distribution systems by integrating local distributed energy resources (DERs) and ... studies with various portions of renewable generation are illustrated to provide .... List of Figures . ...... different types of renewable energy resources [1].
RESILIENT DISTRIBUTION SYSTEMS WITH COMMUNITY MICROGRIDS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By Chen Yuan Graduate Program in Electrical and Computer Engineering
The Ohio State University 2016
Dissertation Committee: Dr. Mahesh S. Illindala, Advisor Dr. Jin Wang Dr. Jiankang Wang
Copyrighted by Chen Yuan 2016
Abstract Large-scale power outages are rare but extreme accidents. They are usually caused by severe weather events and overloading caused cascading failures. Nowadays, with climate change and ever-increasing load demand, power blackouts are happening more frequently. In order to ensure reliable power delivery to customers, resilient distribution systems are envisaged, because of their characteristics of high reliability, power quality, advanced protection, and optimal restoration. During extreme events, they can provide uninterruptible power supply to critical loads, quickly detect and accurately isolate fault areas, and reestablish with an optimal restoration plan. This dissertation first proposes to develop community microgrids within distribution systems by integrating local distributed energy resources (DERs) and neighboring load centers, especially critical loads. Community microgrids can be useful means of providing resilient electricity service by enabling sustainable operations and supporting critical loads in the event of power disruptions. When an extreme event happens, the distribution system can be seamlessly partitioned into several energyindependent community microgrids. Then, the important customers are supplied with uninterrupted power by local DERs. After fault isolation, distribution systems are restored by reconnecting these community microgrids. The DER selection for community microgrids is mainly determined by the levelized cost of energy (LCOE) based quantitative assessment in conjunction with the quality functional deployment (QFD) tool. ii
Subsequently, the capacity planning of dispatchable generation units, like natural gas gensets and battery energy storage system (BESS), is elaborated. The goal of this sizing scheme is to keep adequate reserve margin to ride through unforeseen events, like uncertainties from loads and renewables, loss of generation, etc. This is because when community microgrids work in the islanded mode, the critical loads completely rely on the power generated by DERs. Therefore, the resource adequacy is a key requirement to handle unexpected incidents. Discrete-time Fourier transform (DTFT) and particle swarm optimization (PSO) are employed to find the optimal sizing solution by satisfying reserve margin requirement and minimizing annualized cost. The loss of load expectation (LOLE) is used to ensure the reliable operation of islanded community microgrids during blackouts. In addition, the impacts of reserve margin on system reliability and case studies with various portions of renewable generation are illustrated to provide guidance for the sizing of dispatchable generators. To ensure the resilience of distribution systems, advanced protection schemes that can fast detect and accurately isolate fault areas are needed. However, many protection challenges exist in making the shift away from conventional distribution systems. For example, with large penetrations of DERs and microgrids, the power flow within a distribution system becomes bi-directional and the fault current level varies significantly. In this dissertation, a multilayered protection strategy is presented for distribution systems with community microgrids. The proposed strategy is verified by simulation studies in MATLAB/Simulink against various fault conditions. A comparison between the proposed strategy and existing distribution protection schemes is also provided. iii
After fault isolation, because of the radial topology in distribution systems, the loads downstream are interrupted. Therefore, a modified Viterbi algorithm is presented to identify the optimal distribution system restoration plan by maximally re-energizing the load through least switching operations. Moreover, an improved flexible switching pair operation is employed to maintain the radial structure of distribution system. Case studies are presented to verify the performance of the proposed strategy. Furthermore, the effects of integrating distributed energy resources and microgrid systems are analyzed in this dissertation.
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Dedication This document is dedicated to my family.
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Acknowledgments First of all, I want to thank Prof. Mahesh S. Illindala, my advisor, for his guidance, patience, encouragements, and support during the course of this journey. He taught me research skills and gave me opportunities to explore different research topics. He shared with me his experience in life selflessly and helped me build the path to my future career. I would also like to thank my Ph.D. defense, candidacy and qualifying exam committee members, Prof. Jin Wang, Prof. Jiankang Wang, Prof. Rama K. Yedavalli, Prof. Vadim Utkin, Prof. Kevin Passino for their support and advice. I am grateful to Mr. Krishna D. Ramamoorthy and Dr. Osama Alkhouli at Caterpillar Research for their guidance and financial support to my research. I would like to thank Mr. Amrit S. Khalsa for his advice and kind help from American Electric Power. My thanks are extended to my fellow colleagues Mr. Abrez Mondal, Ms. Jieying Zhang, Dr. Ajit A. Renjit, Dr. Mohammed Haj-Ahmed, Mr. Kexing Lai, Dr. Hussam Khasawneh, Mr. Daijiafan Mao, Mr. Lixing Fu, Dr. Feng Guo, Dr. Cong Li, Dr. Xuan Zhang, Mr. He Li, Mr. Chengcheng Yao, Dr. Haiwei Cai, Dr. Dakai Hu, Dr. Miao Wang and Mr. Jianyu Pan for sharing this journey at The Ohio State University. Thank you all for those joys and shared memories.
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I own my deepest gratitude to my parents, Zhiping Yuan and Hongxiu Lin. Without your love and support, I would not have been where I am today.
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Vita Sept. 2008 - Jun. 2012....................................B.S.
Electrical
Engineering,
Wuhan
University, Wuhan, China Aug. 2012 - Present .......................................Ph.D. Student, Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH
Publications [1]
C. Yuan, M. Haj-ahmed, M. Illindala, “An MVDC microgrid for a remote area mine site: protection, operation and control,” in Proc. of 2014 IEEE Industry Applications Society Annual Meeting, Vancouver, BC, 5-9 Oct 2014.
[2]
C. Yuan, M. Haj-ahmed, M. Illindala, “Protection strategies for medium voltage direct current microgrid at a remote area mine site,” in IEEE Transactions on Industry Applications, vol. 51, no. 4, pp. 2846-2853, July-Aug. 2015.
[3]
C. Yuan, M. Illindala, M. Haj-ahmed, A. Khalsa, “Distributed energy resource planning for microgrids in the United States,” in Proc. of 2015 IEEE Industry Applications Society Annual Meeting, Addison, TX, 18-22 Oct. 2015. viii
[4]
C. Yuan, K. Lai, M. Illindala, M. Haj-ahmed, A. Khalsa, “Multilayered protection strategy for developing community microgrids in village distribution systems,” in IEEE Transactions on Power Delivery, vol. 31, pp. 1-8, 2016.
[5]
C. Yuan, M. Illindala, and A. Khalsa, “Modified Viterbi algorithm based distribution system restoration strategy for grid resiliency,” in IEEE Transactions on Power Delivery, vol. 31, pp. 1-8, 2016.
