method aims at developing the basis of an industrial tool aiming to assess the reliability of a grid plan in the short-term planning. The method accounts for errors ...
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20 Congrès de maîtrise des risques et de sûreté de fonctionnement - Saint-Malo 11-13 octobre 2016
The DIFERS (DIscrete Forecast ERror Scenarios) method for grid reliability assessment in short-term planning Evaluation de la fiabilité du réseau électrique en planification opérationnelle par la méthode DIFERS (DIscrete Forecast ERor Scenarios) Dogan Gamze, Labeau Pierre-Etienne and Maun Jean-Claude Université libre de Bruxelles Av F. D. Roosevelt 50, CP 165/84, 1050 Bruxelles
Sprooten Jonathan, Galvez Manuel and Sleurs Kristof Elia system operator SA Blvd de l’Empereur 20, 1000 Bruxelles
Summary The present paper presents a method developed to evaluate the reliability of a planned electrical grid submitted to errors of forecast, in a context of operational planning i.e. short-term planning than spans from week – 5 to day-ahead operations. Indeed, the context of electricity supply has changed a lot due to the increasing amount of renewable generation. As those generations depend on meteorological conditions, they are subject to errors of forecast that are not accounted for in the current evaluation process of a planning performed by Transmission System Operators (TSOs). Therefore, the combined impact of forecasting errors on renewables, load demand and cross-border flows has induced an increase in the methodological bias entailed by using deterministic methods based on best-estimate values and a predefined list of contingencies that the grid has to be able to withstand. The impact of those forecast errors has already been investigated in the literature but mostly in long-term planning. In lots of those studies, Monte Carlo Sampling (MCS) is used to sample the probability density function (pdf) of the renewable production. Nevertheless, as mentioned above, the method presented here targets the short-term planning and it is thus subjected to stronger time constraints. Therefore, the use of direct MCS is not suitable for the purpose of our study. The present method aims at developing the basis of an industrial tool aiming to assess the reliability of a grid plan in the short-term planning. The method accounts for errors of forecasts on the load demand, the weather-dependent renewable generation and the status of lines and generators. The tool will be used as a decision-aiding tool by the planners to better plan the grid based on a risk assessment and for the operator to have more reliable information on the grid vulnerabilities in a given planning.
Résumé Cet article présente une méthode permettant d’évaluer la fiabilité d’une planification du réseau électrique soumise à des erreurs de prévisions, dans le contexte de la planification opérationnelle (planification court-terme qui s’étend de 5 semaines à l’avance au jour avant les opérations du réseau). En effet, le contexte d’approvisionnement en électricité a subi de grands changements dus à l’introduction des énergies renouvelables. Ces productions étant dépendantes des conditions météorologiques, elles sont soumises à des erreurs de prévision qui ne sont actuellement pas prises en compte par les gestionnaires du réseau de transport lors de l’évaluation d’une planification. De ce fait, l’impact combiné des erreurs de prévision sur les productions renouvelables ainsi que la demande et les flux transfrontaliers induit un plus grand risque d’erreur fait sur la validation d’une planification. En effet, la méthode utilisée pour cette validation est jusqu’ici purement déterministe ; elle se base sur la meilleure prévision des variables du réseau et sur une liste de contingences que le réseau doit être capable de supporter. Dans la littérature, l’impact des variations possible des prévisions a déjà été étudié ; principalement pour la planification long-terme et en utilisant l’échantillonnage Monte Carlo afin d’échantillonner les densités de probabilité des productions renouvelables. Cependant, la planification court-terme étant sujette à des contraintes temporelles beaucoup plus strictes, l’utilisation directe du Monte Carlo ne peut se faire dans cette étude. La méthode proposée vise donc à développer les bases d’un outil industriel capable d’évaluer la fiabilité d’une planification court-terme du réseau. La méthode tient compte des erreurs de prévision sur les productions renouvelables, la charge, et le statut des lignes et générateurs. L’outil sera utilisé en tant qu’outil d’aide à la décision afin de permettre au planificateur de planifier au mieux le réseau sur base d’une évaluation du risque.
Introduction 1. Context Traditionally, the electricity generation has been mostly ensured by centralized units (nuclear, gas, coal). The production of those units can be forecast with a high level of confidence. Those forecasts have therefore been used to calculate the margins necessary to ensure a reliable electricity supply, that is, a supply that can overcome contingencies that could appear on the grid. Nevertheless, as it is not possible to cover all contingencies, TSOs test the reliability of the grid when subjected to the loss of any of its active elements (or set of k active elements) given best-estimate (BE) forecasts of load and generation. This policy is known as the “N-1 (or N-k) policy” and is thus fully deterministic in nature. Nevertheless, the increase of the share of renewable energies, the production of which differs a lot from the conventional units, and their integration into the electrical grid, present major challenges for the TSO. Indeed, the production from Renewable Energy Sources (RESs) is variable, weather-dependent and its forecast is subject to errors (in magnitude and time). Therefore, the increasing penetration of RESs in power system is likely to entail undesirable effects on the grid operation, as well as on the quality of the power produced (stability of the grid, voltage control…). The policies used so far in the domain of electricity supply have thus to be adapted to those new generation types. Indeed, the consideration of a discrete contingency on those generations would led us to consider events such as the loss of an entire wind park due to weather conditions. This involves large amounts of production and thus, the cost to cover that loss would be very high. Therefore, the well-known N-1 policy could easily become very costly if applied as it is currently. Moreover, this policy does not account for the low probability of occurrence of such events. Therefore, TSOs will have to make a shift in paradigm: going from the N-1 criterion, which entails reliance on costly preventive measures, to a reliability-based approach with risk management and integration of errors on forecast values. This amounts to shifting from deterministic techniques to probabilistic approaches capable of quantifying this risk.
