Autonomous Voltage Control Strategies in Distribution ...

Autonomous Voltage Control Strategies in Distribution Grids with Photovoltaic Systems - Technical and Economic Assessment Dissertation (Dr.-Ing.) by Thomas Stetz Master of Science The Dissertation was Submitted to the Faculty of Electrical Engineering and Computer Science at the University of Kassel - Department of Energy Management and Power System Operation -

Supervisor: Prof. Dr.-Ing. Martin Braun (University of Kassel) Co-Supervisor: Prof. Dr.-Ing. Bernd Engel (TU Braunschweig) Day of Defense: 18th of December 2013

Erklärung ”Hiermit versichere ich, dass ich die vorliegende Dissertation selbstständig, ohne unerlaubte Hilfe Dritter angefertigt und andere als die in der Dissertation angegebenen Hilfsmittel nicht benutzt habe. Alle Stellen, die wörtlich oder sinngemäß aus veröffentlichten oder unveröffentlichten Schriften entnommen sind, habe ich als solche kenntlich gemacht. Dritte waren an der inhaltlich-materiellen Erstellung der Dissertation nicht beteiligt; insbesondere habe ich hierfür nicht die Hilfe eines Promotionsberaters in Anspruch genommen. Kein Teil dieser Arbeit ist in einem anderen Promotions- oder Habilitationsverfahren verwendet worden.”

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Danksagung Die Dissertation ist ein weiterer Meilenstein im Rahmen einer akademischen Karriere; der offizielle Nachweis der Befähigung zum wissenschaftlichen Arbeiten. Nicht mehr, aber auch nicht weniger. Das Verfassen einer Dissertation erfordert bekanntermaßen ein hohes Maß an Motivation, einer selbstständigen Arbeitsweise, Ausdauer und natürlich einem soliden Fachwissen. Dies kann ich rückblickend auf die letzten vier Jahre nur bestätigen. Weniger präsent hingegen sind die externen Faktoren, deren Existenz mindestens im selben Umfang zum Gelingen einer Dissertation beitragen, deren Ausbleiben in den meisten Fällen aber frühzeitig zum Scheitern eines Dissertationsvorhabens führen dürfte. Für mich sind diese externe Faktoren eine professionelle Begleitung, ein interaktives und förderndes Arbeitsumfeld, eine gesicherte Finanzierung sowie die langfristige Unterstützung durch Freunde und Familie. Ich hatte das große Glück, dass mir diese externe Unterstützung zuteil wurde, gewährt von Menschen die sich aktiv (und manchmal ohne es zu wissen) für das Gelingen meiner Dissertation eingesetzt haben. Ihnen möchte ich hiermit herzlichst danken. Für die professionelle Begleitung meiner Dissertation, die vielen damit verbunde¨ nen Uberstunden und für die zahlreichen wertvollen Anregungen möchte ich mich zunächst bei meinen beiden Gutachtern, Herrn Professor Martin Braun von der Universität Kassel und Herrn Professor Bernd Engel von der Technischen Universität Braunschweig, herzlich bedanken. Ferner bedanke ich mich bei den Beisitzern meiner Prüfungskommission, Herrn Professor Clemens Hoffmann und Herrn Pro¨ fessor Peter Zacharias von der Universität Kassel, für die Ubernahme dieser Aufgabe. Verfasst habe ich diese Dissertation im Rahmen meiner Forschungstätigkeiten am Fraunhofer IWES. Dort fand ich ein kreatives, interaktives und kontruktives Arbeitsumfeld vor und einen Kollegenkreis den ich fachlich wie auch persönlich sehr zu schätzen gelernt habe. Namentlich hervorheben möchte ich bei dieser Gelegenheit die Herren Jan von Appen, Dr. Konrad Diwold, Dr. Alexander Scheidler und Dr. Frank Marten für ihre fortwährende Diskussionsbereitschaft und ihre kritischen aber stets konstruktiven Anmerkungen. Ich danke auch meinen Studenten für ihren persönlichen Einsatz im Rahmen ihrer Abschlussarbeiten. Unsere Zusammenarbeit habe ich stets als gewinnbringend erlebt. Des Weiteren möchte ich mich ganz herzlich bei Herrn Sebastian Schmidt, von der Bayernwerke AG, für die aktive Unterstützung meiner Forschungstätigkeiten und sein hohes Interesse an meinen Forschungsergebnissen bedanken. Die Finanzierung meiner Dissertation wurde durch die Mitarbeit in zahlreichen, o¨ ffentlich geförderten Projekten gesichert. Den Projektinitiatoren, den Fördermittelgebern und den Projektpartnern möchte ich hiermit herzlich danken.

VI Von all den oben genannten Faktoren gebührt mein größter Dank allerdings meinem Freundeskreis und meiner Familie. Ohne ihre langjährige Unterstützung und Ermutigung wäre diese Dissertation sicherlich niemals entstanden. Ich danke meinen Eltern, Sigrid und Alfred Stetz, für ihre nunmehr 30-jährige Einsatzbereitschaft und vielfältige Unterstützung. Zum Schluss bedanke ich mich bei meiner langjährigen Partnerin, Anna Beck. Dafür, dass sie im selben Zeitraum ihre Dissertation geschrieben hat wie ich, für ihr Verständnis u¨ ber zahlreiche entbehrungsreiche Wochenenden und letztlich dafür das sie so ist, wie sie ist.

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Author’s Publications Peer Reviewed Journal Publications (Listed) Stetz, T., Diwold, K., Kraiczy, M., Braun, M., Geibel, D., Schmidt, S. (2013), ”Techno-Economic Assessment of Voltage Control Strategies in Low Voltage Grids”, IEEE Transactions on Smart Grids - Special Issue on Control Theory and Technology in Smart Grid, Accepted: 04/2014. von Appen, J., Stetz, T., Braun, M., Schmiegel, A. (2013), ”Local Voltage Control Strategies for PV Storage Systems in Distribution Grids”, IEEE Transactions on Smart Grids, TBP, accepted 10/2013. Stetz, T., Kraiczy, M., Braun, M., Schmidt, S. (2013), ”Technical and Economical Assessment of Voltage Control Strategies in Distribution Grids”’, Progress in Photovoltaics: Research and Applications, DOI: 10.1002/pip.2331 Stetz, T., Marten, F., Braun, M. (2012), ”Improved Low Voltage Grid-Integration of Photovoltaic Systems in Germany”, IEEE Transactions on Sustainable Energy, Vol.4, Issue 2, pp.534-542, DOI: 10.1109/TSTE.2012.2198925 Braun, M., Stetz, T., Bründlinger, R., Mayr, C., Ogimoto, K., Hatta, H., Kobayashi, H., Kroposki, B., Mather, B., Coddington, M., Lynn, K., Graditi, G., Woyte, A. and MacGill, I. (2012), ”Is the distribution grid ready to accept large-scale photovoltaic deployment? State of the art, progress, and future prospects”, Progress in Photovoltaics: Research and Applications, 20:681-697, DOI: 10.1002/pip.1204

Peer Reviewed Journal Publications Büdenbender, K., Braun, M., Stetz, T., Strauss, P. (2011), ”Multifunctional PV Systems offering additional Functionalities and Improving Grid Integration”, International Journal of Distributed Energy Resources, Vol.7,pp.109-128, Kassel, 2011 Speckmannm, M., Schlögl, F., Hochloff, P., Lesch, K., Stetz, T., Braun, M. (2011), ”The RegModHarz Architecture - Facing Challenges caused by the Transformation to a Distributed Energy System”, International Journal of Distributed Energy Resources, Kassel, 2011

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Publications in Proceedings of Scientific Conferences Stetz, T., Kraiczy, M., Diwold, K., Kämpf, E., Töbermann, J.-C., Braun, M., Schmidt, S., Schmiegel, A.U., Premm, D., Jung, A., Bröscher, S., ”Parallel Operation of Photovoltaic Systems and Transformer with OLTC”, in Proc. VDE ETG Conference, Berlin, 2013 Kraiczy, M., Braun, M., Wirth, G., Stetz, T., Brantl, J., Schmidt, S., ”Unintended Interferences of Local Voltage Control Strategies of HV/MV Transformer and Distributed Generators”, 28th European Photovoltaic Solar Energy Conference, Paris, 2013 Idlbi, B., Diwold, K., Stetz, T., Braun, M., ”Cost-Benefit Analysis of Central and Local Voltage Control Provided by Distributed Generators in MV Networks”, in Proc. IEEE PowerTech Conference, Grenoble, 2013 Löther, S., Stetz, T., Braun, M., ”Voltage Control Capabilities of Biogas Plants in Parallel Operation - Technical and Economical Assessment”, in Proc. IEEE PowerTech Conference, Grenoble, 2013 Braun, M., Kämpf, E., von Appen, J., Kraiczy, M., Stetz, T., Töbermann, J.-C., Brantl, J., Schmidt, S., Bröscher, S., Premm, D., Schmiegel, A., ”Forschungsprojekt ”‘PV-Integrated”’ - technisch und wirtschaftlich verbesserte Netzintegration von PV-Anlagen in Verteilnetze”, in Proc. 28th Symposium on Photovoltaic Solar Energy, Bad Staffelstein, 2013 Kraiczy, M., Stetz, T., Braun, M., Schmidt, S., ”Untersuchung der Wechselwirkungen zwischen der lokalen Spannungsregelung des Umspannwerks-Transformators und der lokalen Blindleistungsregelung dezentraler Erzeugungsanlagen im Verteilnetz”, in Proc. 28th Symposium on Photovoltaic Solar Energy, Bad Staffelstein, 2013 Stetz, T., Wolf, H., Probst, A., Eilenberger, S., Braun, M., Saint-Drenan, Y.-M., Kämpf, E., Schmidt, S., Schöllhorn, D., ”Stochastical Analysis of Smart-Meter Measurement Data”, in Proc. VDE ETG Conference, Stuttgart, 2012 Stetz, T., Braun, M., Nehrkorn, H.-J., Schneider, M., ”Methods for Maintaining Voltage Limitations in Medium Voltage Systems”, in Proc. VDE ETG Conference, Würzburg, 2011 Yan, W., Braun, M., von Appen, J., Kämpf, E., Kraiczy, M., Ma, C., Stetz, T., ”Operation Strategies in Distribution Systems with high level PV penetration”, in Proc. ISES Solar World Congress, Kassel, 2011

IX Stetz, T., von Appen, J., Braun, M., Wirth, G., ”Cost-Optimal Inverter Sizing for Ancillary Services - Field Experience in Germany and Future Considerations”, in Proc. 26th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, 2011 Stetz, T., Braun, M., Künschner, J., Engel, B., ”Cost-Optimal Sizing of Photovoltaic Inverters”, in Proc. 25th European Photovoltaic Solar Energy Conference and Exhibition, Valencia, 2010 Stetz, T., Yan, W., Braun, M., ”Voltage Control in Distribution Systems with high level PV-Penetration”, in Proc. 25th European Photovoltaic Solar Energy Conference and Exhibition, Valencia, 2010 Braun, M., Stetz, T., ”Wirtschaftlich optimierte Blindleistungsbereitstellung durch Photovoltaikanlagen in Niederspannungsnetzen”, in Proc. 25th Symposium on Photovoltaic Solar Energy, Bad Staffelstein, 2010 Braun, M., Büdenbender, K., Stetz, T., Thomas, U., ”Activation of Energy Management in Households - The Novel Local Consumption Tariff for PV Systems and its Influence on Low Voltage Distribution Grids”, in Proc. VDE ETG Conference, Düsseldorf, 2009 Arnold, G., Braun, M., Reimann, T., Stetz, T., Valov, B., ”Optimal Reactive Power Supply in Distribution Networks - Technological and Economic Assessment for PV Systems”, in Proc. 24th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, 2009 Braun, M., Stetz, T., ”Multifunctional Photovoltaic Inverters - Economic Potential of Grid-Connected Multifunctional PV-Battery-Systems in Industrial Environments”, in Proc. 23rd European Photovoltaic Solar Energy Conference and Exhibition, Valencia, 2008

Publications in Technical and Scientific Magazines von Appen, J., Braun, M., Stetz, T., Diwold, K., Geibel, D., ”Time in the Sun”, IEEE Power&Energy Magazine, March/April 2013 Stetz, T., Braun, M., ”Decentralized approaches for voltage rise mitigation in low voltage grids - a case study”, Elektrotechnik&Informationstechnik, 128/4, pp.105109, 2011

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Supervised Bachelor and Master Theses • Dipl.-Ing. Wei Yan, ”Netzsimulationen zur Blindleistungsbereitstellung in Verteilnetzen durch Photovoltaikwechselrichter”, Diploma Thesis at the Technical University of Darmstadt, 2010 • M.Sc. Jochen Künschner, ”Optimized PV inverter sizing considering reactive power supply”, Masters Thesis at the University of Kassel, 2010 • M.Sc. Markus Kraiczy, ”Technische Bewertung von Netzbetriebsführungsverfahren anhand eines realen Mittelspannungsnetzes mit hoher dezentraler Erzeugungsdichte”, Masters Thesis at the University of Kassel, 2012 • Dipl.-Ing. (Diplom I) Hendrik Wolf, ”Stochastische Analyse von Smart Meter Messdaten”, Diploma Thesis at the University of Kassel, 2012 • Dipl.-Ing. (FH) Stefan Löther, ”Netzparallelbetrieb von Biogasanlagen in Verteilnetzen”, Diploma Thesis at the University of Applied Sciences Schweinfurt, 2012 • M.Sc. Thomas Kral, ”Implementierung und Analyse von Regelungsalgorithmen zur Spannungshaltung durch Photovoltaik-Wechselrichter mittels Rapid Control Prototyping”, Masters Thesis at the University of Kassel, 2013 • M.Sc. Wolfgang Kehrer, ”Autonomous Voltage Control Strategies in a real US Distribution Grid with a high PV-penetration - Technical Assessment to increase the PV Hosting Capacity”, Masters Thesis at the University of Kassel, 2013

Abstract Maintaining local voltage limitations in distribution grid sections with high penetration by residential scale photovoltaic systems is still a major issue for German distribution system operators who are in charge of maintaining a secure and reliable grid operation. In many highly penetrated distribution systems, cost intensive grid reinforcement measures become or have already become necessary in order to properly host the additional generation capacity. However, the application of alternative measures at distribution system level, such as the active usage of local voltage support provided by photovoltaic inverters and distribution transformers with on-load tap changer is still an emerging topic. It is accompanied by pending questions on the technical effectiveness and the economic efficiency of different kinds of autonomously operating voltage control strategies. First, this thesis analyzes the simultaneity of load consumption and photovoltaic generation in residential low voltage grids, based on smart meter measurement data. In this context, a focus is set on determining the expected low load of domestic loads in times of high solar irradiation. The superimposition of load and generation time series allows deriving potential reverse power flows by local power generation, which can be used by distribution system operators for the sizing of conductor and transformer. Second, the theoretical potential of local voltage control strategies at low voltage level is investigated. Based on a total of 40 real low voltage grids, the theoretical potential of different autonomous voltage control strategies, in terms of increasing the grids hosting capacity, is analyzed using a probabilistic assessment approach. It becomes obvious that the application of distribution transformers with on-load tap changer (OLTC) is a technically effective measure to increase the voltage related hosting capacity of low voltage grids. A combination of voltage dependent active power control and reactive power provision (so-called Q(V)/P(V)) by photovoltaic inverters promises a high theoretical potential for increasing the hosting capacity of low voltage grids as well. It could be shown that a parallel operation of inverter-based and OLTC-based voltage control strategies do not lead to significant increases of a gridâs hosting capacity, compared to a sole application of either OLTC- or inverter-based control strategies.

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ABSTRACT

Third, two different control concepts for a simultaneous voltage dependent active power control and reactive power provision by photovoltaic inverters are compared. The two control concepts are a common Q(V)/P(V) droop control and a so-called automatic voltage limitation. The investigations highlight the robustness of the droop controller against variations of controller and process parameter and its more distinct load-sharing capability compared to the concept of automatic voltage limitation. Finally, the economic efficiency of applying autonomous voltage control strategies is analyzed and compared against traditional grid reinforcement approaches. An example using two real low voltage grids with high local photovoltaic penetration shows that the application of autonomous voltage control strategies can reduce the grid integration costs of photovoltaic systems by up to 75% compared to the costs of traditional grid reinforcement measures. The study analyses investment costs as well as grid losses and maintenance costs for OLTCs over a period of ten years. Here again, distribution transformers with on-load tap changer and Q(V)/P(V) inverter control show the highest savings potential.

Management Summary The steadily increasing number of residential scale photovoltaic systems, installed at distribution system level, leads to new challenges for distribution system operators in terms of maintaining a secure and reliable grid operation. The high simultaneity of local photovoltaic feed-in during times of low load consumption causes reverse power flows over feeder impedances and hence leads to increased voltage magnitudes within distribution grids. Today, maintaining local voltage limitations in grids with high photovoltaic penetration has become one of the main drivers for cost intensive grid reinforcement measures at distribution system level. An alternative to traditional grid reinforcement measures could be the incorporation of additional voltage control capabilities, provided by modern photovoltaic inverters (e.g. active power control and reactive power provision) and distribution transformers with on-load tap changer, into the distribution system operation without using additional information and communication technology (autonomous control strategies). However, the new degrees of freedom have to be properly addressed and carefully tuned during grid planning processes, in order to maximize the utilization of existing grid infrastructure. At this point, several questions concerning a technically effective and economically efficient implementation of voltage control strategies arise, of which the following ones are addressed by this thesis: • To what extend can local photovoltaic generation be considered to be compensated by local consumption? • What is the theoretical potential of different voltage control strategies in terms of increasing a grid’s hosting capacity for additional photovoltaic generation and can different voltage control strategies be combined beneficially? • How can a combined voltage dependent active and reactive power control be implemented in the control structure of photovoltaic inverters and how can their performance be assessed? • How significant is the cost savings potential of voltage control strategies compared to traditional grid reinforcement measures? This thesis contributes to answering the aforementioned questions. In the following, the major findings and contributions of this thesis are summarized.

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MANAGEMENT SUMMARY

Local compensation of photovoltaic power generation and expected reverse power flows: Many photovoltaic impact studies analyze the effect of photovoltaic feed-in in low voltage grids based on worst-case assumptions for the local load and the local generation, while neglecting the simultaneity of generation and consumption. Conservative worst-case assumptions, such as no load and 100% photovoltaic feed-in, over-estimate the impact of photovoltaic on the grid and lead to a less efficient utilization of grid infrastructure. An analysis of 143 smart meter data sets, recorded at private H0 customers over a period of one year, and 283 data sets, recorded at the point of common coupling of residential scale photovoltaic systems over the same period, reveals that the expected low load during times of high solar irradiation is a crucial parameter for photovoltaic impact studies. Compared to the expectable minimum load of H0 customers the low load during times of high solar irradiation can be considered to be 2 to 3 times as high, depending on the number of households and the day of the year. For photovoltaic impact studies the low load and peak load conditions, depending on the number of H0 customers, and the expectable reverse power flows by photovoltaic feed-in, depending on the number of H0 customer and the installed photovoltaic capacity, can be empirically expressed by the equations listed in Table 1. Their application during photovoltaic impact studies allows to utilize existing grid infrastructure more efficiently than conservative approaches. Table 1: Summary of the findings of Chapter 2. n =number of households, PPV =installed PV capacity.

Equation (Time Interval)

Parameter

Worst-Case Period

α = 1.16221 β = −7.14717 κ = 1.39203

Winter/ Sunday

Low load √ Ll(n) = α + κ n (11 a.m. to 3. p.m.)

α = −0.989711 κ = 14.8996

Summer/ Workday

Reverse power flows PRV (PPV , n) = α · nβ·PPV + γ · PPV + δ

α = −2.22996 β = −0.0264108 γ = −0.872303 δ = 2.41438

Transition/ Workday

Peak load Pl(n) = α −

β √ κn

(whole day)

MANAGEMENT SUMMARY

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The technical potential of voltage control strategies to increase the hosting capacity of low voltage grids for additional photovoltaic generation: The term hosting capacity describes the maximum amount of generation capacity or load that can be interconnected to a particular distribution grid or distribution grid section (e.g. a particular low voltage grid) while maintaining the quality of electricity supply. Autonomous voltage control strategies can be used to support maintaining the local voltage quality, especially for suppressing technically critical voltage rises over the low voltage grid impedances, and hence can contribute to increase the hosting capacity of low voltage grids for additional generation capacity. An assessment approach was introduced that allows for comparing the theoretical potential of the following voltage control strategies during photovoltaic impact studies at low voltage level. • Reactive power provision by photovoltaic inverters – Fixed power factor – cosϕ(P) characteristic according to VDE AR 4105 – Q(V) droop characteristic • Combined active and reactive power control of photovoltaic inverters (Q(V)/P(V) droop characteristics) • Distribution transformer with additional on-load tap changer. The assessment approach was applied on a total of 40 real low voltage grids in the context of a probabilistic investigation. The results highlight the case sensitivity of the structure of real low voltage grids on the achievable additional hosting capacity. For low voltage grids, which experience mainly voltage issues, an on-load tap changer based voltage control strategy usually led to the best results in terms of increasing the grid’s hosting capacity. Also a combined Q(V)/P(V) PV inverter control strategy performed well, compared to a sole reactive power provision by photovoltaic inverter. A sensitivity analysis on the on-load tap changer controller parameterization suggests that the theoretical potential of an on-load tap changer based voltage control strategy is limited by the permissible voltage rise over the downstream feeder impedances. On average, the hosting capacity of the investigated low voltage grids could be increased by lowering the voltage set value of the on-load tap changer controller until a voltage rise of 9.5% VN over the feeder impedances was realized. Higher photovoltaic penetration level often caused current related cable overloadings within the investigated low voltage grids. The accumulated additional reactive power flows over the distribution transformer, caused by photovoltaic inverter operated in under-excitation mode, usually lead to a larger voltage drop over the transformer impedance than over the downstream feeder impedances. For a parallel operation of on-load tap changer based and reactive power based voltage control strategies, the voltage drop over the transformer impedance cannot be utilized for increasing a grid’s hosting capacity, since

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autonomously operated on-load tap changers control the voltage at their low voltage busbar and hence neutralize voltage drops over the transformer impedance. This effect plus the fact that a sole application of on-load tap changer often utilizes the hosting capacity of the existing grid infrastructure to its full extent leads to the conclusion that in many cases a parallel operation of on-load tap changer based and reactive power based voltage control strategies do not increase the hosting capacity of low voltage grids significantly.

Implementation and assessment of a combined voltage dependent active and reactive power control provided by photovoltaic inverters: In the context of this thesis, two different variations of a combined voltage dependent active and reactive power control by photovoltaic inverters are discussed: • Based on active and reactive power droop characteristics (Q(V)/P(V)) • Based on a single voltage threshold value (automatic voltage limitation) For both variations, investigations were undertaken in order to assess their robustness against variations of control and process variables and to compare their general load-sharing capability for a parallel operation of photovoltaic inverters. The results show that the common Q(V)/P(V) droop controller performance is relatively robust against variations of controller gains and the implementation of additional damping in the outer voltage control loop (e.g., voltage measurement filter and power gradient limitations). For the parallel operation of Q(V)/P(V) control approaches the consideration of additional damping is a crucial element to avoid undamped power oscillations caused by high proportional gains. As expected, the Q(V)/P(V) control approach shows a relatively good load-sharing behavior for photovoltaic inverters, connected in electrically close distance. The general applicability of the automatic voltage limitation approach under parallel operation could also be demonstrated by the conducted simulations. However, this control approach shows a relatively high parameter sensitivity compared to the Q(V)/P(V) control approach. Especially the implementation of additional damping might reduce the overall controller performance considerably. Moreover, the introduction of a single voltage threshold value weakens the general loadsharing capability of this approach.

MANAGEMENT SUMMARY

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Cost savings potential by applying autonomous voltage control strategies compared to traditional grid reinforcement measures: Increasing a grid’s hosting capacity by applying autonomous voltage control strategies means utilizing the existing grid infrastructure more effectively without the need for additional information and control infrastructure. The economical relevance of the cost savings potential, associated with the application of autonomous voltage control strategies, could be identified in the context of this thesis. The structures of two real low voltage grids and a period of time of 10 years with constant photovoltaic growth were the basis for this investigation. As a result, the application of autonomous voltage control strategies shows a significant cost reduction potential for the two investigated LV grids. The net present value of the investment costs could be reduced by up to 82% for grid No. 20 and 60% for grid No. 39, compared to traditional grid reinforcements. A high savings potential yields from deferring investment costs to later points in time. For both grids, the on-load tap changer based voltage control strategies and the combined Q(V)/P(V) control strategy showed the highest savings potential for investment costs. The network losses and the associated photovoltaic feed-in losses are determined by means of one-year root-mean-square simulation with one minute resolution. Additional costs due to increased network losses or higher on-load tap changer maintenance costs are considered but only play a minor role for the two low voltage grids. A remarkable savings potential for photovoltaic plant operators was identified by applying a voltage driven active power curtailment P(V) instead of a fixed active power limitation according to § 6 of the German Renewable Energy Sources Act (EEG). The maximum overall cost reduction potential was identified to be up to 75% of the conventional grid reinforcement scenario by applying the Q(V)/P(V) control strategy for grid No. 20 and 50% by applying on-load tap changer based voltage control strategies for grid No. 39. Figure 1 and Table 2 summarize the results of the cost-benefit analysis. Sensitivity analyses on the cost assumptions and the discount factor underlined the robustness of the gained results. Table 2: Total savings by the application of autonomous voltage control strategies compared to pure grid reinforcements. OLTC VSet = 1.0p.u.

OLTC VSet = 0.98p.u.

Cosϕ(P)

Q(V)

Q(V)/ Pmax = 70%

Q(V)/P(V)

Grid No. 20 No. 39

62% 50%

66% 50%

46% 42%

60% 43%

68% 44%

75% 47%

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MANAGEMENT SUMMARY

Figure 1: Comparison of net present values NPV of the cash flow time series, comprising investment costs NPVINV and operational costs NPVOP (network losses NPVOP1 and photovoltaic opportunity costs NPVOP2 ), referred to the beginning of year t1 .

The results of this thesis clearly suggest that autonomous voltage control strategies should be used to improve the technical and economic grid integration of PV systems. If applied appropriately, they are capable of deferring grid reinforcement measures and hence shift investment costs to future points in time. In addition, autonomous voltage control strategies gain extra time for the DSOs until voltage driven grid reinforcements become necessary, if at all. During this time the extent of local PV penetration might be more advanced and hence enable DSOs to size their grids more efficiently. Of all investigated autonomous voltage control strategies, the on-load tap changer based voltage control strategies and the combined Q(V)/P(V) PV inverter control strategy showed the most promising results, from a technical as well as from an economic perspective.

Contents 1 Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Objective and Structure of the Thesis . . . . . . . . . . . . . . . . 1.3 Autonomous Control in the Context of Distribution System Operation 2 Smart Meter Data Analysis 2.1 Load Data Sets . . . . . . . . 2.1.1 Standard Load Profiles 2.1.2 Equivalent Load . . . 2.2 Generation Data Sets . . . . . 2.3 Reverse Power Flows . . . . . 2.4 Summary and Outlook . . . .

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3 Hosting Capacity of Distribution Grids 3.1 Definition of Hosting Capacity . . . . . . . . . . . . . . . . . 3.2 Strategies for Increasing the Hosting Capacity . . . . . . . . . 3.2.1 Traditional Grid Reinforcements . . . . . . . . . . . . 3.2.2 Voltage Support by Controllable PV Inverter . . . . . 3.2.3 Distribution Transformer with On-Load Tap Changer . 3.3 Improved Parameterization for PV Impact Studies . . . . . . . 3.3.1 Basic Approach . . . . . . . . . . . . . . . . . . . . . 3.3.2 Modifications for PV Inverter Operation Methods . . . 3.3.3 Modifications for OLTC Operation Methods . . . . . . 3.3.4 Summary of Modifications . . . . . . . . . . . . . . . 3.4 Probabilistic Assessment for Increasing the Hosting Capacity Autonomous Voltage Control Strategies . . . . . . . . . . . . 3.4.1 Methodology and Structure . . . . . . . . . . . . . . . 3.4.2 Basic Configuration Assessment . . . . . . . . . . . . 3.4.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . 3.5 Summary and Outlook . . . . . . . . . . . . . . . . . . . . .

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4 Parallel Operation of Photovoltaic Inverters 4.1 Modeling of Photovoltaic Inverters with Voltage Support Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Model Description . . . . . . . . . . . . . . . . . . . . . 4.1.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . 4.2 The Concept of Automatic Voltage Limitation . . . . . . . . . . . 4.3 Single Operation of Photovoltaic Inverters - Controller Parameter Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Parallel Operation of Photovoltaic Inverters . . . . . . . . . . . . 4.4.1 Stability of Parallel Operation and Controller Parameter Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Load Sharing Capability . . . . . . . . . . . . . . . . . . 4.5 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . .

62 64 65 69 72 75 82 84 91 95

5 Economic Assessment 97 5.1 Investigated LV grids and PV Expansion Scenarios . . . . . . . . 100 5.2 Calculation of Grid Reinforcement Costs . . . . . . . . . . . . . . 104 5.3 Calculation of Operational Costs . . . . . . . . . . . . . . . . . . 107 5.3.1 Simulation Assumptions and Settings . . . . . . . . . . . 108 5.3.2 Calculation of the Net Present Value of the Operational Costs112 5.3.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . 117 5.4 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . 122 6 Conclusion and Outlook

124

A ANNEX to Chapter ’Smart Meter Data Analysis’

129

B ANNEX to Chapter ’Hosting Capacity of Distribution Grids’

130

C ANNEX to Chapter ’Parallel Operation of Photovoltaic Systems’

136

D ANNEX to Chapter ”Economic Assessment”

146

List of Figures

156

List of Tables

163

Bibliography

165

List of Units and Symbols

177

Nomenclature

181

Project Support for the Thesis

183

Chapter 1

Introduction 1.1 Motivation Undoubtfully, mitigating climate change is one of today’s most urgent challenges of humankind. A worldwide reduction of greenhouse gas emissions is necessary to prevent global warming sustainably. In 2010, 40% of Germany’s total CO2 emissions were caused by the energy supply industries [1]. Hence, restructuring the electrical power supply system from fossil fuel based energy generation towards an energy generation based on renewable energies can help to reduce greenhouse gas emissions significantly. To accelarate the restructering process, the German Federal Government passed the so-called Renewable Energy Sources Act (EEG) in 2004, setting a mandatory goal to archieve a renewable energy penetration of at least 20% by 2020. This goal was later on revised and increased to 35% by 2020 (§1 (2) EEG 2012). As an incentive to stimulate the deployment of renewable energies, a feed-in tariff mechanism for different renewable energy sources (RES) was introduced. The relatively high feed-in tariff for photovoltaic (PV) power generation resulted in booming installation rates over the past years, despite regularly adapted feed-in degressions (compare Fig. 1.1). As of September 2013, a total of more than 35 GW of PV capacity [2], distributed among more than 1.2 Mio. PV plants [3], were connected to the German mains. A remarkable feature of PV installations in Germany is the voltage level of their point of common couplings (PCC). Most of the PV systems are directly connected to the distribution grid, which comprises the low voltage (LV) level, the medium voltage (MV) level, and in some service areas also the high voltage (HV) level. Currently, about 70% of the total installed PV capacity in Germany are connected to the low voltage (LV) level and about 25% to the medium voltage (MV) level, highlighting the fact that PV is a highly distributed RES [4]. Due to a non-uniform spatial distribution across Germany, some regions are already experiencing a local PV penetration of more than 200 kWp/km2 while the nationwide average is about 39 kWp/km2 (compare [5], [6]). In this highly PV dominated grid sections a transformation process from consumption to supply grids is taking place (see Fig. 1.2).