Fields of Study Major Field: Electrical and Computer Engineering
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Table of Contents Abstract ............................................................................................................................... ii Acknowledgments.............................................................................................................. vi Vita................................................................................................................................... viii Table of Contents ................................................................................................................ x List of Tables ................................................................................................................... xiii List of Figures .................................................................................................................. xvi Chapter 1: Introduction ...................................................................................................... 1 1.1 Background and Motivation .................................................................................. 1 1.2 Literature Review ................................................................................................ 17 1.3 Chapter Review ................................................................................................... 21 Chapter 2: Community Microgrid Development in Distribution System........................ 23 2.1 Introduction ......................................................................................................... 23 2.2 Electricity Mix in the United States Current Status and Trends..................... 24 2.3 Community Power System .................................................................................. 25 2.4 Distributed Energy Resources Selection for Community Microgrids ................. 27 x
2.5 Community Microgrid Development .................................................................. 32 2.6 Summary .............................................................................................................. 34 Chapter 3:
Sizing of Gensets and Battery Energy Storage System for Islanded
Community Microgrid ...................................................................................................... 36 3.1 Introduction ......................................................................................................... 36 3.2 Reliability Metrics ............................................................................................... 37 3.3 Stochastic Models of Load and Renewable Energy Resources ........................... 40 3.4 Planning Reserve Margin .................................................................................... 46 3.5 Sizing of Gensets and BESS ................................................................................ 51 3.6 Optimization Algorithm....................................................................................... 55 3.7 Case Studies and Sensitivity Analysis ................................................................. 62 3.8 Summary .............................................................................................................. 84 Chapter 4: Multilayered Protection Strategy for Resilient Distribution System ............. 85 4.1 Introduction ......................................................................................................... 85 4.2 Community Microgrid within 69-Bus Distribution System ................................ 86 4.3 Multilayered Protection Strategy ......................................................................... 89 4.4 Summary ............................................................................................................ 107 Chapter 5: Modified Viterbi Algorithm based Restoration for Resilient Distribution System ............................................................................................................................. 108 xi
5.1 Introduction ....................................................................................................... 108 5.2 Problem Formulation ......................................................................................... 109 5.3 Modified Viterbi Algorithm for Distribution System Restoration .................... 117 5.4 Restoration Performance Investigation with the Integration of Community Microgrids ......................................................................................................... 123 5.5 Summary ............................................................................................................ 137 Chapter 6: Conclusions and Future Work ...................................................................... 138 6.1 Conclusions ....................................................................................................... 138 6.2 Contributions ..................................................................................................... 140 6.3 Future Work ....................................................................................................... 143 References ....................................................................................................................... 145
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List of Tables Table 2. 1 Costs and performance characteristics for electric generating technologies ... 30 Table 2. 2 QFD evaluation of DERs for community microgrids development ................ 32 Table 3. 1 Cost parameters of DERs ................................................................................. 65 Table 3. 2 Cost parameters of BESS ................................................................................. 65 Table 3. 3 Results of gensets and BESS sizing without consideration of renewable energy in the first case .................................................................................................................. 69 Table 3. 4 Results of gensets and BESS sizing with consideration of 20% renewable energy in the first case ...................................................................................................... 70 Table 3. 5 Results of gensets and BESS sizing with consideration of 50% renewable energy in the first case ...................................................................................................... 71 Table 3. 6 Results of gensets and BESS sizing with consideration of 80% renewable energy in the first case ...................................................................................................... 72 Table 3. 7 Results of gensets and BESS sizing with consideration of 90% renewable energy in the first case ...................................................................................................... 73 Table 3. 8 Results of gensets and BESS sizing with consideration of 100% renewable energy in the first case ...................................................................................................... 74 Table 3. 9 Comparison of different situations in the first case ......................................... 75
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Table 3. 10 Results of gensets and BESS sizing without consideration of renewable energy in the second case .................................................................................................. 77 Table 3. 11 Results of gensets and BESS sizing with consideration of 20% renewable energy in the second case .................................................................................................. 78 Table 3. 12 Results of gensets and BESS sizing with consideration of 50% renewable energy in the second case .................................................................................................. 79 Table 3. 13 Results of gensets and BESS sizing with consideration of 80% renewable energy in the second case .................................................................................................. 80 Table 3. 14 Results of gensets and BESS sizing with consideration of 90% renewable energy in the second case .................................................................................................. 81 Table 3. 15 Results of gensets and BESS sizing with consideration of 100% renewable energy in the second case .................................................................................................. 82 Table 3. 16 Comparison of different situations in the second case .................................. 83 Table 4. 1 Protection levels for distribution and microgrid layer ..................................... 91 Table 4. 2 Qualitative evaluation of various approaches for protection ........................... 91 Table 4. 3 Comparison between existing and proposed protection schemes for community microgrids ....................................................................................................................... 106 Table 5. 1 Best switching pair operations for the case shown in Figure 5. 1 ................. 115 Table 5. 2 Results of restoration for 33-bus distribution system .................................... 124 Table 5. 3 Results of restoration for 69-bus distribution system .................................... 127 Table 5. 4 Locations and generation capacities of DERs ............................................... 130 Table 5. 5 Results of restoration for 69-bus distribution system with DER integration. 131 xiv
Table 5. 6 Generation capacities of community microgrids ........................................... 134 Table 5. 7 Results of restoration for 69-bus distribution system with community microgrids ....................................................................................................................... 135