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This paper presents a method that aims at making a soft shift of paradigm that will ease the industrial development of a support tool for this evolution. In that spirit, the method combines the advantages of deterministic and probabilistic evaluations. It has been developed for the operational planning and therefore it accounts for strong computational time constraints. 2. State of the art In the literature, several authors investigated the influence of wind generation uncertainty on power system, essentially in the perspective of long-term planning. Some papers focus on the adequacy of power balance with a high penetration of wind generation at hierarchical level I (i.e. without considering network constraints) (Billinton et al., 2004; Olsina et al., 2007; MacCormack et al., 2010 and Degeilh et al., 2011). Others consider also capacities and availabilities of transmission lines to compute the reliability evaluation of a composite generation and transmission system (hierarchical level II) with a large amount of wind generation (Billinton et al., 2004; Do et al., 2010; Wangdee et al., 2007 and Wen et al., 2009). Both linear and nonlinear approaches are used. However, as the power system contains nonlinear factors (e.g. line congestion and non-linear load-flow equations) and as the relation between the wind speed and the output power of a wind turbine is also a nonlinear function, the use of a linear approach is not appropriate to study a power system with massive integration of variable wind generation, given the wide range of possible operating conditions. To study uncertainties in the power system, there are two main approaches: response variability methods and reliability methods. The response variability methods aim at calculating the first statistical moments (mean, standard deviation…) and/or the Probability Density Function (pdf) of the output variables either directly, with the help of numerical simulations, such as Monte Carlo Sampling (MCS) (Billinton et al., 1994 and Dimitrovski et al., 2006), or from the statistical moments (analytical approaches) (Hu et al., 2006 and Su et al., 2005). However, as the probability of failure in a power system is usually small, MCS requires a large number of system evaluations in order to achieve accurate results. This makes the method very time-consuming, even when resorting to techniques to reduce the variance of the output such as Latin Hypercube Sampling, antithetic sampling or importance sampling (Hammersley et al., 1964). If analytical approaches are used to reconstruct the pdf from the statistical moments, the results are not accurate: indeed, failure corresponds usually to values of the uncertain parameters located at the tails of their pdf’s, which cannot be modelled properly with only the first statistical moments (mean, variance, skewness). The second approach, based on reliability methods, aims only at evaluating the probability of failure of the system. This approach was used to evaluate this failure probability in a system with wind production and for short-term planning (Do, 2012). The method couples the first order reliability method (FORM) with the law of total probability to determine the failure probability of a system, i.e. the probability of load shedding, considering errors on wind production forecasts. 3. Operational planning Operational planning aims at verifying whether a proposed grid plan is reliable. Nowadays, this consists in applying the N-k criterion and check if the grid can keep operating within predefined limits after the occurrence of any contingency of the N-k list. This list gathers the events that are considered as being most challenging for the grid; they are mainly N-1 events. The timeframe of interest in our study is the short-term operational planning which spans, for the Belgian Transmission System Operator, Elia, from five weeks ahead (W-5) to close to real-time operations. Therefore, the maintenance plan is already known at the time of the assessment. The N-k approach is thus performed based on a list of elements or sets of elements, whose loss is tested to see its effect on the grid. In order for a planning scheme to be acceptable, the loss of up to k active elements should be acceptable (i.e. the grid is still operable after the considered loss). If an N-k event leads to overloaded lines, the planner has to propose actions that solve the issue. The actions can be of two types: corrective or preventive. In practice, the corrective actions can only be applied for N-k events that led to overloads of less than 120% of line rating. These actions, once applied on the planned grid, should be able to decrease the line loading below its rating in less than 15 minutes. For events leading to overloads higher than 120%, preventive actions need to be proposed. Once a preventive action has been chosen by the planner, it is applied on the N state of the grid and a new N-k security analysis is performed to check for new possible issues and violations of constraints. To that purpose, the planner uses presumed grid topology and production plans; along with best-estimate load demand, wind and solar production forecasts. Currently, the operational planning does not account for the uncertainties on those variables. Nonetheless, with the increasing penetration of RES, these uncertainties on renewable production will become more and more challenging to the grid if the operational planning does not evolve along with this evolving environment. Therefore, the development of a probabilistic tool capable of accounting for the uncertainties of all input variables would allow the TSOs to be more prepared to changes in the predicted values on inputs. The development of such a tool represents a challenge in order to meet the time constraints of operational planning. A tool developed for the long-term planning (i.e. which takes place up to several years before real-time operation) is not suitable for solving the short-term planning problem. Indeed, the response variability methods are not adapted due to their important computational cost and their low accuracy. Moreover, the uncertainty considered for the long-term is the variability range of the variables whereas for the short-term the uncertainty is the forecast error on the variables. An operational version of the method needs thus to be developed to tackle the issue of forecast errors in the operational planning. Moreover, it represents a challenge for the operators to adapt and use a tool based on a risk evaluation and therefore, to make the shift from deterministic to probabilistic. 4. Objectives This paper presents the work carried out in a project that aims at developing a probabilistic method compatible with the operational planning of the Belgian power system (in terms of time constraints and available information). The method has to be able to determine the reliability of a grid plan given the uncertainties on input variables (load, production and cross-border flow forecasts and grid topology). The tool under development is a decision-support tool that supports the planner for sound decisions. A first version of the methodology (Dogan et al., 2015) was developed using MCS and its application on a modified version of the 14-bus IEEE test case. A second methodology based on DIscrete Forecast ERror Scenarios (DIFERS) was presented in (Dogan et al., 2016) along with the first results of its implementation on a 69-bus test case. As the target is to set up the basis of an industrial tool, it is important to develop the method in an industrial perspective. Therefore, the tool has not been developed as a black box but rather as a decision-aiding tool for the planner, which will be
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presented in the following section. To better help the planner, the method calculates several risk indicators in order for the planner to know if the grid plan is reliable or has to be subjected to changes. Those indicators will be presented in a second time. Then the DIFERS method will be detailed. It aims at discretizing the pdf of continuous variables (like e.g. wind speed, load forecasts…) into a finite number of possible states - or trends with respect to the BE values. Therefore, the method collects information not only for the BE (as it is done nowadays using the N-k criterion) but also for possible representative states of the continuous variables that could appear in real-time. It allows thus to respond to questions such as: What happens if we have more wind than predicted? Or more load? Finally, the first results of the implementation of the methodology will be detailed. The test case used in a modified version of the 69-bus test case in order to include circuit-breakers, thus leading to a 75-bus test case.