1

2

CHAPTER 1. INTRODUCTION

Figure 1.1: Installed capacity of renewables in Germany. Data derived from [4].

This transformation process offers new challenges for the distribution system operator (DSO), who, according to § 14 EnWG (German Energy Industry Act), is responsible to provide a certain quality of electricity supply to its customers. Reverse power flows towards upstream voltage levels, in times of high solar irradiation, lead to voltage rises along MV and LV feeder as well as to the possibility of temporal equipment overloadings and hence might risk a violation of current technical requirements (e.g. the voltage quality defined by DIN EN 50160). According to § 9 EEG and § 14 EEG, the German DSOs are obliged to increase the local hosting capacity of their grid for additional generation capacity at their own costs, if technically necessary. Often, ”traditional” grid reinforcement measures (aiming at increasing the local short-circuit power, compare section 3.2.1) are conducted to allow additional generation capacity to be connected to the grid. Of course, this approach can be very cost intensive, especially as the local development of additional PV installations is hard to predict, what makes a pro-active grid planning difficult to conduct. A study published in 2012 assess the necessary grid reinforcement costs for further RES deployment in Germany, based on the so-called ”grid development plan 2012” (”Netzentwicklungsplan 2012”’) [7] to 27.5 Mrd. EUR until 2030 [8]. According to the authors, 41.5% of the total investment costs can be associated with grid reinforcement measures at LV and MV levels, where most of the total PV capacity is currently installed.

1.2. OBJECTIVE AND STRUCTURE OF THE THESIS

3

In order to keep the overall extend of grid reinforcement measures as low as possible, innovative grid planning and operation strategies are necessary. For example, by using the control capabilities of state-of-the-art PV inverter (e.g. reactive power control), ancillary services such as local voltage support could be provided by PV plants themselves. These additional functionalities might increase the local hosting capacity for additional generation capacity and hence can contribute to lower the overall costs for PV grid integration in the nearby future [9], [6], [10], [8]. This thesis contributes to answer the question, whether autonomous voltage control strategies, provided by PV inverter, are an technically effective and economically efficient alternative to increase the hosting capacity of distribution grids for additional generation capacity.

Figure 1.2: Measured power flow over HV/MV substation transformer, recorded from 2009 to 2013. The data is a courtesy of the Bayernwerk AG.

1.2 Objective and Structure of the Thesis In the previous section, the necessity for alternative technical solutions to traditional grid reinforcement measures is argued against the background of steadily increasing PV grid integration costs. Out of this general need the overall goal of this thesis is derived.

4


It is the goal of this thesis, to identify technical effective and economic efficient control strategies, which can be applied during normal grid operation and without the need for additional information and communication infrastructure, while aiming at maximizing the utilization of the existing grid infrastructure for the interconnection of increasing shares of dispersed PV generation capacity. From the requirement for no additional information and communication technologies (ICT) the scope of technical solutions can be narrowed down to autonomous voltage control strategies, provided by PV inverter and distribution transformer with on-load tap changer (OLTC) (see Section 1.3). The investigations are carried out for balanced LV grids under the consideration of the current regulatory framework conditions in Germany. The thesis is divided into 5 chapters. An overview about the structure gives Fig. 1.3. Chapter 2: During PV impact studies, the extend of necessary grid reinforcements is determined. In order to improve the utilization of existing grid infrastructure it is therefore a crucial element to perform PV impact studies with realistic worst-case assumptions. These assumptions include the expected PV generation during times of high solar irradiation as well as the local load consumption during that time. Load and generation might partially compensate each other and hence unload feeders and transformers to a certain degree. However, existing information from literature on peak load and low load conditions are usually not differentiated by time slices, but refer to the overall peak load and low load of certain load types. In order to identify realistic load assumptions for PV impact studies at LV level, the thesis starts with an analysis of smart-meter measurement data, recorded over a period of one year at the sites of 143 private household customers by the Bayernwerk AG. Calculation relevant information, such as the expected low load and peak load conditions during times of high solar irradiation are statistically derived from that data. The results can be used in the context of PV impact studies and deal as a base for subsequent investigations within this thesis. Chapter 3: Besides realistic worst-case assumptions for load and generation, a proper calculation frame is required to account for the theoretical and/or technical potential of autonomous voltage control strategies during PV impact studies. This chapter gives an overview on the investigated autonomous voltage control strategies and introduces a calculation methodology for PV impact studies. Based on the derived calculation frame and the load and generation assumptions from the smart meter analysis, the theoretical potential of different autonomous voltage control strategies in terms of mitigating voltage rises is investigated. To do so, the additional hosting capacity of 40 real LV grids from the Bayernwerk AG is calculated, using a probabilistic assessment approach and taking into account the definition of voltage quality in distribution systems according the DIN EN 50160 standard.

1.2. OBJECTIVE AND STRUCTURE OF THE THESIS

5

Chapter 4: In this chapter, the stability and load-sharing capability of voltage dependent active and reactive power control strategies is studied for parallel operation scenarios. This investigation becomes necessary, as the voltage feedback signals of the autonomously operating controller are indirectly coupled via the local grid impedances. Although the locally measured voltage signal is used for control purposes of single PV inverters there might be change of occurring unintended interferences between different PV inverter. Besides the droop-based Q(V)/P(V) voltage control strategy a novel concept of a so-called automatic voltage limitation strategy is introduced. In contrast to the Q(V)/P(V) strategy, the automatic voltage limitation strategy relays on a single voltage threshold value only. Based on a validated model of a three-phase current controlled voltage source inverter (VSI), the performance during single operation and the controller parameter robustness of both control approaches is studied. In a second step, their stability and loadsharing capability are analyzed for parallel operation scenarios using time-domain simulations. Chapter 5: This chapter finally deals with the investigation of the economic potential of autonomous voltage control strategies as an active part in the operation of distribution systems. A cost-benefit analysis for the investigated autonomous voltage control strategies is conducted, considering investment costs as well as operational costs (additional grid losses, reactive power compensation costs and opportunity costs for reduced active power feed-in) over a period of 10 years. The cost-benefit analysis is conducted for two real LV grids with high PV penetration. For the determination of the operational costs one-year root mean square (RMS) simulations are used. Chapter 5 closes with an outlook on the potential economic benefit by network loss minimization at LV level by means of coordinated control.

Figure 1.3: Structure of the thesis.

6


1.3 Autonomous Control in the Context of Distribution System Operation This section defines the meaning of autonomous voltage control strategies in the context of distribution system operation that is used within this thesis. In general, autonomous control is a discipline of control engineering and control theory.

”Autonomous means having the power for self government. Autonomous controllers have the power and ability for self governance in the performance of control functions. They are composed of a collection of hardware and software, which can perform the necessary control functions, without external intervention, over extended time periods.” [11] ”The objective of Autonomous Control is the achievement of increased robustness and positive emergence of the total system due to disturbed and flexible coping with dynamics and complexibility.”[12] These two statements provide us with a frame to define the meaning of autonomous voltage control in the context of distribution system operation. The assigned objective of autonomous voltage control strategies is to support the voltage quality in distribution systems or distribution system sections. In the context of this thesis, the term distribution system refers to the MV and LV grids that can be dedicated to one particular HV/MV substation. A distribution system section is then defined as a part or subsystem of the distribution system (e.g., a LV grid served by a MV/LV distribution transformer). The required absence of external intervention is a crucial element for the definition of autonomous control that needs to be studied more closely for the operation of distribution systems. For this, additional hierarchical dimensions have to be introduced. Figure 1.4 shows that the control structure of distribution systems (also called ”Distribution Management System” (DMS) , see [13; 14]), which could serve one or more special control purposes (e.g. voltage control), can be hierarchically categorized into centralized, decentralized and local control levels [15]. According to IEC IEV 60050-351-26 the following definitions can be applied [16]: Centralized Control: ”Structure of a control in coupled subsystems at which each controller considers output variables from all subsystems to form its output variables.” Decentralized Control: ”Structure of a control in coupled subsystems at which each controller considers only output variables from that subsystem attached to itself to form its output variables.”

1.3. AUTONOMOUS CONTROL

7

In this context, a centralized controller receives measurement values from entities and sends set values to chosen entities within its control level. In contrast, decentrailzed control approaches cover only chosen sections (or subsystems) of the distribution system. In such cases, the controller (so-called Micro Distribution Management System (Micro-DMS)) communicates only with entities within its subsection. However, a decentralized controlled subsystem itself can be a part of superior centralized control approach, if the exchange of information is limited to communication between the control center and the micro DMS units. Local control approaches instead do not involve any communication between single entities at all. Measurement values are recorded, processed and interpreted by the respective controlling entity itself. For example, a PV inverter (the entity) measures the local voltage magnitude at its output terminal and uses this information to change its active or reactive power operating points accordingly. All three hierarchic control approaches can be considered as autonomously operating, if they do not exchange any information with devices or entities outside their respective control level. For example, a centralized control approach can be considered as autonomously operating, if it does not exchange any information with superior management and optimization systems or if it does not require frequent interventions via human machine interfaces (HMI). However, in the context of distribution system management, a local control approach can be always considered as operating autonomously. This thesis will focus on the investigation of local and hence autonomously operating voltage control strategies for distribution grids with high local PV penetration. The term ”strategy” specifies a concrete measure to achieve the goal of supporting the voltage quality in distribution systems. This can be the usage of PV inverter control capabilities or the installation of autonomously operating OLTC at distribution transformer, for example. For autonomous voltage control by PV inverter and OLTC various operation modes exist (compare section 3.2). It has to be noticed that the investigated autonomous voltage control strategies in this thesis have a relatively low degree of freedom, since their behavior is usually predefined by initial parameter settings and do not include any form of artificial intelligence (for further reading on degrees of freedom in the context of autonomous control see [11]).

8


Figure 1.4: Differentation between centrally, decentrally and locally structured intelligence of voltage control strategies. Modified version of original graphic presented in [15]

.

Chapter 2

Smart Meter Data Analysis It is the reverse power flows, due to a local mismatch of consumption and generation, which cause voltage rises over the grid impedances and hence can limit the hosting capacity of distribution grids (see Chapter 3). Before assessing the leverage effect of autonomous voltage control strategies on a grids hosting capacity, assumptions have to be made according to the expected simultaneity of load and PV generation. In this chapter, the results of a statistical smart meter measurement data analysis for Bayernwerk’s AG official Smart Grid region ”Seebach” [17] will be presented. The smart meter data sets can be distinguished in load data sets for private households and generation data sets for residential scale PV systems. The shown results were partially presented in [18]. State-of-the-Art: For sizing issues of conductors and transformers in load dominated LV grids, expected values for the maximum power flows are of interest. In [19; 20; 21] expected values for the aggregated maximum power flows, depending on the number of private end customers, are presented. These values are typically derived from customer type specific peak load conditions and already consider the simultaneity for different numbers of aggregated customers. In LV grids with high local PV penetration, the magnitudes of reverse power flows might exceed the peak load conditions and hence become crucial for the sizing of grid elements. Because of this, additional information on the low load conditions during times of high solar irradiations are required in order to assess reverse power flows properly and to set up realistic PV impact studies. Realistic low load values of German private end customers, correlating with times of high solar irradiation, have yet to be determined. These load values together with statistically processed generation data can be used as a basis for probabilistic grid planning approaches (compare [22; 23; 24]). Goal of the Chapter: It is the goal of this chapter to derive assumptions for the simultaneity of load and generation, which can be used for grid simulations and sizing issues in the context of PV impact studies, as shown in chapter 3 and 5.

9

10

CHAPTER 2. SMART METER DATA ANALYSIS

Realistic expected values for low load conditions during times of high solar irradiation and the extend of reverse power flows for different PV penetration level are of special interest for PV impact studies, which aim at maximizing the utilization of existing grid infrastructure. Methodology and Structure: At first, standard load profiles are derived from the measured load data in order to analyze, if the recorded data sets show a similar load pattern among themselfs and hence can be classified accordingly. In a second step, values for peak load and low load conditions are derived for different representative days and different time intervals. In Section 2.3, the load data is superimposed with measured generation data for different PV penetration level and a mathematical relationship between the installed PV capacity, the number of households and reverse power flows is derived. Scientific Novelty and major Findings: In this chapter, realistic low load values of private end customers are derived for times with high solar irradiation. These values can be used in the context of PV impact studies, as exemplary applied in Chapter 3 and 5. Furthermore, an equation for the expected reverse power flows by local PV generation is derived, which requires the locally installed PV capacity and the number of considered household customers as variables. This equation can be used for sizing issues of transformer and branch feeders within LV grids.

2.1 Load Data Sets The analyzed electrical consumption data was recorded over the period of one year at the interconnection points of LV end customer and PV systems within the Bayernwerk’s AG official Smart Grid region ”Seebach” [17]1 . After preprocessing the raw data [25], data sets for a total of 143 measured domestic loads are available for the analysis. The recorded values are 10 minute averages of active power consumption in UCT/GMT+1 time format. For validation purposes of the load data sets, the standard load profiles, simultaneity factors and peak load values are derived from the measured data and compared with existing values from literature.

2.1.1

Standard Load Profiles

Standard load profiles describe the characteristic consumption profiles of certain customer groups over one reference day. The reference days are typically defined 1 The

data is a courtesy of the Bayernwerk AG. The installation of the smart meter and the development of the measurement concept were conducted within the project ”Netze der Zukunft” by the Bayernwerk AG, the University of Applied Sciences Munich and the Technical University of Munich

2.1. LOAD DATA SETS

11

by a combination of weekdays (workdays, Saturdays and Sundays) and time intervals (winter period, transition period, summer period). For Germany, a total of 9 different types of so-called VDEW2 standard load profiles for domestic loads (so-called H0-Profiles) are available. Their main purpose is to provide a simplified calculation basis for the energy consumption forecast of a DSO balancing group. According to §12 StromNZV, DSOs are obliged to use standard load profiles for accounting issues of end customer at LV level with an annual energy consumption of up to 100,000 kWh. From 100,000 kWh annual energy consumption on, specific power measurement data needs to be recorded. Within this subsection, the VDEW standard load profiles are used as a basis to validate the recorded smart meter load data of the ”Seebach” region. It is of interest, if the majority of the recorded data sets for private end customer show distinct characteristics at certain points in time. Figure 2.1 compares the standard load profiles of VDEW and ”Seebach” for winter and summer workdays. Both profiles are normalized for an energy consumption of 1,000 kWh/yr. Detailed information on the construction of the VDEW standard load profiles can be found in [27]. Motivated by this approach, the standard load profiles from the smart meter measurement data are derived as follows: 1. For each recorded data set (i.e. each household), a subset containing the measured data of the respective VDEW period (e.g. all workdays of the winter period) is extracted. 2. The respective subsets are filtered for days with data gaps, which are excluded from further evaluation. The remaining data covers a total of m completely filled single day profiles for each VDEW period (e.g. m = 7809 for winter workdays [25]). In the following, m is considered to be the base population of each characteristic day. 3. For every 10 minute time slice, the mean over m consumption values is calculated. 4. The derived profile is normalized for an energy consumption of 1,000 kWh/yr, following the approach described in [18] and [25]. Although only 143 measured data sets are available for this analysis, the direct comparison of the VDEW standard load profile and the mean of the ”Seebach” data shows a good match. Fig. 2.1 shows the VDEW standard load profile and its ”Seebach” equivalent, exemplary for winter workdays. The Box-Whisker plots, which are depicted separately for every 10 minute time slice, indicate, that the smart meter data of the domestic loads are not normally distributed. Similar analysis show that a log-normal distribution [23] or a Beta or Weibull distribution [28] 2 The

German Association of Energy and Water Industries VDEW (today BDEW) published the standard load profiles after a broad measurement campaign in 1985 (see [26] and [21]).

12


are appropriate to describe the distribution of domestic loads. Additional statistical information on the robustness of the sample distribution is given by the standard error σm (see equ. 2.1, σ is the standard deviation of the respective time slice samples). Figure 2.2 shows the standard error for each of the 10 minute time slices of the winter workday subset, which is based on m = 7809 single day profiles. As the calculated standard errors are small compared to mean values of the base population, the amount of smart meter data is considered to be appropriate for further analysis. σ σm = √ m

(2.1)

Figure 2.1: Standard load profiles derived from smart meter data, exemplary shown for winter workday.

Figure 2.2: Standard error of the smart meter data, exemplary shown for winter workday.

2.1. LOAD DATA SETS

13

In the next subsection, values for the equivalent load (e.g. peak load and low load conditions) for residential areas are derived from the smart meter data.

2.1.2

Equivalent Load

For grid planning purposes (e.g. the sizing of transformer and cables), information on the equivalent load of a particular service area with a certain number of end customer n are of interest. This information can be either the expected peak load in consumption dominated grids or the expected low load in grid sections with high generation capacity. In this subsection, the equivalent peak load and low load values are derived, using the smart meter data recorded at private end customer sites. In general, two different approaches for the calculation of equivalent loads can be distinguished: • Direct deviation of equivalent loads from smart meter data. • Equivalent loads calculated from simultaneity factors in combination with information on the installed load. Both approaches are discussed in the following. Direct Deviation of Peak Load and Low Load: For each VDEW period, information about the peak and low load conditions can be derived from the respective base populations m. To show the dependency of peak load and low load values on the number of households n = 1, 2, ..., 100, a total of 10, 000 · n profiles without gaps are randomly drawn from the respective base population m (drawn profiles are no not put back to the base population within one iteration in order to avoid multiple considerations). The n drawn load profiles are accumulated and the respective low load and peak load values are saved. As this procedure is repeated 10,000 times for every number of n, k = 10, 000 single peak load pL and low load lL samples are available for n = 1, 2, ..., 100 households. The respective values are saved in form of the matrices PL and LL for further evaluation. PL = [pLi, j ]i=1,...,k; j=1,...,n

(2.2)

LL = [lLi, j ]i=1,...,k; j=1,...,n

(2.3)

Figure 2.3 shows the development of the peak load subsets PLn [pLi, j ]i=n; j=1,...,10000 over the number of households n, exemplary for winter Sundays (characteristic day with highest peak load values of the analyzed smart meter data sets) and summer workdays (characteristic day with lowest low load values of the analyzed smart meter data sets).

14


Figure 2.3: Peak load variation for summer workday (solid lines) and winter Sunday (dashed lines) data sets. Application of different percentiles.

For a more convenient applicability of the derived information, a parameter fit is conducted based on the 99% smart meter peak load percentiles for winter sundays, using a nonlinear least square fitting method on equ. 2.43 . This delivers a function for the 99% peak load percentil, depending on the number of considered households Pl(n). β Pl(n) = α − √ κ n

(2.4)

The fitted parameters are α = 1.16221, β = −7.14717 and κ = 1.39203. Equation 2.4 can be used for grid planning issues in load dominated LV grids. Here, the 99% percentile accounts for a reliability of 99%. Or in other words, sizing grid elements based on values from the 99% peak load percentil contains a 1% risk of exceeding the maximum loading of conductors and transformers. Using such a planning approach means that on average 1% of the LV grids need to be reinforced at a later stage [24].

3 The

parameter fits for this chapter were conducted by using the open source software c Gnuplot .

2.1. LOAD DATA SETS

15

Figure 2.4: Parameter fit using smart meter data from the characteristic day with highest peak load (winter Sunday).

Figure 2.5 depicts the characteristics of chosen percentiles for the derived low load subsets LLn [lLi, j ]i=n; j=1,...,10000 , for summer workdays and winter Sundays.

Figure 2.5: Low load variation for summer workday (solid lines) and winter Sunday (dashed lines) data sets. Application of different percentiles.

16


In LV grids with high level PV penetration, low load values in times of high solar irradiation can become of special interest for grid planning issues (e.g. for the determination of a grids hosting capacity as discussed in Chapter 3). Because of this, the low load values for the time slices 11 a.m. to 3 p.m and 11 a.m. to 1 p.m. are studied more closely, since high PV feed-in power can be expected to occur within these time intervals (see Section 2.2). Figure 2.6 shows the derived 1% low load percentiles for winter Sundays and summer workdays for the analyzed time slices, using the same procedure as for the peak load. In addition, a parameter fit on the low load data (summer workday) is conducted for the 11 a.m. to 3 p.m time slice, using equ. 2.5. The Ll11,3 (n) dependency will be used in Chapter 3 for the calculation of the hosting capacity of LV grids as it represents a worst-case assumption for grids with high local PV penetration. √ Ll11,3 (n) = α + κ n

(2.5)

The fitted parameters are α = −0.989711 and κ = 14.8996.

Figure 2.6: 1% low load percentiles for summer workday (solid lines) and winter Sunday (dashed lines) data sets for different time slices (UCT/GMT+1).

An alternative methodology to derive values for equivalent loads is using simultaneity factors together with assumptions on the installed load.

2.1. LOAD DATA SETS

17

Simultaneity Factors and Installed Load: Simultaneity factors SF are a measure for the temporal correlation of the peak load of n individual end customers within a certain time interval ∆t (typically one day). According to equ. 2.6 they are expressed as the ratio of the maximum of the accumulated load demand over the sum of the respective individual maximum load demand Px of n customers. SF =

max∆t {∑nx=1 Px (t)} ∑nx=1 max∆t {Px (t)}

(2.6)

The simultaneity factor varies with the number of loads. This dependency is expressed by equ. 2.7 [19], with g∞ as the simultaneity for an infinite number of loads (compare equ. 2.8). For the determination of the peak load equivalent for domestic loads, PlSF (n), SF(n) has to be multiplied by a value for the average installed load P(n). In literature, values from 5 kW to 30 kW, depending on the extend of electric loads (e.g. electric heating) can be found [19; 20]. SF(n) = g∞ + (1 − g∞ ) · n

−3 4

(2.7)

lim SF(n) = g∞

(2.8)

PlSF (n) = P(n) · SF(n)

(2.9)

n→∞

To extract SF(n) from the smart meter data, the base population m of each VDEW period is used. For n = 1, 2, ..., 100 households, 10, 000 · n single day profiles are randomly drawn from the base population m. For each of the 10,000 iterations, the simultaneity is calculated according to equ. 2.6. Again, drawn profiles are not put back to the base population within one iteration in order to avoid multiple considerations. Following this approach, 10,000 simultaneity factors are available for n = 1, 2, ..., 100 households, respectively. Figure 2.7 shows the average of 10,000 simultaneity factors, depending on the number of accumulated profiles n (i.e. number of households) for the base population of summer workday and winter Sunday as well as the threefold standard error 3σm . All simultaneity factors of the other VDEW periods lie between both curves.

18


Figure 2.7: Upper Figure: Simultaneity factor depending on the number of household loads n, exemplary for summer Workday (SU/WD) and winter Sunday (WI/SUN). Lower Figure: Threefold standard error based on m = 10, 000 samples.

The simultaneity factor alone does not deliver an equivalent load and hence has to be extended by information on the installed load (see equ. 2.9). This installed load depends on the peak and low load conditions of the characteristic days, as shown in the previous section. The installed load PInst (n) is gained by dividing the 99% peak load percentile Pl(n) by the respective SF(n). Figure 2.8 shows PInst (n) for winter Sundays as the characteristic day with the highest peak load values over the investigated year. As a result of the chosen approach, PInst is not constant but varies with the number of considered households.

2.1. LOAD DATA SETS

19

Figure 2.8: Installed load PInst (n) depending on the number of households for characteristic winter Sundays.

A comparison of the 99% peak load values of the smart meter data (winter Sunday) and the respective values from literature is presented in Fig. 2.9. Here, equ. 2.4 (from smart meter data) and equ. 2.9 (compare [19; 20]) are used. Because of the good match of the equivalent peak load from both data sets, it is assumed that the derived low load equivalent values are also usable for deeper analysis.

Figure 2.9: Comparison of peak load equivalent values derived from smart meter data (winter Sunday) and equivalent values from [19] and [20].

20


2.2 Generation Data Sets This section briefly discusses the characteristic values of the recorded PV generation data sets. The active power output of a total of 283 residential scale PV systems with an average installed capacity of 13.7 kWp (maximum 56.7 kWp) was measured over the period of one year. The resolution of the data is 10 minutes consisting of average values. The single profiles were normalized regarding their installed module capacity PSTC in [25]. Time stamps of the daylight saving time period were transformed into UTC/GMT+1 format in order to bring the load and generation time series in line. For grid planning issues, days with high accumulated PV feed-in are of interest, as high reverse power flows might occur during those days, which in turns can lead to high voltage rises and/or equipment overloading in particular grid sections (compare chapter 3). Because of this, the day with the highest accumulated PV feed-in ′ over all measured PV systems is determined for each of the characteristic Pmax VDEW periods (compare section 2.1), respectively. For this, the average feed-in over a total of nPV,i single day profiles PPV (t) without gaps is calculated for every time stamp t (PV profiles with a normalized feed-in higher than 1.3 p.u. are rated as suspicious and hence filtered out, compare Fig. A.1 in the Annex). For each day i of the particular VDEW period the highest accumulated feed-in value PPV max,i is saved according to equ. 2.10. ( ) n 1 PV,i PPV max,i = maxt (2.10) ∑ PPV,x (t) nPV,i x=1 In equ. 2.10 t = [1; 144] stands for the 10 minute time stamps and i = [1; k] for each day of a particular VDEW period with k as the total number of all days ′ of a VDEW period is belonging to this period. The highest PV feed-in value Pmax ′ Pmax = maxi {PPV max,i } .

(2.11)

Consequently, the day with the highest accumulated PV feed-in per VDEW period is defined by ′ . imax = i|PPV max,i = Pmax

(2.12)

Figure 2.10 shows the active power feed-in PPV (t) for nPV,i measured profiles ′ over the recorded year over the day imax with the highest accumulated feed-in Pmax (4th of May 2011, transition period, workday). This particular day started with clear sky conditions in the morning and shows some feed-in reductions in the afternoon, due to cloud movements.

2.2. GENERATION DATA SETS

21

Figure 2.10: Measured active power feed-in of PV systems at the day with the highest accumulated power feed-in during the recorded year (4th of May 2011, transition period/ workday). ′ and their particular date of occurrence for each Table 2.1 lists the values Pmax VDEW period, respectively. It should be considered that a 10 minute averaging time can filter high feed-in values considerably (compare chapter 5). Site specific aspects, such as tilt and orientation angle, inverter sizing and partial shading effects are also contributing to a relatively low accumulated feed-in over n PV systems. The lower feed-in values during the summer period are most likely due to a smaller module efficiency at relatively high ambient temperatures (a good overview on temperature/performance correlations of PV modules gives [29]). ′ over all n measured PV systems. Table 2.1: Days with highest accumulated PV feed-in Pmax

VDEW Period Winter/ Workday Winter/ Saturday Winter/ Sunday Transition/ Workday Transition/ Saturday Transition/ Sunday Summer/ Workday Summer/ Saturday Summer/ Sunday

′ Pmax

Date

0.7179 p.u. 0.6753 p.u. 0.6754 p.u. 0.7663 p.u. 0.7617 p.u. 0.7319 p.u. 0.6764 p.u. 0.6925 p.u. 0.6626 p.u.

04.03.2011 05.03.2011 13.11.2011 04.05.2011 09.04.2011 10.04.2011 03.06.2011 04.06.2011 04.09.2011

The PV feed-in values presented above cannot be directly used for grid simu-

22


lations, as they represent average values over n measured PV systems, respectively (extreme values are filtered out with this approach). In a next step, probabilistic analyses have to be conducted in order to derive more realistic values for the expected residual load, considering a smaller number of PV systems and hence more extreme feed-in scenarios.

2.3 Reverse Power Flows In this section, realistic worst-case assumptions for the expected reverse power flows in LV grid sections, depending on the level of PV penetration, are determined. For this, the derived low load values (compare section 2.1) and peak PV feed-in values (compare section 2.2) are superimposed and statistically analyzed. Figure 2.11 exemplary shows how low load and peak load values can be affected, if load profiles are superimposed with PV feed-in characteristics [18].

Figure 2.11: Effect of superimposition of PV feed-in and local load consumption on accumulated active power flows [18].

For each VDEW period, the following algorithm is applied in order to calculate the expected reverse power flows for particular LV grid sections, depending on the load pattern of n domestic loads (H0-Profiles) and the locally installed PV capacity PPV . • Randomly select n load profiles from each VDEW base population m (pulled profiles are not put back to the base population). • Randomly select n normalized PV generation profiles PPV (t) from the day ′ of each VDEW period. imax with the highest accumulated feed-in Pmax

2.3. REVERSE POWER FLOWS

23

• Scale the PV profiles PPV (t) from PPV = 1 kW p up to PPV = 10 kW p. • Superimpose load and PV time series and detect the peak and low load values of the accumulated power flows (low load values might actually become reverse power flows). This procedure is repeated 10,000 times for n = 1, 2, ..., 100 domestic loads and finally, the 99% peak load percentiles and 1% low load percentiles are saved. In contrast to peak load values, PV generation has a significant influence on the accumulated low load power flows as it has already been presented in [18]. Figure 2.12 exemplary shows the effect of an average installed PV capacity of 5 kWp per household on the resulting 1% low load percentile, depending on the number of private households n. Negative values stand for reverse power flows. In this analysis, the worst-case scenario by reverse power flows occurs during workdays within the transtition period. Because of this, the data set of the transition period will be studied in more detail below.

Figure 2.12: 1% low load percentile for different VDEW periods considering an installed PV capacity of 5 kWp per household.

In general, the dependency of the expected 1% low load percentile (i.e. the reverse power flows) in residential areas PRF on the number of households n and the average installed PV capacity per household PPV can be empirically expressed by equ. 2.13. PRF = f (n, PPV ) = α · nβ·PPV + γ · PPV + δ

(2.13)

Figure 2.13 compares PRF as derived from the smart meter data sets with the calculation results using equ. 2.13, exemplary for the worst-case scenario (workdays within the transition period). The parameters used are: α = −2.22996, β = −0.0264108, γ = −0.872303 and δ = 2.41438.

24

CHAPTER 2. SMART METER DATA ANALYSIS Transition Period/ Workday

Figure 2.13: Smart meter data (blue dots) and parameter fit (red grid) for 1% low load percentiles depending on the installed PV capacity [kWp/HH] and the number of households (n).

The application of equ. 2.13 leads to a relative error compared to the 1% low load percentiles directly derived from the smart meter data Pre f . The relative error for the transition period is shown in Fig. 2.14 for installed PV capacities from 1 kWp to 10 kWp per household. Equation 2.13 seems to represent a good approximation of the expected reverse power flows in residential areas with n = [2; 100] households and an average installed PV capacity of PPV = [2 kW p/HH; 10 kW p/HH], if a relative error of ±4% is acceptable. Relative Error = f (PPV , n) =

Pre f (PPV , n) − PRV (PPV , n) · 100% Pre f (PPV , n)

(2.14)

2.4. SUMMARY AND OUTLOOK

25

Transition Period/ Workday

Figure 2.14: Relative error between smart meter data and equation 2.13.