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List of Figures Figure 1. 1 Net electricity generation in the United States [1] ........................................... 2 Figure 1. 2 Renewable generation in the United States [1] ................................................ 2 Figure 1. 3 A simplified conventional power grid [6] ........................................................ 4 Figure 1. 4 Microgrid with DERs [17], [25] ..................................................................... 11 Figure 1. 5 Power outages caused by extreme weather [26]............................................. 12 Figure 2. 1 Electricity mix in different regions of the United States [109] ...................... 25 Figure 2. 2 Single line diagram of a distribution network ................................................ 26 Figure 2. 3 Curves of LCOE vs. capacity factor for DERs based on Table 2. 1 .............. 31 Figure 2. 4 Single line diagram of a community microgrid.............................................. 34 Figure 3. 1 Commercial Load Profile ............................................................................... 42 Figure 3. 2 PV power output in a sample day during summer ......................................... 43 Figure 3. 3 Wind turbine power output in a sample during summer ................................ 44 Figure 3. 4 Curve of LOLE vs. planning reserve margin when the largest dispatchable generation unit is 10% of total available generation ......................................................... 49 Figure 3. 5 Curve of SAIFI vs. planning reserve margin when the largest dispatchable generation unit is 10% of total available generation ......................................................... 50 Figure 3. 6 Curves of LOLE vs. planning reserve margin with different proportions of the largest dispatchable generation unit .................................................................................. 50 xvi
Figure 3. 7 Curves of SAIFI vs. planning reserve margin with different proportions of the largest dispatchable generation unit .................................................................................. 51 Figure 3. 8 Flowchart of gensets and BESS sizing with assumption of identical gensets 59 Figure 3. 9 Flowchart of gensets and BESS sizing in general .......................................... 61 Figure 3. 10 Weekday and weekend representative load profile in four seasons ............. 63 Figure 3. 11 Net load profile and its spectrum for a weekday in summer ........................ 66 Figure 3. 12 Tendencies of annualized cost and gensets total capacity without consideration of renewable energy in the first case .......................................................... 69 Figure 3. 13 Tendencies of annualized cost and gensets total capacity with consideration of 20% renewable energy in the first case ........................................................................ 70 Figure 3. 14 Tendencies of annualized cost and gensets total capacity with consideration of 50% renewable energy in the first case ........................................................................ 71 Figure 3. 15 Tendencies of annualized cost and gensets total capacity with consideration of 80% renewable energy in the first case ........................................................................ 72 Figure 3. 16 Tendencies of annualized cost and gensets total capacity with consideration of 90% renewable energy in the first case ........................................................................ 73 Figure 3. 17 Tendencies of annualized cost and gensets total capacity with consideration of 100% renewable energy in the first case ...................................................................... 74 Figure 3. 18 Tendencies of minimum annualized cost and minimum gensets total capacity with counted portion of renewable energy........................................................................ 75 Figure 3. 19 Tendencies of annualized cost and gensets total capacity without consideration of renewable energy in the second case ..................................................... 78 xvii
Figure 3. 20 Tendencies of annualized cost and gensets total capacity with consideration of 20% renewable energy in the second case.................................................................... 79 Figure 3. 21 Tendencies of annualized cost and gensets total capacity with consideration of 50% renewable energy in the second case.................................................................... 80 Figure 3. 22 Tendencies of annualized cost and gensets total capacity with consideration of 80% renewable energy in the second case.................................................................... 81 Figure 3. 23 Tendencies of annualized cost and gensets total capacity with consideration of 90% renewable energy in the second case.................................................................... 82 Figure 3. 24 Tendencies of annualized cost and gensets total capacity with consideration of 100% renewable energy in the second case.................................................................. 83 Figure 3. 25 Tendencies of minimum annualized cost and minimum gensets total capacity with counted portion of renewable energy........................................................................ 84 Figure 4. 1 Schematic diagram of (a) the community microgrid (b) the 69-bus distribution system with integration of the community microgrid. Note: An extra line (shown in blue) was added to the benchmark 69-bus distribution system to form a mesh network. ......... 87 Figure 4. 2 Fault current during a bus fault in grid-connected mode ............................... 93 Figure 4. 3 Fault current during a loop fault in grid-connected mode .............................. 97 Figure 4. 4 Fault current during a loop fault in islanded mode......................................... 98 Figure 4. 5 Load-line fault current with failure of relay-e1 in grid-connected mode ..... 101 Figure 4. 6 Load-line fault current with the failure of relay-e1 in islanded mode .......... 103 Figure 4. 7 Protection scheme implementation............................................................... 105 Figure 5. 1 33-bus distribution system............................................................................ 113 xviii
Figure 5. 2 System restoration with number of switching pair operations ..................... 114 Figure 5. 3 Optimality principle of Viterbi algorithm .................................................... 118 Figure 5. 4 State diagram of the modified Viterbi algorithm ......................................... 120 Figure 5. 5 Flowchart of modified Viterbi algorithm based distribution system restoration ......................................................................................................................................... 122 Figure 5. 6 Bus voltage distributions in 33-bus distribution system............................... 125 Figure 5. 7 69-bus distribution system............................................................................ 126 Figure 5. 8 Bus voltage distributions in 69-bus distribution system............................... 128 Figure 5. 9 69-bus distribution system with integration of DERs .................................. 129 Figure 5. 10 Bus voltage distributions in DERs integrated 69-bus distribution system . 131 Figure 5. 11 69-bus distribution system with community microgrids. ........................... 134 Figure 5. 12 Bus voltage distributions in 69-bus distribution system with the presence of community microgrids .................................................................................................... 136
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CHAPTER 1: INTRODUCTION 1.1
Background and Motivation With industrial development and population growth, a surge in global demand for
energy has triggered energy crisis in last decades. In addition, human activities of utilizing fossil fuels are causing massive emissions of greenhouse gasses, including carbon dioxide and nitrogen oxide, which mainly result in global warming and climate change. The increasing concern about the energy shortage and climate change has stimulated applications of renewable energy, particularly the use of solar and wind energy. Dramatic technology development has promoted its popularity. Figure 1. 1 shows the U.S. net electricity generation from 1990 to 2040 with projections [1]. Renewable generation is increasing and will surpass coal after 2030 according to annual energy outlook 2016 (AEO2016), taking the clean power plan (CPP) into consideration. In comparison, if not considering CPP, renewable generation increases more slowly and will not surpass coal by 2040. In addition, Figure 1. 2 presents the electricity generation from different types of renewable energy resources [1]. Among them, wind and solar have the largest potential for growth and will take the lead in future renewable energy generation. On the other hand, utilization of conventional distributed energy resources (DERs), 1
having much less air pollution than coal plants, is another efficient and cost-effective way to relieve the status quo of energy shortage and climate change. For example, natural gas DERs can be aggregated to provide the local demand, replacing the role of central coal power plants. Then the transmission and distribution (T&D) losses in power delivery to
Net Electricity Generation (TWh)
consumers, accounting for 6% gross generation [2], can be much reduced.
Renewable Generation (TWh)
Figure 1. 1 Net electricity generation in the United States [1]
Figure 1. 2 Renewable generation in the United States [1]
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However, high penetrations of DERs including renewable resources will cause bidirectional power flow within distribution systems and even on transmission lines. It brings new challenges to system operators, needing more advanced and intelligent control schemes to ensure the robustness of power systems. Microgrids, as entities to coordinate DERs in a more decentralized way, are capable of addressing these challenges and reducing control burdens on the grid side [3]–[5]. On the other hand, in recent years, extreme weather events and overloading accidents are more frequent, resulting in severe damages and economic loss to utilities, customers, and other electricity related industries. Therefore, resilient distribution systems are being encouraged to maximally ensure the uninterruptible power supply for end-users, particularly the critical part. With the development of community microgrids by integrating local DERs, distribution systems can be partitioned into several small electricity independent communities during unexpected events and reunited via postevent restoration. 1.1.1
Conventional Power Grid: Centralized Generation Conventionally, a power grid consists of electric utilities, large central generators,
long-distance transmission lines, distribution systems, and end-users. Most electricity today is generated in large, central stations, which is a cluster of large power plants, with power capacities in hundreds and thousands of megawatts. Figure 1. 3 presents a simplified conventional power grid [6]. In real power grids, there are multiple transmission paths between generating stations and customers.