The discrete forecast error scenarios method 5. Decision support tool The methodology developed in the project aims at giving the planner a tool to make sound decisions regarding the validation of a given grid plan, the topology of which is known. The tool will use, as input variables, the forecasts of load, conventional generation (Conv. Gen.), renewable generation (Ren. Gen.) and cross-border flows (C-B flows) along with their forecast errors, represented by their pdf, and the Force Outage Rate (FOR) of elements of the grid (see Fig. 1). Based on those inputs, a probabilistic assessment will be performed. This will lead to the computation of indicators of reliability that will help the planner decide whether the planning scheme s/he submitted to the tool can be accepted, i.e. whether or not it meets the reliability objectives with minimum operating costs and market limitations.
Figure 1. Flowchart of the decision support tool
If it is not the case, the planner will be able, based on the results of the first iteration, to introduce preventive or corrective actions to be tested, to perform a second evaluation and to determine which one is meeting the reliability targets and/or is the least costly and has the lowest impact on market actors. There is thus an interaction between the tool and the user; the assessment is performed by a joint work of the tool and the planner. The proposed methodology based on this flowchart aims at combining the advantages of both deterministic and probabilistic approaches. Attention has been paid to limit the computational time in order for the method to be consistent with the operational planning and to allow the planner-tool interaction. The DIFERS methodology is divided in three steps that are performed either off-line or on-line in order to meet the above mentioned requirements. The on-line step ensures the tool-planner interaction, while the off-line steps have limited planner interaction. In each step, a calculation routine will be used in order to analyze the possible states of the grid. This routine will be described hereafter. 6. Calculation routine In each step, states of the grid, or samples, will be studied using a fixed calculation routine. First, for each of these states/samples, a load flow (LF) calculation will be performed. If this calculation does not converge or leads to overloaded lines, the sample is submitted to an optimal power flow (OPF) calculation. The objective function of the OPF is to minimize the cost of operation. The OPF makes use of several actions in order to solve the problem. The costs associated to each of these actions will determine the ranking of the use of these actions by the OPF and were chosen so that they lead to a near real-time order of magnitude for each action. Therefore, the first action that will be implemented by the OPF is reactive power redispatch on units; this solution, if sufficient to solve the network constraint, will be referred to as “OPF1-solved”. Then, the next action is active power redispatch on running conventional units; it is referred to as “OPF2-solved”. Thirdly, the OPF will consider starting up and shutting down conventional units, leading, if successful, to an “OPF3-solved” situation. Then power control of renewable units will be performed (“OPF4-solved”). As a last resort, load shedding will be applied (“LS-solved”). Once all the needed samples have been analyzed, risk indicators are calculated to help the planner analyze the grid plan. Those indicators are presented hereafter. 7. Risk indicators In order to analyze the results of each step of the methodology and support the planner in proposing preventive or curative actions, indicators have been developed and are presented in the following section. The probability of solving a sample, using the LF (P-LF), the OPF (P-OPF1 to 4) and load shedding (P-LS), respectively, are given hereafter. 𝑁𝑠 is the total number of samples.