2.4 Summary and Outlook In this section, a statistical analysis of smart meter measurement data for domestic loads and residential scale PV systems has been presented. The recorded smart meter data was checked for characteristic load patterns by deriving standard load profiles from the measured data and comparing the results with the VDEW standard load profiles as known from literature. Based on this, worst-case assumptions for the expected peak load and low load power flows were derived. For practical reasons, parameters of mathematical equations were fitted to the gained results. These equations could be used by DSOs in the context of PV impact studies to determine the expected equivalent load in residential areas. In a next step, the recorded generation data sets were prepared and days with the highest accumulated PV feed-in were filtered for each characteristic VDEW period. By applying a probabilistic approach, the load data sets and the generation data sets were superimposed and information on the expected reverse power flows for different PV penetration level was extracted. A mathematical expression was fitted to this extracted data, which allows for a good approximation of the expected reverse power flows in residential areas, depending on the average installed PV capacity and the number of households. Table 2.2 summarizes the derived equations for peak load, low load and reverse power flows, which can be applied to evaluate sizing issues of transformers of branch feeder sections, for example.

26


Table 2.2: Summary of the findings of Chapter 2.

Equation (Time Interval)

Parameter

Worst-Case Period

α = 1.16221 β = −7.14717 κ = 1.39203

Winter/ Sunday

Low load √ Ll(n) = α + κ n (11 a.m. to 3. p.m.)

α = −0.989711 κ = 14.8996

Summer/ Workday

Reverse power flows PRF (PPV , n) = α · nβ·PPV + γ · PPV + δ

α = −2.22996 β = −0.0264108 γ = −0.872303 δ = 2.41438

Transition/ Workday

Peak load Pl(n) = α −

β √ κn

(whole day)

The above listed equations should be validated by using measured power flow data from aggregation nodes (e.g. transformer or feeder sections) in LV grids of residential areas with high local PV penetration. In addition, statistical analysis on reactive power flows in LV grid should be addressed as well in order to derive additional valuable information for grid planning issues and economic analyses. In the next chapter, the gained results will be used in the context of PV impact studies to analyze the hosting capacity of real LV grids for additional PV capacity.

Chapter 3

Hosting Capacity of Distribution Grids In the past, distribution grids and especially LV grids were often designed to serve local loads only. Decentralized generation capacity was not foreseen to be interconnected to those systems on large scale. Nowadays, with steadily increasing numbers of dispersed generators on distribution level, such grids often need to be reinforced in order to host the additional generation capacity. However, there are alternative measures besides traditional grid reinforcements, whose application could be technically reasonable in order to increase a systems hosting capacity on short notice. Some of these measures involve autonomous control capabilities of PV inverters and distribution transformer with OLTC. State-of-the-Art: For Germany, the first comprehensive investigation on the hosting capacity (in 2002 it was called ”maximale Netzanschlussleistung”) of electricity grids for PV installations and measures for increasing the hosting capacity was published in 2002 by [30]. In 2005, [31] presented a definition for the term ’hosting capacity’ of distribution grids for DER, based on performance indices for different quality aspects of electricity supply. With the increasing share of installed PV capacity across Europe, investigations on measures for increasing a grid’s hosting capacity for additional PV capacity became more frequent. Depending on the availability of grid data, studies were presented based on either generic LV grid structures [32; 21; 33; 34; 35; 36] or real distribution grid structures [37; 38; 39]. Often, the generic grid studies for Germany refer to investigations on grid characteristics, published by [40; 21; 30]. Regarding their assessment approach the studies can be distinguished between those using deterministic approaches (i.e., simulation of specific scenarios) [37; 32; 38; 33] and those based on probabilistic approaches (e.g., using Monte-Carlo simulations) [39; 34; 35; 36]. Properties, such as the PCCs of PV systems and their installed capacity, have a significant influence on the hosting capacity of a particular grid (compare [33]). Because of this, probabilistic assessment approaches gain

27

28

CHAPTER 3. HOSTING CAPACITY OF DISTRIBUTION GRIDS

in importance for the analysis of a grid’s hosting capacity for PV installations and hence can be considered as state-of-the-art. Figure 3.1 gives an overview on the field of research on hosting capacity of electricity grids for PV capacity.

Figure 3.1: Overview on field of research on hosting capacity of electricity grids for PV capacity.

Goal of the Chapter: It is the goal of this chapter to discuss the technical potential of autonomous voltage control strategies in terms of increasing the hosting capacity of LV grids for additional PV capacity. The additional value of the presented analysis is that the gained results are based on a total of n = 40 real LV grids from Germany. Besides reactive power provision by PV inverter the study also investigates the impact of an autonomously voltage driven active power curtailment by PV inverter and distribution transformer with OLTCs. Moreover, the additional technical potential of combinations of OLTC-based and PV inverterbased autonomous voltage control strategies is investigated. Sensitivity analysis show the influence of control parameter variations on the hosting capacity of the investigated grids. Methodology and Structure: The investigation starts with a general definition of hosting capacity in distribution grids (Section 3.1). Section 3.2 discusses on a theoretical level, how the autonomous voltage control strategies could be used to increase the hosting capacity of LV grids. In a second step, a separate methodology will be presented for each operation method, which allows to assess their impact on the hosting capacity of a particular LV grid by using load-flow calculations. In Section 3.4 the developed methodologies are applied in the context of a probabilistic approach, which assesses the effect of chosen operation methods on the hosting capacity of a set of 40 real LV grids from Germany. Sensitivity analy-

3.1. DEFINITION OF HOSTING CAPACITY

29

sis on the parameter settings of the single operation methods are carried out as well. Scientific Novelty and major Findings: The results highlight the technical potential of applying autonomous voltage control strategies at LV level. Especially OLTC-based voltage control strategies and a combined voltage dependent active and reactive power control of PV inverter (so-called Q(U)/P(U)) show a significant technical potential to increase the hosting capacity of voltage limited LV grids. Based on the analysis of 40 real LV grids, it is shown that a combined operation of OLTC-based and PV inverter-based voltage control strategies leads to no significant additional improvement for most of the investigated LV grids. For some of the grids, the combined application even leads to a reduced technical potential, as the OLTC alone is already capable of fully utilizing the hosting capacity of the grid, whereas the additional reactive power flows increase the loading of local equipment and hence might cause over-loading issues.

3.1 Definition of Hosting Capacity The term hosting capacity describes the maximum amount of generation capacity or load, that can be interconnected to a particular distribution grid or distribution grid section (e.g. a particular LV grid) while maintaining the quality of electricity supply. Schwaegerl et al. [31] use performance indices to illustrate the principle of hosting capacity depending on the penetration level of DER in electricity grids (see Fig. 3.2). In this context, the term ’performance index’ has to be considered as a placeholder, which can be exchanged by different quality aspects of electricity supply and whose limits are typically defined by requirements of technical standards and guidelines. For steady-state interconnection studies of PV in distribution grids, two major technical categories for the limitation of a grid’s hosting capacity can be derived: • The local voltage quality (voltage limitations) and • the maximum loading of conductors and transformer (current limitations).

30


Figure 3.2: Illustration of hosting capacity principle according to [31].

The required voltage quality in distribution grids is defined by the DIN EN 50160 standard, which, among others, limits the maximum voltage magnitude of slow voltage deviations at any node within the grid to ± 10% of its nominal voltage VN , for 95% of the 10 minutes intervalls of one week and to +10% and −15% at any time. In order to meet this requirement, a limitation of the voltage rise in LV grids to +3% (compared to the voltage magnitude without generation) is recommended by the German guideline for the connection to the LV grid [41]. This value can be considered as a worst-case approach, as it assumes a voltage rise over the MV impedances of already +2% compared to no generation (value defined in [42]) and a voltage offset of +4% VN at the MV busbar of the HV/MV substation transformer (including a voltage buffer of 1% VN and a MV/LV transformer ratio of 50). Figure 3.3 shows a typical voltage bandwidth for German distribution grids with OLTC at the HV/MV substation transformer. The segmentation of the single per unit values might differ from DSO to DSO. It has to be noticed that the above mentioned voltage rise of +2% resp. +3% VN compared to no generation is not the same as a voltage rise of +2% resp. +3% VN , as in most cases the voltage magnitude without generation will be below VN .

Figure 3.3: Example of permissible voltage rises along MV and LV impedances.

Depending on the focus of the investigation, the voltage related hosting capacity can be determined by either referring to absolute voltage values (e.g. according to DIN EN 50160) or by referring to the permissible voltage rise per voltage level (according to [42],[41]). In the context of this thesis, absolute voltage values are

3.2. STRATEGIES FOR INCREASING THE HOSTING CAPACITY

31

chosen (compare Subsection 3.3.1). Additional voltage quality criteria, such as harmonics, imbalances or flicker can also limit the voltage related hosting capacity of distribution grids, but are excluded from the scope of this thesis. For additional literature on voltage imbalances in LV grids, the reader can refer to [43] and [44], for example. The maximum acceptable equipment loading is not centrally defined by binding rules. In literature, values for the maximum transformer loading of up to 150% of the rated transformer power SrT can be found [45]. In the context of this thesis the current related hosting capacity will be reached as soon as the loading of conductors and transformer exceeds or can be expected to exceed 100% of their respective rated power. Table 3.1 summarizes the quality aspects of electricity supply, which are considered for the following investigations. Table 3.1: Summary of quality aspects limiting the hosting capacity for additional PV capacity as used for the following investigations. Applicable for steady-state analysis and investigation with separate voltage levels. Criteria Voltage Current

MV Level

LV Level

∆V = ±2%VN Vmax = 1.06 p.u. 100% of rated power (conductor and transformer)

∆V = ±3%VN Vmax = 1.09 p.u. 100% of rated power (conductor and transformer)

3.2 Strategies for Increasing the Hosting Capacity In this section, measures for increasing the hosting capacity of distribution grids for additional generation capacity are introduced. Subsection 3.2.1 starts with an introduction of the effectiveness of traditional grid reinforcement measures, such as the exchange of transformer and the laying of additional cables. Subsections 3.2.2 and 3.2.3 introduce the operation principle of autonomously controlled PV inverter and OLTC.

3.2.1

Traditional Grid Reinforcements

Traditional grid reinforcement describes measures which increase the local shortcircuit power Ssc of particular grid sections. Given VN as the nominal grid voltage, Ssc can be increased by lowering the respective short-circuit impedance Zsc according to Ssc =

VN 2 . Zsc

(3.1)

32


Equation 3.7 in subsection 3.2.2 will show that the lower the real part of the short-circuit impedance the less vulnerable a PCC becomes for active power feedin in terms of voltage deviations. A simplified example illustrates the sensitivity of Ssc along a LV feeder, depending on the short-circuit power at the upstream MV level SMV , the rated power of the transformer SrT and the cable type (Rcable and Xcable ). Therefore, the electrical equivalent circuit of single LV feeder is depicted in Fig. 3.4.

Figure 3.4: Equivalent circuit of single LV feeder

Figure 3.5 shows that Ssc decrease exponentially with the distance from the LV busbar of the distribution transformer. In close electrical distance to the LV busbar, Ssc can be increased significantly by substituting the transformer type from 250 kVA (usc =4%) to 630 kVA (usc =6%). With increasing distance from the transformer, an exchange of the transformer type becomes technically less effective in terms of increasing the local short-circuit power. If the respective LV grid consists of single long branch feeders, an exchange of cable types or a laying of additional cables is required. It is remarkeble that measures which increase the short-circuit power at upstream voltage level have almost no effect on the short-circuit power of PCCs at LV level 1 . The equations to calculate the respective impedances are given in the annex B.

1 Grid

reinforcement measures at MV level limit voltage rises along the MV impedances and hence lower the voltage offset at the LV busbar of the MV/LV transformer. This can contribute to increase the voltage related hosting capacity of downstream LV grids, although the short-circuit power within the LV grids is not effected explicitly.


33

Figure 3.5: Effect of different grid reinforcement measures on the short-circuit power along a LV feeder.

Although traditional grid reinforcement measures, such like laying of additional cable or exchanging of transformer types, increase the local hosting capacity of distribution grid sections for additional generation capacity, they lock up capital for a relatively long time. Hence, measures to increase the voltage related hosting capacity, e.g. by autonomously controllable PV inverter or OLTC, are desirable for a cost efficient distribution grid operation (compare chapter 5). Such measures could be applied on short-notice and can help saving time for the DSO to develop sophisticated grid planning approaches [6], [10]. The following subsection provides the reader with the technical background knowledge to understand the operation principle of chosen voltage control strategies.

3.2.2

Voltage Support by Controllable PV Inverter

In cases of high local distributed generation (DG) penetration reverse power flows occur in times when the local power generation exceeds the local power consumption (compare Section 2). These reverse power flows will lead to voltage drops over the upstream grid impedances, which means that the terminal voltage of a generator will rise depending on the injected current (compare [46], [47]). Figure 3.6 depicts a simplified electric schematic of a generator connected to the mains. In case of a current controlled voltage source inverter, the generator can be modeled as a current source whose terminal voltage VG is defined by its feed-in current I G as well as by the upstream grid impedance Z. For this example, the nominal grid voltage VN is assumed to depict an infinite bus with a fixed voltage magnitude of |VN | and a phase angle ϕVN of 0◦ . The voltage drop V Z over the grid impedance Z is V Z = Z · IG

(3.2)

34


Figure 3.6: Simplified schematic of a current source connected to the mains.

Taking into account the apparent power output of the PV system SG = P + jQ, the injected current I G becomes

IG =

SG VG

∗

=

P ·VGd + Q ·VGq +j 2 +V 2 VGd Gq

Q ·VGd − P ·VGq 2 +V 2 VGd Gq

!!∗

(3.3)

where VGd is the direct component of the generators terminal voltage and VGq the quadrature component. The grid impedance Z can be expressed in cartesian form by its resistance R and its reactance X. Z = R + jX

(3.4)

Assuming |VG | ≈ |VN | and ϕVN − ϕVG ≈ 0◦ (compare [48; 49] and Fig. B.2 in the Annex), and substituting I G and Z in equ. 3.2, the voltage drop over the grid impedance V Z can be approximated by P · X − (±)Q · R P · R + (±)Q · X = VZd + jVZq (3.5) +j VZ = |VN | |VN | Figure 3.7 shows a phasor diagram of the voltages and the current for an exemplary situation of a single generator in parallel operation (it should be noticed that the respective phasors are not drawn in scale due to a better readability). For each component a specific complex reference frame is indicated in order to help visualizing, if the current is leading or lagging its respective voltage phasor. In most cases (|VN | +VZd ) >> VZq , which means that the imaginary part of equ. 3.5 can be neglected. q 2 ≈ |V | +V |VG | = (|VN | +VZd )2 +VZq (3.6) N Zd This assumption allows to simplify equ. 3.5 in order to calculate the voltage magnitude at the generators terminal, depending on its active and reactive power feed-in. |VG | ≈ ℜ {V G } =

P · R + (±)Q · X |VN |

(3.7)


35

Figure 3.7: Phasor diagram for single PV system (Grid and Load = Load Perspective, Generator = Generator Perspective)

Equation 3.7 shows that feeding-in active power will contribute to rise the voltage at the generators terminal, while the reactive power capabilities of the generator (under-excitation) could be used to lower the terminal voltage (generators perspective: -Q = under-excited, +Q = over-excited, compare section B in the Annex). In contrast to voltage control at high voltage levels, where the X/R ratio of the grid impedance is >> 1, the influence ability of the voltage magnitude at medium and low voltage levels is usually considerably lower. In most cases |VN | >> VZd which means that the voltage angle ϕV G can be described using the imaginary part of V Z . VZq ϕV G = arctan (3.8) |VN | VZq =

P · X − (±)Q · R |VN |

(3.9)

From equ. 3.7 and 3.9 it becomes visible that controlling the active and reactive power output of a generator means influencing the voltage magnitude and the voltage phase angle, depending on the local grid impedance (X/R ratio). Table 3.2 summarizes the effect of active and reactive power control on the local voltage magnitude |V | and the local voltage phase angle ∠ (compare [50]).

36


Table 3.2: Influence of active and reactive power on the voltage magnitude and the voltage phase angle depending on the local X/R ratio.

Active power provision Reactive power provision

X/R >> 1

X/R VDB+ the voltage difference will be integrated over time, starting at t1 , until VLV drops back below VDB+ at time t2 again. The state variable x is reset as soon as VLV ≤ VDB+ (compare equ. 3.10). The transmission ratio of the transformer is increased (tap change is triggered), if x ≥ xmax becomes true. The same principle applies for lowering the transmission ratio in cases of low local voltages. In [52] and [53] more insights on the OLTC control concept are given. The parameters VDB+ and xmax are configurable and together determine the dynamics of the OLTC control.

38


x=

R t2 t1

(VLV −VDB+ ) dt i f VLV > VDB+ (3.10) 0 i f VLV ≤ VDB+

Figure 3.10: Autonomous local control principle for OLTC.

3.3 Improved Parameterization for PV Impact Studies It is the goal of this section to present a harmonized methodology, which could be used by DSOs in the context of PV impact studies to account for the positive effect of voltage control strategies. The derived approaches are later on applied in the context of Section 3.4 and the economical analysis in Chapter 5.

3.3.1

Basic Approach

If the leveraging effect of different autonomous voltage control strategies on a grid’s hosting capacity has to be compared, an alternative voltage criteria to the +3% voltage rise criteria of [41] needs to be considered. Operation methods, such as Q(V) and Q(V)/P(V) require the local voltage magnitude to adjust their power output, which is not addressed properly by the voltage rise criteria of [41]. In order to provide a unified base for the evaluation of the hosting capacity, it is suggested to set the slack bus voltage at the MV busbar of the distribution transformer to 1.06 p.u.. This will account for voltage offsets at the upstream MV level and hence provides a worst-case scenario for the additional voltage rise over the distribution transformer and the feeder impedances. The upper voltage limitation within the LV grid should be set to 1.09 p.u., which leaves a voltage buffer for measurement errors (compare Fig. 3.3). Besides the changes in the evaluation procedure, a harmonization of the parameter settings for the local load consumption and power feed-in by dispersed generation are necessary.

3.3. IMPROVED PARAMETERIZATION FOR PV IMPACT STUDIES 39

Load Consumption of Domestic Loads:For the parameterization of the active power consumption of domestic loads, the low load conditions during the time interval from 11 a.m. to 3 p.m. are of special interest. This is the time slice, when the maximum reverse power flows by PV have to be expected (compare chapter 2). In order to represent a worst-case scenario for the grid operation of residential areas, low load conditions for typical summer workdays should be considered (for the classification of typical consumption days refer to [27]). For the setting of the simultaneous active power consumption of private households equ. 2.6 from section 2.1 should be applied. In the case of commercial and/or agricultural loads a more individual approach becomes necessary, since their temporal power consumption might differ considerably over the period of one year. PV Feed-In: In cases of pure active power feed-in and without any additional voltage control functionalities, a simultaneous active power feed-in of 0.85 · PSTC seems to be appropriate for residential scale PV systems, installed in south-eastern Bavaria (expected value for maximum generation over x samples). This factor already accounts for generator specific inefficiencies, such as the overall module orientation and tilt angle, partial module shadings and dust coverings as well as the sizing of the inverter [54]. If certain operation methods for PV inverter have to be considered, additional assumptions for PV impact studies become necessary.

3.3.2

Modifications for PV Inverter Operation Methods

This subsection introduced the required parameter settings for PV impact studies considering the application of autonomous voltage control strategies. Cosϕ(P) Characteristic The cosϕ(PAC ) characteristic is suggested in [41]. Based on investigations described in [55], it is assumed that the average inverter sizing fsizing of residential scale PV systems Smax /PSTC is about 0.9 for south-eastern Bavaria. If reactive power has to be provided by those PV systems, the inverter sizing needs to be adjusted for guaranteeing that no additional feed-in losses occur due to a limited inverter capacity. The adjusted inverter sizing Smax,Q can be calculated using equ. 3.11. q (3.11) Smax,Q = PSTC · fsizing · 1 + tan (phi)2min PAC,100% = PSTC · fsizing

(3.12)

Because the simultaneity of the PV feed-in within the LV grid is still considered to be 85% of the installed module capacity PSTC (compare with basic approach), the provided reactive power Q has to be assumed to be 88.8% of the maximum reactive power Qmax according to equ. 3.13 and equ. 3.14, if the vertices of the char-

40


acteristic are set according to [41] (begin of Q provision at PAC,100% /2 and Qmax at PAC,100% ) and fsizing = 0.9 is assumed. The minimum power factor cos(phi)min depends on the installed capacity of the PV system [41]. s 1 −1 (3.13) Q = PSTC · 0.9 · 0.88 · cos(phi)2min s 1 Qmax = PAC,100% · −1 (3.14) cos(phi)2min Figure 3.11 visualizes these considerations.

Figure 3.11: Parameterization of reactive power provision by PV, considering a simultaneity factor of 0.85 (expected value) and an adjusted inverter sizing ( fsizing = 0.9).

Q(V) Characteristic One particular autonomous operation method for PV inverter, that aims at utilizing the reactive power control capabilities of an inverter, is a voltage dependent reactive power provision, the so-called Q(V) method, as depicted in Fig. 3.12. For distribution system operation in Germany, this operation method was first suggested for generators connected to the MV level in 2008 [42]. A discussion on the applicability of this operation method for LV grid operation is still ongoing in Germany (compare chapter 4.4).


Figure 3.12: Typical characteristic of a Q(V) static for a voltage dependent reactive power provision by PV inverter.

Before the Q(V) characteristic can be utilized as a measure for an improved LV grid operation, an adaption of [41] becomes necessary. As depicted in Fig. 3.12, the Q(V) characteristic can be parameterized by tuning V1 , V2 and Qmax . As a change of the inverters reactive power output is only subject to its locally measured voltage, the power factor at the PCC of the inverter will vary with different active power feed-in conditions. However, [41] limits the power factor of generating units to 0.95 resp. 0.9 depending on their installed capacity. Because of this contradiction, two different modes of the Q(V) operation method are possible: • The reactive power capabilities of the inverter are limited by the minimum power factor. Hence, Qmax can only be provided in times of maximum active power feed-in PAC,100% . • The reactive power capabilities are limited by Qmax . Hence, lower power factor than currently required by [41] are possible. Figure 3.13 visualizes the respective reactive power capabilities for both modes. The Q(V) operation method varies from the aforementioned cosϕ(P) method, as it represents a closed-loop control structure, with the local PCC voltage as the control variable. For the determination of inverter operation points, an iterative algorithm, considering the chosen Q(V) characteristic and local PCC voltage, has to be applied for load flow calculations. The suggested algorithm is divided into two major parts. First, the calculation of the reactive power set value Q′k for each inverter according to the Q(V) characteristic and the local PCC voltage (Part I) and second, an additional damping term in order to avoid numerical oscillations between different operation points (Part II). Such numerical oscillations might occur, if the local PCC voltage shows a good controllability by reactive power provision (compare Section 3.2.2) and/or if steep Q(V)-characteristics are chosen. Figure 3.14 shows the flow chart of the applied algorithm. The following calculation have to be conducted for all controlled PV systems.

42


Figure 3.13: PQ diagram of state-of-the-art PV inverter with reactive power control capability. The figure compares the possible area of operation for both, a reactive power provision restricted by a minimum power factor and a reactive power provision restricted by Qmax .

Figure 3.14: Flow chart for the iterative calculation of the reactive power output by applying a Q(V) characteristic.

Part I: For each iteration k, the respective terminal voltage Vk at the clamps of the controlled inverter are used to calculate the reactive power set values Q′k according to equ. 3.15.  Qmax  V2 −V1 · (Vk −V1 ) i f V1 ≤ Vk ≤ V2 ′ (3.15) Qk = Qmax i f Vk > V2  0 i f Vk < V1

Part II: The additional damping is realized as stated by equ. 3.16. Its purpose is to avoid possible numerical oscillations due to the interference between the local PCC voltage and the inverter’s reactive power provision.


Qk =

Q′k − Qk−1 δQ

+ Qk−1

(3.16)

The damping coefficient δQ needs to be adjusted for the respective droop. Values from 2 to 5 seem to be sufficient for most characteristics. The algorithm can be stopped if |Q′k − Qk−1 | ≤ ζQ for all controlled PV systems. For all iterations, Pk = PSTC · 0.85 remains constant. Q(V)/P(V) Characteristic For the application of a combined Q(V)/P(V) characteristic, as exemplary depicted in Fig. 3.15, an even more complex methodology for the determination of the inverters operation point has to be used.

Figure 3.15: Typical characteristic of Q(V)/P(V) statics for a voltage dependent reactive power provision and a voltage dependent active power output limitation.

The methodology of Fig. 3.14 has to be extended by an additional calculation block for the active power output (compare Fig. 3.16). The active power set value is then calculated according to equ. 3.17. It is important to feed the calculated active power set value Pk′∗ to the reactive power calculation block, as in cases of power factor restrictions, Pk′∗ needs to be considered for the determination of the reactive power set value Q′∗ k (compare equ. 3.19 and Fig. 3.13). h i  1−P   PAC,100% · 1 − V4 −Vmin3 · (Vk −V3 ) i f V3 ≤ Vk ≤ V4 Pk′ = (3.17) PSTC · 0.85 i f Vk < V3   Pmin i f Vk > V4

As Pk′ needs to remain smaller than PSTC · 0.85, an additional limitation of Pk′ might become necessary. ′ PSTC · 0.85 i f Pk′ > PSTC · 0.85 Pk′∗ = (3.18) else Pk′

44


Q′∗ k =

(

Pk′∗ ·

q

1 cos(phi)2crit Q′k

h ′ i Q < cosϕmin − 1 i f cos atan P′∗k k

(3.19)

else

′∗ Both set values, Q′∗ k and Pk , are then damped according to equ. 3.16. The ′ algorithm can be canceled if |Q′∗ k − Qk−1 | ≤ ζQ AND |Pk − Pk−1 | ≤ ζP becomes true for all controlled PV systems.

Figure 3.16: Flow chart for the iterative calculation of the reactive power output by applying a Q(V) characteristic and a voltage dependent active power limitation P(V).

3.3.3

Modifications for OLTC Operation Methods

The voltage rise limitation in LV grids of +3% according to [41] can be considered as outdated, if an OLTC is used. Permissible values for slow and fast voltage deviations are now limited by ∆VPV 1 = (Vmax −VBu f f er −VDB+ ) VN VN

(3.20)

with the maximum voltage magnitude Vmax , an optional voltage buffer VBu f f er and the upper controller deadband VDB+ for autonomous operation methods. For the calculation of the hosting capacity in LV grids, the slack bus should be moved to the LV busbar of the distribution transformer and its voltage magnitude should be set to VDB+ . This accounts for the worst-case scenario, in which the LV busbar voltage is at the higher end of the control deadband VDB+ . Figure 3.17 depicts the reshaped voltage band segmentation. It has to be considered that if ∆VPV has to be wholly utilized, fast voltage fluctuations at the MV level should be limited. Otherwise, a temporary overshoot of the control deadband could lead to violations of voltage limitations within the downstream LV level.


Figure 3.17: Decoupling of MV and LV level by using a distribution transformer with OLTC. The ± 10% VN EN50160 criterion is used here.

3.3.4

Summary of Modifications

Table 3.3 summarizes the set values for particular operation methods of different autonomous voltage control strategies. Although, the fixed power factor operation method Cosϕ f ix was not explicitly discussed before, it can also be found in the table below as the calculation of its set values is straight forward. The set values and methodologies in table 3.3 can be used to calculate the voltage related hosting capacity of LV grids. In the next section, these settings will be used to demonstrate the technical capability of autonomous voltage control strategies for increasing the hosting capacity for additional PV generation.

46


Table 3.3: Summary of set values for the calculation of the hosting capacity of LV grids. Operation Method

Set Value QPV

Set Value PPV

Base

-

PSTC · 0.85

Cosϕ f ix Cosϕ(P)V DE Q(V) Q(V)/P(V)

PSTC · 0.85 ·

q

1 cos(phi)2min

PSTC · fsizing · 0.88 ·

q

−1

1 cos(phi)2min

Iterative algorithm equ. 3.15 and Fig. 3.14 Iterative algorithm equ. 3.15, equ. 3.19 and Fig. 3.16

PSTC · 0.85

MV-busbar VSL = 1.06p.u. MV-busbar VSL = 1.06p.u. MV-busbar VSL = 1.06p.u. MV-busbar VSL = 1.06p.u.

equ. 3.17 and Fig. 3.16

MV-busbar VSL = 1.06p.u.

PSTC · 0.85 −1

Slack Bus (SL)2

PSTC · 0.85

OLTC

-

PSTC · 0.85

LV-busbar VSL = VDB+

Private Households

0

Low Load 11 a.m.-3. p.m. (compare Chapter 2)

-

3.4 Probabilistic Assessment for Increasing the Hosting Capacity by Autonomous Voltage Control Strategies In this section, the leveraging effect on the hosting capacity of real LV grids is determined for the autonomous voltage control strategies of Table 3.3.

3.4.1

Methodology and Structure

This investigation is divided into two major parts. At first, the additional hosting capacity by applying autonomous voltage control strategies is calculated for a set of n = 40 real LV grids from the official Smart Grid region ”Seebach” of the Bayernwerk AG. This approach avoids to work with generic standard grid types (i.e. classification into rural, suburban, urban etc.), as the transition between these types might be blurry and could lead to misinterpretations of the results. For further reading on statistical investigations on typical LV grid structures [30], [40] and [21] are recommended. The second part deals with sensitivity analysis on the parameterization of different operation methods. R The investigations within this section are conducted using Matlab and the power system simulation package MATPOWER [56]. Figure 3.18 shows the flow chart for the probabilistic assessment of the hosting capacity.

2 MV-busbar

and LV-busbar refer to the MV or LV side of the distribution transformer

3.4. PROBABILISTIC ASSESSMENT

47

Step 1: At the beginning, one of the total n = 40 real LV grid structures has to be chosen. Step 2: The slack bus needs to be redefined according to the assumptions of Table 3.3. Step 3: It is assumed that every designated private household load is theoretically capable of hosting a PV system. Hence, a total of m bus numbers (buses at which private households are connected to) are initially saved in the array PVBUS in random order. Step 4: The total number of w calculation relevant PV systems (PV systems which are activated during consecutive load flow calculation) are chosen from PVBUS . In order to speed up the iteration time, a so-called binary search algorithm is applied. For the first iteration, the total of w = m buses is considered. The steps 4 to 6 are conducted in parallel for all investigated control strategies. This allows a direct comparison of the gained results, as the initial configuration PVBUS is the same for all control strategies. Step 5: The power feed-in of the PV systems needs to be set according to the introduced methodology in section 3.3. For the installed PV capacity PSTC a value of 10 kWp is defined (average installed capacity for H0-customer in the Smart Grid region ”Seebach” [57]). Step 6: After setting the PV output power, a load flow calculation is performed to derive voltages and currents for the simulated configuration. In case that the hosting capacity (for its definition compare sections 3.1 and 3.3) has been exceeded for the particular configuration, the number of calculation relevant PV systems gets corrected following the procedure in Fig. 3.18. It has to be considered that agricultural and commercial loads are treated as normal H0-customer. As a result, the hosting capacity of each control strategy Sx is gained for n = 40 grids with m = 1000 random configurations, respectively. Sx = [sx,i, j ]i=1,...,m; j=1,...,n

(3.21)

The applied assessment approach calculates the theoretical potential of autonomous voltage control strategies for increasing a grid’s hosting capacity, as all PV inverters are assumed to be controllable. In contrast, for the calculation of the technical potential one would consider existing non-controllable PV inverters, meaning that only additionally installed PV inverters are assumed to provide reactive power or curtail their active power output for voltage support purposes.3 The presented investigations focus on the determination of the theoretical potential, as existing non-controllable PV inverters might be gradually replaced by ’smart inverters’ during future repowering processes.