3
Figure 1. 3 A simplified conventional power grid [6]
With the rapid growth of power demand, it is inevitable to upgrade existing central generators, build more power plants and plan new transmission lines. However, this is not cost-effective and environmentally friendly. In the United States, approximate 90% of electricity is generated via the energy conversion of “chemical → heat → mechanical → electrical”. However, electricity from fossil fuels based power plants is the main cause of air pollution and the whole generation process is not efficient. In the year of 2015, fossil fuels such as coal and natural gas account for 66.8% of total electricity generation in U.S. [7]. According to the U.S. Environment Protection Agency (EPA), in 2014, approximately 31% of greenhouse gas and 37% of total carbon dioxide emissions came from the electricity sector [8]. Within the electricity sector, coal power plants contribute 77% of CO2 emissions with only 38.5% of electricity generation [7]. Though the issues are eased to a certain extent when the coal power plants approach their retirement, there is still great pressure further cutting the emissions and increasing energy efficiency. Therefore, a movement toward DERs is gaining more attention, and many emission-reduction targets have been set forth by both federal and state governments [9]– 4
[11]. In addition, T&D losses associated with power delivery to consumers account for 6% of gross generation [2]. This makes a strong case for installing DERs near the load centers to improve energy efficiency. In addition, load centers can be categorized into the residential load, commercial load, industrial load, municipal load, etc. Their requirements of power demand are diverse. Hospitals demand the high-reliability power supply, while manufacturing industries need the high-quality power supply. Under such circumstances, it is attractive to develop microgrids as they can be designed and controlled for specific applications, improving grid reliability and resilience. 1.1.2
Distributed Energy Resources DERs are smaller power generation units that can be aggregated and dispatched to
meet load demand, including diesel generators, microturbine, combine heat and power (CHP), photovoltaic (PV), wind turbine (WT), fuel cell, battery energy storage system (BESS), etc. [12], [13]. They are usually decentralized, modular, flexible and located very close to end-users. Due to this proximity, it reduces transmission line losses associated with delivering electricity over long distances and lowers the chance of a power interruption caused by faults on the transmission and distribution lines. In addition, as the grid modernization, DERs can help facilitate the transition to smarter grids. On the other hand, because of small inertia of DERs, particularly inverter based DERs, grid systems and microgrids are more likely to experience frequency variations caused by load changes, renewable output intermittence and loss of generation [14]–[16]. Furthermore, by cogitating stochastic natures of load demand and renewable power output, reserve margin planning and resilient system operation become more difficult 5
with the increase of uncertainties. Another issue is, with penetrations of DERs, the bidirectional power flow, which makes conventional protection schemes and relay settings of distribution systems outdated [17]. 1.1.2.1 Reciprocating engine driven DERs A reciprocating engine is often known as a piston engine, using reciprocating pistons to convert pressure to mechanical rotating power for driving electric generator [18], [19]. Because the reciprocating engine driven DER is a proven, mature and competitive technology with low-cost capital base and simple maintenance needs, it is one of the most popular types of DERs in the U.S. with power capacity ranging from few kilowatts (kW) to several megawatts (MW). It is able to use gasoline, diesel, natural gas and propane/methane to power the engine and spin the generator. Its main member is the internal combustion engine, used extensively in automobiles and industries, steam engine and Stirling engine. 1.1.2.2 Turbine driven DERs A turbine is a rotary mechanical device that extracts energy from fluid flow and converts it to drive an electric generator. For DERs, gas turbines are commonly used ones. Advantages of the gas turbine over reciprocating engine are continuous combustion without reciprocating motion, high power-to-weight ratio and environmentally friendly [20]. In addition, the gas turbine is becoming more favored because of the vast deposits of oil shale around the world [21]. But, the gas turbine is more expensive and has less response to changes in power demand [20].
6
1.1.2.3 Fuel cell A fuel cell is able to convert the chemical energy inside the fossil fuel into electricity via chemical reactions. Instead of burning fossil fuels, it oxidizes the hydrogen and causes ion migration to create electric current and electric power. So it works silently and efficiently with no air pollution. Depending on the operation mechanism, fuel cells can be categorized into five groups: proton exchange membrane fuel cell (PEMFC), alkaline fuel cell (AFC), phosphoric acid fuel cells (PAFC), molten carbonate fuel cells (MCFC), and solid oxide fuel cells (SOFC). Except for AFC, which is often used in spacecraft, the other four types are viable for DER applications. The output of the fuel cell is direct current (DC) power. Therefore, it needs at least a power electronic inverter to feed alternating current (AC) power to the grid, or it can be directly used in DC power systems. Although the concept of the fuel cell is simple, the actual execution is much more complicated. This is because the fuel-to-electric efficiency depends on the internal temperature. A higher internal temperature can assist to achieve a higher efficiency of energy conversion [18]. Therefore, it needs robust design and high-temperature tolerant materials to ensure high efficiency. Although over three decades development and improvement, the three barriers to fuel cell widespread applications high cost, insufficient durability and the need for advanced service infrastructure are still in the way. 1.1.2.4 Combined heat and power CHP, also known as a cogeneration unit, generates electricity and useful thermal energy in a single unit. Conventional fossil fuel-based generators, like gas turbines and 7
diesel generators, emit hot exhaust gasses without energy harvest. CHP is capable of harnessing the remaining energy resided in waste heat to provide additional value. Because of its high efficiency and cost-effective characteristics, CHP is becoming a widely used and very popular type of DERs in the United States [22]. 1.1.2.5 Renewable energy Renewable energy generally indicates the energy which is collected from resources that can be naturally replenished on a human timescale, like solar, wind, biomass, etc. [23]. Renewable energy resources are becoming popular and rapidly growing due to the energy crisis, global warming, government regulations, the applicability over wide geographical areas and zero consumption of fossil fuel [23]. The capital cost for renewable energy has decreased drastically over the last decade, and this trend is expected to continue due to various technological developments. But, compared with biomass, wind, and solar energy cannot be stored for future use. In order to make full use of the free energy, PV and wind turbine are often allowed to generate electricity as much as possible, and categorized into non-dispatchable resources. Besides, since the power output of PV and wind turbine highly depend on weather conditions, they have stochastic natures and cannot well support peak shaving. So, they have a negative influence on system frequency response, resulting in system stability issues. This is because most of the renewable resources connect to the grid system via power electronics interfaces, which brings down the whole system inertia. A solution to ensure system stability and resilience is integrating BESS to act as spinning reserve and compensate system inertia loss. Another common solution is controlling renewable resources output 8
below their available maximum generation. So there has some reserve margin with PV and WT, but it causes energy waste and the forecast error might hurt the effectiveness of this methodology. 1.1.2.6 Battery energy storage system BESS is a special type of DERs and also an indispensable component in modern power systems, particularly microgrids. It acts as the role of “spinning reserve” with a very large inertia, so it can immediately respond to the mismatch between the power supply and load demand by charging and discharging. BESS is able to assist the system in three general ways. First, it can be used for the purpose of system stability improvement by quickly following load changes. Then other DERs can operate at a relatively stable level with high efficiencies and adequate reserve margin. Second, BESS can benefit the system stability and resilience by riding through contingencies like loss of generation and sudden large load change. At last but not the least, non-dispatchable renewables can be seen as dispatchable generation units with the assist of BESS. This is because BESS can be controlled to compensate power imbalance between renewable output and the expectation. 1.1.3
Microgrid A microgrid is a cluster of loads and DERs operating as a controllable unit [3]–[5],
[24]. It is a localized and small-scale grid, contrary to the conventional and centralized power grid. The concept of microgrid provides an alternative to resolve many emerging challenges in the conventional power grids. The primary purpose of microgrids is to ensure reliable power supply to load centers and mitigate grid disturbances. 9
Therefore, it can reduce the odds of power outages by continuously supporting customers with local DERs. In addition, the capability of operation mode conversion is able to strengthen the grid resilience. For example, microgrids can isolate themselves by disconnecting from the grid, when there is a fault happening outside microgrids. After the fault isolation, microgrids can quickly reconnect to the grid systems and restore power to external consumers. A distribution system based community microgrid system is shown in Figure 1. 4 [17], [25]. It has a mixture of DERs located close to critical loads. When the point of common coupling (PCC) is closed, it works in the grid-connected mode and has power exchange with the utility. It is a positive load when the electric power flows into the microgrid. Otherwise, it can be seen as a negative load. When the microgrid system is in islanded operation, it has no power exchange with grid utility, acting as a zero load.