P-LF = P-OPFj =
P-LS =
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1 Ns 1 Ns
1 Ns
s ∑N i=1 xi
Ns ∑i=1 xi
s ∑N i=1 xi
xi = 1, if sample i is LF-solved xi = 0, otherwise x = 1, if sample i is OPFj -solved with { i xi = 0, otherwise for 𝑗 = 1, … 4 x = 1, if sample i is LS-solved with { i xi = 0, otherwise with {
{1} {2}
{3}
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The Mean Cost of Operation (MCO) of the hourly grid plan has been calculated using near real-time redispatching costs of reactive power (1€/MVArh), active power (50€/MWh for conventional units and 100€/MWh for renewable units) and load shedding (3000€/MWh) as proposed by the TSO. MCO =
1 𝑁𝑠
𝑠 ∑𝑁 𝑖=1(1 × |∆𝑄𝑖 | + 50 × |∆𝑃𝑐𝑜𝑛𝑣𝑖 | + 150 × 𝑛𝑐𝑜𝑛𝑣𝑖 + 100 × |∆𝑃𝑟𝑒𝑛𝑖 | + 3000 × |∆𝐿𝑖 |)
{4}
where ∆𝑄𝑖 , ∆𝑃𝑐𝑜𝑛𝑣𝑖 , ∆𝑃𝑟𝑒𝑛𝑖 and ∆𝐿𝑖 are respectively the modifications of mean hourly reactive power, active power and the load shedding needed to solve sample i. 𝑛𝑐𝑜𝑛𝑣𝑖 is the number of shut-downs and/or start-ups of conventional units to account for the start-up and shut-down costs. This indicator will also be developed under specific conditions/events that will allow a ranking of events with regard to their related cost. For instance, the MCO can be calculated for the special condition “more wind than predicted” or “generator 1 out of service”… Further information on the possible overloads and voltage drops will be given to the planner in order for him/her to identify the main issues. This information will be detailed in section Results of the DIFERS method. 8. Step 1: Off-line probabilistic assessment The aim of the first step of the DIFERS method is to determine the list of the most critical sets of events (N-1, N-k …) that will be referred to as the dynamic contingency list. The aim of this step is to replace the permanent N-1 list by a dynamically-defined contingency list that accounts for the error on forecast values and for the probability of events. Indeed, in the current practice, the same N-1 list is mostly used no matter the situation (some N-2 events are added in case of possible storm) even though situations could be very different between two different days or from summer to winter conditions. The aim of this first step is thus to determine a contingency list adapted to the situation at hand. Therefore, this assessment will be performed once per set of similar operating conditions, which can typically cover a month. The contingency list will thus be determined one month in advance (M-1). As mentioned, this calendar has to consider that the contingency list for a summer day will differ from the list of a winter day. Therefore, between those two states, a new assessment of the dynamic contingency list has to be performed. This assessment will receive as inputs the forecasts and the forecast errors to determine the most challenging events for which the system must have a safe response in order to ensure a minimal risk level. Therefore, this assessment has to be precise in determining the most challenging events for the grid. Thus, a method with high precision had to be used. The use of MCS has thus been chosen. MCS allows using continuous and discrete variables while ensuring a reliable level of precision. The main disadvantage of the use of MCS is that it requires a long calculation time. Nevertheless, as this assessment does not need any planner intervention once it is launched, it can be performed off-line, what relaxes the time constraint. Using MCS, the following variables are sampled: wind speeds (from which wind generation can be obtained (Do, 2012)) and loads. So far, neither cross-border flows nor solar production have been considered. The uncertainties on loads and wind speeds are modelled using normal distributions (Do, 2012) centered on their best-estimate forecasts, with a standard deviation embodying the error estimated on these forecasts. The status of lines and generators is determined using the FOR of each element. The values used for these parameters are the same as those used in (Do, 2012). Nevertheless, more pertinent data for the uncertainties can be obtained using historical data analysis but the present paper does not focus on this subject. In order to reduce the computational time induced by MCS, stratified sampling has also been implemented on the pdf of the wind speed. Stratified sampling consists in drawing samples from the various truncated pdf’s defined on a partition in intervals of the range of the random variable at stake. The estimation in each interval is then weighed by the probability to lie in this specific interval. Doing so, more samples can be studied from less probable regions that are likely to lead to problematic situations corresponding to the probability of being in that particular area. After the sampling of each input variable, each sampled case is studied using the calculation routine described in section 6. The simulation is stopped either when the relative standard deviation on the probability of load shedding reaches 0.01% or when a maximum number of samples (2,000,000 samples) is reached. This way, the accuracy on the indicators and results is ensured. 9. Step 2: On-line semi-deterministic assessment The aim of this step is to guide the user towards helpful (preventive and/or corrective) actions. A deterministic evaluation will be performed as it is currently done by TSOs using no longer the N-1 list but the dynamic contingency list evaluated in step 1. This evaluation will consider newly acquired forecasts for the week (W-1) or the days to come. Moreover, the evaluation will be performed not only for the BE forecast of the continuous variables (wind speed, load…), but also for other possible discretized states of those variables. Therefore, the evaluation will be performed more than one time for each contingency. Indeed, the pdf of a variable, see Fig 2, will be discretized (e.g. in five points) in order for the evaluation to consider possible evolutions in trends compared to the BE case. The evaluation of the grid planning will thus be performed on the BE, but also for the points: less than estimated (LE), much less than estimated (MLE), more than estimated (ME) and much more than estimated (MME). The ME and LE points are located at one standard deviation from the right and left respectively of the BE. The MLE and MME points are distanced by 3 standard deviations, that way the discretization is performed in the confidence interval of 99%.