3 For

OLTC based voltage control strategies the theoretical potential and the technical potential are the same. For consistency reasons, the term theoretical potential will be used as well.

48


Figure 3.18: Flow chart for probabilistic assessment of hosting capacity.

3.4.2

Basic Configuration Assessment

Following the methodology described in Section 3.3 and Fig. 3.18, the hosting capacity of n = 40 real LV grid from the Bayernwerk AG is calculated. The initial parameter setting of the single autonomous voltage control strategies is depicted in Table 3.4.


49

Table 3.4: Initial parameter settings of the investigated autonomous voltage control strategies. Control strategy

Parameter

Value

OLTC

VSet VDB+ VDB− CosPhi Characteristic CosPhimin CosPhimin CosPhicrit V1 V2 Q(V) as before Pmin V3 V4 PSTC fsizing

1.0 p.u. 1.02 p.u. 0.98 p.u. 0.95 VDE AR 4105 0.95 0.95 0.2 1.05 p.u. 1.08 p.u.

Cosϕ f ix Cosϕ(P) Q(V)

Q(V)/ P(V)

PV Settings

PSTC · 0.7 1.08 p.u. 1.09 p.u. 10 kWp 0.9

Figure 3.19 and Fig. 3.20 show box-whisker plots of the relative additional hosting capacity ∆HC (see equ. 3.22), which can be utilized by applying autonomous voltage control strategies (hosting capacity with voltage control strategy x applied Sx ) instead of pure active power feed-in (hosting capacity without voltage control strategies applied SnoControl ) in the investigated LV grids. The lower and upper limitation of the solid box depict the lower and upper quartile of the gained population (i.e., 50% of the medium values lie in between both quartiles). The range between both quartiles is called inter quartile range (IQR) . The outer whiskers have a maximum length of 1.5 · IQR, respectively. Outliers are surpressed for illustration purposes. ∆HCx =

Sx − SnoControl · 100% SnoControl

(3.22)

It has to be considered that all PV systems are assumed to be controllable. Consequently, the depicted results represent the bandwidth of the full theoretical potential, depending on the location of the PV systems within the respective grids.

50

CHAPTER 3. HOSTING CAPACITY OF DISTRIBUTION GRIDS Assessment Part I

Figure 3.19: Relative additional hosting capacity by autonomous voltage control strategies. The number below the grid name represents the number of nodes within the respective grid.


51

Assessment Part II

Figure 3.20: Relative additional hosting capacity by autonomous voltage control strategies. The number below the grid name represents the number of nodes within the respective grid.

52


In general, three different grid types can be observed in Fig. 3.19 and Fig. 3.20. First of all, there are 9 LV grids where no improvement could be achieved by applying autonomous voltage control strategies (Grids: 3, 6, 11, 12, 17, 18, 22, 24, 35). These grids simply did not experience any hosting capacity issues at all, since all PCC could be equipped with an uncontrolled 10 kWp PV system, respectively. Another 11 grids have to be considered as mostly current limited, as in more than 75% of all simulations with uncontrolled PV systems, current problems led to hosting capacity limitations instead of voltage issues (Grids: 2, 7, 10, 15, 16, 25, 29, 31, 36, 37, 38). For the same reason, 17 LV grids have to be considered to be voltage limited (Grids: 1, 4, 5, 9, 13, 14, 19, 20, 21, 23, 26, 30, 32, 33, 34, 39, 40). Here, the additional benefit of voltage control can often be utilized to full extend by the application of the investigated autonomous voltage control strategies. Finally, three grids (Grids: 8, 27, 28) experienced frequent voltage and current issues. For a better comparison of the theoretical potential, the additional relative hosting capacities ∆HCSx,Sy are determined between the hosting capacity of voltage control strategy Sx and the hosting capacity of an alternative voltage control strategies Sy (see equ. 3.23). Equation 3.23 delivers a matrix containing m = 1000 values for ∆HCSx,Sy for the n = 31 LV grids, respectively (the 9 LV grids where no improvement could be observed are excluded from the following discussions). In a next step, the median of each grid (over m = 1000 values) is calculated in order to gain more compact results. Figure 3.21 to Fig. 3.25 finally show the histogram of the calculated medians, grouped into fixed intervals. The intervals can be interpret as the additional technical benefit that can be achieved by applying a particular voltage control strategy instead of one of the alternative voltage control strategies. The depicted frequencies show the number of LV grids for which a certain additional hosting capacity could be observed.

∆HCSx,Sy =

Sx − Sy · 100% Sy

(3.23)


53

Figure 3.21: Cosϕ f ix : Additional hosting capacity that can be utilized by applying a Cosϕ f ix voltage control strategy compared to alternative voltage control strategies.

Figure 3.22: Cosϕ(P): Additional hosting capacity that can be utilized by applying a Cosϕ(P) voltage control strategy compared to alternative voltage control strategies.

54


Figure 3.23: Q(V): Additional hosting capacity that can be utilized by applying a Q(V) voltage control strategy compared to alternative voltage control strategies.

Figure 3.24: Q(V)/P(V): Additional hosting capacity that can be utilized by applying a Q(V)/P(V) voltage control strategy compared to alternative voltage control strategies.


55

Figure 3.25: OLTC: Additional hosting capacity that can be utilized by applying a OLTC voltage control strategy compared to alternative voltage control strategies.

Figures 3.21 to 3.25 show that the highest additional hosting capacities can be utilized by a combined Q(V)/P(V) approach and OLTC-based voltage control strategies. It should be noticed, that the presented results have to be interpreted as tendencies only, since grid specific characteristics may have significant effects on the realizable hosting capacity. This can be pointed out by comparing the grid specific distribution of the result values. For this, the qq-plot of the Q(V) voltage control strategy is exemplary depicted in Fig. 3.26 (see [58] for further reading). Here, the quantiles of the hosting capacity distribution of LV grid No.1 are plotted against the quantiles of the other 16 LV grids, which have been identified before to experience frequent voltage limitations. An exact match between the distribution of any of the 16 LV grids and the distribution of grid No.1 would exist, if the plotted points of a particular color were wholly covering the reference line. As this is not the case in this study, general statements about the expected additional hosting capacity, due to the Q(V) voltage control strategy, cannot be made. Instead, LV grids should be studied individually to ensure that grid specific characteristics can be taken into account.

56


Figure 3.26: QQ-plot for the results of the Q(V) voltage control strategy.

3.4.3

Sensitivity Analysis

This subsection discusses the outcome of sensitivity analyses on the parameterization of the Q(V) and Q(V)/P(V) characteristics as well as a combined application of OLTC and inverter based voltage control strategies. The sensitivity analyses are based on the 17 real LV grids, which have been identified before to experience frequent voltage limitations. It is the goal to show whether a certain controller parameter has a significant influence on the technical potential and therefore needs to be studied more in detail. Parameterization of Q(V) and Q(V)/P(V) Characteristic: Figure 3.27 shows beanplots of the additional hosting capacity for different starting points of the Q(V) characteristic V1 . The plot shows the distribution over all 17 investigated LV grids. It becomes clear that shifting V1 towards higher voltage values reduces the ability of the Q(V) voltage control strategy to increase a grids hosting capacity. This is due to lower accumulated reactive power flows, as less PV inverters will measure voltages above V1 and hence will not provide any reactive power. Figure 3.28 shows the effect of varying the parameter Plim of the Q(V)/P(V) control strategy. The lower Plim , the higher the active power curtailment in cases of high voltages. Although, this parameter can be quite sensitive for a grid’s hosting capacity its economic impact on the performance of the PV system has yet to be investigated (see Chapter 5).


57

Figure 3.27: Beanplot showing the distribution of the additional hosting capacity for different starting points of the Q(V) characteristic. The bold black line represents the median of the distributions. The plot was conducted using the beanplot package in R [59].

Figure 3.28: Beanplot showing the distribution of the additional hosting capacity for different active power limitations Plim . The bold black line represents the median of the distributions. The plot was conducted using the beanplot package in R [59].

58


Parameterization of OLTC Controller: Figure 3.29 and Fig. 3.30 show the results of a sensitivity analysis on the parameterization of the OLTC controller for two exemplary LV grids. By varying the set voltage VSet and the controller deadband [VDB− ,VDB+ ] of the OLTC, the permissible voltage rise over the downstream feeder impedance can be influenced. Lowering the set voltage and the controller deadband allows for a higher voltage rise over the feeder impedances and hence might lead to an increased hosting capacity until current problems can be observed (saturation in Fig. 3.29 and Fig. 3.30).4

Figure 3.29: Sensitivity analysis: Parameterization of OLTC controller (grid No. 5). The plot was conducted using the beanplot package in R [59].

Figure 3.30: Sensitivity analysis: Parameterization of OLTC controller (grid No. 9). The plot was conducted using the beanplot package in R [59].

The distributions over all 17 LV grids are combined in Fig. 3.32 for different OLTC controller parameterizations. The illustration shows that on average, a voltage rise of more than 9.5% VN does not utilize any additional hosting capacity, due to current limitations of the LV conductors. The slight decrease in hosting capacity, from 10.5% VN on, can be explained by higher currents, caused by lower grid voltages.

4 The lower OLTC set values are limited by the expected peak load conditions and the associated voltage drops over the feeder impedances. Power flow dependent set values for the OLTC controller promise a greater flexibility in this regards (compare [60], for example).


59

Figure 3.31: Sensitivity analysis: Parameterization of OLTC controller. Distribution over all 17 LV grids. The plot was conducted using the beanplot package in R [59].

Combination of OLTC and Inverter Based Voltage Control Strategies: The aforementioned OLTC based control strategy is applied in combination with the inverter based control strategies. For this investigation, the 17 LV grids are used as well. The assessment methodology is the same as introduced in Section 3.3 using the same initial controller parameterizations. As OLTCs are applied, the slack bus has to be moved to the LV busbar of the distribution transformer and its voltage magnitude is set to VDB+ in order to simulate a worst-case scenario. Hence, the additional reactive power flows, provided by controllable PV inverter, can only interact with the reactance of the cables, as the OLTC controller automatically corrects high voltage drops over the transformer impedance. Figure 3.32 shows the additional hosting capacity (median of distributions, compare subsection 3.4.2) that can be utilized by combining OLTC-based and inverterbased voltage control strategies, compared to a sole OLTC application. It is remarkable that only for few grids slight improvements could be achieved. These are grids, where the sole application of an OLTC cannot solve all voltage problems appropriately (e.g. due to single long branch feeders). In these cases, the additional reactive power flows cause additional voltage drops over the cable impedances and hence contribute to increase the grids hosting capacity. In contrast, there are also grids where the additional reactive power flows lead to an over-loading of cables

60


and hence decrease the grid’s hosting capacity, compared to a sole OLTC application. However, most of the grids showed no improvements at all, since the OLTC application alone is sufficient to equip all PCC’s with a 10 kWp PV system, respectively. Significant performance differences between the single PV inverter control strategies cannot be observed for the investigated LV grids.

Figure 3.32: Additional hosting capacity by combinations of OLTC and inverter based voltage control strategies compared to a sole OLTC application.

Altogether, it can be concluded that a combined operation mode of OLTC and local reactive power provisioning is rarely useful for the majority of investigated LV grids. Before combinations of OLTC-based and PV inverter-based voltage control strategies are applied, an accurate a priori analysis becomes necessary to assure the additional technical benefit of such control strategies on the real network.


61

3.5 Summary and Outlook In this chapter, the theoretical potential of autonomous voltage control strategies to increase the hosting capacity of LV grids has been discussed for balanced grid conditions. At first, the theoretical background has been briefly presented. Second, an assessment approach was introduced that allows for comparing the theoretical potential of different voltage control strategies during PV impact studies. This assessment approach has been applied on a total of 40 real LV grids in the context of a probabilistic investigation. The results highlight the case sensitivity of real applications. For LV grids which experience mainly voltage issues, an OLTC based voltage control strategy usually achieves the best results in terms of increasing the grid’s hosting capacity. Also a combined Q(V)/P(V) PV inverter control strategy performed well, compared to a sole reactive power provision by PV inverter. A sensitivity analysis on the OLTC controller parameterization suggests, that the theoretical potential of an OLTC-based voltage control strategy can be improved until a voltage rise of 9.5% VN over the LV feeder impedances is realized. Higher PV penetration level often caused current related cable over-loadings within the investigated LV grids. A combined application of OLTC and inverter based control strategies does not lead to significant increases of the hosting capacity for most of the investigated LV grids. Here, detailed a priori studies become necessary in order to assess the additional technical benefit of combined voltage control strategies and to minimize the possibility of unintended interferences between reactive power flows and the OLTC control. In further studies, the interferences between OLTC and PV inverter based voltage control strategies should be investigated in more detail. Of special interest are short term reactive power fluctuations caused by different reactive power based voltage control strategies and spatial balancing effects (that is the simultaneity of PV feedin for different weather conditions). The same investigations become necessary for MV grids where the OLTC controller of the HV/MV substation transformer could interfere with the accumulated reactive power flows from residential scale PV systems at downstream LV grids and utility scale PV systems at the MV level. First results on this topic were already presented by [61] and [62].

Chapter 4

Parallel Operation of Photovoltaic Inverters The previous chapter demonstrated the technical potential of autonomously controlled PV inverters for a grid’s hosting capacity. However, this technical potential can only be fully utilized, if the parallel operation of multiple autonomously controlled PV inverters remains stable under normal grid conditions. Especially voltage dependent active and reactive power control strategies of PV inverters (i.e. Q(V) and Q(V)/P(V) control) have to be studied more in detail, as unintended interferences between different controllable PV inverters needs to be avoided. This investigation demonstrates the technical feasibility of voltage dependent active and reactive power control by PV inverters under parallel operation. State-of-the-Art: Recently published studies were analyzing the parallel operation of residential scale PV systems with Q(V) voltage support [63; 64] in laboratory environment. The laboratory demonstration was set up using Q(V) controlled PV inverters from different manufacturer. The investigated scenarios showed no instabilities for and between Q(V) controlled PV inverters. In [65] results from laboratory tests and field tests were presented for an extended autonomous Q(V)/P(V) voltage control strategy, applied by PV inverters. Although [65] could show an oscillating reactive and active power output for very high controller gains and undamped inverter settings, it can be assumed that the tested PV inverters will find stable operation points, if practically reasonable gain and damping settings are used. Moreover, the reactive power output stability of a single utility scaled PV plant with Q(V) voltage support functionality and MV PCC was investigated in [66]. Further previously conducted studies investigated the stability of a single threephase droop-controlled (f(P) and U(Q)) PV inverter using dynamic phasor models [67] and the stability of two parallel operated PV inverters with Q(V) control in Micro Grids [68].

62

63

Goal of the Chapter: It is the main objective of this Chapter to compare the performance of two different autonomously operating voltage control strategies, based on a voltage dependent reactive and active power control of PV inverters. The investigated voltage control strategies are a combined Q(V)/P(V) droop control and the so-called automatic voltage limitation strategy. The latter one is a novel concept, which will be introduced in this Chapter as well. The performance of the respective voltage control strategies will be measured by their overall voltage support capability and the load-sharing capability under parallel operation. From a PV plant operators perspective a good load-sharing capability between PV inverters might be desirable to ensure a non-discriminatory plant operation, especially when active power curtailment is part of the applied voltage control strategy. Finally, the robustness of the control strategies against variations of process and control parameters will be analyzed. Methodology and Structure: This chapter is divided into four main sections. In Section 4.1, the PV inverter model with outer Q(V)/P(V) voltage support loop is described and validated by laboratory tests. Based on the validated PV inverter model an alternative voltage support approach is introduced in Section 4.2. This approach aims at limiting the PCC voltage of the PV inverters to a preset voltage threshold value by controlling the inverter’s active and reactive power output. The robustness of the two voltage control strategies against variations of process and control parameters is then investigated in Section 4.3 by simulating the timedomain response of the controlled inverter on sinusoidal voltage disturbances with different frequencies. Sensitivity analyses are conducted for the controller gains, PT1 filter time constants and power output gradient limitations. Section 4.4 deals with the assessment of the parallel operation of multiple voltage supporting PV inverters. The stability under parallel operation is analyzed in Subsection 4.4.1 and the load-sharing capability of the investigated voltage support approaches in Subsection 4.4.2. Scientific Novelty and major Findings: This chapter presents the results of a simulation based stability analysis for the parallel operation of PV inverter with Q(V)/P(V) voltage support functionality. In addition, a novel control concept of a so-called automatic voltage limitation by PV inverter is introduced. The results show that the common Q(V)/P(V) droop controller performance is relatively robust against variations of controller gains and the implementation of additional damping in the outer voltage control loop (e.g., voltage measurement filter and power gradient limitations). For the parallel operation of Q(V)/P(V) control approaches the consideration of additional damping in form of input or output filter and/or power gradient limitations is a crucial element to avoid undamped power oscillations caused by high proportional gains. As expected, the Q(V)/P(V) control approach shows a relatively good load-sharing behavior for PV inverter, connected in electrically close distance. The general applicability of the automatic voltage limitation approach under paral-

64

CHAPTER 4. INVERTER CONTROL

lel operation could also be demonstrated by the conducted simulations. However, this control approach shows a relatively high parameter sensitivity compared to the Q(V)/P(V) control approach. Especially the implementation of additional damping might reduce the overall controller performance considerably. Moreover, the introduction of a single voltage threshold value weakens its load-sharing capability.

4.1 Modeling of Photovoltaic Inverters with Voltage Support Functionality This section presents a detailed description of the PV inverter model, that is used as a basis for the investigations within this chapter. Depending on their contribution to the grid operation, PV inverters can be classified as either grid forming, grid feeding or grid supporting components [67]. In this context, autonomously controlled PV inverters with voltage control functionality act as grid supporting components. In contrast to pure grid feeding inverter they contain an additional outer voltage support loop, often realized in form of Q(V) and/or P(V) droops (see [67], [69], [70], [71] and [47] for additional information). Figure 4.1 gives an overview on the cascaded control structure of an autonomously controlled grid supporting inverter. If the inverter model is realized as a current controlled voltage source inverter (VSI), it requires an internal current control loop with current output filter (e.g. of type LC or LCL) in addition to the actual outer grid supporting controller. The grid impedance model is necessary to study the effect of different grid coupling scenarios (e.g. distinguishing between mostly resistive or reactive grid coupling impedances).

Figure 4.1: Block diagram showing the cascaded control structure of grid supporting current controlled voltage source inverter.

For the inverter’s inner current control loop and current output filter various examples in literature exist (see [72; 73; 74; 75; 76; 77], for example). For the following investigations, the model from [73] is chosen to represent the inner current control loop and current output filter of the overall PV inverter model (see Subsection 4.1.1 for further details). The basic features of this model are the following:

4.1. MODELING

65

• The model represents a three-phase inverter topology, which becomes more and more state-of-the-art also for small scale residential PV systems in Germany (e.g. see SMA TRIPOWER series with maximum apparent power ranges from 5 kVA to 20 kVA [78]). • The model is based on a detailed mathematical description, allowing for further extensions (e.g. outer voltage support loops) and independence from the inverter’s rated power. • The model is described in DQ and DQ0 reference frameDQ0Direct-QuadratureZero Components, which allows to effectively control direct quantities instead of alternating quantities. • The model comprises a current output filter of LC-type. • The model can be implemented in various simulation environments. The current control loop and output filter model is then complemented by a model for the voltage support functionality and a grid impedance model. A detailed description of the overall PV inverter model is presented in the following subsection. All simulations presented in this chapter are conducted with MATLAB Simulink.

4.1.1

Model Description

This subsection introduces the PV inverter model, comprising the inner current control loop and current output filter, the grid coupling impedance and the outer voltage control loop for voltage support functionalities by means of active and reactive power control. Inner Current Control Loop and Current Output Filter: Figure 4.2 shows the control scheme of the inverter’s inner current control structure with LC output filter and power reference conversion block, as introduced in [73]. The model represents the control structure of a three-phase VSI in the DQ reference frame with P∗ and Q∗ as external active and reactive power set values. The power reference conversion block calculates the direct and quadrature output current set values ∗ and I ∗ (in the following summarized as I ∗ ) depending on inverter’s output Io,d o,q o,dq voltage Vc,dq , measured over the LC filter capacitor. The current controller itself controls the inverter’s output current Io,dq Io Inverter Output Current by regulating Vdq . However, as the current controller effectively controls the filter inductor current ∗ IL,dq , the filter current set value IL,dq first needs to be derived from the output cur∗ rent set values Io,dq . A second order butterworth filter (BW-Filter) then filters the current set values before passing them to the actual current controller. For the following simulations, a cut-off frequency of 50 Hz is chosen. The current controller is made up of two separate PI-controller together with cross-axis decoupling and feed-forward terms (see [73] and [79] for more information). The phase-locked loop (PLL) is used for PCC voltage phase detection and phase synchronization

66


purposes. To limit the complexity of the overall PV inverter model, switching losses, MPP tracker and direct link voltage controller are neglected. Within the context of this thesis, the inverter’s inner current control loop and the current output filter are not subject to any sensitivity analysis and hence remain unchanged once they are set up.

Figure 4.2: Inverter’s inner current control model with LC current output filter as presented by [73].

Grid Impedance Model: In a balanced three-phase system, the coupling of the inverter with the grid impedance p can be modeled as depicted in Fig. 4.3. The grid coupling impedance Zc = R2c + ω2 Lc2 and the external ideal voltage source vN are modeled in the abc coordinate system. The inverter output current is io,abc and the voltage over the filter capacitor is vC,abc . The capacitance of the conductor is neglected in this approach.

Figure 4.3: Equivalent circuit for electric coupling of PV inverter in a balanced three-phase system. The grid impedance is modeled in the abc coordinate system.

The system of first order differential equations of the coupling impedance is described by equ. 4.1. Here, only balanced conditions are covered by the model. dio,abc 1 = · (vC,abc − vN,abc − io,abc · RC ) . dt LC

(4.1)

As the PV inverter model uses DQ-quantities, an abc-DQ0 transformation needs to be applied on the state variables. The used abc-DQ0 transformation matrices can

4.1. MODELING

67

be found in equ. C.1 and equ. C.2 in the Annex. Voltage Control Loop: In order to provide voltage support functionalities with the PV inverter model, the inner current control and current output filter model, introduced in Fig. 4.2, has to be extended by an outer voltage control loop as depicted in Fig. 4.4. The extended model can be optionally equipped with a low-pass filter that is used to filter short-term voltage fluctuations (see Section C in the Annex). The filtered voltage signal Vmea˜ is then used by the active and reactive power control block as an input signal for the P(V) and Q(V) control. It should be noticed that the filter could as well be placed in the forward loop of the controlled inverter system for smoothing the inverter’s output power, without changing the dynamics of the overall inverter system (see Section C in the Annex).

Figure 4.4: Inverter control scheme with inner current control and current output filter (green), the grid coupling impedance (black) and the outer voltage support loop (orange).

Figure 4.5 and Fig. 4.7 depict chain structure of the Q(V) and P(V) voltage support functionality, respectively. Both controller are set up in order to realize static active and reactive power droop characteristics, as introduced in Chapter 3. At first, a voltage dead band is applied on the measured and optionally filtered voltage signal Vmea˜, passing ∆V = V1 −Vmea˜, for Vmea˜> V1 and ∆V = 0 for Vmea˜ ≤ V1 . The reactive power control gain kq is determined according to equ. 4.2. Depending on the measured voltage signal, VN can be either the nominal line to line (LL) or the nominal line to neutral (LN) voltage. The voltage magnitudes at the beginning and at the end of the Q(V) characteristic are expressed by V1 and V2 for absolute values and v1 and v2 for per unit values (compare Fig. 3.12 in Section 3.3.2). kq =

|Qmax | Smax · sin (acos(cosϕmin )) h var i = VN · (v2 − v1 ) VN · (v2 − v1 ) V

(4.2)

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If necessary, the reactive power set value QSet gets limited by Qmax for Vmea˜≥ V2 and 0 for Vmea˜≤ V1 . Finally, an optional rate limiter can be applied to limit the reactive power gradients of the inverter.

Figure 4.5: Q(V) control scheme with Vmeaãs the measured and filtered voltage reference signal and Q∗ as the reactive power set value.

Figure 4.6 shows the inverter model’s reactive power output for increasing voltage magnitudes Vmea˜. For this simulation, no additional voltage measurement filter and gradient limitation are applied. Using additional damping elements, such as voltage measurement filter or gradient limitation, can cause deviations between the measured inverter output and the preset droop characteristic for the transition time between two operation points [80].

Figure 4.6: Reactive power output of inverter model for increasing voltage magnitudes Vmea˜(negative values = under-excitation).

The active power control has to modeled differently. Here, the active power control gain kp is used to set an upper limitation for the instantaneous active power feed-in, according to the P(V) droop characteristic of equ. 4.3 (compare Section 3.3 in Chapter 3). The upper active power limitation Plim,up = Pmax − kp · ∆V is kept between [0; Pmax ] in case that Vmea˜exceeds V4 or stays below V3 , respectively. ′ The output of the controller limitation block Plim,up is used as a dynamic limitation

4.1. MODELING

69

for the active power feed-in of the inverter. An optional rate limiter can be used to apply an active power gradient limitation for P∗ , too. W Pmax − Pmin (4.3) kp = VN · (v4 − v3 ) V

Figure 4.7: P(V) control scheme with Vmea˜ as the measured and filtered voltage reference signal and P∗ as the active power set value.

Figure 4.8 shows the inverter model’s active power output for increasing voltage magnitudes Vmea˜ . Again, no additional voltage measurement filter and rate limitations are applied.

Figure 4.8: Active power output of inverter model for increasing voltage magnitudes Vmea˜.

The interoperability of the P(V) control with the PV DC-power control (i.e. off-MPP mode, see [81]) is out of the scope of this investigation.

4.1.2

Model Validation

The expanded model of the three-phase current controlled VSI with outer voltage support loop and grid coupling impedance is validated in this subsection. As a basis for the validation, the real-time prototyping platform 3PExpressTM ,

70


comprising a 5 kVA three-phase power module of type PM5 from Triphase NV, is used (additional information are available on [82]). The power module is fed by a DC voltage source and operated as a three-phase inverter connected to the laboratory grid as schematically depicted in Fig. 4.3. For the coupling impedance, a resistance of R = 0.9Ω and a inductance of L = 1.75mH are assumed according to the ’extreme scenario’ as defined in [63]. The laboratory set up and demonstration were conducted by [80]. Additional information on the inverter settings are listed in Table 4.1. The vertices of the Q(V) and P(V) characteristics are set to v1 = 1.05 p.u., v2 = 1.08 p.u., v3 = 1.08 p.u. and v4 = 1.09 p.u., as depicted in Fig. 4.6 and Fig. 4.8, respectively. In order to influence the voltage magnitude at the inverter’s output clamps, the voltage offset profile depicted in Fig. 4.9 was artificially added to all three phases of the measured laboratory voltage in order to stimulate the inverter’s active and reactive power controller. The measured magnitude of the laboratory voltage was recorded during the test run with a sampling frequency of 50 Hz and later on used as the input profile for the external voltage source VN of the inverter model. Table 4.1: System parameter for the validation of the three-phase current controlled VSI with Q(V)/P(V) voltage support with the 5kVA power module of type PM5 from Triphase NV.

Parameter Inverter Type Current output filter topology Rated power Active power operating point Minimum power factor Cosϕmin Maximum reactive power slew rate Maximum active power slew rate Voltage measurement filter

Model

PM5

I-controlled VSI LC-Filter 5 kVA 4750 W 0.95 ±310 var/s ±950 W /s deactivated

I-controlled VSI LCL-Filter 5 kVA 4750 W 0.95 ±310 var/s ±950 W /s deactivated

4.1. MODELING

71

Figure 4.9: Voltage offset signal of external voltage source VN , which has been used to stimulate the inverters voltage dependent active and reactive power controller.

Figure 4.10 compares the response of the active and reactive power output of the inverter model and the Triphase system on the voltage test signal and Fig. 4.11 the measured voltages at the inverter’s output terminal. Both figures show an acceptable accuracy between model and hardware and hence confirm the model as a basis for further studies.

Figure 4.10: Comparison of simulated active and reactive power output of the 3 phase voltage source inverter model with the measured step responses of the Triphase system in laboratory environment.

The slight deviations between the measured inverter voltage can be caused by measurement errors and the different current filter topologies. The active and reac-

72


tive power spikes of the model are due to the sudden voltage changes and could be overcome by the application of more sophisticated decoupling methods within the current controller (see [81] for further reading).

Figure 4.11: Comparison of simulated and measured voltages.

4.2 The Concept of Automatic Voltage Limitation An alternative approach for autonomously supporting the grid voltage by means of active and reactive power output control is presented in this section. The idea of the automatic voltage limitation is to reduce the overall time a PV inverter operates in voltage support mode by introducing a single fixed voltage threshold at which the voltage controller gets enabled. This voltage threshold can be set to relatively high voltages and thus avoids active and reactive power control in times when the local grid voltage is still within permissible tolerances. The control concept is inspired by studies presented in [83] and [84]. First investigations dealing with the automatic voltage limitation have been already presented in [85] and [86]. The automatic voltage limitations has also been part of economical analysis, which can be found in [6] for PV systems at LV level and in [10] for PV systems at MV level. In [87] the concept was adapted for biogas plants and in [88] it was implemented in an energy management strategy for PV-battery systems. Operation principle: As soon as the measured and filtered voltage signal Vmea˜ exceeds a predefined voltage threshold Vtrsh , the VSI changes from grid-feeding mode (Mode 1) into grid-supporting mode (Mode 2 and Mode 3). At first, the in-

4.2. THE CONCEPT OF AUTOMATIC VOLTAGE LIMITATION

73

verter will try to bring Vmea˜back to Vtrsh by increasing its inductive reactive power consumption until either Vmea˜= Vtrsh is achieved or its reactive power capability Qmax is reached (Mode 2). If the reactive power provision alone is not sufficient to lower Vmeaãppropriately, its active power output is reduced (Mode 3). The VSI switches back to normal grid-feeding operation (Mode 1), if Vmea˜≤ Vtrsh and the active power reduction dP and reactive power provision dQ are both zero. For the implementation of the control algorithm two consecutive major function blocks are required; the selection of the operation mode and the actual active and reactive power control. Figure 4.12 provides an overview on the control structure of the automatic voltage limitation.

Figure 4.12: Overview on control structure of the automatic voltage limitation.

The switching between the operation modes is realized by a logic state inquiry in the ’Operation Mode’ function block. The respective set and reset conditions are listed in Table 4.2. For operation mode 2, two different set conditions need to be distinguished. Here, Mode 2-1 accounts for the transition from Mode 1 to Mode 2 and Mode 2-3 accounts for the transition from Mode 3 to Mode 2. Table 4.2: Logical set and reset conditions for switching between the operation modes of the automatic voltage limitation. Mode

Set condition

1 2-1 2-3 3

Vmea˜≤ Vtrsh Vmea˜> Vtrsh Vmea˜≤ Vtrsh Vmea˜> Vtrsh

∧ ∧ ∧ ∧

Reset condition dQ = 0 ∧ dP = 0 dQ = 0 ∧ dP = 0 dQ = |Qmax | ∧ dP = 0 dQ = |Qmax | ∧ dP = 0

Mode2 = 1 Mode1 = 1 Mode1 = 1 Mode1 = 1

∨ ∨ ∨ ∨

Mode3 = 1 Mode3 = 1 Mode3 = 1 Mode2 = 1

The detailed control structure of the ’Q Control’ block is depicted in Fig. 4.13. The reactive power controller gets enabled as soon as the operation mode changes into Mode 2. In this case, the voltage deviation ∆V serves as an input for a PIcontroller with anti wind-up limitation and downstream saturation block. A rate limiter can be optionally used for gradient limitation purposes. If required, the controller output dQ can be added to an external reactive power set value QSet , which should be set to zero for most applications.