10
Figure 1. 4 Microgrid with DERs [17], [25]
1.1.4
Power Systems Blackouts and Importance of Resilience Power systems blackouts are uncommon but extreme occurrences. Natural
disasters and cascading failures caused by overloading are the two main causes of large blackouts in North America.
11
In recent years, because of climate change, severe weather events, like hurricanes, typhoons, and floods, are becoming more common. These extreme weather events are posing significant threats to power systems, especially electrical facilities, and presenting serious challenges to grid operators. Climate Central, a nonprofit organization focusing on the impacts of climate change, analyzed 28 years power outage data in the United States and charted a tenfold increase in weather related major power outages affecting over fifty thousand customers in Figure 1. 5 [26].
Figure 1. 5 Power outages caused by extreme weather [26]
In addition, as the other main cause of blackouts, cascading failures, like the 2003 northeast blackout [27], were triggered by a set of overloading events that caused further 12
outages. With penetrations of renewable energy resources, microgrids and distribution systems are more likely to have issues of instability and overloading. This is because renewable power output is intermittent and highly depending on weather conditions, which are very stochastic and hard to predict. Plus load demand uncertainties, the unknown factors increase, leading to a weakened controllability. Hence, there is a critical need to incorporate resilience into the power grid [28]– [30]. The principal aim of having a resilient system is trying to keep from power outages, quickly detect and isolate the fault area, and restore power right after fault isolation. Therefore, this dissertation proposes to form community microgrids within distribution systems by integrating local DERs. Then distribution systems can be partitioned into small but power independent community microgrids when extreme incidents happen. The load, at least the critical load, could be uninterruptedly power supplied to a maximum extent. In addition, an efficient protection strategy and an optimal restoration plan are necessary for quickly bringing back power to the un-faulted but interrupted portions. In the following chapters, efforts on community microgrids creation, DERs selection, dispatchable DERs capacity planning, protection improvement and innovative system restoration algorithm have been made for resilient distribution systems. 1.1.5
Challenges in Resilient Distribution Systems Resilience expresses the ability of a system to adapt to and recover from a
disruptive event. A resilient distribution system can respond to extreme events, ensure uninterrupted power supply for critical loads, avoid unnecessary losses, fast detect and
13
accurately isolate fault areas, and quickly spring back to normalcy after power disruptions. But there are still some challenges needing extra efforts to deal with: 1.1.5.1 Radial topology In the existing distribution systems, when a blackout happens, the downstream customers will also get disrupted after fault isolation, because of the radial topology. In this dissertation, community microgrids are formed within distribution systems to mainly support critical load centers without interruptions. When a fault or an extreme event happens, microgrids are able to disconnect from the main power system and continuously support their loads. 1.1.5.2 Planning reserve margin versus annualized cost For community microgrids in islanded operation mode, there is no support from the grid side. Local DERs have to well follow load variations and keep system frequency within the acceptable range. However, with large penetrations of DERs, especially the inverter based DERs, the system inertia is brought down. Distribution systems and microgrids are becoming more likely to experience frequency variations by load changes, renewable output intermittence and loss of generation [14]–[16]. The power utility employs a simple strategy for maintaining system reliability and resilience: always has more available power supply than needed, which is the concept of reserve margin [31], [32]. Even though the concept is simple to understand, how to design it appropriately and cost-effectively in the planning horizon is not an easy thing. This stage reserve margin is also named as planning reserve margin (PRM). It has to identify whether the planning capacity is large enough to cover peak load demand, loss of one generation, and 14
uncertainties from load and renewables. Besides, the planning cost should be the least when guaranteeing the availability of power supply. Moreover, as it is a capacity based metric, an accurate performance assessment cannot be ensured for energy limited resources, e.g., reciprocating engine driven generators with limited fossil fuel. Also, the portion of renewable generation considered in PRM has a large impact on system reliability and cost because of its intermittency and uncertainty. 1.1.5.3 Protection and restoration With high penetration of DERs, power flow that was unidirectional is now becoming bi-directional, outdating conventional protection schemes and protective relay logic [17]. In addition, the fault current levels have changed drastically, especially those from inverter based DERs. Therefore, power systems protection and protective relay settings need adjustments and improvements to well protect modern distribution systems and microgrids. After fault isolation, automated restoration plans have to be implemented immediately to improve system resilience. This needs real time update of system topologies and advanced algorithms to ensure distribution systems maximum recovery with the minimum switching operation. 1.1.5.4 Reliable not equal to resilient The system reliability is measured by indices like customer average interruption duration index (CAIDI), customer average interruption frequency index (CAIFI), system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI), loss of load expectation (LOLE), etc. These reliability indices mainly care about the influence of power interruptions on the customer side but pay little attention to 15
system protection and restoration. In highly automated distribution systems, service restoration can be realized by remotely controlled devices within a very short time. Therefore, the frequency and duration of outages are much lower and system reliability is improved. This is because if the fault duration is limited to one to five minutes, it will not be counted in the measurement of reliability indices. However, from the view of system resilience, power interruptions still exist. Also, system resilience is mainly defined to measure the system ability to respond to extreme events, like hurricanes, earthquakes, and terrorist attacks. Different from a typical outage, an extreme event could cause catastrophic outages, like multiple faults within a distribution system. Numerous components may be damaged, power sources may not be available, and a large number of customers could be affected. A resilient system should be able to handle such situations and at least guarantee that critical loads are power supplied uninterruptedly. So, with the existing reliability indices, a highly reliable system is not equal to a highly resilient system [33]. 1.1.5.5 Resilient metrics Based on the discussion in the previous section, standardized resilient metrics are needed to evaluate and quantify the system capability of withstanding severe contingencies and its fast restoration from an extreme event [33], [34]. However, presently, there is no standard and unified metrics for resilient power systems design and assessment. Reference [35] proposed a general framework to assess the resilience of infrastructure and economic systems. Besides, the conceptualization of the resilience of
16
the future power infrastructure is presented in [36] via a conceptual curve of the resilience level as a function of time associated with a disturbance event.