Figure 2. Discretization of the pdf of a forecast quantity
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This is another difference with the N-1 criterion. It will help the planner see what could happen if the BE case considered in the planning phase turns out to be the actual situation in real-time but it will also prepare him/her if it is not the case. The variables considered here are the wind speed and the load. We considered that all renewable productions are submitted to the same wind change, and the same goes for the loads. 9.1. Evaluation for LE, BE and ME This assessment will be made for each possible combination of discretized input variables. Firstly, the evaluation is performed for the LE, BE and ME points of the wind speed and the load, and for each possible combination of the states of those variables (9 possible combinations). That way the user to have the information on the most probable cases. As the probability of each event in the contingency list and the probability of each discretized input (LE, BE and ME) are known, the risk for each combination can be calculated. Therefore, there is a risk evaluation in this assessment that is not accurate but can be used as a first approximation which will be verified in step 3. As mentioned, other indicators will also be computed to have information on the overloads and voltage drops (see section Results of the DIFERS method). The aim of this step is to give the user the necessary information to find and propose actions that might improve the grid plan. The planner has thus the responsibility of studying the results and proposing actions to be tested by the tool. Step 2 is then relaunched with the added actions and new estimates of the indicators are calculated. Comparing the results of the first iteration to the next one, the user can determine which grid plan ensures the most reliable grid. The method allows thus comparing two grid plans, a feature that the N-1 criterion does not offer. Indeed, using the N-1 criterion, we are only able to say whether or not the criterion is respected, but we are not able to choose the best grid plan. The indicators developed here allow this comparison to ensure a safer grid planning. Of course, the interaction between the planner and the tool stops once the actions proposed allow reaching an acceptable level of risk. The interaction between the tool and the planner is thus based on a risk evaluation. 9.2. Evaluation for MLE and MME As the probability of occurrence of the MLE and MME points is very low, there is no point of ensuring that those cases are safe for the whole contingency list. Nevertheless, a reliable situation in N should be ensured by the user. 10. Step 3: Off-line semi-probabilistic assessment A second probabilistic assessment is performed that will use as input the preventive and/or corrective actions tested and validated by the planner in step 2 and the newly acquired forecasts on the input variables, as we get nearer real-time. The aim of the probabilistic assessment is to get more information on the possible trends of evolution with regard to the most recent forecasts obtained days before operation (in D-2 for instance). This information will be used by the planner to know which events are the most challenging and under which conditions. This information is of high importance as, when getting closer to real-time, the user will have more reliable and accurate forecasts. Based on the newly acquired forecasts, s/he will be able to use the assessment made with previous forecasts to put on preventive actions under specific conditions determined by the new forecasts. Indeed, the assessments in step 1 and step 2 will determine challenging events for the grid plan and will test actions to resolve the issues revealed. Nevertheless, the choice of enforcing those actions will be delayed until we get more accurate forecasts. This feature is very important, as when considering the error made on forecasts at a given time, various evolution scenarios can take place. Those scenarios being different from each other, they can lead to selecting very different actions to solve an issue. Those actions could even be opposite to one another. Therefore, the choice of those actions to be performed is made as follows. Simplifying the problem and considering only one variable, the planner could face possible corrective actions solving very different risky situations, e.g. corresponding to the opposite tails of the pdf of this variable, (see Fig. 3).
Figure 3. Corrective actions at the tail of the distribution Instead of enforcing the two corrective actions at a large cost, the planner could wait before acting to base his/her decision on the evolution of these risks. Indeed, as we get closer to real-time, we have a better knowledge on the forecasts. Based on the previous forecast, three scenarios could appear. First, if the best-estimate forecast is kept and the accuracy on it has increased, we observe a shrinking of the pdf embodying the forecast error. In that case, as the probability of being at any of the tails of the input distribution has lowered a lot, compared to the initial pdf of the data, there is no interest of enforcing any of the actions.
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Then, we could observe a shift of the pdf to the left or to the right. In Figure 4, where the shift is to the left, action 2 becomes irrelevant, as the risk it is meant to cover has significantly decreased; in the meantime, as the risk possibly covered by action 1 has increased, the user could decide to perform it preventively.
Figure 4. Delaying decision on action to be performed We are thus using and updating the assessment made with less accurate forecasts as soon as we have more reliable information on our forecasts. There is thus no need of re-running the tool as soon as we get new forecasts. The indicators can also be recalculated once we get those new forecasts and thus the corresponding new pdf. 11. Flowchart of the DIFERS method Given those three steps, the flowchart of the method is presented in Fig. 5. Each step is performed closer to real-time operation and uses newly acquired forecasts to have at each step a more precise evaluation.
Figure 5. Flowchart of DIFERS
Results of DIFERS method
The results will be presented per step of the methodology. A previous study analyzed (Henneaux, 2013) the impact of cascading failures on blackout risk using a 69-bus that comprised renewable production. The DIFERS method has been tested on a modified version of this test case: buses have been added in order for the grid to comprise circuit-breakers. The final version of the test case is a 75-bus test case presented in Fig. 6. Renewable productions are depicted by a green triangle. The slack bus is located at bus 15. The tested area is defined by the term “grid zone”. Other areas are considered as cross-border zones and are assumed to be known in this work.