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Figure 4.13: Control structure of reactive power control block.

Figure 4.14 show the detailed control structure of the ’P Control’ block. As soon as Mode 3 becomes active, ∆V is passed to a PI-controller in parallel structure with anti wind-up limitation, downstream saturation and rate limiter. The output of the actual controller, dP, is then subtracted from the instantaneous DC power generation in order to determine the active power set value P∗ .

Figure 4.14: Control structure of active power control block.

Figure 4.15 illustrates the response of the automatic voltage limitation to a voltage ramp applied on the external grid voltage VN . The considered parameter settings are listed in Table 4.3. The grid coupling impedance remains the same as introduced in Subsection 4.1.2. Table 4.3: System parameters for the demonstration of the automatic voltage limitation control strategy.

Parameter Rated power Active power operating point Minimum power factor Cosϕmin Maximum reactive and active power slew rate Voltage measurement filter Q controller proportional gain k1 Q controller integral gain k2 P controller proportional gain k3 P controller integral gain k4 Voltage threshold Vtrsh

Value 5 kVA 4750 W 0.95 ±10, 000 W (var)/s deactivated 1, 000 var/V 10, 000 var/V 1, 000 W /V 10, 000 W /V 1.05 p.u.

It should be noticed that the damping of the PV inverter system has been sig-

4.3. SINGLE OPERATION

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nificantly reduced for general demonstration purposes (this comprises the voltage measurement filter and the active and reactive power rate limitation). A detailed sensitivity analysis on the controller parameters is presented in Section 4.3.

Figure 4.15: Simulation based visualization of operation principle of the automatic voltage limitation control strategy demonstrated by applying a voltage ramp on the external grid voltage VN .

4.3 Single Operation of Photovoltaic Inverters - Controller Parameter Sensitivity This section will analyze the sensitivity of the Q(V)/P(V) and automatic voltage limitation controller performance on control parameter variations. With regards to the inverter’s overall dynamic behavior, the following control parameters are considered to be of special interest for this analysis: • Active and reactive power controller gains. • Voltage reference signal filter time constant (realized as PT1 low-pass filter). • Active and reactive power gradient limitation. Active and reactive power controller gain: The active and reactive power controller gains for the Q(V)/P(V) control strategy are varied by changing the beginning of the Q(V) droop characteristic v1 and the end of the P(V) droop characteristics v4 according to equ. 4.3 and equ. 4.2. The vertices v2 and v3 are kept constant at 1.08 p.u. for the following simulations. For the automatic voltage limitation strategy the proportional gains kp and kq of the active and reactive power controller are varied directly. Voltage filter time constant: A simple PT1 element is applied to serve as a low-pass filter for the measured voltage signal. It’s time constant T f is varied in the

76


context of this sensitivity analysis. The standard first order differential equation and the bode-plot of a PT1 element can be found in Section C in the Annex. Active and reactive power gradient limitation: The active and reactive power gradient limitations are set in the rate limiter block of Fig. 4.5 and Fig. 4.7 as well as of Fig. 4.13 and Fig. 4.14. As both voltage control strategies comprise different non-linear function blocks, such as rate limitations, saturations blocks and dead bands, common analysis techniques for linear time-invariant (LTI) systems in frequency domain fall short in this case. Instead, the whole control structure, as introduced in Section 4.1.1 and Section 4.2, will be stimulated by a sinusoidal disturbance signal, which is added on top of the external voltage magnitude VN according to equ. 4.4 (see also Fig. 4.4 for an schematic overview). The controllers response is then simulated for different parameter settings and different disturbance signal frequencies in steady state. With this approach, the gain and phase response of the control structure on certain disturbance frequencies can be analyzed. v′N = [vˆN + vˆdist · sin(ωdist t)] · sin(ωt)

(4.4)

ωdist = 2 · π · fdist

(4.5)

The amplitude of the disturbance signal vˆdist and the amplitude of the external voltage vˆN are adjusted in a way that they lead to a voltage magnitude VC at the output clamps of the inverter, which oscillates by 0.01 p.u. around the value of 1.08 p.u., if no voltage control is applied. Time domain simulations are conducted using a disturbance frequency fdist of 0.1 Hz, 0.5 Hz and 1 Hz, respectively. Table 4.4 summarizes the test cases for this sensitivity analysis. The parameter settings of the base configuration are highlighted (the PT1 low-pass filter is neglected in the base configuration). Table 4.4: Parameter settings for the sensitivity analysis. The highlighted values represent the base configuration of the controller. The droop vertices v2 and v3 of the Q(V)/P(V) control strategy remain constant at 1.08 p.u.. Test Case

Q(V)/P(V) v1 = 1.06/ 1.07/ 1.075 p.u. v4 = 1.10/ 1.09/ 1.085 p.u.

Automatic Voltage Limitation kp = 500/ 1,000/ 5, 000 W/V kq = 500/ 1,000/ 5, 000 var/V

Filter time constant

T f = 1/ 2/ 3s

T f = 1/ 2/ 3s

Gradient limitation

dP = 500/ 1, 000/ 10,000 W/s dQ = 500/ 1, 000/ 10,000 var/s

dP = 500/ 1, 000/ 10,000 W/s dQ = 500/ 1, 000/ 10,000 var/s

Proportional gain

The results for the Q(V)/P(V) voltage control strategy and the automatic voltage limitation strategy are presented in Fig. 4.16 and Fig. 4.17.


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Figure 4.16: Sensitivity of Q(V)/P(V) voltage control strategy on voltage fluctuations at the external grid. The black curves represent the uncontrolled inverter voltage Vc .

78


Figure 4.17: Sensitivity of automatic voltage limitation control strategy on voltage fluctuations at the external grid. The black curves represent the uncontrolled inverter voltage Vc .


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The results clearly highlight the importance of fast acting voltage controller dynamics for successfully mitigating voltage disturbances with frequencies of 0.1 Hz and above. Both investigated voltage control strategies performed well for a voltage disturbance frequency of 0.1 Hz. The peak shaving capability of the automatic voltage limitation can be clearly recognized in Fig. 4.17 (upper part). Increasing the proportional gains only lead to slight improvements for both voltage control strategies in terms of maintaining the voltage magnitude below 1.08 p.u.. However, for higher disturbance frequencies than 0.1 Hz and by introducing additional damping terms in the control feedback loop (e.g., voltage filter time constant, gradient limitation), significant performance differences between both voltage control strategies can be observed. In case of the automatic voltage limitation strategy one can clearly recognize the transition from operation mode 2 (reactive power provision only) to operation mode 3 (reactive and active power control), due to the highly resistive coupling of the inverter. As the automatic voltage limitation comprises two additional PI-controller in the P and Q control block, a sinusoidal disturbance signal can be considered as a worst-case scenario. Due to the relative slowness of the integral control in combination with the relative ineffectiveness of reactive power flows over the investigated coupling impedance (R/X ≈ 1.64), the introduced controller is not able to smooth out disturbance signals with relatively high frequencies, especially, if additional damping terms are considered. Figure 4.18 and Fig. 4.19 show the application of the automatic voltage limitation in combination with a real measured and highly fluctuating PV DC-power time series (one second resolution) and the measured laboratory voltage time series of Section 4.1.2. The voltage threshold was set to Vtrsh = 1.08 p.u.. The DC-power data was recorded in 2008 at a 1 kWp PV site, located in the city of Stuttgart, with mono crystalline modules [89]. The previous simulations suggest that the automatic voltage limitation strategy requires relatively fast controller dynamics in order to provide its full voltage support capability. This can be underlined by a time-domain simulation of the automatic voltage limitation controller, which has been parameterized aiming at highly dynamic performance (proportional gains k1 = 1, 000 var/V and k3 = 1, 000 W /V ; gradient limitation dQ = 10, 000 var/s and dP = 10, 000 W /s; no additional voltage filter). As a result, the inverter’s output voltage could be satisfactory limited to the predefined voltage threshold value with only minor overshoots, as Fig. 4.18 shows. As discussed before, the implementation of additional damping terms in the control feedback loop worsens the performance of the automatic voltage limitation strategy significantly. Figure 4.19 shows that in such a case, the inverter’s output voltage highly fluctuates around the preset voltage threshold value (here dQ = 500 var/s and dP = 500 W /s and a voltage measurement filter with T f = 3s are applied). The performance of the Q(V)/P(V) voltage control strategy with highly dynamic and slow controller parameterization is depicted in Fig. 4.20 and Fig. 4.21. In both

80


cases, the same droop settings are used (v1 = 1.07 p.u., v2 = v3 = 1.08 p.u. and v4 = 1.09 p.u.). As a result, the inverter’s output voltage is maintained below the upper voltage limitation of 1.09 p.u.. Implementing additional damping terms by changing the active and reactive power gradient limitation from dQ = 10, 000 var/s to dQ = 500 var/s and dP = 10, 000 W /s to dP = 500 W /s as well as adding a voltage measurement filter with T f = 3s, effects the performance of the control strategy only insignificantly. This makes the Q(V)/P(V) voltage control strategy relatively robust against varying controller parameterization.

Figure 4.18: Time domain simulation of single PV inverter system with automatic voltage limitation strategy and fast controller dynamics (proportional gains k1 = 1, 000 var/V and k3 = 1, 000 W /V ; gradient limitation dQ = 10, 000 var/s and dP = 10, 000 W /s; no additional voltage filter).


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Figure 4.19: Time domain simulation of single PV inverter system with automatic voltage limitation strategy and slow controller dynamics (dQ = 500 var/s and dP = 500 W /s and a voltage filter with T f = 3s).

Figure 4.20: Time domain simulation of single PV inverter system with Q(V)/P(V) voltage control strategy and fast controller dynamics (dQ = 10, 000 var/s and dP = 10, 000 W /s; no additional voltage filter).

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Figure 4.21: Time domain simulation of single PV inverter system with Q(V)/P(V) voltage control strategy and slow controller dynamics (dQ = 500 var/s and dP = 500 W /s; voltage filter with T f = 3s).

The conducted sensitivity analysis highlights the robustness of a Q(V)/P(V) voltage control strategy against varying inverter dynamics. For the automatic voltage limitation strategy, two different scenarios have to be distinguished. By neglecting additional damping terms, such as active and reactive power gradient limitations and voltage measurement filter, a well performing voltage peak-shaving functionality is observed. However, the automatic voltage limitation strategy showed only a poor robustness against slower inverter dynamics, resulting in significant voltage oscillations around the preset voltage threshold value. The following sections will analyze the performance of the Q(V)/P(V) voltage control strategy and the automatic voltage limitation for two parallel operated PV inverter.

4.4 Parallel Operation of Photovoltaic Inverters In recognition of the preliminary work in [63], [64] and [66], this section will complete the stability considerations by analyzing the stability of combined Q(V)/P(V) control strategies and the automatic voltage limitation strategy under parallel operation. An additional focus is set on the load sharing capability of both voltage control strategies, as it can be assumed that active power reduction of a PV system will almost always be followed by financial losses for the PV system operator (see investigations of Chapter 5). For the following analyses, time domain simulations using the PV system model of Section 4.1 will be conducted.

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83

In order to study interferences of PV inverter in voltage support mode, a two inverter network is set up in the abc coordinate system according to Fig. 4.22. By varying the coupling resistances (RC1 and RC2 ) and the coupling reactances (LC1 and LC2 ) different configurations can be set up. For this analysis, only balanced conditions are assumed.

Figure 4.22: Single line diagram for a two inverter network with external voltage source VN as the slack bus.

The dynamic system model for the electric network of Fig. 4.22 can be derived by applying Kirchhoff’s first and second law according to equ. 4.6 (currents at node K), equ. 4.7 (mesh ’Feeder’ → ’Coupling Branch 1’) and equ. 4.8 (mesh ’Feeder’ → ’Coupling Branch 2’). 0 = iC1 + iC2 − iFT 0 = −vN − iFT · RFT − LFT

diC1 diFT − iC1 · RC1 − LC1 + vC1 dt dt

(4.6) (4.7)

diFT diC2 − iC2 · RC2 − LC2 + vC2 (4.8) dt dt Rewriting and substituting equ. 4.6 to 4.8 yields a system of first order ordinary differential equations in form of equ. 4.9, with x as the state vector containing the branch currents and u as the input vector with the bus voltages. The detailed description of the deriviation is presented in Section C in the Annex. 0 = −vN − iFT · RFT − LFT

x˙ = A · x + B · u

(4.9)

Equation 4.10 describes the system of first order ordinary differential equations of the electric network of Fig. 4.22, where λ = LC1 LC2 + LC1 LFT + LC2 LFT . The transformer impedance can be considered by substituting the resistance RFT and ′ =L LFT by R′FT = RFT + RTra f o and LFT FT + LTra f o . Here, RTra f o and LTra f o are the resistance and reactance of the MV/LV transformer, related to the transfromer’s LV side, according to in Section B in the Annex.

84


 diC1 

 −R

dt  diC2  =   dt diFT dt

4.4.1

C1 (LC2 +LFT )

λ RC1 ·LFT λ −RC1 ·LC2 λ

  RC2 ·LFT ) −RFT ·LC2 iC1 λ λ    −RC2 (LC1 +LFT ) −RFT ·LC1  · iC2 + λ λ −RFT (LC1 +LC2 ) −RC2 ·LC1 iFT λ λ     LC2 +LFT −LC2 −LFT vC1 λ λ λ LC1 +LFT −LC1    −LFT · vC2  λ λ λ LC2 LC1 LC1 +LC2 vN − λ λ λ 

(4.10)

Stability of Parallel Operation and Controller Parameter Sensitivity

Based on the dynamic grid model of equ. 4.10 a configuration scenario for the parallel operation of two 20 kVA PV inverters is set up. The PV inverter settings as well as the grid and transformer data are listed in Table 4.5. Methodology: The two parallel connected PV inverter are parameterized according to the specification of Table 4.5 and are operated at a constant active power output of Smax · cosϕmin . At t=0.5s a voltage step of 1%VN /s is triggered at the external voltage source. This voltage step raises the measured inverter voltage and stimulates the voltage controller. As the grid coupling branches of the inverters are of the same length, their coupling impedances are the same, too. This can be considered as a worst-case scenario for the parallel operation, since both inverter measure the ’same’ voltage amplitude and hence react simultaneously on voltage fluctuations. The following simulations are conducted in the time domain.


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Table 4.5: Initial scenario parameterization for parallel operation stability investigations. Inverter power rating Smax 20 kVA cosϕmin 0.95 P operation point Smax · cosϕmin = 19 kW Initial voltage controller settings - Q(V)/P(V) Parameter Scenario 1 Scenario 2 Scenario 3 v1 1.075 p.u. 1.07 p.u. 1.06 p.u. v2 1.08 p.u. 1.08 p.u. 1.08 p.u. v3 1.08 p.u. 1.08 p.u. 1.08 p.u. v4 1.085 p.u. 1.09 p.u. 1.1 p.u. dP and dQ limitation dP = dQ = 2 · Smax /s Tf Voltage measurement filter deactivated Initial voltage controller settings - Automatic voltage limitation Parameter Scenario 1 Scenario 2 Scenario 3 k1 Smax 20% · Smax 10% · Smax k2 k1 · 10 k1 · 10 k1 · 10 k3 Smax 20% · Smax 10% · Smax k4 k3 · 10 k3 · 10 k3 · 10 dP and dQ limitation dP = dQ = 2 · Smax /s Tf Voltage measurement filter deactivated Cable data Cable type NAYY 3x95mm2 / 70sm/ sm 0.6kV / 1kV , data from [90] Specific resistance R′ = 0.3208 Ω/km Specific reactance L′ = 0.24 mH/km Length feeder C1 200m →RC1 = 0.064 Ω and LC1 = 0.048 mH Length feeder C2 200m →RC2 = 0.064 Ω and LC2 = 0.048 mH Length feeder FT 800m →RFT = 0.257 Ω and LFT = 0.192 mH Transformer data Transformer type 0.1 MVA 20kV/0.4kV DOTE 100/20 SGB, data from [51] Resistance RTra f o = 0.028 Ω 1 Reactance LTra f o = 0.183 mH

Results for Q(V)/P(V) Control Strategy: Figure 4.23 exemplary depicts timeseries plots of the output voltage of inverter 1 for the three test scenarios (application of different droop parameters) of Table 4.5. The network of equ. 4.10 is used. Each sub-figure shows the voltage magnitude of a certain setting of droop parameters and different controller dynamics. The blue line stands for the initial parameter settings according to Table 4.5, which represent relatively fast controller dynamics. The green and orange line show the sensitivity of the active and reactive power gradient limitation and the voltage measurement filter, while all other parameters are kept constant. The applied droop settings of scenario 1 and 2, together with the fast controller dynamics and the specific grid configuration can cause the inverter’s output voltage 1 For

the calculation of RTra f o and LTra f o see Section B in the Annex.

86


to oscillate after being stimulated by a voltage step. The inverter’s power output resembles a two-position controller, as the measured and processed voltage jumps from one end of the droop-characteristic to the other. By introducing an additional active and reactive power gradient limitation of 20% · Smax /s the amplitude of the oscillation can be reduced significantly, but not wholly suppressed. Only the application of an additional voltage measurement filter adds the required damping, that is necessary for the voltage controller to find a new steady operation point after the initial stimulation. For the simulated case-study, a voltage measurement filter time constant of T f = 1s is already able to provide sufficient damping to the system and in turns allows for higher controller gains, if required. In general, the simulation results have to be interpret as a worst-case scenario since absolute identical inverter control structures and dynamics as well as identical grid coupling impedances are assumed. A more realistic scenario is presented in Fig. 4.27. Here, the same recorded voltage time-series and DC-power generation profile as of Subsection 4.3 are applied. Furthermore, heterogeneous inverter settings are used (the settings are listed in Table 4.6). The effectiveness of voltage control by means of active and reactive power depends on the short-circuit power and the grid impedance angle at the inverter’s PCC (compare Chapter 3). Consequently, the grid impedance is an additional influencing factor that should be covered by stability analysis. Figure 4.24 exemplary shows that no voltage oscillations can be observed for scenario 1, if the cable diameter is changed from 3x95mm2 to 3x150mm2 (cet. par.). The higher X/R ratio of the 3x150mm2 cable lessens the effectiveness of active power output changes on the local inverter voltage and hence provides additional damping compared to lower X/R ratios. A similar effect can be observed by increasing the amount of controllable reactive power Qmax by lowering cosϕmin . In this case, the additional reactive power provision can already reduce the inverter voltage more sufficient and hence reduce the necessity of additional active power curtailment (Figure C.5 in the Annex exemplary compares the results of scenario 1 for different cosϕmin ). In general, the same argumentation is valid for reactive power control at PCCs with high X/R ratio.


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Figure 4.23: Measured voltage at the output clamps of inverter 1 before and after a 2.5%VN voltage step at the external voltage source while applying the Q(V)/P(V) voltage control strategy.

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Figure 4.24: Measured voltage at the output clamps of inverter 1 before and after a 2.5%VN voltage step at the external voltage source by simulating scenario 1. Cable data of type NAYY 3x150mm2 / 70sm/ sm 0.6kV / 1kV : R′ = 0.2075 Ω/km; L′ = 0.23 mH/km, [90].

Results for the Automatic Voltage Limitation Strategy: Figure 4.25 exemplary depicts time-series plots of the voltage magnitude at inverter 1 for the three test scenarios of Table 4.5 by applying the automatic voltage limitation strategy. While varying the active and reactive power gains k1 and k3 showed no significant influence on the dynamics of a single inverter system (see Section 4.3), they turn out to be crucial parameters for the parallel operation scenarios. Similar to the Q(V)/P(V) control strategy, the inverter voltage oscillates around the voltage threshold value Vtrsh if the initial controller parameter settings of scenario 1 are applied (k1 = k3 = Smax , fast controller dynamics). This oscillation can be suppressed by lowering the proportional gain values to 20%Smax and 10%Smax , respectively (see blue line of scenario 2 and 3). Adding additional damping to the voltage controller worsens the dynamic behavior of the automatic voltage control strategy, as already presented in Section 4.3. By introducing an active and reactive power gradient limitation of ± 20%Smax /s the control settling time increases significantly (green lines), while minor oscillations around Vt rsh still remain. Finally, the additional time delay of a voltage measurement filter with Ts = 1s leads to significant voltage overshoots by the automatic voltage limitation strategy. This is caused by the relatively high integral gains k2 and k4 of the active and reactive power controller, which lead to high active and reactive power output changes as they integrate the voltage deviation over a relatively long period compared to a direct voltage measurement input.


89

Figure 4.25: Measured voltage at inverter 1 before and after a 2.5%VN voltage step at the external voltage source while applying the automatic voltage limitation strategy.

90


From the previous results it follows, that reducing the integral gain of the active and reactive power controller can be an adequate measure to enhance the overall inverter system performance, if filtered voltage measurement signals are used. Figure 4.26 compares step response of the automatic voltage limitation for different integral gain values. It should be noticed that this does not affect the inverter system’s capability for smoothing out sinusoidal voltage noise signals as Fig. C.6 in the Annex exemplary shows.

Figure 4.26: Measured voltage at inverter 1 before and after a 2.5%VN voltage step at the external voltage source while applying the automatic voltage limitation strategy with different integral gains.


4.4.2

91

Load Sharing Capability

This subsection compares the load sharing capability of the proposed Q(V)/P(V) voltage control strategy with the automatic voltage limitation strategy exemplary for a heterogeneously parameterized two-inverter system. In the context of this study, the term load sharing is characterized by the inverter’s capability to counteract voltage rises by means of active and reactive power control, while simultaneously balance the controlled active and reactive power among multiple inverters. From a PV plant operator’s perspective, a good load-sharing capability is desirable if they do not get any monetary compensations for active power curtailments and hence feed-in losses. Active and reactive power droop controller are widely used for voltage and frequency control by generation units at transmission levels [91; 92], and were proposed for the operation of micro-grids in [93; 71; 94; 69; 95] as well as for island grids in [50; 96; 97]. Basically, voltage support via droop characteristic can be considered as sharing the controllable load between multiple inverters [70; 96; 47; 98]. For the automatic voltage limitation concept the load-sharing capability is assumed to be less distinct, as the following investigation will show. Methodology: A two-inverter system is set up for this analysis using the balanced grid impedance model of equ. 4.10. In contrast to the approach of the previously conducted stability analysis of Subsection 4.4.1, a heterogeneous system parameterization with slightly different feeder lengths and inverter dynamics is assumed. This accounts for the differing dynamics of commercially available PV inverters from different manufacturers, as used in [63], for example. Table 4.6 summarizes the inverter and grid settings for the following time-domain simulations. For the external voltage source and the DC-power generation of the PV inverter, the measurement profiles of Section 4.3 are used. Starting at t = 2s the external voltage magnitude is ramped up with a slope of 0.05p.u./s until t = 10s, enabling the inverter’s voltage controller. The total simulation period is 3 minutes.

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Table 4.6: Scenario parameterization for the load sharing simulations. For the transformer data see Table 4.5. Inverter power rating for inverter 1 and 2 Smax 20 kVA cosϕmin 0.95 P operation point Smax · cosϕmin = 19 kW Voltage controller settings - Q(V)/P(V) Parameter Inverter 1 Inverter 2 v1 1.07 p.u. 1.07 p.u. v2 1.08 p.u. 1.08 p.u. v3 1.08 p.u. 1.08 p.u. v4 1.09 p.u. 1.09 p.u. dP and dQ limitation 2 · Smax /s 20% Smax /s Tf deactivated 1s Voltage controller settings - Automatic voltage limitation Parameter Inverter 1 Inverter 2 Vtrsh 1.08 p.u. 1.08 p.u. k1 20% · Smax 10% · Smax k2 1 · k1 1 · k1 k3 20% · Smax 10% · Smax k4 1 · k3 1 · k3 dP and dQ limitation 2 · Smax /s 20% Smax /s Tf deactivated 1s Cable data Cable type NAYY 3x95mm2 / 70sm/ sm 0.6kV / 1kV , data from [90] Specific resistance R′ = 0.3208 Ω/km Specific reactance L′ = 0.24 mH/km Length feeder C1 20m →RC1 = 0.0064 Ω and LC1 = 4.8 µH Length feeder C2 15m →RC2 = 0.0048 Ω and LC2 = 3.6 µH Length feeder FT 300m →RFT = 0.096 Ω and LFT = 0.072 mH

Results for the Q(V)/P(V) Control Strategy: Figure 4.27 compares the inverter’s output power and their local voltage magnitudes for the simulated twoinverter system. Due to its parameterization, the active and reactive power output of inverter 1 show a faster transient response than the active and reactive power output of inverter 2. For the local inverter voltage, a continuous steady state error, which is typical for a proportional controller without integrating elements, can be observed.


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Figure 4.27: Load-sharing capability of Q(V)/P(V) voltage control strategy with heterogeneous inverter parameterization (Inverter 2: T f = 1s).

Results for the Automatic Voltage Limitation Strategy: The initial hypothesis of a less distinct load-sharing capability of the automatic voltage limitation strategy can be confirmed by the simulation results. Due to the clear voltage threshold and the faster transient response of inverter 1, a significant deviation of the

94


inverter’s output power can be clearly recognized from Fig. 4.28.

Figure 4.28: Load-sharing capability of automatic voltage limitation strategy with heterogeneous inverter parameterization (Inverter 2: T f = 1s).

Table 4.7 quantitatively summarizes the results of the load-sharing simulations. It clearly shows that the inverter with faster controller dynamics (inverter No. 1)


95

has to provide more reactive energy and to curtail more active power than the inverter with slower dynamics. The provided reactive energy is measured by the ratio (EQ1 /EQ2 ) ∗ 100% and the active power curtailment by (EP1 /EP2 ) ∗ 100%. The time-domain plots for the 3s and 5s filter time constant can be found in Section C in the Annex. As the energy missmatch between both inverters mainly depends on differences in their dynamics, it should be considered of defining a frame for the parameterization of the outer voltage control loop in the context of standardization processes. Fast inverter dynamics could eventually discriminate single PV systems, when it comes to active power curtailment for over-voltage mitigation. Table 4.7: Summary of load sharing capability of the Q(V)/P(V) voltage control strategy and the automatic voltage limitation strategy. EQ1 EQ2

Inverter 2: T f Q(V)/P(V) AVL

EP1 EP2

· 100%

1s 3s 5s 100% 99.9% 99.9% 117.6% 135.3% 171.5%

1s 98.3% 59.2%

· 100%

3s 96.2% 53.5%

5s 94.0% 48.4%

4.5 Summary and Outlook The parallel operation of PV inverter using a Q(V)/P(V) voltage control and a automatic voltage limitation strategy has been discussed in this Chapter. In the context of this analysis, the following technical aspects were considered to be of special interest for a parallel operation of voltage supporting PV inverter: • Analyze the controller performance regarding its general voltage support capability. • Analyze the robustness of the investigated voltage control strategies against variations of control and process parameter. • Analyze the load-sharing capability of the investigated voltage control strategies. As a basis for this investigation a detailed dynamic model of a three-phase current controlled VSI with outer voltage support loop was set up in MATLAB/Simulink and validated against measured data from laboratory demonstrations. Based on the validated inverter model the control concept of the so-called automatic voltage limitation strategy was introduced. From the perspective of DSOs it might be desirable to apply PV inverter with relatively slow acting voltage support loops to ensure a smooth transient operation during times of high local voltages. Since the dynamics of the voltage support loop are predominantly influenced by the controller gain, optional power gradient limitations and voltage measurement filter, sensitivity analysis were conducted by varying these controller parameters. The investigated Q(V)/P(V) voltage control strategy shows a sufficient robustness

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against variations of the aforementioned controller parameter and could also be parameterized to ensure a relatively slow time response (by enabling power gradient limitations and voltage measurement filter). On the one hand, the inverters lose their ability to mitigate fast transient voltage fluctuations, if additional damping elements are applied. One the other hand, additional filter and/or power gradient limitations stabilize the parallel operation of PV inverter with Q(V)/P(V) voltage support functionality. For the simulations, such a stabilization effect could already be achieved by applying relatively low filter time constants (here 1s for a low-pass filter of type PT1). One drawback of the Q(V)/P(V) control is the steady-state error, which is typical for control structures without integrating elements. The general functioning of the automatic voltage limitation concept for single and parallel operation could be demonstrated by the conducted simulations. However, fast acting inverter dynamics are essential to ensure its proper applicability. The implementation of additional damping elements can have a significant influence on the inverter’s overall time response and hence make this control concept less robust against parameter variations, as sensitivity analyses showed. As it is the nature of the applied Q(V)/P(V) droop characteristics to provide its control functionality over the voltage range [V1 ;V4 ], it shows a better load-sharing capability than the automatic voltage limitation concept, which is enabled by exceeding a predefined voltage threshold Vtrsh . However, different inverter dynamics reduce the inverter’s load-sharing capability and hence can lead to energy mismatches between inverter with voltage support functionality, even if they are installed in electrically close distance. Due to its higher robustness against variations of controller and process parameter and its more distinct load-sharing capability it can be concluded that the Q(V)/P(V) voltage control strategy should favored over the alternative automatic voltage limitation strategy. Outlook: Besides the gained results from this study, it can be expected that unbalanced grid conditions in combination with different types of voltage measurements and measurement processing will influence the load-sharing capability of parallel operated PV inverters with voltage support functionality. This effect should be analyzed more in detail in future studies, possibly triggering discussions on a standardized usage of feedback variables. In a next step, the simulations should be also complemented by laboratory demonstrations in order to confirm the gained results and to evaluate the interferences of the embedded voltage controller with other internal inverter control structures (e.g., DC/DC converter control and DC-link voltage controller).

Chapter 5

Economic Assessment The previous chapters demonstrated the technical potential of applying autonomous voltage control strategies in terms of increasing the hosting capacity of distribution grids. It was claimed that traditional grid reinforcement measures, such as laying of parallel cables and/or replacing distribution transformers, can be deferred or even wholly avoided by applying autonomous voltage control strategies. However, the application of autonomous voltage control strategies will also affect the power flows within the distribution system (e.g., by additional reactive power provision or active power curtailment) and hence can lead to increased network losses or reduced active power feed-in by PV systems. For an encompassing cost-benefit analysis of autonomous voltage control strategies it is therefore necessary to take operational costs into account as well. This chapter will present a cost-benefit analysis for chosen autonomous voltage control strategies, which are based on the control capabilities of PV inverter and distribution transformer with OLTC. Based on the example of two real LV grids it will be shown that the application of distribution transformer with OLTC and PV inverter with Q(V)/P(V) voltage control can enable a significant cost reduction potential from the DSO perspective. Parts of this investigation have been already presented in [6; 10; 99]. State-of-the-Art: Figure 5.1 gives an overview on different approaches for an economic assessment of voltage control strategies in distribution grids. Depending on the availability of real grid data, studies based on generic grid data [33; 9; 6; 100] and real grid data [101; 10] can be found in literature. Concerning the considered cost categories, one can differentiate between investigations on investment costs (e.g., reinforcement of grid section by exchanging transformer or by parallel cables) and operational costs (e.g., additional feed-in losses due to active power curtailment and additional network losses). In [101] the accruing investment costs of several centralized control strategies(i.e., coordinated voltage control and substation OLTC control based on remote measurement data) were compared with the investment costs of traditional grid reinforcement measures over several years, based on real MV grid data (for further reading see also [102; 103; 104]). The eco-

97

98

CHAPTER 5. ECONOMIC ASSESSMENT

nomic assessment is based on net present value calculations, considering the time value of future cash-flow time-series. In [100] results of cost-benefit analysis for different local and de-centralized voltage control strategies, based on generic MV and LV feeder, are presented. The results of the investment costs are based on a static annuity method while operational cost are derived from 15 minute steady-state time-series analysis. Recently, [105] presented an economic assessment of different local voltage control strategies, applied within a real LV grid. The focus of this study is set on analyzing the additional feed-in losses for PV plant operators, which can be associated with a voltage dependent active power curtailment (P(V)). Investment costs were not considered here. Besides the aforementioned detailed grid specific cost-benefit analysis, several studies focusing on a nation-wide or state-wide estimation of grid reinforcement costs exist [8] or are currently in progress [106; 107]. These studies rely on simplified assessment approaches in order to cope with the vast amount of data and hence are considered of minor relevance for this thesis.