1.2
Literature Review A review of hybrid renewable energy power generation systems affecting the
energy sustainability was presented in [37]. It also discussed important issues and challenges in the distribution system design and energy management. The long-term viability, scalability and sustainability of renewable energy resources were presented in [38] vis-a-vis non-renewable resources. Sustainable energy policies made for China and India were put forward in [39], [40]. The Unites States promoted energy independence and many states have released their renewable energy standard portfolios [11]. Reference [41] features the U.S. department of energy (DOE) smart grid research and development projects. Distributed generation can help meet the growing energy demands without expanding the conventional large centralized fossil fuel power plants [42]. But, with large penetration of intermittent renewables, the power balance is affected within the distribution system [43]–[46]. A microgrid could be designed with the optimal mix of DERs and energy storage. In order to guarantee the power balance between power demand and supply, a system design with the optimal mix of DERs is a necessity before the operation management. There has been a lot of works focusing on the capacity planning of DERs, with the main consideration of total cost [47]–[50], while an adaptive genetic algorithm based DER allocation strategy that minimizes network power loss and node voltage 17
deviation is proposed in reference [51]. For the sizing of energy storage, how to optimally manage energy imbalance has been extensively studied to compensate forecast errors of load demand and renewable DERs power output [52]–[54]. Numerous works related to energy management have been conducted to minimize economic cost, reduce CO2 emissions, improve system reliability and increase renewable energy utilization [55]–[68]. In order to achieve optimal solutions under different conditions and constraints, previous works have employed and improved many advanced optimization algorithms, like heuristic methods [55]–[60], multi-level optimization [61]–[63], stochastic programming [62]–[64], dynamic programming [65], [66], linear and non-linear programming [67], [68], etc. However, very few attentions have been paid to resilience-oriented capacity planning. Community microgrids can be formed by integrating locally available DERs with power distribution systems. They are able to support higher penetration of DERs. Furthermore, if unexpected disruptions occur, the power grid can be partitioned seamlessly into self-sustaining islanded networks for uninterruptedly supporting critical loads and improving system resilience. However, the operation of community microgrid, in particular, has many unresolved challenges, particularly in the protection aspects [69]– [71]. Existing distribution systems at the outset are mostly passive and radial networks with unidirectional power flow. With the large integration of DERs, the power flow is becoming bi-directional. The fault current level could also change mainly depending on the system topology and its operation mode. Also, it was shown in [72], [73] that the fault currents are much different in grid-connected and islanded modes. Thus, the existing 18
conventional protection schemes are incapable of implementing faults detection and isolation accurately. Reference [74] discussed the protection challenges in a microgrid that can be operated in both grid-connected and islanded modes. Selected protection problems related to DERs integration have been investigated in [75], which has emphasized the necessity for a change to the existing distribution systems protective logic. The references [76], [77] explored dynamic behavior of microgrid systems and developed the protection strategies for satisfying given specifications. A wide-ranging and thorough survey of antiislanding schemes was conducted in [78]. Current limiters were employed to protect distribution systems by limiting short-circuit current under fault conditions in [69]. Besides, it illustrates that an optimal relay setting could be acquired to satisfy the operations in both grid-connected and islanded modes. However, a tradeoff is often needed with compromise and the optimal solution may not be suitable to all individual conditions. In addition, meshed/looped architecture is effective to improve system resilience and usually employed in microgrids. Earlier work on forming microgrids within distribution systems was carried out by Zamani et. al. in [79]. However, it is only applicable for radial distribution systems, and the meshed loop network has increased the dimension of complexity for coordinated protection. Hence, in this dissertation, a multilayered protection strategy is favored to ensure system reliability and resilience. In [80]–[82], the concept of adaptive protection was proposed for microgrids. Although it was effective for different operations, a central controller is however needed to monitor 19
the system topology in real time and send coordinating commands. Therefore, it is inevitable to result in extra time delays. In addition, the challenges of high impedance faults detection and communication-assisted protection were discussed in [70]. After detection and isolation of unexpected faults, rapid restoration plans were elaborated in [83], [84] to build more resilient power grids. Restoration strategies for distribution systems to recover electricity service to interrupted loads were illustrated in [85], [86]. The restoration plan optimization is a nonlinear problem with constraints of power operation and network topology. Several works were published to solve this problem, using heuristic methods [87]–[89], expert system [90], [91], multi-agent system [92]–[94], fuzzy logic [95]–[97], neural network [98], mathematical programming [99]– [101], and graph theory [102], [103]. However, many of them only included real power flow analysis and neglected the reactive portion. This is not correct because a reactive power fluctuation could lead to the instability of bus voltage, and even system collapse. Moreover, the emphasis of previous literature was on single fault and finding its restoration plan. Very few work ever tested the restoration scheme in worse cases that involve multiple faults in a distribution system. The reference [104] employed a spanning tree search method to find the restoration plan and proposed a topology simplification strategy for large distribution systems. Microgrids were considered as virtual feeders in the distribution system. But, this paper only assumed these microgrids as some unknown resources and did not give enough details about the microgrids architecture and capabilities. In [105]–[107], remote-controlled switches were installed to reduce the restoration time with minimum switch upgrade cost. However, the authors only 20
investigated single-fault conditions. Reference [108] presents a restoration plan using dynamic programming. The number of states is reduced to simplify the restoration problem by grouping adjacent states and screening out the best one for each group. However, such a simplification strategy impacts the power flow analysis and compromises the speed of restoration, thus violating the primary goal of restoring the maximum load as soon as possible.
1.3
Chapter Review This dissertation focuses on resilient distribution systems with community
microgrids. Based on appropriate PRM, community microgrids can provide uninterruptible power supply to critical loads during unexpected contingencies. Advanced multilayered protection strategy is able to fast detect and accurately isolate faulted segments. After fault isolation, an innovative restoration algorithm is able to find the optimal solution to fast re-energize disrupted load customer. The organization of the rest dissertation is as follows. Chapter 2 illustrates the development of community microgrids within distribution systems. It first describes the current status and trend of electricity mix across the United States. Then a distribution system based community power network is presented. With the help of quantitative assessment and qualitative evaluation, specific types of DERs are selected and installed within community microgrid. Based on the result in Chapter 2, Chapter 3 presents a DER sizing strategy to guarantee the uninterruptible power supply to critical loads. In this chapter, discrete-time 21
Fourier transform (DTFT) and particle swarm optimization (PSO) algorithms are employed to achieve the optimal planning reserve margin with least annualized cost. In the case studies, sensitivity analysis is conducted to investigate the influence of renewable generation on DERs capacity planning and annualized cost. Chapter 4 presents a multilayered protection scheme to cover distribution systems and community microgrids. It employs an adaptive over-current protective method combined with differential protection scheme. Furthermore, the adaptive over-current protection is implemented with a centralized approach while the differential protection uses a distributed scheme. Case studies are carried out to validate its effectiveness. After fault-isolation, distribution systems should be restored immediately to recover de-energized areas. An innovative modified Viterbi algorithm is proposed in Chapter 5 to find the optimal restoration plan. In this way, the maximum load restoration is guaranteed with the minimum number of switching operations. Furthermore, an improved flexible switching pair operation is presented to keep the radial topology of distribution systems. Various case studies are presented to verify the effectiveness of the proposed restoration algorithm. The system restoration performance with the presence of DERs and microgrids is also investigated in this chapter. In Chapter 6, contributions of the work are summarized and future work is recommended.