Figure 6. 75-bus test case
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The methodology has been implemented on Matlab and uses Matpower (Zimmerman et al., 2011). The calculations were performed on a standard computer (Asus core i5). 12. Results of step 1 The calculation time is of 2 days. For this first step the calculation is not a large issue as the assessment has to be performed once per month. The maximum number of samples was reached, thus, 2,000,000 samples were studied using the calculation routine. The relative standard deviation on the probability of load shedding is of 0.06%. The mean cost of operation (MCO) for this hourly planning is of 5.40 k€. Table 1 presents the percentage of each solution type needed to solve the samples. Table 2 presents the six most challenging issues in terms of related cost. LF-solved
OPF1-solved
97.41%
0%
OPF2-solved
OPF3-solved
OPF4-solved
LS-solved
0.01% 0.12% 2.35% Table 1. Probabilities of each solution in step 1
0.11%
%MCO
Eventsa
%MCO
Events
1.79%
G11 – G13
1.43%
G13 – L at nodes 36-17
1.71%
G6 – G13
1.22%
G2 – G3
1.54%
G9 – G13
1.12%
G3 – G13 a. G stands for generator & L for line
Table 2. Six most challenging events and related %MCO Those are the first events of the contingency list. This list will be established by considering the most challenging events to cover 75% of the total MCO. Doing so, the 1,214 first N-k events have been considered. Therefore, costs related to those events represent 75% of the total MCO. In order to stay coherent with the N-1 principle, the N-1 events were added to the contingency list. Therefore, the contingency list gathers 1,313 events that will be studied and analyzed given their probability of appearance in step 2. 13. Results of step 2 We will now launch the evaluation for a particular state of the grid using the general contingency list established in step 1. In our case, we considered a grid plan in which 3 maintenance actions were planned. We considered the maintenance of lines between nodes 35-45, 61-36 and 19-68, respectively. In the first loop of step 2, the evaluation of the points LE, BE and ME of the wind speed and the load is launched. Thus, as there are only 3 possible states for the wind and the load (LE, BE and ME), 32 combinations were studied. Therefore, 9 * 1,313 = 11,817 samples were analyzed. The calculation time is of 1 hour. This computer time will have to be decreased in order to optimize the tool-planner interaction in this on-line step of DIFERS. The MCO for this first evaluation is of 10.89 k€. Table 3 presents the percentages of each solution type. Table 4 presents the contribution of each combination of wind and load state to the total MCO. Table 5 presents the 5 N-k events that contribute most to the total MCO. LF-solved
OPF1-solved
22.36%
0%
OPF2-solved
OPF3-solved
OPF4-solved
LS-solved
0.39% 3.54% 52.21% Table 3. Probabilities of each solution in step 2
21.50%
LOAD
WIND %MCO
LE
BE
ME
LE
4.82%
11.65%
5.09%
BE
12.07%
29.07%
11.86%
ME
5.69%
13.69%
6.06%
Table 4. Relative contributions to MCO per combination of wind and load states N-k
G13
G12 -G13
L at 17-43
L at 43-44
L at 17-13
%MCO
30.34%
6.29%
1.71%
1.62%
1.52%
Table 5. Five main contributors to MCO This table shows that the risk is not uniformly distributed among the N-k events. Indeed, the loss of generator 13 appears to have a very large impact on the total MCO compared to other events. In order to help the planner propose useful actions, additional information on the main issues encountered is given. Table 6 presents the analysis of the overloads that led to the use of an OPF. Because of space constraints, only the three main overloads are presented. This table presents the main overloads that are classified given their contribution to the MCO of the grid
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plan. The probability of appearance of those overloads is also given. Moreover, for each overload, the table presents which N-k events contribute most to the MCO of that specific overload. OVERLOAD
% MCO
Line at bus 36-75
65.38%
Line at bus 40-41
13.33%
Line at bus 18-42
9.21%
Others
…
% MCO per contingency and order of importance G13 30.34% G11 – G13 1.43% G11 – G13 1.43%
G12 – G13 6.29% G9 – G13 1.10% G11 – G12 – G13 0.55%
L at nodes 17-13 1.52% G6 – G13 0.97% G10 – G12 – G13 0.31%
% APPEARANCE Others 27.23% Others 9.83% Others 6.92%
21.33% 42.88% 34.42%
… Table 6. Analysis of the main overloads
…
The analysis of this table shows that the overload of line 36-75 contributes most to the MCO. Moreover, it shows that the loss of generator 13 induces this overload at a large cost (30.34% MCO). The planner should thus focus on reducing the risk related to the overload of this line. Moreover, the contribution of other contingencies appears mostly distributed, for the three main overloads. Therefore, as the line in parallel with line 36-75 is in maintenance (line 36-61), the planner should test the cancellation of this maintenance as a preventive action to improve the risk indicators. The same analysis can be carried out for the voltage drops, the results are presented in Table 7. VOLTAGE DROPS
% MCO
Bus 2
15.39%
Bus 49
14.19%
Bus 40
14.19%
Others
…
% MCO per contingency and order of importance G5 – G13 0.78% G5 – G13 0.78% G5 – G13 0.78%
G2 – G13 0.77% G2 – G13 0.77% G2 – G13 0.77%
G8 – G13 0.77% G8 – G13 0.77% G8 – G13 0.77%
% APPEARANCE Others 13.07% Others 11.87% Others 11.87%
…
40.71% 43.65% 43.04% …
Table 7. Analysis of the main voltage drops This table shows that the main voltage drops have a mostly equal share in contribution to MCO. Moreover, the contribution of the contingencies is also mostly distributed and small. To reduce the cost related to the voltage drop at bus 2, the planner could enforce a preventive action on the transformer tap at bus 2. Therefore, the planner can implement those two preventive actions (cancellation of maintenance on line 36-61 and change transformer tap at bus 2) to be tested by the tool in a second iteration. Those actions will be validated by the planner if it leads to a smaller MCO. The results show that implementing preventively those actions improves indeed the indicators. The total MCO for this evaluation is of 4.73 k€, it has thus decreased of 56.57% compared to the MCO in the first evaluation. Table 8 shows the improvements of the use of each type of solution. Table 9 shows the 5 main contributors to the total MCO.