Figure 5.1: Overview on field of research on economic assessments of voltage control strategies.

Goal of the Chapter: The goal of this chapter is to analyze, whether autonomous voltage control strategies are an economically reliable alternative to traditional grid reinforcement measures in order to host additional PV generation capacity at LV level. A focus is set to provide a comprehensive comparison of the additional costs and benefits over a period of 10 years, associated with different autonomous voltage control strategies. In this context, it is important to consider the economic perspectives of the DSO as well as of the DG operators by investigating the economic effects on investment costs and operational costs for both parties.

99

Methodology and Structure:The following autonomous voltage control strategies and variations of their parameter settings are economically assessed in the context of this investigation: • Distribution transformer with on-load tap changer • Reactive power provision by PV inverter – Power factor depending on active power feed-in (cosϕ(P)) – Voltage dependent reactive power provision (Q(V)) • Active power curtailment and reactive power provision by PV inverter – Fixed 70% power limitation (§ 6 EEG) and Q(V) – Voltage dependent reactive power provision and active power curtailment Q(V)/P(V) The presented cost-benefit analysis bases on net present value calculations, considering investment and operational costs. With this dynamic assessment approach it is possible to determine the time value of future cash-flow time-series and hence to calculate the value of deferred investments. Simulations are conducted exemplary for two real LV grids from the Bayernwerk AG Smart Grid region ”Seebach” (see [17]). The overall cost-benefit analysis is structured in four consecutive Sections (see fig. 5.2). A special focus is set on presenting a voltage dependent active power curtailment as an economically beneficial alternative to the fixed 70% limitation according to § 6 EEG (status: 2012). Section 5.1 defines the simulation scenarios for the cost-benefit analysis. Here, PV expansion scenarios are defined for each LV grid, assuming a continuous PV growth rate over a period of 10 years. In Section 5.2 the extend of necessary grid reinforcement measures is determined for each of the 10 simulated years. As the installed PV capacity will exceed the initial hosting capacity of the investigated grids, the DSO would have to be forced to take corrective actions, either in terms of traditional grid reinforcements or by also applying autonomous voltage control strategies. This section presents the annually required extend of grid reinforcement measures with and without the application of autonomous voltage control strategies, using the calculation methodology introduced in Chapter 3. The economic assessment of the investment costs is based on net present value (NPV) analysis.

100


The calculation of the operational costs is presented in Section 5.3. For this, one-year RMS simulation are parameterized and conducted in order to gain time-series for the resulting network losses and the PV power feedin over 10 consecutive years. These time-series deal as a basis for the calculation of the annual operational costs. The NPV of the investment costs and the NPV of the operational costs together will then be used to compare the economic potential of the investigated autonomous voltage control strategies. Sensitivity analysis on different cost categories will be presented in order to deal with the uncertainty of future price developments. Scientific Novelty and major Findings: This chapter compares and ranks Figure 5.2: Flow chart of the structure of chapter 5. the economic potential of different autonomous voltage control strategies for an improved LV grid operation. The investigation demonstrates, on the example of two real LV grids, how the application of autonomous voltage control strategies can be used to defer the time of invest for additional grid reinforcement measures and thus gain additional value for the DSO compared to traditional grid reinforcements. The presented cost-benefit analysis also considers the perspective of PV plant operators, as feed-in losses are also part of the economic assessment. It can be shown that a savings potential of up to 75% can be achived by the application of autonomous voltage control strategies compared to traditional grid reinforcements. By using a voltage dependent active power curtailment instead of a fixed active power feed-in limitation (as currently optionally required by the German EEG) the opportunity costs for PV plant operators can be drastically reduced.

5.1 Investigated LV grids and PV Expansion Scenarios The investigated LV grids are located in the official Bayernwerk AG Smart Grid region ”Seebach” [17]. Figure 5.3 (Grid No. 20) and Fig. 5.4 (Grid No. 39) show their single line diagrams with possible PCCs for PV systems (red markers) and the MV/LV distribution substation (green). In their initial configuration, both LV

5.1. INVESTIGATED LV GRIDS AND PV EXPANSION SCENARIOS 101

grids are served by a 400 kVA delta-wye distribution transformer, respectively. The grids are operated as a three-phase radial system with a nominal line to line voltage of 400 V. For the following simulations, balanced conditions are assumed. These LV grids are chosen because they were identified in Chapter 3 to experience frequent voltage problems in high PV penetration scenarios. The results also showed that the application of local, autonomous voltage control strategies is capable of increasing the grid’s hosting capacity significantly (see Section 3.4) and are therefore expected to also gain an economic benefit for the DSOs.

Figure 5.3: Single line diagram of LV grid No. 20.

Figure 5.4: Single line diagram of LV grid No. 39.

Figure 5.5 and Fig. 5.6 graphically compare the distribution of the additional hosting capacity that can be enabled by applying different autonomous voltage control strategies. The gray beanplot in the foreground visualizes the distribution of the additional hosting capacity explicitly for one of the two chosen LV grids. The colored beanplot in the background however depicts the accumulated distribution over all 17 LV grids, which could be identified in Section 3.4 to experience frequent voltage limitations. It can be assumed that the differences of the respective variances and medians are due to the different grid layouts1 . However, from the ”similarity” of the depicted distributions it is assumed that the two chosen LV grids 1 Applying

a two-sample Wilcoxon test (also known as Mann-Whitney test) will reject the nullhypothesis that is that both sample populations belong to the same base population.

102


do not represent any extreme scenarios and hence can be used for the cost-benefit analysis within this chapter.

Figure 5.5: Beanplot showing the distribution of the additional hosting capacities by applying different autonomous voltage control strategies. Background: All 17 voltage limited grids from Section 3.4.2; Foreground: Grid No. 20. The plot was conducted using the beanplot package in R [59].

The presented cost-benefit analysis covers a period of 10 years, assuming a fixed PV growth rate. It is considered that at the end of the base year t0 a total of 25 PV systems are installed at grid No. 20 and 35 PV systems at grid No. 39, each with an installed module capacity PSTC of 10 kWp (average for residential scale PV systems in the ”Seebach” region [57]). These PV systems were randomly assigned among the available PCCs by using a uniform distribution. For both ”base scenarios” it was assured that the grid’s initial hosting capacity is not exceeded by the installed PV capacity, following the methodology described in Section 3.3. One of the mayor issues for German DSOs is the difficulty to precisely predict the extend and time of local PV deployment. In the context of this investigation, this is accounted for by setting up annual PV expansion scenarios, assuming a fixed PV installation rate of 50 kWp per year (equals 5 additional PV systems with 10 kWp PSTC each). Again, the additionally installed PV systems are randomly installed among the remaining PCCs. Table 5.1 gives an overview on the annual PV penetration. It has to be noticed that only the additionally installed PV systems

5.1. INVESTIGATED LV GRIDS AND PV EXPANSION SCENARIOS 103

Figure 5.6: Beanplot showing the distribution of the additional hosting capacities by applying different autonomous voltage control strategies. Background: All 17 voltage limited grids from Section 3.4.2; Foreground: Grid No. 39. The plot was conducted using the beanplot package in R [59].

are considered to be equipped with voltage support functionalities, meaning that 25 PV systems within grid No. 20 and 35 PV systems within grid No. 39 remain uncontrolled during the economic evaluation. This assumption leads to a more conservative cost-benefit analysis, as it is based on the technical potential of autonomous voltage control strategies rather then their theoretical potential (compare Section 3.4). However, it should be noticed that existing, non-controllable inverters could be replaced in future by state-of-the-art inverters in the context of repowering measures. This additional effect is not considered in the assessment approach.

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Table 5.1: Investigated PV expansion scenarios using LV grid No. 20 and No. 39.

Year t0 t1 t2 ... t10

Additionally installed PV capacity No.20 No.39 50 kWp 50 kWp 50 kWp 50 kWp ... ... 50 kWp 50 kWp

Total PV capacity No.20 No.39 250 kWp 350 kWp 300 kWp 400 kWp 350 kWp 450 kWp ... ... 750 kWp 850 kWp

No. of PV systems No.20 No.39 25 35 30 40 35 45 ... ... 75 85

In a next step, the technical impact of the installed PV capacity on the grid is assessed for every year, grid and voltage control strategy, following the methodology of Section 3.3.

5.2 Calculation of Grid Reinforcement Costs The assumed continuously increasing installed PV capacity requires for measures to increase the grid’s hosting capacity over the investigated period of time. As shown in Chapter 3, this can be either done by performing traditional grid reinforcement measures or by a mixture/ sole application of voltage control strategies. In order to quantify the extend of necessary grid reinforcements, the following simplified approach is applied for each year t1 − t10 and voltage control strategy: 1. Randomly install additional PV systems among remaining PCCs. 2. Check, if the grid’s hosting capacity has been exceeded by applying the assessment procedure for the different voltage control strategies as described in Section 3.3 (for the definition of hosting capacity in the context of this thesis see Section 3.1). 3. In case that the hosting capacity has been exceeded, grid reinforcement measures need to be conducted (compare fig. 5.7): (a) In cases of local over-voltages or over-loadings, a parallel cable (of cable type 4x150mm2 NAYY) is installed between distribution cabinets within the respective feeder, starting at the distribution substation2 . (b) If 3 (a) does not sufficiently increase the hosting capacity, the 4x150mm2 cables from the closest distribution cabinet to the critical node are replaced by 4x240mm2 cables. (c) In cases of transformer over-loadings or in situations where the exchange of the transformer solves multiple voltage issues in different branch feeder simultaneously, an exchange of the transformer is realized. 2 The

particular cable type is chosen because it has been already frequently installed in the investigated grid and parallel installation generally requires the same cable type.

5.2. CALCULATION OF GRID REINFORCEMENT COSTS

105

4. Calculate the NPV of the grid reinforcement costs, referred to the beginning of year t1 . It should be noticed that network restructuring and placing of additional distribution substations are also technically effective measures to increase a grids hosting capacity. However, to keep the economic assessment comprehensible these approaches are not considered in this study.

Figure 5.7: Simplified grid reinforcement approach of cost-benefit analysis.

By the application of the investigated autonomous voltage control strategies, the time of invest in additional grid infrastructure can be deferred, as Fig. D.1 and Fig. D.2 in the Annex show. This gains additional value for the DSO as the requisite money can be invested elsewhere within the company (the assumed unit prices for the different grid reinforcement measures are also listed in Table D.1 in the Annex). A classical tool to describe this present value of future cash flows is the net present value (NPV). A good overview on this topic is given in [108]. Net Present Value Calculation of Investment Costs: The following paragraph describes the calculation of the NPV for the investment costs. For a better readability, Table 5.2 lists the acronyms which are used in this section. Table 5.2: List of acronyms used in this section. Acronym

Describtion

a(t; i) C f3 i n

Discount Factor (year; Discount Rate) Total Investment Costs Present Value Factor f3 - Infinitely Repeated Reinvestment Discount Rate Lifetime of Investment

Unit [-] [EUR] [-] [%] [yr]

For each of the investigated autonomous voltage control strategies, the NPV of the total investment cash flow time series NPVINV EST is calculated using equ. 5.1. Here, Cy stands for the total investment costs at the beginning of year y, a(y; i) equ. 5.2 represents the discount factor considering the discount rate i and f 3(n; i), equ. 5.3, describes the present value factor of an infinitely repeated investment (n

106


= lifetime of invest). It is assumed that the cash flows for the investment in grid infrastructure accrue at the beginning of each year. For this study, a discount rate i of 8% is assumed, covering the long-term investment rate and the inflation rate. ! 10

NPVINV EST = f3 (n; i) ·

∑ Cy · a(y − 1; i)

(5.1)

y=1

a(y; i) = ((1 + i)y )−1

(5.2)

(1 + i)n (1 + i)n − 1

(5.3)

f3 (n; i) =

Figure 5.8 compares the NPV of the total investment cash flow time series for grid No. 20 and grid No. 39, discounted at the beginning of year t1 . It is clearly visible that all studied autonomous voltage control strategies are capable of reducing the NPVINV EST considerably, compared to the reference scenario pure grid reinforcement. The higher NPVs for grid No. 39 result from the fact that relatively high investments accrue already at the beginning of year t1 (see also Fig. D.1 and Fig. D.2 in the Annex). Table 5.3 lists the additional savings that can be realized for the two test-grids by applying autonomous voltage control strategies. For the Q(V) voltage control strategy, a scenario with power factor limitation to 0.95 and without power factor limitation are distinguished (compare Section 3.3). The OLTC based voltage control strategies are calculated for a LV busbar set value vSet of 1.0 p.u. and 0.98 p.u., respectively. For the OLTC control strategies, an exchange of the OLTC controller (only the electronic parts) every 15 years is assumed as well.

5.3. CALCULATION OF OPERATIONAL COSTS

107

Figure 5.8: Comparison of net present values of the total investment cash flow time series, referred to the beginning of year t1 .

Table 5.3: Investment costs savings by the application of autonomous voltage control strategies. OLTC VSet = 1.0p.u.


Cosϕ(P)

Q(V) with PF limitation

Q(V) without PF limitation

Q(V)/ Pmax = 70%

Q(V)/P(V)

Grid No. 20 No. 39

74% 60%

70% 60%

50% 49%

66% 49%

66% 49%

82% 59%

82% 54%

The following Section deals with the calculation of the operational costs.

5.3 Calculation of Operational Costs In order to determine the operational costs that can be associated with the application of different autonomous voltage control strategies, one-year RMS simulations R are conducted, using the power system analysis software PowerFactory from DIgSILENT. To gain valuable information from the simulations, realistic load and generation models, load and generation time-series and general simulation settings are required.

108

5.3.1


Simulation Assumptions and Settings

For the presented cost-benefit analysis, the following models and simulation assumptions were considered to be of special interest for the calculation of operational costs: • • • • •

PV system model and generation time-series. OLTC model. Load model and load time-series. MV profile at MV-busbar of distribution transformer. General simulation settings.

Figure 5.9 provides an schematic overview of the applied simulation model and the input values, used for the different unit models. The properties of the unit models are described in the following paragraphs.

Figure 5.9

PV system model and generation time-series: A simplified illustration of the PV system model is given by Fig. 5.10 [33]. The model requires DC-power profiles as an input and calculates the instantaneous active and reactive power output of the inverter, taking into account plant specific properties, such as the inverter sizing, the inverter efficiency curve and the applied voltage controller, if required. Table D.7 in the Annex summarizes the model parameter settings and Subsection D in the Annex describes the implementation of the efficiency curve.


109

A measured DC-power generation profile of a utility scale PV system, located in Southern Bavaria, is used as an input timeseries for the PV system model3 . The generation time-series comprises per-unit values and has a resolution of one-minute, which Figure 5.10: Simplified illustration of applied can be considered to be a good RMS PV system model [33]. compromise between the required simulation time for one-year simulations on the one hand and the consideration of short-term generation peaks on the other hand (compare Fig. A.1 in the Annex). In Fig. 5.13 the load duration curve of the applied DC-power generation profile is depicted. OLTC model: The OLTC model is set up according to the descriptions of Subsection 3.2.3. During the simulations, the LV-busbar voltage VLV of the MV/LV transformer is measured and passed to the OLTC controller. If VLV exceeds the preset control deadband [VDB− ,VDB+ ], a tap change event is triggered according to equ. 3.10. The applied controller parameter settings can also be found in Table D.7 in the Annex. Load model and load time-series: A general load model from PowerFactory [110] is used to represent the load consumption at the different PCCs. The voltage dependency of the load model was disabled to account for the increasing share of low voltage loads with electronic ballasts. Measured smart meter data timeseries for H0-customer in 10 minute resolution (see Chapter 2) are assigned to the single PCCs dealing as consumption profiles. Possible measuring gaps were filled by interpolating between two points in time, following the approach introduced in [25]. As the number of PCCs is lower than the actual number of households within the investigated test grids (due to the presence of semidetached houses and apartment buildings), the active power consumption at each PCC is scaled up by the ratio of households and PCCs. For the reactive power consumption, a constant power factor of 0.95 under-excited is assumed (see Table D.7 in the Annex). 4 Figure 5.11 shows the load duration curves of the accumulated load profiles. 3 The measures DC-power generation profile is a courtesy of the Solarenergief¨ orderverein Bayern

e.V.. More information on the measured PV plant can be found in [109] 4 A own investigation of power measurements, recorded at the LV busbars of a total of 137 distribution transformers within the ”Seebach” region showed, that the accumulated power factor at the LV busbars actually depends on the active power flow over the distribution transformer [10]. However, the investigation also shows that in times of load consumption, the measured power factor converges against 0.95 (under-excited) already for relatively small active power flows. In order to improve this assumption for future simulations, detailed smart meter analysis need to be conducted in order on the power factors of domestic loads.

110


Figure 5.11: Load duration curves of the accumulated load profiles of grid No. 20 and grid No. 39.

MV profile at MV-busbar of distribution transformer: A crucial element for realistic one-year simulations, especially when simulating voltage dependent active and reactive power provision, is to account for the voltage deviations at the upstream MV grid. In case of an area-wide high PV penetration considerable voltage rises can already occur at MV level (compare [10; 111; 112]). In the context of this thesis, simulated 5 one-year MV profiles in one minute resolution are available for a total of 187 MV/LV distribution substations of the ”Seebach” MV grid [10]. In order to make the resulting operational costs less dependent from the actual short-circuit power and R/X ratio of the MV PCC of LV Grid No. 20 and LV Grid No. 39, sensitivity analysis with different MV profiles are conducted. To do so, three different voltage categories are defined: • Category A: The 99% voltage percentile of 10 minute averages is lower than 1.04 p.u. (applies to 41.7% of all MV nodes). • Category B: The 99% voltage percentile of 10 minute averages is between 1.04 p.u. and 1.05 p.u. (applies to 53.8% of all MV nodes). • Category C: The 99% voltage percentile of 10 minute averages is higher than 1.05 p.u. (applies to 4.5% of all MV nodes). For the following simulation, one particular one-minute voltage profile is chosen from Category A, B and C, respectively. The MV slack bus of the simulations, located at MV busbar of the MV/LV transformer, is modeled by an AC voltage 5 The

simulated voltage profiles originate from a separate one-year RMS simulation, using the real ”Seebach” MV grid topology. For validation purposes, measured power flows at the HV/MV substation were compared with the simulated power flows over the period of one year. The comparison showed a good match between the measured and the simulated power flows. Because of this, it is assumed that the simulated voltage profiles can be used in the context of LV grid simulations within the ”Seebach” region. Detailed information on the MV study can be found in [10].


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source using the chosen MV profiles as input data. Figure 5.12 visualizes the three voltage categories and exemplary depicts the single percentiles for the arbitrarily chosen category B profile. Figure 5.13 shows the load duration curves of the three different voltage profiles. Within the upstream MV grid, 41.7% of all nodes were identified by time domain analyses to belong to category A, 53.8% to belong to categroy B and 4.5% to belong to category C [10].

Figure 5.12: Percentiles of an exemplary category B voltage profile.

Figure 5.13: Load duration curves of applied external voltage profile and PV DC-power generation profile.

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General simulation settings: The performed RMS simulations read the aforementioned load, generation and voltage time-series as input data. In between two consecutive time steps, PowerFactory linearly interpolates the input data in 4 second steps. The output of the one-year RMS simulations (e.g., network losses, PV feed-in etc.) is again saved using a one-minute step size.

5.3.2

Calculation of the Net Present Value of the Operational Costs

The following paragraph describes the calculation of the NPV for the operational costs. For a better readability, Table 5.4 lists the acronyms which are used in this section. Table 5.4: List of acronyms used in this section. Acronym

Describtion

a(t; i) closs cmain cPV Eloss EPV f1 f2 f3 i qPV t Tx x z(y; qPV )

Discount Factor (year; Discount Rate) Costs for Compensation of Network losses Maintenance Costs for OLTC Photovoltaic Feed-In Tariff Network Losses PV Feed-In Losses Present Value Factor f1 - Specific Period of Time Present Value Factor f2 - Infinite Extrapolation of Costs Present Value Factor f3 - Infinitely Repeated Reinvestment Discount Rate Monthly Feed-In Degression Year of Calculation Period Year of Photovoltaic Installation Number of Investigated PV System Feed-In Degression Factor (year; Discount Rate)

Unit [-] [EUR/kWh] [EUR] [EUR/kWh] [kWh] [kWh] [-] [-] [-] [%] [%/Mon] [-] [-] [-] [-]

For a better understanding, the total annual operational costs are split into two groups. The annual operational costs NPVOP is the sum of the net present value NPVOP1 and the annual operational costs over all PV plant operators NPVOP2 , which are due to a temporal PV feed-in reduction (so-called opportunity costs [9; 6; 10]). The lost PV energy of PV system No. x in year t is defined as EPV x,t . The annual operational costs comprise the compensation of network losses Eloss and additional maintenance costs for the OLTC every 10 years, if applied 6 . Table D.2 in the Annex summarizes the price assumptions for the calculation of the annual operational costs. For the calculation of NPVOP1 it is assumed that all payments accrue at the end of a year. Equation 5.4 describes the net present value NPVOP1 of the cash flow time series.

6 Additional

costs for the compensation of additional reactive power flows are not considered. In [33] these could be identified of playing only a minor role for the overall cost-benefit analysis.


113

!

(5.4)

9

NPVOP1 =

∑ closs,y · Eloss,y · a(y; i)

y=1

+ closs,10 · Eloss,10 · a(10; i) · f2 (i)

The present value factor f2 equ. 5.5 is used to extrapolate the operational costs of year t10 infinitely. 1 (5.5) i For OLTC control strategies, the net present value of the operational costs needs to be extended by the discount factor f3 , equ. 5.3, taking into account the 10 year maintenance interval. f2 (i) =

NPVOP1,OLTC = NPVOP1 + cmain · a(10; i) · f3 (10; i)

(5.6)

The calculation of NPVOP2 is expressed by equ. 5.7. Here, the feed-in losses of a total of m individual PV systems have to be taken into account. m

NPVOP2 =

∑

′ ′′ ′′′ NPVOP2,x + NPVOP2,x + NPVOP2,x

x=1

(5.7)

At first, the individual feed-in tariff for each PV system cPV,x needs to be determined according to the German EEG (see equ. 5.8). Among others, the feed-in tariff depends on the year of the PV installation Tx , considering a monthly feed-in degression qPV (see equ. 5.9), starting at the beginning of year t1 . In the context of this thesis, it is assumed that the feed-in tariff remains constant once it reaches a value of 10cEUR/kWh at year ty (see equ. 5.10). Furthermore, it is assumed that an end of the feed-in tariff system, due to the German 52 GWp installation scenario, does not occur during the investigated time interval ([113] assume this to happen in 2020 according to their ”2011 A” scenario).

cPV,x (Tx ) =

cPV · z(Tx ; qPV ) 0.1 · EUR kW h

f or Tx < ty,x (5.8) f or Tx ≥ ty,x

z(Tx ; qPV ) = (1 + qPV )−(12·Tx −12)

(5.9)

10cEUR/ kW h 1 ty,x = 1 − log1+qPV 12 cPV,x

(5.10)

′ (equ. 5.11), describes the feed-in losses The first term of equ. 5.7, NPVOP2,x for PV system No. x, EPV x , until the end of the simulated period t10 .

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′ NPVOP2,x = cPV,x (Tx ) ·

10

∑ EPV x,y · a(y; i)

(5.11)

y=Tx

′′ (equ. 5.12), takes into account that the respective The second term, NPVOP2,x feed-in tariff is paid for a total of 20 years, which is beyond the simulated time span. For this, the feed-in losses of year t10 are assumed to occur for the following years as well. The present value factor f1 (n; i) is used in this context to account for the remaining feed-in tariff period.

′′ NPVOP2,x = cPV,x (Tx ) · EPV x,10 · f1 (10 + Tx ; i) · a(10; i)

f1 (n; i) =

(1 + i)−n − 1 −i

(5.12) (5.13)

′′′ (equ. 5.14), finally considers the value of PV energy The third term, NPVOP2,x after the 20 years of guaranteed feed-in payment. For this, it is assumed that a sales price of 10cEUR/kWh can be realized at the energy market.

EUR · EPV x,10 · f2 (i) · a(Tx + 20; i) (5.14) kW h This procedure is necessary to refer NPVOP1 and NPVOP2 to an identical time frame and hence making both values comparable. All variables are listed in Table D.2 in the Annex. Figure 5.14 shows the NPVOP for grid No. 20 and grid No. 39. ′′′ NPVOP2,x = 0.1

The opportunity costs for the PV plant operators visualize the benefit of a voltage dependent active power curtailment over the fixed active power limitation according to § 6 EEG. In both scenarios a maximum active power feed-in of 70% PSTC is guaranteed and the grid has been reinforced accordingly. But instead of continuously limiting the active power feed-in to 70% PSTC , the Q(V)/P(V) control strategy needs to reduce the plants active power output only occassionaly, leading to insignificantly low opportunity costs over all PV plant operators. Moreover, it should be considered that the results are based on the assumption of a category C MV profile (worst-case condition), as introduced in Subsection 5.3.1. A sensitivity analysis on different MV profiles is presented in Subsection 5.3.3. The OLTC-based voltage control strategies show the highest operational costs in this study. This has two main reasons: First, deferred grid reinforcements lead to higher line and transformer loadings and hence to higher network losses and second, the additional maintenance costs for the OLTC (compare Table D.2).


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Figure 5.14: Comparison of net present values of the operational costs cash flow time series NPVOP (network losses and PV opportunity costs), referred to the beginning of year t1 .

In the context of local reactive power provision by DG, concerns regarding increasing network losses due to higher transformer and line loadings are often expressed (compare [86; 114; 115; 116] for example). These concerns seem to be legitimate for a particular PV penetration scenario, but need to be reconsidered if the economic efficiency of reactive power based voltage control strategies has to be compared to alternative approaches. For example, reactive power provision by PV inverters increase the network losses, but an alternative approach for increasing the grid’s hosting capacity might require a transformer exchange at a relatively early PV expansion stage, which in turns leads to higher no-load losses and hence increased network losses over time. Figure 5.15 depicts the time dependent development of the annual network losses of grid No. 20 for the investigated scenarios. It can be clearly seen that an early transformer exchange (400 kVA usc = 4% → 630kVA usc = 6%, compare also Table D.3 and Table D.4 in the Annex) can cause a significant offset in network losses compared to the alternative voltage control strategies. In this particular investigation, the network losses were highest for the grid reinforcement scenario until year 6 to 8, depending on the alternative voltage control strategy. From an economic perspective this means to deferr operational costs, if reactive power control strategies are applied. Figure D.3 in the Annex shows the time dependent development of the network losses for grid No. 39.

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Figure 5.15: Time dependent development of network losses for grid No. 20.

Figure 5.16 finally compares the total NPV of the investigated voltage control strategies, comprising investment costs in grid infrastructure and smart grid technologies as well as network loss costs, maintenance and reduced PV feed-in. The results highlight the significant savings potential, which can be achieved by applying autonomous voltage control strategies instead of pure grid reinforcement. Among the investigated voltage control strategies, the OLTC-based approaches and the Q(V)/P(V) control strategy show the highest savings potential for both grids.

Figure 5.16: Comparison of net present values of the operational costs cash flow time series NPVOP (network losses and PV opportunity costs), referred to the beginning of year t1 .


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Table 5.5 lists the total savings by the application of autonomous voltage control strategies compared to pure grid reinforcement 7 . The fact that the investigated autonomous voltage control strategies are capable of deferring investment costs as well as operational costs (compare results on network losses) suggest that autonomous voltage control strategies are an economically efficient measure for LV grids which are in a transition process from being load dominated to being generation dominated. As soon as a saturation in PV installations can be observed, or if the local PV potential (e.g., limited by available roof area) is fully utilized, the DSO can start an optimization process aiming at permanently reducing network losses. Table 5.5: Total savings by the application of autonomous voltage control strategies compared to pure grid reinforcement. OLTC VSet = 1.0p.u.


Cosϕ(P)

Q(V) with PF limitation

Q(V) without PF limitation

Q(V)/ Pmax = 70%

Q(V)/P(V)

Grid No. 20 No. 39

62% 50%

66% 50%

46% 42%

60% 43%

60% 43%

68% 44%

75% 47%

The next subsection presents sensitivity analysis on the price assumptions and discusses the affect of voltage dependent active power curtailment for the economic reliability of PV systems.

5.3.3

Sensitivity Analysis

This section describes the calculation methodology for the sensitivity analysis. For a better readability, Table 5.6 lists the acronyms which are used in this section. Table 5.6: List of acronyms used in this section. Acronym

Describtion

a(t; i) closs Eloss f2 f3 i qPCR s(t; qPCR ) t

Discount Factor (year; Discount Rate) Costs for Compensation of Network losses Network Losses Present Value Factor f2 - Infinite Extrapolation of Costs Present Value Factor f3 - Infinitely Repeated Reinvestment Discount Rate Price Change Rate Price Change Factor (year; Discount Rate) Year of Calculation Period

7 It

Unit [-] [EUR/kWh] [kWh] [-] [-] [%] [%/yr] [-] [-]

should be noticed that due to the diversity of grid structures and penetration scenarios, the presented results should be interpreted as tendencies only.

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The calculation of the net present value over an interval of 10 years is subject to many uncertainties. In order to develop an understanding of the sensitivity of changes in the calculation assumptions, sensitivity analyses are presented in this subsection. At first, the price change rate sensitivity of material costs and network losses is studied, followed by a sensitivity analysis on the affect of the Q(V)/P(V) controller parameterization on the additional PV feed-in losses. Price Change Rate Sensitivity: The following changes in the calculation assumptions are studied: • Network loss compensation costs: Price change rate from -2%/yr to +2%/yr. • Material costs: Price change rate from -2%/yr to +2%/yr. • Discount factor: From 6% to 10%. Sensitivity analysis on the maintenance costs for the OLTC are not conducted, as they play only a minor role for the total NPV (compare Fig. 5.16). For the consideration of a constant price change rate qPCR , equ. 5.1 and equ. 5.4 have to be extended by a price change factor s(t; qPCR ), equ. 5.17, and hence need to be rewritten as follows (cet. par.): 10

NPVINV EST = f3 (n; i) ·

∑ Cy · a(y − 1; i) · s(y; qPCR) +C1

y=2

9

NPVOP1 =

∑ closs,y · Eloss,y · a(y; i) · s(y; qPCR)

y=1

!

!