22
CHAPTER 2: COMMUNITY MICROGRID DEVELOPMENT IN DISTRIBUTION SYSTEM 2.1
Introduction In the year of 2015, fossil fuels such as coal and natural gas account for 66.8% of
total electricity generation in U.S. [7]. According to the U.S. EPA, in 2014, approximately 31% of greenhouse gas and 37% of total CO2 emissions came from the electricity generation [8]. Within the electricity sector, coal power plants contribute 77% of CO2 emissions with only 38.5% of electricity generation [7]. Though the issues are eased to a certain extent when the coal power plants approach their retirement, there is still great pressure further cutting the emissions and increasing energy efficiency. Therefore, a movement toward DERs, particularly renewable generation, is gaining more attention, and many emission-reduction targets have been set forth by both federal and state governments [9]–[11]. The principal goal of this dissertation is to build resilient distribution systems with community microgrids [25]. Microgrids can well support higher penetration of DERs for increasing system energy efficiency and system controllability. Moreover, if any unexpected event occurs, distribution systems can be partitioned into several selfsufficient community microgrids without interrupting critical loads. 23
This chapter mainly focuses on how to form community microgrids by integrating local DERs and load centers within distribution systems. It is organized as follows. Section 2.2 presents the current status and trend of electricity mix in the U.S. A distribution system based community network is displayed in Section 2.3. The selection of DERs including quantitative and qualitative comparison will be elaborated in Section 2.4. In Section 2.5, a community microgrid is formed within a distribution system. The summary of this chapter is in Section 2.6.
2.2
Electricity Mix in the United States Current Status and Trends According to the data in 2014 from National Renewable Energy Laboratory
(NREL) [7], fossil fuels are a major source of electric power generation in the United States. The electricity generation from coal is about 38.5%, and natural gas provides another 27.3% of the total electricity produce. Renewable energy contributes approximately 13.5% of the total electricity with the breakup as hydropower 6.3%, wind 4.4%, solar 0.8% and others 2%. However, these did not consider factors like climate and topographical conditions that range wildly in different parts of the U.S. Figure 2. 1 shows the distribution discrepancy of the locally available energy resources in different regions across the United States. In addition, the electricity mix is expected to differ from this figure as many coal-fired power plants, especially those located in Midwest, are planned for retirement in the near future. This is a necessity to meet the targets of emission reduction and energy efficiency regulated by federal and state governments. Under such circumstances, microgrids are becoming appealing as they make use of local energy 24
resources, with few T&D losses, and thereby can improve energy efficiency and system resilience by replacing large central generators with small DERs.
Figure 2. 1 Electricity mix in different regions of the United States [109]
2.3
Community Power System The distribution system is the receiving portion of power delivery. It distributes
the electricity from transmission lines to customers. Distribution substation is a PCC between the transmission system and distribution system. It lowers the transmission voltage to medium voltage. The community power network shown in Figure 2. 2 is 25
typical in the majority of the United States. It is a portion of a distribution system and has a 34.5/12 kV main transformer with a maximum capacity of 13.85 MVA. Within the community, it has a hospital, a university, government & commercial buildings, industrial manufacturing loads and a wastewater treatment plant.
Figure 2. 2 Single line diagram of a distribution network
26
2.4
Distributed Energy Resources Selection for Community Microgrids This section illustrates the selection of DERs based on quantitative assessment
and qualitative evaluation for establishing cost-effective and qualified community microgrids. The levelized cost of energy (LCOE) is employed to financially compare different types of DERs. After the quantitative comparison, a quality functional deployment (QFD) is used to further assist the DERs selection cogitating environmental factors, customer requirements, and government regulation. 2.4.1
LCOE Quantitative Assessment LCOE is one of the utility industry’s primary metrics for measuring the cost of
electricity produced by a generator. It calculates the value of a generator’s annualized total cost divided by its estimated annual energy output, as expressed in (2.1). The annualized total cost consists of annualized capital cost, annual operation and maintenance (O&M) cost including fixed and variable portions, annual fuel cost and also renewable energy tax incentive payback. In this dissertation, the tax incentive is the production tax credit (PTC). It is a federal tax incentive that provides financial support for the development of renewable energy [110], [111]. Power generation from wind, solar, geothermal and “closed-loop” bioenergy [112], which uses dedicated energy crops, is eligible to receive $23 per megawatt-hour (MWh) PTC incentive payback for the first ten years of operation. Other renewable technologies, such as “open-loop” biomass using wastes, are able to receive a lesser value tax credit, $12 per MWh. In addition, the annual energy output of an energy resource is equal to its year-round energy generation at full power multiplies its capacity factor (CF). If we use the per unit value, for example, the 27
capital cost per kW or MW, then the power rating, 𝑃𝑃𝑅𝑅 , can be taken away and all numerators in (2.1) become per unit values, 𝑈𝑈𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑈𝑈𝑈𝑈 𝑂𝑂&𝑀𝑀 , 𝑈𝑈𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 , 𝑈𝑈𝑈𝑈 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 .