Base case
Preventive action on transformer at bus 2 & maintenance of line 36-61 cancelled
22.36%
+ 2.01%
OPF1-solved
0%
/
OPF2-solved
0.39%
/
OPF3-solved
3.54%
+ 0.34%
OPF4-solved
52.21%
+ 4.36%
LF-solved
LS-solved
21.50% - 6.72% Table 8. Probabilities of solution found: comparison between base case and preventive actions N-k
L at 17-43
L at 43-44
G11 - G13
L at 35-45
L at 38-46
%MCO 3.87% 3.67% 3.16% 3.13% 2.97% Table 9. Five main contributors to MCO after implementing preventive actions From those charts, we see that there is globally an improvement of the grid plan. First, the MCO has decreased a lot. Secondly, the probability of using load shedding has also decreased. Finally, we see in Table 9 that the risk is mainly distributed among the N-k events, which proves that the grid plan is more reliable. Given the detailed analysis of the results, the planner can once again launch an iteration of the method by proposing new actions to be tested. The iterations stops once the MCO reaches an acceptable value. This value has yet to be determined for practical
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applications. The validated actions will be used as input to the final step of the methodology, the results of which are not presented here. Moreover, the results presented can be declined for specific initial conditions. For example, if the planner wants to only have the information for the BE case, the charts can be computed considering only the samples where the wind and the loads are at their BE values. 14. Results of the N-1 analysis An N-1 analysis was also launched in order to compare the results of the current method to the proposed DIFERS method. First, the N-1 analysis was carried out for the base case considering the maintenance actions on the 3 lines at nodes 35-45, 61-36 and 19-68, respectively. This evaluation revealed problems with the outage of six N-1 events. Table 10 presents the overloads in this analysis and Table 11 presents the voltage drops. N°
N-1
Overload
Value
Snoma
1
L at 43-44
L at 35-45
112.10%
950
2
L at 17-43
L at 35-45
109.29%
950
3
L at 38-46
L at 35-45
103.19%
950
4
L at 53-47
L at 35-45
100.37%
950
5
L at 23-24
L at 68-21
100.06%
700 a
Snom is the nominal power
Table 10. Overloads in the N-1 analysis N° 6
N-1
Bus
Value
Bus
L at 35-45 44 0.88 39 Table 11. Voltage drops in the N-1 analysis
Value 0.89
From this analysis, it can clearly be seen that the main issue is with the overload of line 35-45. As there is a maintenance planned in between those nodes, the planner would have cancelled preventively the maintenance of the second line between nodes 35-45. The resulting overloads after this action are presented in Table 12: there is no voltage drops anymore. As the overload is very small, a curative action can simply be performed in real-time if the N-1 event appears. N°
N-1
Overload
Value
Snom
1’
L at 23-24 L at 68-21 100.06% 700 Table 12. Overloads in the N-1 analysis after preventive action
Therefore, the results show that the N-1 analysis guided us toward the cancellation of the maintenance of line 35-45. On the other hand, the DIFERS method led us to cancel the maintenance of line 36-75. Therefore, those methods lead to different actions to perform in order for the grid plan to be reliable. 15. Comparison of the results In order to fully compare the method, the DIFERS method was launched considering the cancellation of the maintenance of line 35-45 as the N-1 analysis suggested. Table 13 and Table 14 show the improvements of the type of solution found and the main contributors to the MCO respectively. Base case
Preventive action: cancel maintenance of L 36-61
Preventive action: cancel maintenance of L 35-45
MCO
10.89 k€
- 56.57%
- 7.53%
LF-solved
22.36%
+ 2.01%
+0.52%
OPF1-solved
0%
/
/
OPF2-solved
0.39%
/
+0.01%
OPF3-solved
3.54%
+ 0.34%
+0.02%
OPF4-solved
52.21%
+ 4.36%
-0.44%
LS-solved 21.50% - 6.72% -0.12% Table 13. Improvements on the results after cancelling maintenance of line 36-61 & line 35-45 N-k
G13
G12 - G13
L at 17-13
G13 - R4
G11 - G13
%MCO 32.57% 6.57% 1.63% 1.59% 1.54% Table 14. Five main contributors to MCO after cancelling maintenance of line 35-45 Those results show that cancelling the maintenance of line 35-45 is less beneficial for the grid. Indeed, the MCO reduction is very low compared to the one resulting from the cancellation of the maintenance of line 36-61, as suggested by the DIFERS method.