+

(5.15)

(5.16)

c10 · Eloss,10 · a(10; i) · s(10; qPCR ) · f2 (i) s(t; qPCR ) = (1 + qPCR )t−1

(5.17)

Figure 5.17 shows that the additional savings by voltage control strategies vary only insignificantly, if different price change rates and discount factors are assumed. Hence, the results gained by the cost-benefit analysis can be considered as relatively robust against variations of material costs, network loss compensation costs and the chosen discount factor.


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Figure 5.17: Sensitivity of additional savings on variations of unit prices and discount factor, exemplary for grid No. 39.

Q(V)/P(V) MV Sensitivity: Figure 5.14 shows a significant savings potential by applying a voltage dependent Q(V)/P(V) control strategy instead of a fixed active power limitation of 70% PSTC , according to § 6 EEG (status 2012)8 . Figure 5.18 shows the development of the additional annual PV feed-in losses over all controllable PV systems by using the different MV profiles for the slack bus according to Subsection 5.3.19 The 70% limitation reference line clearly shows that although a worst-case scenario has been set up, the application of the Q(V)/P(V) voltage control strategy leads to sginificantly lower annual feed-in losses over all controllable PV systems. In the first years almost no voltage driven feed-in losses accrue, which in turns lowers the NPV in addition.

8 According

to § 6 subsection 2 EEG the 70% limitation represents an alternative option to a remote control interface which is obligatory for PV systems with more than 30 kWp PSTC . 9 The results are based on a worst-case scenario with P lim = 0% PSTC (i.e., the PV systems can theoretically cease feeding-in active power completely.). Furthermore, no voltage driven grid reinforcements were conducted.

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Figure 5.18: Accumulated annual PV feed-in losses due to active power curtailment in relation to the total annual energy generation of all controllable PV systems.

Although, the total annual feed-in losses over all controllable PV system are lower compared to the 70% PSTC limitation, some PV systems might be discriminated by this approach due to their PCC (compare also [105]). Figure 5.19 shows the top ten PV systems with the hightest feed-in losses during year t10 (category C MV profil applied). Together, these ten PV systems represent 79% of the total feed-in losses of grid No. 20 and 60% of grid No. 39. The reference value for the 70% limitation is 2.7% for each PV system. The presented feed-in losses should be interpret as aproximate values only, as they are based on 1 minute RMS simulations. Higher temporal resolutions and PV site specific characteristics might result in higher feed-in losses, as described in detail in [89]. Figure D.5 in the Annex visualizes the annual feed-in losses over the ten years and for the different MV profiles.


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Figure 5.19: Top ten PV systems with highest additional feed-in losses due to active power curtailment during year t10 .

The presented results clearly highlight the economic benefit by applying a combined Q(V)/P(V) voltage control strategy. However, the application of a Q(V)/P(V) voltage control strategy (and any other voltage dependent control strategy that relays on active power curtailment) always bears an economic risk for either the plant operators or the responsible DSO 10 . PV system specific boundary conditions (e.g., orientation, inverter sizing, PCC), grid specific boundary conditions (e.g., local DG penetration level, load situation at LV and MV level) and meteorological boundary conditions influence the extent of incurring feed-in losses and beyond that might be subject to changes over time. These effects make it extremely difficult to predict the expected feed-in losses with appropriate preciseness. One practical approach to limit the extent of voltage driven feed-in losses can be to set a lower active power limitation for the P(V) controller Plim , as applied in the previous Sections of this Chapter. Although, using Plim as a base to calculate a PV system’s expected energy feed-in would most likely underestimate its actual performance as the presence of over-voltages will be limited to certain points in time, if occurring at all. Lowering Plim would mean to increase the grid’s hosting capacity, as more active power can be temporarily reduced in cases of local over-voltages (compare Fig. 10 This depends on the interpretation of § 12 EEG (status 2012). A legal review should be carried out to identify the responsibilities of DSOs and plant operators for the application of autonomous voltage control strategies.

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3.28 in Chapter 3). On the other hand, more frequent active power curtailments will increase the feed-in losses of controlled PV systems. If DSOs are responsible to compensate plant operators for feed-in losses, an appropriate compensation strategy needs to be identified. Three common compensation approaches for PV systems are discussed in [117] (based on (a) local solar irradiation measurements; (b) local reference modules or (c) reference PV systems in close distance). Further studies should build on this investigation and check the applicability of compensation approaches in the context of autonomous voltage control.

5.4 Summary and Outlook In this Chapter, a detailed cost-benefit analysis for applying autonomous voltage control strategies in two real LV grids with high PV penetration is presented. A PV expansion scenario with a fixed annual PV installation rate has been set up and analyzed over a period of 10 years. The cost-benefit analysis covers investment cost for conventional grid reinforcement measures (parallel cables and transformer exchanges) and the installation of smart grid technologies (e.g., distribution transformer with OLTC). Furthermore, the costs for the compensation of network losses, additional PV feed-in losses due to active power curtailment and additional maintenance cost for the OLTC are considered. As a result, the application of autonomous voltage control strategies shows a significant cost reduction potential for the two investigated LV grids. The net present value of the investment costs could be reduced by up to 82% for grid No. 20 and 60% for grid No. 39. A high savings potential can be achieved by deferring investment costs to later points in time and hence avoiding piecewise grid reinforcement measures. For both grids, the OLTC-based voltage control strategies and the combined Q(V)/P(V) control strategy showed the highest savings potential for investment costs compared to conventional grid reinforcement measures. The network losses and PV feed-in losses are determined by one-year RMS simulation in one minute resolution. Additional costs due to increased network losses or higher OLTC maintenance costs play only a minor role for the two test LV grids. A remarkable savings potential could be identified by applying voltage driven active power curtailment P(V) instead of a fixed active power limitation. The maximum overall cost reduction potential is identified to be 75% of the conventional grid reinforcement costs by applying the Q(V)/P(V) control strategy in grid No. 20 and 50% of the conventional grid reinforcement costs by applying OLTC-based voltage control strategies for grid No. 39. Sensitivity analysis on the cost assumptions and the discount factor underlined the robustness of the gained results. In further studies the sensitivity analysis should be extended to load and generation assumptions as well. Imbalanced power flows, distinct reactive power consump-


123

tion profiles and individual PV generation profiles could improve the preciseness of the cost-benefit analysis. Their actual influence on the economic results has yet to be determined. Besides steady improvements of simulation assumptions, the focus of future studies should be also set at aiming at automatic or semi-automatic solutions for the introduced methodology. This could help to speed up the economic assessment process and could lead to cover a larger number of grids in a reasonable amount of time.

Chapter 6

Conclusion and Outlook Technically effective and economically efficient voltage control is a major issue in distribution systems with lots of installed capacity from dispersed generators, such as residential scale PV systems. Especially in rural service areas, where the majority of Germany’s installed PV capacity can be found, the distribution system operators in charge often have to take corrective actions in order to maintain the local voltage quality as defined by the EN 50160 standard. These corrective actions typically comprise cost intensive grid reinforcement measures, such as laying of additional cables and exchanging of transformers, which in turn increase the overall system integration costs of PV. During recent years, the required amount of ancillary services provided by PV has been continuously expanded by revised grid codes and standards. Technical solutions for local voltage support, such as additional reactive power capabilities by PV inverter and active power curtailment, have become state-of-the-art. And yet, many uncertainties regarding the technical effectiveness and the economic efficiency of these autonomous voltage control strategies remain. The adaption of design criteria for PV impact studies, the revision of current regulatory framework and the quantification of the additional benefit by applying autonomous voltage control strategies are necessary steps towards fully utilizing their respective voltage support potential. The present work has dealt with the technical and economic assessment of chosen voltage control strategies in distribution systems with high local PV penetration. The focus was set on the investigation of autonomous control strategies for PV inverters and distribution transformer with on-load tap changer, which rely on locally measured feedback signals only. The goal was to present methodologies which can be applied to account for the full voltage support potential of autonomous voltage control strategies during PV impact studies and to quantify their additional monetary benefit for distribution system operators as well as for PV plant operators. The results highlight that autonomous voltage control strategies are an economically

124

CONCLUSION AND OUTLOOK

125

reliable alternative to conventional grid reinforcement measures, if applied appropriately. In Chapter 2 statistical analyses based on smart meter measurement data from domestic loads and residential scale PV systems were presented. By probabilistic superimpositions of load and generation data, the expected extend of reverse power flows by PV generation could be extracted from the smart meter data for different penetration level in residential service areas. Worst-case analyses suggest that the extracted low load conditions between 11 a.m. and 3 p.m. should be used for PV impact studies in order to allow the local consumption of PV generation to be taken into account appropriately. This consideration can be used to improve PV impact studies and hence make the grid design process technically more effective. Based on the analyzed smart meter data mathematical expressions for low load, peak load and reverse power flows are provided. Chapter 3 dealt with the technical potential of autonomous voltage control strategies of increasing the hosting capacity of LV grids. A detailed methodology for PV impact studies was presented, which aims at utilizing the full voltage support potential of autonomous voltage control strategies during the grid design process. At this stage, also the results of the smart meter analyses were incorporated into the methodology. The derived methodology was then applied to a total of 40 real LV grids from the Bayernwerk AG, using a probabilistic assessment approach. The investigation showed that OLTC-based voltage control strategies usually achieve the best results in terms of increasing a grid hosting capacity compared to PV inverterbased voltage control strategies. However, a combined Q(V)/P(V) inverter control also performed well in the context of this study. Analyses on a combined application of OLTC and inverter-based voltage control strategies showed that no significant improvements can be expected for most of the investigated LV grids compared to a sole OLTC application. This is mainly due to the fact that the sole application of OLTCs is capable of sufficiently solving overvoltage problems and in turn increasing the grid’s hosting capacity in a way that causes local current congestions. As a combined voltage dependent active and reactive power control by PV inverter could be identified to be technically effective in terms of increasing a grids hosting capacity, the single performance and parallel operation of two different active and reactive power control strategies were analyzed in detail in Chapter 4. The two investigated autonomous voltage control strategies are the Q(V)/P(V) voltage control and the so-called automatic voltage limitation strategy which is aiming at limiting the local inverter voltage to a fixed upper voltage value instead of using a droop characteristic.

126


Both voltage control strategies were assessed regarding their • controller performance and overall voltage support capability, • their robustness against variation of control and process parameters and • their load-sharing capability. Due to its higher robustness against variations of controller and process parameter and its more distinct load-sharing capability, the Q(V)/P(V) voltage control strategy seems to be much easier to implement and hence should be favored over the automatic voltage limitation concept for grids with high PV penetration. In order to ensure its proper functionality, the automatic voltage limitation requires for relatively high controller dynamics. However, the performed simulations indicate that both voltage control strategies perform stable under parallel operation, if parameterized appropriately. The economic benefit of applying autonomous voltage control strategies was quantified in Chapter 5 by the example of two real LV grids. The results were discussed from the DSO’s as well as from the PV plant operator’s perspective. Encompassing PV expansion scenarios and one-year RMS simulations, in one minute resolution, were used to determine the extend of necessary grid reinforcement costs for the PV grid integration and the operational costs (i.e., network losses and PV feed-in losses) during grid operation. The results clearly highlight the additional savings potential that can be achieved by applying autonomous voltage control strategies instead of pure grid reinforcement measures. For example, by applying the Q(V)/P(V) voltage control strategy a savings potential of up to 75% resp. 47% of the total costs for conventional grid reinforcement measures was identified. Besides the inverter-based Q(V)/P(V) voltage control strategy also the OLTC-based voltage control strategies showed a high savings potential for DSOs. By applying a voltage dependent active power curtailment P(V) instead of a fixed feed-in limitation according to § 6 EEG, a significant feed-in loss reduction can be realized for PV systems, making their operation economically more reliable. However, single PV systems could be economically discriminated due to the individual location of their PCC. This circumstance requires for appropriate compensation approaches to cover experienced feed-in losses and hence to guarantee secure investments for PV plant operators. One practical approach could be to limit the active power curtailment to 70% PSTC according to the current requirements of § 6 EEG. Sensitivity analyses on varying unit prices and the discount factor showed the robustness of the gained results.


127

The results of this thesis clearly suggest that autonomous voltage control strategies should be used to improve the technical and economic grid integration of PV systems. If applied appropriately, they are capable of deferring grid reinforcement measures and hence shift investment costs to future points in time. In addition, autonomous voltage control strategies gain extra time for the DSOs until voltage driven grid reinforcements become necessary, if at all. During this time the extent of local PV penetration might be more advanced and hence enable DSOs to size their grids more efficiently. Of all investigated autonomous voltage control strategies, the OLTC-based voltage control strategies and the combined Q(V)/P(V) PV inverter control strategy showed the most promising results, from a technical as well as from an economic perspective. Outlook: The results of the smart meter data analysis of Chapter 2 should be verified by smart meter data from other project regions. The derived dependency between PV penetration level, the number of private end customer and the expected reverse power flows should be validated by aggregated power flow measurements at representative nodes within LV grids. Therefore, it is necessary to run at least one year measurement campaigns. Additional load characteristics, such as imbalanced power flows, reactive power consumptions and higher temporal resolutions promise additional value for an improved grid planning. It should also be considered to set up a study covering small commercial sites and farms as well. In Chapter 3 the voltage drop caused by reactive power flows over a transformer impedance was discussed. In the context of an autonomous local voltage support by means of reactive power provision unintended interferences between the reactive power flows and a local OLTC controller could occur. Especially at HV/MV substation transformer with relatively high short-circuit impedance, the risk of triggering unintended and counterproductive tap settings by bulk reactive power flows needs to be studied. The simulation based results of Chapter 4 should be verified by laboratory demonstrations. Therefore, the Q(V)/P(V) voltage control strategy and the automatic voltage limitation strategy need to be implemented in the control structure of real inverters. An upstream DC/DC converter with MPP tracker and off-MPP controller is important to adjust the dynamics of the voltage dependent active power controller appropriately. A minimum of two voltage supporting inverters should be operated in electrically close distance to evaluate their stability under parallel operation and to assess their load-sharing capability. The presence of different inverter dynamics could financially discriminate owners of PV inverters with relatively fast acting active and reactive power control loops. Once this effect has been proven in laboratory demonstrations, it should be considered to start a harmonization process for the outer voltage control loop of PV inverters. The results of the cost-benefit analysis of Chapter 5 are based on two real LV grids. The applied assessment methodology, comprising PV expansion scenarios and parameterized one-year RMS simulations, turned out to be a very time consuming

128


process. In future studies, the overall assessment process should be divided into automated or semi-automated subprocesses, in order to speed up the cost-benefit analysis. If successfully applied, the economic analysis could be extended to cover a statistically significant number of grids.

Appendix A

ANNEX to Chapter ’Smart Meter Data Analysis’ Figure A.1 shows the maximum DC power generation of a 1 kWp mono crystalline reference module, installed in Stuttgart, Germany, for different averaging time intervals. The data was recorded in 2010. Detailed information on the measured data can be found in [89].

Figure A.1: Maximum DC power generation for different averaging time intervals.

129

Appendix B

ANNEX to Chapter ’Hosting Capacity of Distribution Grids’ Calculating the Short-Circuit Power in LV Grids This section lists the equations used to calculate the short-circuit power in LV grids as presented in chapter 3.2.1. The short-circuit power at any PCC can be calculated by Ssc =

VN 2 [VA], Zsc

(B.1)

with VN as the nominal grid voltage and Zsc as the local short-circuit impedance. For a PCC within a radial LV feeder (compare Fig. 3.4), Zsc can be determined using equ. B.2. q zSC = (RCable + RTra f o + RMV )2 + (XCable + XTra f o + XMV )2 [Ω]

(B.2)

The values of the respective resistances R and reactances X can be calculated as follows: Cable Impedance: ′ RCable = RCable · l [Ω] ′ XCable = XCable · l [Ω]

R’Cable =Specific cable resistance [Ω/km] ′ XCable =Specific cable reactance [Ω/km] l = Length of cable [km]

130

(B.3) (B.4)

APPENDIX B. HOSTING CAPACITY OF DISTRIBUTION GRIDS 131

Transformer Impedance: The transformer impedance is determined using the following equations 2 usc ·VLV [Ω] (B.5) ZTra f o = 100% · SrT ur RTra f o = ZTra f o · [Ω] (B.6) usc q 2 2 (B.7) XTra f o = ZTra f o − RTra f o [Ω] with VLV =Nominal Grid Voltage [V ] SrT =Rated Transformer Capacity [VA] usc =Specific short-circuit impedance [%] ur =Specific short-circuit impedance (resistive part) [%] Medium-Voltage Impedance: The medium voltage impedance is determined using the following equations 2 c ·VMV [Ω] SMV s 2 ZMV XMV = [Ω] 1 + XR q 2 − X 2 [Ω] RMV = ZMV MV

ZMV =

(B.8)

(B.9) (B.10)

with VMV =Nominal Grid Voltage [V ] SMV =Short-Circuit Power at MV Level [VA] c =Voltage Factor [−] R/X =R/X Ratio of MV Level [−]

Generator Perspective of PQ-Diagram Figure B.1 shows the PQ-diagram as used in the context of this thesis. The PQdiagram is depicted from a generator’s perspective.

132 APPENDIX B. HOSTING CAPACITY OF DISTRIBUTION GRIDS

Figure B.1: PQ-Diagram, depicted from a generator’s perspective

Deviation of Voltage Angle Figure B.2 shows the deviation of the voltage angle between two LV-busbars, depending on active and reactive power flows over the connecting cable impedance. The two busbars are connected by a cable of type NAYY 95mm2 . Cable Type: NAYY 95mm², R’=0.3208Ω/km, X’=0.0754Ω/km, length = 1 km 2

Deviaition of Voltage Angle over Cable Impedance [ °]

0 −2 −4 −6 −8 −10 −12

Active Power Flow Reactive Power Flow 10

20 30 40 50 60 70 80 90 Active and Reactive Power Flow over Cable Impedance [MW, Mvar]

100

Figure B.2: Deviation of voltage angle over a cable impedance at low voltage level, depending on active and reactive power flows.


Calculating the Voltage Drop over the Transformer Impedance This sections lists the equations used to calculate the voltage drop over the transformer impedance.

Figure B.3: Transformer equivalent circuit

Methodology: 1. Calculate Impedance Values for Transformer Equivalent Circuit 1.1 Calculate per-unit Values Short-circuit impedance zsc =

usc [p.u.] 100

(B.11)

rsc =

PCU [p.u.] Sr

(B.12)

q 2 [p.u.] z2sc − rsc

(B.13)

Winding resistance

Leakage reactance xsc = No-load impedance

zm = Iron-loss resitance rFE = Main reactance

v u u xm = t

1

[p.u.]

(B.14)

SrT [p.u.] P0

(B.15)

I0 ·IN 100

1 1 2 12 zm − rFE (B.16)

1.2 Calculate real Values Definition of reference impedance ZHV re f =

2 VHV [Ω] Sr

(B.17)

134 APPENDIX B. HOSTING CAPACITY OF DISTRIBUTION GRIDS

ZLV re f =

2 VLV [Ω] SrT

(B.18)

Conversion of per-unit values to real values. Impedance values are split equally to HV and LV windings. 1 (B.19) RHV = · rsc · ZHV re f [Ω] 2 XHV =

1 · xsc · ZHV re f [Ω] 2

(B.20)

RLV =

1 · rsc · ZLV re f [Ω] 2

(B.21)

XLV =

1 · xsc · ZLV re f [Ω] 2

(B.22)

RFE = rFE · ZHV re f [Ω]

(B.23)

Xm = xm · ZHV re f [Ω]

(B.24)

1.3 Transform real Values to reference Voltage Level Transformation ratio n=

VHV VLV

(B.25)

Transformation from HV level to LV level R∗HV

2 1 = RHV · n

2 1 = XHV · n 2 1 ∗ RFE = RFE · n 2 1 ∗ Xm = Xm · n

∗ XHV

(B.26)

(B.27)

(B.28)

(B.29)

2. Calculate Voltage Drop over Transformer Impedance ∗ Z ∗sc,HV = R∗HV + jXHV

(B.30)


Z ∗0 =

R∗FE · jXm∗ R∗FE + jXm∗

(B.31)

Figure B.4: Transformer equivalent circuit - simplified

To calculate the voltage at the LV busbar of the transformer, depending on the active and reactive power flows, a recursive algorithm with k iteration is applied until convergency is reached at ε < ξ, with ξ as the required accuracy. The current at the LV side of the transformer is defined by the active and reactive power flows and the voltage at the LV busbar. For the first iteration the respective nominal voltage can be assumed. P + jQ ∗ I LV,k = (B.32) V LV,k I HV,k = I LV,k ·

Z ∗HV ·Z ∗0 Z ∗HV +Z ∗0 Z ∗HV

1 + I HV,k · Z ∗HV + I LV,k · (RLV + jXLV ) U LV,k+1 = U HV · n P + jQ ∗ I LV,k+1 = V LV,k+1 ε = I LV,k − I LV,k+1

(B.33) (B.34)

(B.35) (B.36)

Appendix C

ANNEX to Chapter ’Parallel Operation of Photovoltaic Systems’ Inverter Model Figure C.1 shows the block diagram of the general inverter control scheme, as implemented in MATLAB Simulink.

Figure C.1: Overview on inverter control scheme, implemented in MATLAB Simulink.

136

APPENDIX C. INVERTER CONTROL

137

Figure C.2 shows the block diagram of the automatic voltage limitation control scheme, as implemented in MATLAB Simulink.

Figure C.2: Overview on automatic voltage limitation control scheme.

138


ABC-DQ0 Transformation Matrices The following set of equations describes the abc-DQ0 transformation (power invariant):   r    ) cos(Θ + 2π ) cos(Θ) cos(Θ − 2π Id Ia 3 3 2π    Iq = 2 −sin(Θ) −sin(Θ − 2π ) −sin(Θ + ) Ib (C.1) 3 3 √ √ √ 3 2 2 2 I0 Ic 2 2 2 The following set of equations describes the DQ0-abc transformation (power invariant): √     r  2 cos(Θ) −sin(Θ) Ia Id 2 √ 2  2   Iq  2π Ib = (C.2) cos(Θ − 2π  ) −sin(Θ − ) 3 3 √2 3 2 2π 2π Ic I0 cos(Θ + 3 ) −sin(Θ + 3 ) 2

PT1 Low-Pass Filter Equation C.3 shows the first order differential equation of a PT1 low-pass filter and Fig. C.3 shows the corresponding Bode plot. 1 dx1 (t) = · (K · x2 (t) − x1 (t)) dt Tf

Figure C.3: Bode plot of PT1 low-pass filter.

(C.3)


139

Whether placing the filter in the feedback loop for smoothing out voltage measurement fluctuations or to place it in the forward loop for smoothing out the inverter’s output power, does not effect the dynamics of the controlled inverter system (see Fig. C.4) for external voltage changes. In both cases the transfer function remains the same. ∆v(s) GCT RL (s) · GINV (s) · GFILT ER (s) = VN (s) 1 + GCT RL (s) · GINV (s) · GFILT ER (s)

(C.4)

Figure C.4: Simplified feedback control structure of VSI with voltage support functionality. A) Structure with filter for voltage measurements. B) Structure with inverter output filter.

Dynamic System Model of two Inverter Network The dynamic system model is based on the equation of Kirchhoff’s first and second law (see equ. C.5 to C.7). 0 = iC1 + iC2 − iFT

(C.5)

0 = −vN − iFT · RFT − LFT

diC1 diFT − iC1 · RC1 − LC1 + vC1 dt dt

(C.6)

0 = −vN − iFT · RFT − LFT

diFT diC2 − iC2 · RC2 − LC2 + vC2 dt dt

(C.7)

Equation C.5 can be rewritten as diC1 diC2 diFT = + . dt dt dt Substituting equ. C.8 into equ. C.6 and equ. C.7 yields

(C.8)

140


0 = −vN − iFT · RFT −

diC2 diC1 (LC1 + LFT ) − LFT − iC1 · RC1 + vC1 dt dt

diC2 diC1 (LC2 + LFT ) − LFT − iC2 · RC2 + vC2 dt dt and rewriting equ. C.9 and equ.C.10 to

0 = −vN − iFT · RFT −

(C.9)

(C.10)

diC1 vN iFT · RFT LFT diC2 iC1 · RC1 vC1 =− − − · − + dt LC1 + LFT LC1 + LFT LC1 + LFT dt LC1 + LFT LC1 + LFT (C.11) vN iFT · RFT LFT diC1 iC2 · RC2 vC2 diC2 =− − − · − + dt LC2 + LFT LC2 + LFT LC2 + LFT dt LC2 + LFT LC2 + LFT (C.12) Now, substituting equ. C.11 into equ. C.12 and equ. C.12 into equ. C.11 leads to vN · LC2 iFT · RFT · LC2 iC2 · RC2 · LFT diC1 =− − + dt λ λ λ iC1 · RC1 (LC2 + LFT ) vC1 (LC2 + LFT ) vC2 · LFT − + − λ λ λ

(C.13)

diC2 vN · LC1 iFT · RFT · LC1 iC1 · RC1 · LFT =− − + dt λ λ λ (C.14) iC2 · RC2 (LC1 + LFT ) vC2 (LC1 + LFT ) vC1 · LFT − + − λ λ λ with λ = LC1 LC2 + LC1 LFT + LC2 LFT . Finally, equ. C.13 and equ. C.14 are substituted into equ. C.8. diFT vN (LC1 + LC2 ) iFT · RFT (LC1 + LC2 ) iC2 · RC2 · LC1 =− − − dt λ λ λ (C.15) iC1 · RC1 · LC2 vC1 · LC2 vC2 · LC1 + + − λ λ λ Equations C.13, C.14 and C.15 form the system of first order differential equations for the two inverter network.  diC1 

 −R

dt  diC2  =   dt diFT dt

C1 (LC2 +LFT )

λ RC1 ·LFT λ −RC1 ·LC2 λ

  RC2 ·LFT ) −RFT ·LC2 iC1 λ λ    −RC2 (LC1 +LFT ) −RFT ·LC1 iC2 + ·  λ λ −RFT (LC1 +LC2 ) −RC2 ·LC1 iFT λ λ     LC2 +LFT −LC2 −LFT vC1 λ λ λ LC1 +LFT −LC1    −LFT vC2  · λ λ λ LC1 LC1 +LC2 LC2 vN − λ λ λ 

(C.16)


141

Parallel Operation of PV Inverter - Sensitivity Analysis

Figure C.5: Variation of minimum power factor of Q(V)/P(V) control strategy

Figure C.6: Variation of integral gain of automatic voltage limitation control strategy.

142

APPENDIX C. INVERTER CONTROL Inverter 2: T f = 3s

Figure C.7: Load-sharing capability of Q(V)/P(V) voltage control strategy with heterogeneous inverter parameterization (Inverter 2: T f = 3s).


143

Inverter 2: T f = 5s

Figure C.8: Load-sharing capability of Q(V)/P(V) voltage control strategy with heterogeneous inverter parameterization (Inverter 2: T f = 5s).

144

APPENDIX C. INVERTER CONTROL Inverter 2: T f = 3s

Figure C.9: Load-sharing capability of the automatic voltage limitation strategy with heterogeneous inverter parameterization (Inverter 2: T f = 3s).


145

Inverter 2: T f = 5s

Figure C.10: Load-sharing capability of the automatic voltage limitation strategy with heterogeneous inverter parameterization (Inverter 2: T f = 5s).

Appendix D

ANNEX to Chapter ”Economic Assessment” Unit Prices for Cost-Benefit Analysis The listed prices represent orientation prices and hence may vary from DSO to DSO. Table D.1: Investment costs assumptions

Cables

Transformer

Object

Price per unit

400 kVA incl. installation 8, 000 EUR/PC 630 kVA incl. installation 11, 000 EUR/PC 800 kVA incl. installation 13, 500 EUR/PC OLTC upgrad 15, 000 EUR/PC OLTC controller exchange 2, 500 EUR/PC 4x150mm2 NAYY 13 EUR/m 4x240mm2 NAYY 18.5 EUR/m Surfacce restoration 55 EUR/m Discount rate i = 8%

Lifetime n

40 years 15 years 40 years

Table D.2: Operational costs assumptions Cost category

Price per unit

Power loss compensation OLTC maintenance PV feed-in

closs = 0.07 EUR/kW h cmain = 1, 000 EUR/10yr cPV = 0.17 EUR/kW h q = 1% monthly degression 20 year of guaranteed payment

146

Table D.3: GRID NO. 20: Required grid reinforcement measures for the investigated voltage control strategies provided by PV inverters. Year 3

Cable 150mm2 [m] Cable 240mm2 [m] Surface restoration [m] 630 kVA Transformer 800 kVA Transformer

166.2 0 166.2 1 0

91.3 0 91.3 0 0

247.7 201.9 449.6 0 0


166.2 0 166.2 0 0

91.3 0 91.3 0 0


0 0 0 0 0

166.2 0 166.2 0 0


0 0 0 0 0

166.2 0 166.2 0 0


0 0 0 0 0

0 0 0 0 0


0 0 0 0 0

0 0 0 0 0

4

5

6

7

8

Grid reinforcement only 0 0 166.2 48.7 272.9 296.4 30.7 345.1 0 246.3 296.4 30.7 511.3 48.7 519.2 0 0 0 0 0 0 1 0 0 0 CosPhi(P) 247.7 0 0 0 0 0 0 474.1 0 133.6 0 0 247.7 474.1 0 133.6 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Q(V) without power factor limitation 0 0 91.3 0 166.2 247.7 0 0 0 0 299.8 0 0 0 91.3 0 466 247.7 0 0 1 0 0 0 0 0 0 0 0 0 Q(V) with power factor limitation 0 0 91.3 166.2 0 247.7 0 0 0 296.4 0 0 0 0 91.3 462.6 0 247.7 0 0 1 0 0 0 0 0 0 0 0 0 Q(V)/P(V) with Plim = 70% PSTC 0 0 166.2 0 91.3 0 0 0 0 0 0 0 0 0 166.2 0 91.3 0 0 0 0 0 1 0 0 0 0 0 0 0 Q(V) Pmax = 70% PSTC 0 0 166.2 0 91.3 0 0 0 0 0 0 0 0 0 166.2 0 91.3 0 0 0 0 0 1 0 0 0 0 0 0 0

9

10

247.7 132.9 380.6 0 0

410.5 0 410.5 0 0

0 0 0 0 1

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

247.7 0 247.7 0 0

0 0 0 0 0

247.7 0 247.7 0 0

0 0 0 0 0

147

2

APPENDIX D. ECONOMIC ASSESSMENT

1

148


Table D.4: GRID NO. 20: Required grid reinforcement measures for the investigated OLTC-based voltage control strategies.

1

2


166.2 0 166.2 1 0

91.3 0 91.3 0 0

Cable 150mm2 [m] Cable 240mm2 [m] Surface restoration [m] 400 kVA Transformer 630 kVA Transformer 800 kVA Transformer OLTC upgrade

0 0 0 1 0 0 1

0 0 0 0 0 0 0


0 0 0 1 0 0 1

0 0 0 0 0 0 0

3

4

5

Year 6

7

8

Grid reinforcement only 247.7 0 0 166.2 48.7 272.9 201.9 296.4 30.7 345.1 0 246.3 449.6 296.4 30.7 511.3 48.7 519.2 0 0 0 0 0 0 0 0 1 0 0 0 On-load tap changer with VSet = 1.0 p.u. 0 0 0 0 166.2 0 0 0 0 0 0 0 0 0 0 0 166.2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 On-load tap changer with VSet = 0.98 p.u. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0

9

10

247.7 132.9 380.6 0 0

410.5 0 410.5 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

Table D.5: GRID NO. 39: Required grid reinforcement measures for the investigated voltage control strategies provided by PV inverters.