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Moreover, table 14 shows that the risk is not equally distributed among the N-k events and that it is very similar to the distribution of the base case (with the three maintenance actions). 16. Conclusion With the increasing amount of renewable and difficult-to-forecast generation units, TSO are facing new challenges to operate the grid properly. Indeed, renewable energies are subject to forecasting errors which, being combined to the forecasting errors on load demand and cross-border flows, can be challenging for the grid. As the present N-1 method used to assess grid reliability does not account for forecasting errors, a new method is needed for system operation planning The DIFERS method aims at taking into account forecast errors on the loads and the renewable productions for risk-based assessment in short-term planning. It combines the advantages of a probabilistic evaluation to estimate a risk measure of the proposed grid planning; and those of a deterministic evaluation to meet the time constraints of the operational planning. In the first step, the method computes a dynamically-defined contingency list, instead of the quasi-static list proposed in the N-1 method. Therefore, errors on forecasts are accounted for and a more significant contingency list is obtained. Secondly, this contingency list is used to perform a semi-deterministic evaluation of the grid plan. This evaluation is based on a discretization of the pdf of the continuous variables. That way, the planner has information on the BE case but also for possible evolution in trends (LE and ME cases, and combination of those evolutions). In this step, the method allows a tool-planner interaction which is similar to the actual work of the planners, i.e. testing each element of the N-1 list to ensure a safe grid. In the DIFERS method, the N-1 list is replaced by a contingency list and elements of this list are tested by the planner. The interaction is thus very similar but the contingency list is tested for each combination of the possible discretized states of input variables (LE, BE and ME states). Therefore, the method allows a smooth change from deterministic to probabilistic that will ease its integration within a TSO. The indicators developed help the planner to locate where the main issues lie. That way, the planner is able to propose actions to be tested by the tool in order to get better indicators. Therefore, the planner is able to see the impact of his/her choices and actions on the indicators which will help him/her better understand the grid. Moreover, the planner is able to compare different grid plans in order to select the most reliable one based on a risk evaluation. This paper illustrated the comparison of the action proposed by the DIFERS method and the action proposed by the N-1 method. The results show that, for this test case and this grid plan, the DIFERS method led to a more efficient action in cost reduction and risk distribution. In the upcoming developments, the last step of the DIFERS method will be finalized and cross-border flows will be added. Finally, the method will be tested on a realistic scenario of the Belgian grid. 17. Acknowledgement This project has been subsidized by the Brussels-Capital region – Innoviris. It is performed in partnership with Elia System Operator SA. 18. References R. Billinton, and G. Bai, "Generating capacity adequacy associated with wind energy," IEEE Trans. on energy conversion, vol. 19, pp. 641646, Sept. 2004. R. Billinton, and A. Sankarakrishnan, "Adequacy assessment of composite power systems with HVDC links using Monte Carlo simulation," IEEE Trans. on energy conversion, vol. 9, pp. 1626-1633, Aug. 1994. R. Billinton, and X. Tang, "Selected considerations in utilizing Monte Carlo simulation in quantitative reliability evaluation of composite power systems," Electric power systems research, vol. 69, pp. 205-211, May 2004. Y. Degeilh, and C. Singh, "A quantitative approach to wind farm diversification and reliability," Electrical power & energy system, vol. 33, pp. 303-314, Feb. 2011. A. Dimitrovski, and K. Tomsovic, "Impact of wind generation uncertainty on generating capacity adequacy," 9th International conference on probabilistic methods applied to power systems, Stockholm, Sweden, 2006. M. Do, "Approche probabiliste pour l’évaluation de la fiabilité du système électrique intégrant des énergies renouvelables peu prévisibles," Ph.D. dissertation, Université de Lille, 2012. M. Do, J. Sprooten, S. Clenet and B. Robyns, "Influence of wind turbines on power system reliability through probabilistic studies," Innovative smart grid technologies conference Europe, Gothenburg, Sweden, 2010. G. Dogan, P.-E. Labeau, J.-C. Maun, J. Sprooten, M. Galvez and K. Sleurs, "Grid reliability for short-term planning," in Proc. 2015 European safety and reliability Conf., Esrel 2015, Zurich, Switzerland, pp. 217, Sept. 2015. G. Dogan, P.-E. Labeau, J.-C. Maun, J. Sprooten, M. Galvez and K. Sleurs, “Monte Carlo sampling vs. discrete forecast error scenarios in grid reliability assessment for short-term planning,” IEEE Energycon Conference, Leuven, Belgium, 4-8 April 2016. J. M. Hammersley and D. C. Handscomb, Monte Carlo methods, London: Methuen & Co Ltd., 1964. P. Henneaux, "A two-level probabilistic risk assessment of cascading failures leading to blackout in transmission power systems," Ph.D. dissertation, Dept. Métrologie nucléaire. Eng., Université libre de Bruxelles, 2013. Z. Hu, and X. Wang, "A probabilistic load flow method considering branch outages," IEEE Trans. on power systems, vol. 21, pp. 507-514, May 2006. J. MacCormack, A. Hollis, H. Zareipour and W. Rosehart, "The large-scale integration of wind generation: Impacts on price, reliability and dispatchable conventional suppliers," Energy policy, vol. 38, pp. 3837-3846, July 2010. F. Olsina, M. Röscher, C. Larisson and F. Garcés, "Short-term optimal wind power generation capacity in liberalized electricity markets," Energy policy, vol. 35, pp. 1257-1273, Feb. 2007. C. L. Su, and C. N. Lu, "Two-point estimate method for quantifying transfer capability uncertainty," IEEE Trans. on power systems, vol. 20, pp. 573-579, May 2005. W. Wandgee, and R. Billinton, "Reliability assessment of bulk electric systems containing large wind farms," International journal of electrical power & energy systems, vol. 29, pp. 759-766, Dec. 2007. J. Wen, Y. Zheng and F. Donghan, "A review on reliability assessment for wind power," Renewable and sustainable energy reviews, vol. 13, pp. 2485-2494, Dec. 2009. R. D. Zimmerman, C. E. Murillo-Sanchez and R. J. Thomas, “MATPOWER: Steady-state operations, planning and analysis tools for power systems research and education,” IEEE Trans. on power systems, vol. 26, no. 1, pp. 12-19, Feb. 2011
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