3


519.4 0 519.4 0 0

0 0 0 1 0

155.4 0 155.5 0 0


519.4 0 519.4 0 0

0 0 0 0 0

0 0 0 1 0


519.4 0 519.4 0 0

0 0 0 0 0

0 0 0 1 0


519.4 0 519.4 0 0

0 0 0 0 0

0 0 0 1 0


519.4 0 519.4 0 0

0 0 0 0 0

155.4 0 155.4 0 0


519.4 0 519.4 0 0

0 0 0 0 0

155.4 0 155.4 0 0

4

5

Year 6

7

8

Grid reinforcement only 208.4 145.5 467.5 633.5 0 0 0 0 103.3 0 208.4 145.5 467.5 736.8 0 0 0 0 0 0 0 0 1 0 0 CosPhi(P) 155.4 0 0 0 185.6 0 0 0 0 0 155.4 0 0 0 185.6 0 0 0 0 0 0 0 0 0 0 Q(V) without power factor limitation 155.4 0 0 0 185.6 0 0 0 0 0 155.4 0 0 0 185.6 0 0 0 0 0 0 0 0 0 0 Q(V) with power factor limitation 155.4 0 0 0 185.6 0 0 0 0 0 155.4 0 0 0 185.6 0 0 0 0 0 0 0 0 0 0 Q(V)/P(V) with Plim = 70% PSTC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 Q(V) Pmax = 70% PSTC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

9

10

0 88.3 88.3 0 0

0 184 184 0 0

0 0 0 0 0

208.4 0 208.4 0 1

0 0 0 0 0

208.4 0 208.4 0 1

0 0 0 0 0

208.4 0 208.4 0 1

0 0 0 0 0

208.4 0 208.4 0 0

0 0 0 0 0

208.4 0 208.4 0 0

149

2


1

150


Table D.6: GRID NO. 39: Required grid reinforcement measures for the investigated OLTC-based voltage control strategies.

1

2


519.4 0 519.4 0 0

0 0 0 1 0


0 0 0 1 0 0 1

0 0 0 0 0 0 0


0 0 0 1 0 0 1

0 0 0 0 0 0 0

3

4

Year 5

6

7

8

Grid reinforcement only 155.4 208.4 145.5 467.5 633.5 0 0 0 0 0 103.3 0 155.5 208.4 145.5 467.5 736.8 0 0 0 0 0 0 0 0 0 0 1 0 0 On-load tap changer with VSet = 1.0 p.u. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 On-load tap changer with VSet = 0.98 p.u. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

9

10

0 88.3 88.3 0 0

0 184 184 0 0

0 0 0 0 0 0 0

0 0 0 0 0 1 1

0 0 0 0 0 0 0

0 0 0 0 0 1 1


151

Figure D.1: Accumulated investment costs over 10 years of grid No. 20 with unit prices of the end of the base year t0 .

Figure D.2: Accumulated investment costs over 10 years of grid No. 39 with unit prices of the end of the base year t0 .

Table D.7: Model parameter settings for one-year RMS simulations.


PV system model Parameter PDC,max Smax Cosϕmin Cosϕcrit v1 v2 v3 v4 Pmin Inverter Efficiency OLTC model Parameter VDB+ VDB− Load model Parameter No.o f Households No.o f PCC

152

Cosϕ

Without control

Cosϕ(P)

10 kWp 9 kVA -

10 kWp 9.47 kVA 0.95 0.2 -

Q(V) without PF lim. with PF lim. 10 kWp 10 kWp 9.47 kVA 9.47 kVA 0.95 0.95 0.95 0.2 1.05 p.u. 1.05 p.u. 1.08 p.u. 1.08 p.u. see Figure D.4

Q(V)/ Pmax = 70%

Q(V)/P(V)

10 kWp 9.47 kVA 0.95 0.2 1.05 p.u. 1.08 p.u. 70% PSTC

10 kWp 9.47 kVA 0.95 0.2 1.05 p.u. 1.08 p.u. 1.08 p.u. 1.09 p.u. 70% PSTC

Scenario VSet = 1.0 p.u. 1.02 p.u. 0.98 p.u.

Scenario VSet = 0.98 p.u. 1.0 p.u. 0.96 p.u.

Grid No. 20 1.4 0.95 ind.

Grid No. 39 1.184 0.95 ind.


153

Figure D.3: Time dependent development of network losses for grid No. 39.

Modeling of Inverter Efficiency The efficiency of the inverter should be taken into account by using a 2nd order polynomial equation [118] for calculating internal inverter losses depending on the instantaneous active and reactive power output [46]. This second order function can be parameterized by tuning the coefficients b1 (no load losses), b2 (voltage dependent losses) and b3 (current dependent losses). The coefficients can be derived from fitting the inverter efficiency curve, which can be provided by the inverter manufacturer. Since equ. D.4 depends on the active power output of the inverter itself, a recursive algorithm is needed to calculate the active power output of the inverter (see equ. D.1 to D.5). 2 S S PLoss (S) = b1 + b2 · · 100% + b3 · · 100% SN SN

(D.1)

PAC,1 = PDC − PLoss,1 (0)

(D.2)

PAC,2 = PDC − PLoss,2 (PAC,1 ; Q)

(D.3)

PAC,k = PDC − PLoss,k (PAC,k−1 ; Q)

(D.4)

The algorithm converges if equ. D.5 becomes true. PAC,k − PAC,k−1 ≤ ε

(D.5)

Figure D.4 depicts the inverter efficiency curve as used for the simulation in Chapter 5. The efficiency curve is parameterized according to the ”98%-Scenario” of [119].

154


Figure D.4: Inverter efficiency curve as used in Chapter 5.


155

Additional Feed-In Losses due to Active Power Curtailment Figure D.5 shows the top ten PV systems with the highest additional feed-in losses due to active power curtailment by applying the Q(V)/P(V) voltage control strategy.

Figure D.5: Top ten PV system with the highest additional feed-in losses due to active power curtailment by applying the Q(V)/P(V) voltage control strategy.

List of Figures 1

Comparison of net present values NPV of the cash flow time series, comprising investment costs NPVINV and operational costs NPVOP (network losses NPVOP1 and photovoltaic opportunity costs NPVOP2 ), referred to the beginning of year t1 . . . . . . . . . . . . XVIII

1.1 1.2

Installed capacity of renewables in Germany. Data derived from [4]. Measured power flow over HV/MV substation transformer, recorded from 2009 to 2013. The data is a courtesy of the Bayernwerk AG. Structure of the thesis. . . . . . . . . . . . . . . . . . . . . . . . Differentation between centrally, decentrally and locally structured intelligence of voltage control strategies. Modified version of original graphic presented in [15] . . . . . . . . . . . . . . . . . . . .

1.3 1.4

2.1 2.2 2.3 2.4 2.5 2.6

2.7

2.8 2.9

Standard load profiles derived from smart meter data, exemplary shown for winter workday. . . . . . . . . . . . . . . . . . . . . . Standard error of the smart meter data, exemplary shown for winter workday. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peak load variation for summer workday (solid lines) and winter Sunday (dashed lines) data sets. Application of different percentiles. Parameter fit using smart meter data from the characteristic day with highest peak load (winter Sunday). . . . . . . . . . . . . . . Low load variation for summer workday (solid lines) and winter Sunday (dashed lines) data sets. Application of different percentiles. 1% low load percentiles for summer workday (solid lines) and winter Sunday (dashed lines) data sets for different time slices (UCT/GMT+1). . . . . . . . . . . . . . . . . . . . . . . . . . . . Upper Figure: Simultaneity factor depending on the number of household loads n, exemplary for summer Workday (SU/WD) and winter Sunday (WI/SUN). Lower Figure: Threefold standard error based on m = 10, 000 samples. . . . . . . . . . . . . . . . . . . . Installed load PInst (n) depending on the number of households for characteristic winter Sundays. . . . . . . . . . . . . . . . . . . . Comparison of peak load equivalent values derived from smart meter data (winter Sunday) and equivalent values from [19] and [20].

156

2 3 5

8 12 12 14 15 15

16

18 19 19

LIST OF FIGURES

2.10 Measured active power feed-in of PV systems at the day with the highest accumulated power feed-in during the recorded year (4th of May 2011, transition period/ workday). . . . . . . . . . . . . . 2.11 Effect of superimposition of PV feed-in and local load consumption on accumulated active power flows [18]. . . . . . . . . . . . 2.12 1% low load percentile for different VDEW periods considering an installed PV capacity of 5 kWp per household. . . . . . . . . . . . 2.13 Smart meter data (blue dots) and parameter fit (red grid) for 1% low load percentiles depending on the installed PV capacity [kWp/HH] and the number of households (n). . . . . . . . . . . . . . . . . . 2.14 Relative error between smart meter data and equation 2.13. . . . . 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

3.10 3.11

3.12 3.13

3.14 3.15

157

21 22 23

24 25

Overview on field of research on hosting capacity of electricity grids for PV capacity. . . . . . . . . . . . . . . . . . . . . . . . . 28 Illustration of hosting capacity principle according to [31]. . . . . 30 Example of permissible voltage rises along MV and LV impedances. 30 Equivalent circuit of single LV feeder . . . . . . . . . . . . . . . 32 Effect of different grid reinforcement measures on the short-circuit power along a LV feeder. . . . . . . . . . . . . . . . . . . . . . . 33 Simplified schematic of a current source connected to the mains. . 34 Phasor diagram for single PV system (Grid and Load = Load Perspective, Generator = Generator Perspective) . . . . . . . . . . . 35 Voltage deviation over grid impedance according to Fig. 3.6. VN =400V, Ssc =1MVA, SPV =30kVA. . . . . . . . . . . . . . . . . . . . . . . 36 Voltage deviation from MV to LV busbar of distribution transformer, caused by active and inductive reactive power flows. The specific transformer type parameter values are taken from the PowR library [51]. . . . . . . . . . . . . . . . . . . . . . . erFactory 37 Autonomous local control principle for OLTC. . . . . . . . . . . . 38 Parameterization of reactive power provision by PV, considering a simultaneity factor of 0.85 (expected value) and an adjusted inverter sizing ( fsizing = 0.9). . . . . . . . . . . . . . . . . . . . . . 40 Typical characteristic of a Q(V) static for a voltage dependent reactive power provision by PV inverter. . . . . . . . . . . . . . . . 41 PQ diagram of state-of-the-art PV inverter with reactive power control capability. The figure compares the possible area of operation for both, a reactive power provision restricted by a minimum power factor and a reactive power provision restricted by Qmax . . . . . . 42 Flow chart for the iterative calculation of the reactive power output by applying a Q(V) characteristic. . . . . . . . . . . . . . . . . . 42 Typical characteristic of Q(V)/P(V) statics for a voltage dependent reactive power provision and a voltage dependent active power output limitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

158

LIST OF FIGURES

3.16 Flow chart for the iterative calculation of the reactive power output by applying a Q(V) characteristic and a voltage dependent active power limitation P(V). . . . . . . . . . . . . . . . . . . . . . . . 3.17 Decoupling of MV and LV level by using a distribution transformer with OLTC. The ± 10% VN EN50160 criterion is used here. . . . 3.18 Flow chart for probabilistic assessment of hosting capacity. . . . . 3.19 Relative additional hosting capacity by autonomous voltage control strategies. The number below the grid name represents the number of nodes within the respective grid. . . . . . . . . . . . . 3.20 Relative additional hosting capacity by autonomous voltage control strategies. The number below the grid name represents the number of nodes within the respective grid. . . . . . . . . . . . . 3.21 Cosϕ f ix : Additional hosting capacity that can be utilized by applying a Cosϕ f ix voltage control strategy compared to alternative voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . 3.22 Cosϕ(P): Additional hosting capacity that can be utilized by applying a Cosϕ(P) voltage control strategy compared to alternative voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . 3.23 Q(V): Additional hosting capacity that can be utilized by applying a Q(V) voltage control strategy compared to alternative voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.24 Q(V)/P(V): Additional hosting capacity that can be utilized by applying a Q(V)/P(V) voltage control strategy compared to alternative voltage control strategies. . . . . . . . . . . . . . . . . . . . 3.25 OLTC: Additional hosting capacity that can be utilized by applying a OLTC voltage control strategy compared to alternative voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . . . 3.26 QQ-plot for the results of the Q(V) voltage control strategy. . . . . 3.27 Beanplot showing the distribution of the additional hosting capacity for different starting points of the Q(V) characteristic. The bold black line represents the median of the distributions. The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . 3.28 Beanplot showing the distribution of the additional hosting capacity for different active power limitations Plim . The bold black line represents the median of the distributions. The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . . . . . . 3.29 Sensitivity analysis: Parameterization of OLTC controller (grid No. 5). The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.30 Sensitivity analysis: Parameterization of OLTC controller (grid No. 9). The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44 45 48

50

51

53

53

54

54

55 56

57

57

58

58

LIST OF FIGURES

159

3.31 Sensitivity analysis: Parameterization of OLTC controller. Distribution over all 17 LV grids. The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . . . . . . . . . . . . 59 3.32 Additional hosting capacity by combinations of OLTC and inverter based voltage control strategies compared to a sole OLTC application. 60 4.1 4.2 4.3

4.4

4.5 4.6 4.7 4.8 4.9

4.10

4.11 4.12 4.13 4.14 4.15

4.16

4.17

Block diagram showing the cascaded control structure of grid supporting current controlled voltage source inverter. . . . . . . . . . Inverter’s inner current control model with LC current output filter as presented by [73]. . . . . . . . . . . . . . . . . . . . . . . . . Equivalent circuit for electric coupling of PV inverter in a balanced three-phase system. The grid impedance is modeled in the abc coordinate system. . . . . . . . . . . . . . . . . . . . . . . . . . Inverter control scheme with inner current control and current output filter (green), the grid coupling impedance (black) and the outer voltage support loop (orange). . . . . . . . . . . . . . . . . . . . Q(V) control scheme with Vmeaãs the measured and filtered voltage reference signal and Q∗ as the reactive power set value. . . . . . . Reactive power output of inverter model for increasing voltage magnitudes Vmea˜(negative values = under-excitation). . . . . . . . P(V) control scheme with Vmeaãs the measured and filtered voltage reference signal and P∗ as the active power set value. . . . . . . . Active power output of inverter model for increasing voltage magnitudes Vmea˜. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage offset signal of external voltage source VN , which has been used to stimulate the inverters voltage dependent active and reactive power controller. . . . . . . . . . . . . . . . . . . . . . . . . Comparison of simulated active and reactive power output of the 3 phase voltage source inverter model with the measured step responses of the Triphase system in laboratory environment. . . . . Comparison of simulated and measured voltages. . . . . . . . . . Overview on control structure of the automatic voltage limitation. Control structure of reactive power control block. . . . . . . . . . Control structure of active power control block. . . . . . . . . . . Simulation based visualization of operation principle of the automatic voltage limitation control strategy demonstrated by applying a voltage ramp on the external grid voltage VN . . . . . . . . . . . Sensitivity of Q(V)/P(V) voltage control strategy on voltage fluctuations at the external grid. The black curves represent the uncontrolled inverter voltage Vc . . . . . . . . . . . . . . . . . . . . . . Sensitivity of automatic voltage limitation control strategy on voltage fluctuations at the external grid. The black curves represent the uncontrolled inverter voltage Vc . . . . . . . . . . . . . . . . . . .

64 66

66

67 68 68 69 69

71

71 72 73 74 74

75

77

78

160

LIST OF FIGURES

4.18 Time domain simulation of single PV inverter system with automatic voltage limitation strategy and fast controller dynamics (proportional gains k1 = 1, 000 var/V and k3 = 1, 000 W /V ; gradient limitation dQ = 10, 000 var/s and dP = 10, 000 W /s; no additional voltage filter). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.19 Time domain simulation of single PV inverter system with automatic voltage limitation strategy and slow controller dynamics (dQ = 500 var/s and dP = 500 W /s and a voltage filter with T f = 3s). 81 4.20 Time domain simulation of single PV inverter system with Q(V)/P(V) voltage control strategy and fast controller dynamics (dQ = 10, 000 var/s and dP = 10, 000 W /s; no additional voltage filter). . . . . . . . . 81 4.21 Time domain simulation of single PV inverter system with Q(V)/P(V) voltage control strategy and slow controller dynamics (dQ = 500 var/s and dP = 500 W /s; voltage filter with T f = 3s). . . . . . . . . . . 82 4.22 Single line diagram for a two inverter network with external voltage source VN as the slack bus. . . . . . . . . . . . . . . . . . . . 83 4.23 Measured voltage at the output clamps of inverter 1 before and after a 2.5%VN voltage step at the external voltage source while applying the Q(V)/P(V) voltage control strategy. . . . . . . . . . . 87 4.24 Measured voltage at the output clamps of inverter 1 before and after a 2.5%VN voltage step at the external voltage source by simulating scenario 1. Cable data of type NAYY 3x150mm2 / 70sm/ sm 0.6kV / 1kV : R′ = 0.2075 Ω/km; L′ = 0.23 mH/km, [90]. . . . . . . . . . . . . 88 4.25 Measured voltage at inverter 1 before and after a 2.5%VN voltage step at the external voltage source while applying the automatic voltage limitation strategy. . . . . . . . . . . . . . . . . . . . . . 89 4.26 Measured voltage at inverter 1 before and after a 2.5%VN voltage step at the external voltage source while applying the automatic voltage limitation strategy with different integral gains. . . . . . . 90 4.27 Load-sharing capability of Q(V)/P(V) voltage control strategy with heterogeneous inverter parameterization (Inverter 2: T f = 1s). . . 93 4.28 Load-sharing capability of automatic voltage limitation strategy with heterogeneous inverter parameterization (Inverter 2: T f = 1s). 94 5.1 5.2 5.3 5.4 5.5

Overview on field of research on economic assessments of voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . Flow chart of the structure of chapter 5. . . . . . . . . . . . . . . Single line diagram of LV grid No. 20. . . . . . . . . . . . . . . . Single line diagram of LV grid No. 39. . . . . . . . . . . . . . . . Beanplot showing the distribution of the additional hosting capacities by applying different autonomous voltage control strategies. Background: All 17 voltage limited grids from Section 3.4.2; Foreground: Grid No. 20. The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . . . . . . . . . . . . . . . . .

98 100 101 101

102

LIST OF FIGURES

5.6

5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14

5.15 5.16

5.17 5.18

5.19

Beanplot showing the distribution of the additional hosting capacities by applying different autonomous voltage control strategies. Background: All 17 voltage limited grids from Section 3.4.2; Foreground: Grid No. 39. The plot was conducted using the beanplot package in R [59]. . . . . . . . . . . . . . . . . . . . . . . . . . . Simplified grid reinforcement approach of cost-benefit analysis. . Comparison of net present values of the total investment cash flow time series, referred to the beginning of year t1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simplified illustration of applied RMS PV system model [33]. . . Load duration curves of the accumulated load profiles of grid No. 20 and grid No. 39. . . . . . . . . . . . . . . . . . . . . . . . . . Percentiles of an exemplary category B voltage profile. . . . . . . Load duration curves of applied external voltage profile and PV DC-power generation profile. . . . . . . . . . . . . . . . . . . . . Comparison of net present values of the operational costs cash flow time series NPVOP (network losses and PV opportunity costs), referred to the beginning of year t1 . . . . . . . . . . . . . . . . . . . Time dependent development of network losses for grid No. 20. . Comparison of net present values of the operational costs cash flow time series NPVOP (network losses and PV opportunity costs), referred to the beginning of year t1 . . . . . . . . . . . . . . . . . . . Sensitivity of additional savings on variations of unit prices and discount factor, exemplary for grid No. 39. . . . . . . . . . . . . . Accumulated annual PV feed-in losses due to active power curtailment in relation to the total annual energy generation of all controllable PV systems. . . . . . . . . . . . . . . . . . . . . . . . . Top ten PV systems with highest additional feed-in losses due to active power curtailment during year t10 . . . . . . . . . . . . . .

161

103 105 107 108 109 110 111 111

115 116

116 119

120 121

A.1 Maximum DC power generation for different averaging time intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 B.1 PQ-Diagram, depicted from a generator’s perspective . . . . . . . B.2 Deviation of voltage angle over a cable impedance at low voltage level, depending on active and reactive power flows. . . . . . . . . B.3 Transformer equivalent circuit . . . . . . . . . . . . . . . . . . . B.4 Transformer equivalent circuit - simplified . . . . . . . . . . . . .

132 132 133 135

C.1 Overview on inverter control scheme, implemented in MATLAB Simulink. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 C.2 Overview on automatic voltage limitation control scheme. . . . . 137 C.3 Bode plot of PT1 low-pass filter. . . . . . . . . . . . . . . . . . . 138

162

LIST OF FIGURES

C.4 Simplified feedback control structure of VSI with voltage support functionality. A) Structure with filter for voltage measurements. B) Structure with inverter output filter. . . . . . . . . . . . . . . . C.5 Variation of minimum power factor of Q(V)/P(V) control strategy C.6 Variation of integral gain of automatic voltage limitation control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.7 Load-sharing capability of Q(V)/P(V) voltage control strategy with heterogeneous inverter parameterization (Inverter 2: T f = 3s). . . C.8 Load-sharing capability of Q(V)/P(V) voltage control strategy with heterogeneous inverter parameterization (Inverter 2: T f = 5s). . . C.9 Load-sharing capability of the automatic voltage limitation strategy with heterogeneous inverter parameterization (Inverter 2: T f = 3s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.10 Load-sharing capability of the automatic voltage limitation strategy with heterogeneous inverter parameterization (Inverter 2: T f = 5s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.1 Accumulated investment costs over 10 years of grid No. 20 with unit prices of the end of the base year t0 . . . . . . . . . . . . . . . D.2 Accumulated investment costs over 10 years of grid No. 39 with unit prices of the end of the base year t0 . . . . . . . . . . . . . . . D.3 Time dependent development of network losses for grid No. 39. . D.4 Inverter efficiency curve as used in Chapter 5. . . . . . . . . . . . D.5 Top ten PV system with the highest additional feed-in losses due to active power curtailment by applying the Q(V)/P(V) voltage control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

139 141 141 142 143

144

145 151 151 153 154

155

List of Tables 1 2 2.1 2.2 3.1

3.2 3.3 3.4 4.1

4.2 4.3 4.4

4.5

Summary of the findings of Chapter 2. n =number of households, PPV =installed PV capacity. . . . . . . . . . . . . . . . . . . . . XIV Total savings by the application of autonomous voltage control strategies compared to pure grid reinforcements. . . . . . . . . . . XVII ′ over all n meaDays with highest accumulated PV feed-in Pmax sured PV systems. . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of the findings of Chapter 2. . . . . . . . . . . . . . . .

Summary of quality aspects limiting the hosting capacity for additional PV capacity as used for the following investigations. Applicable for steady-state analysis and investigation with separate voltage levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Influence of active and reactive power on the voltage magnitude and the voltage phase angle depending on the local X/R ratio. . . . Summary of set values for the calculation of the hosting capacity of LV grids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial parameter settings of the investigated autonomous voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . System parameter for the validation of the three-phase current controlled VSI with Q(V)/P(V) voltage support with the 5kVA power module of type PM5 from Triphase NV. . . . . . . . . . . . . . . Logical set and reset conditions for switching between the operation modes of the automatic voltage limitation. . . . . . . . . . . System parameters for the demonstration of the automatic voltage limitation control strategy. . . . . . . . . . . . . . . . . . . . . . Parameter settings for the sensitivity analysis. The highlighted values represent the base configuration of the controller. The droop vertices v2 and v3 of the Q(V)/P(V) control strategy remain constant at 1.08 p.u.. . . . . . . . . . . . . . . . . . . . . . . . . . . Initial scenario parameterization for parallel operation stability investigations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

21 26

31 36 46 49

70 73 74

76 85

164

4.6 4.7 5.1 5.2 5.3 5.4 5.5 5.6

LIST OF TABLES

Scenario parameterization for the load sharing simulations. For the transformer data see Table 4.5. . . . . . . . . . . . . . . . . . . . Summary of load sharing capability of the Q(V)/P(V) voltage control strategy and the automatic voltage limitation strategy. . . . . . Investigated PV expansion scenarios using LV grid No. 20 and No. 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of acronyms used in this section. . . . . . . . . . . . . . . . . Investment costs savings by the application of autonomous voltage control strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . List of acronyms used in this section. . . . . . . . . . . . . . . . . Total savings by the application of autonomous voltage control strategies compared to pure grid reinforcement. . . . . . . . . . . List of acronyms used in this section. . . . . . . . . . . . . . . . .

D.1 Investment costs assumptions . . . . . . . . . . . . . . . . . . . . D.2 Operational costs assumptions . . . . . . . . . . . . . . . . . . . D.3 GRID NO. 20: Required grid reinforcement measures for the investigated voltage control strategies provided by PV inverters. . . D.4 GRID NO. 20: Required grid reinforcement measures for the investigated OLTC-based voltage control strategies. . . . . . . . . . D.5 GRID NO. 39: Required grid reinforcement measures for the investigated voltage control strategies provided by PV inverters. . . D.6 GRID NO. 39: Required grid reinforcement measures for the investigated OLTC-based voltage control strategies. . . . . . . . . . D.7 Model parameter settings for one-year RMS simulations. . . . . .

92 95 104 105 107 112 117 117 146 146 147 148 149 150 152

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List of Units and Symbols

Chapter 2: Smart Meter Data Analysis σ

Standard Deviation

[-]

σm

Standard Error of Sample m

[-]

g∞

Simultaneity for an infinite Number of Loads

[W]

Ll(n)

Low Load (Number of Households)

[W]

PInst

Installed Load per Household

[W]

Pl(n)

Peak Load (Number of Households)

[W]

PPV

Photovoltaic Active Power Feed-In

[W]

PRF

Reverse Power Flows

[W]

PSTC

Installed Nominal Photovoltaic Module Capacity under Standard Test Conditions

[W]

Chapter 3: Hosting Capacity of Distribution Grids cosϕ

Power Factor

[-]

fsizing

Sizing Factor of Photovoltaic Inverter

[-]

IG

Generator Feed-In Current

[A]

P

Active Power

[W]

PAC

Active Power Feed-In

[W]

177

178

LIST OF UNITS AND SYMBOLS

Pmin

Minimal Active Power Feed-In after Curtailment

[W]

ϕ

Phase Angle

[ ◦]

Q

Reactive Power

[var]

Qmax

Generator Maximum Reactive Power Capability

[var]

R

Resistance

SG

Generator Apparent Power

[VA]

Smax

Generator Rated Power

[VA]

SrT

Transformer Rated Power

[VA]

Ssc

Short-Circuit Power

[VA]

usc

Specific Short-Circuit Impedance

[%]

V

Voltage

[V]

VDB

On-load Tap Changer Control Deadband

[V]

VDB−

On-load Tap Changer Control Deadband - Lower Limitation

[V]

VDB+

On-load Tap Changer Control Deadband - Upper Limitation

[V]

VG

Generator Voltage

[V]

VLV

Voltage at Low Voltage Busbar of Distribution Transformer

[V]

Vmax

Maximum Grid Voltage

[V]

VN

Nominal Voltage

[V]

VSet

On-load Tap Changer Set Voltage

[V]

VZ

Voltage Drop/Rise over Grid Impedance

[V]

X

Reactance

[Ω]

Z

Impedance

[Ω]

Zsc

Short-Circuit Impedance

[Ω]

[Ω]


179

Chapter 4: Parallel Operation of Photovoltaic Inverters dP

Active Power Gradient

[W/s]

dQ

Reactive Power Gradient

[W/s]

IL

Inverter Inductor Filter Current

[A]

IL ∗

Inverter Inductor Filter Current Set Value

[A]

Io

Inverter Feed-In Current

[A]

Io ∗

Inverter Feed-In Current Set Value

[A]

kp

Active Power Gain P(V)

kq

Reactive Power Gain Q(V)

[var/V]

k1

Reactive Power Proportional Gain (AVL)

[var/V]

k2

Reactive Power Integral Gain (AVL)

[var/V]

k3

Active Power Proportional Gain (AVL)

[W/V]

k4

Active Power Integral Gain (AVL)

[W/V]

LC

Grid Coupling Inductance

[H]

P∗

Inverter Active Power Set Value

[W]

Q∗

Inverter Reactive Power Set Value

RC

Grid Coupling Resistance

[Ω]

Tf

PT1 Filter Time Constant

[s]

Vc

Inverter Output Voltage

[V]

Vmea

Measured Inverter Voltage

[V]

Vmea˜

Measured and Filtered Inverter Voltage

[V]

Vtrsh

Threshold Voltage for Automatic Voltage Limitation

[V]

ω

Angular Frequency

[W/V]

[var]

[1/s]

180


Chapter 4: Economic Assessment a(t; i)

Discount Factor (year; Discount Rate)

[-]

C

Total Investment Costs

closs

Costs for Compensation of Network losses

cmain

Maintenance Costs for OLTC

cPV

Photovoltaic Feed-In Tariff

Eloss

Network Losses

[kWh]

EPV

Photovoltaic Feed-In Losses

[kWh]

f1

Present Value Factor f1 - Specific Period of Time

[-]

f2

Present Value Factor f2 - Infinite Extrapolation of Costs

[-]

f3

Present Value Factor f3 - Infinitely Repeated Reinvestment

[-]

i

Discount Rate

[%]

n

Lifetime of Invest

[yr]

qPV

Monthly Feed-In Degression

qPCR

Price Change Rate

[%]

s(t; q)

Price Change Rate Factor (year; Price Change Rate)

[%]

t

Year of Calculation Period

[-]

Tx

Year of Photovoltaic Installation

[-]

x

Number of Investigated PV System

[-]

z(t; qPV )

Feed-In Degression Factor (year; Price Change Rate)

[EUR] [EUR/kWh] [EUR] [EUR/kWh]

[%/Mon]

[%]

Nomenclature BW

Butterworth Filter

DER

Distributed Energy Resources

DG

Distributed Generation

DMS Distribution Management System DSO

Distribution system operator

EEG

German Renewable Energy Sources Act

HC

Hosting Capacity

HMI

Human Machine Interface

HV

High voltage

ICT

Information and communication technology

IQR

Inter Quartile Range

LTI System Linear Time Invariant System LV

Low voltage

Micro-DMS Micro Distribution Management System MPP

Maximum Power Point

MV

Medium voltage

NPV

Net Present Value

OLTC On-load tap changer PCC

Point of common coupling

PLL

Phased-Locked Loop

PV

Photovoltaic 181

182

RES

NOMENCLATURE

Renewable energy sources

RMS Root Mean Square SL

Slack Bus

UCT/GMT Coordinated Universal Time/ Greenwich Mean Time VSI

Voltage Source Inverter

Project Support for the Thesis This thesis was supported by funding from the following projects:

• PV-INTEGRATED: Integration großer Anteile Photovoltaik in die elektrische Energieversorgung - Neue Verfahren für die Planung und den Betrieb von Verteilnetzen German Project supported by the German Federal Ministry for Environment, Nature Conservation and Nuclear Safety FKZ: 0235224A, 0235224B, 0235224C • PV-SYMPHONIE: Untersuchungen zu Netzparallelbetrieb und Netzdienstleistungen von Photovoltaik-Wechselrichtern im Kurzzeitbereich German Project supported by the German Federal Ministry for Environment, Nature Conservation and Nuclear Safety FKZ: 0325313

183