The annualized capital cost, 𝐶𝐶 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , is equal to the overnight capital cost multiplies the capital recovery factor (CRF), as shown in (2.2) and (2.3). In (2.3), r indicates the discount rate referring to the interest rate used in discounted cash flow (DCF) analysis for setting the present value of future cash flows, and y is the number of years in lifetime. The annualized O&M cost, 𝐶𝐶 𝑂𝑂&𝑀𝑀 , consists of fixed and variable parts, as presented in (2.4). In (2.5), the calculation of annualized fuel cost, 𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 , is expressed. Since fuel costs are very volatile and the estimation of levelized cost of fuel over the lifetime is a challenge. One approach introduced in [6] employs a levelizing factor (LF) to estimate future change. The annual tax incentive payback, 𝐶𝐶 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 , is in equation (2.6). 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 =
=
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 ($/𝑘𝑘𝑘𝑘ℎ 𝑜𝑜𝑜𝑜 $/𝑀𝑀𝑀𝑀ℎ) 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂
𝐶𝐶 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + 𝐶𝐶 𝑂𝑂&𝑀𝑀 (+𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 ) (−𝐶𝐶 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 ) = ($/𝑘𝑘𝑘𝑘ℎ 𝑜𝑜𝑜𝑜 $/𝑀𝑀𝑀𝑀ℎ) 𝑃𝑃𝑅𝑅 ∙ 8760 ℎ/𝑦𝑦𝑦𝑦 ∙ 𝐶𝐶𝐶𝐶
(2.1)
𝑈𝑈𝑈𝑈 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑈𝑈𝑈𝑈 𝑂𝑂&𝑀𝑀 (+𝑈𝑈𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 ) (−𝑈𝑈𝑈𝑈 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 ) ($/𝑘𝑘𝑘𝑘ℎ 𝑜𝑜𝑜𝑜 $/𝑀𝑀𝑀𝑀ℎ) 8760 ℎ/𝑦𝑦𝑦𝑦 ∙ 𝐶𝐶𝐶𝐶 𝐶𝐶 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂ℎ𝑡𝑡 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝐶𝐶
(2.2)
𝐶𝐶 𝑂𝑂&𝑀𝑀 = 𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑂𝑂&𝑀𝑀 + 𝐶𝐶 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑂𝑂&𝑀𝑀
(2.4)
𝐶𝐶𝐶𝐶𝐶𝐶 =
𝑟𝑟 ∙ (1 + 𝑟𝑟) 𝑦𝑦 (1 + 𝑟𝑟)𝑦𝑦 − 1
28
(%/𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦)
(2.3)
𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 𝐹𝐹 ∙ � � 𝑜𝑜𝑜𝑜
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
∑𝑖𝑖 𝑃𝑃[𝑖𝑖] ∙ 𝑇𝑇 � ∙ 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 ∙ 𝐿𝐿𝐿𝐿 𝜂𝜂[𝑖𝑖]
($/year)
𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 𝐹𝐹 ∙ 𝑃𝑃𝑅𝑅 ∙ 8760 ℎ/𝑦𝑦𝑦𝑦 ∙ 𝐶𝐶𝐶𝐶 ∙ 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 ∙ 𝐿𝐿𝐿𝐿 (𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝐷𝐷𝐷𝐷𝐷𝐷)
𝐶𝐶 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑃𝑃𝑃𝑃𝑃𝑃 ∙ � �� 𝑃𝑃𝑟𝑟𝑟𝑟 [𝑖𝑖] ∙ 𝑇𝑇� 𝑟𝑟𝑟𝑟
𝑖𝑖
($/𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦)
($/𝑦𝑦𝑦𝑦)
(2.5)
(2.6)
where, 𝐹𝐹 indicates the fuel price, 𝑃𝑃[𝑖𝑖] is the power output at time i, 𝜂𝜂[𝑖𝑖] is the energy conversion efficiency at time i, 𝑇𝑇 is the sampling time, and 𝑃𝑃𝑟𝑟𝑟𝑟 [𝑖𝑖] is the renewable resources power output at time i.
As a financial tool, LCOE is very valuable for the comparison of various energy resources. A low value of LCOE indicates that the electricity is being produced at a low cost. For a conventional fossil fuel plant, the future fuel price is uncertain and depending on a number of factors, while a renewable energy resource has zero fuel cost, although the initial investment cost is very high. In addition, governments have policies to encourage the integration of renewable energy resources, like subsidies/grants, tax incentives, feed-in tariff, net-metering program, renewable portfolio standards, etc. They can be reflected from the last term of the numerator in (2.1), 𝐶𝐶 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 . Figure 2. 3 is the comparison of LCOE vs. capacity factor among different DERs, based on the cost estimation presented in Table 2. 1 [6], [113]–[115]. It clearly presents that renewable energy resources, like PV, WT and biomass genset, are very cost-effective with consideration of tax incentives. Also, natural gas genset is much better than other fossil fuel generators. The integrated gasification combined cycle (IGCC) power plant seems a 29
little bit more economic than combustion turbine at higher capacity factor because of a cheaper price of coal. However, its CO2 emission is much higher than other DERs and its efficiency is very low.
Table 2. 1 Costs and performance characteristics for electric generating technologies Technology
IGCC
Combustion Turbine
Fuel
Coal
Natural Gas
Natural Gas
Biomass
Heat Rate (Btu/kWh)
8700
10850
7050
Overnight Capital Cost ($/kW)
3000
973
917
2500
2000
2346
3490
Fixed O&M Cost ($/kWyear)
62.25
7.34
13.17
70
25
40
3
Variable O&M Cost ($/MWh)
7.22
15.45
3.6
Fuel Cost ($/MMBtu)
2.22
3.08
3.08
LF
1.5
1.5
1.5
Discount Rate
5%
5%
5%
5%
5%
5%
5%
Life-time (year)
20
20
20
20
20
20
20
PTC
12
23
23
($/MWh)
Combined Cycle
30
PV
Wind BESS Turbine
Figure 2. 3 Curves of LCOE vs. capacity factor for DERs based on Table 2. 1
2.4.2
Qualitative Function Deployment Qualitative Evaluation After the LCOE calculations, a qualitative evaluation is able to further assess
DERs soft indices. This evaluation can be made using the method of QFD. It is a method to transform the voice of customers into engineering evaluation for a product service. It prioritizes products or service characteristics [116]. In this section, a QFD is employed to examine the relationships strong (9), medium (3), weak (1) or no relation (0) between each DER option against environmental factors, customer requirements, and government mandates. Furthermore, it also distinguishes between a positive relationship and a negative one. The takeaway from the QFD exercise is able to help better understand which DER(s) need to be taken into consideration for community microgrids development. As seen in Table 2. 2, biomass genset, natural gas genset, PV panel, and wind turbine are more suitable DER options than other choices. Besides, the natural gas genset is very efficient and has ample supplies in the U.S. 31
Importance (1-5)
PV Panel
Wind Turbine
Biomass Genset
Natural Gas Genset
Natural Gas Combustion Turbine
Coal−Fired Power Plant (Base-line)
Table 2. 2 QFD evaluation of DERs for community microgrids development
LCOE
5
9
9
3
3
1
1
CO2 Emission Reduction
5
3
3
9
9
1
0
Fuel Consumption Savings
4
9
9
9
3
1
0
Outage Time Reduction
5
-3
-3
1
3
3
3
Dispatchability
4
-1
-1
1
3
3
1
Equipment Lifetime
3
3
3
1
1
1
3
Comply with the U.S. DOE Target
5
9
9
9
1
1
0
131
131
153
107
49
33
DERs Options
Customer Requirements
Absolute Target
2.5
Community Microgrid Development In previous sections, typical community network in the United States is presented
and suitable DERs have been selected out after quantitative comparison and qualitative evaluation. This section will then present how to form a community microgrid with the integration of DERs and critical load centers. At first, it is planned to develop a community microgrid within the existing distribution system. This is made by distributing locally available DERs in the community network, and tactically placing them near critical load centers, like hospital, university, government building, commercial area, industrial manufacturer, etc. (cf. 32
Figure 2. 4), according to IEEE Industrial and Commercial Systems Standards [117]– [120]. This has also to ensure reliable power delivery to meet the IEEE 1547 Standard [121], [122]. In addition, whenever a fault occurs outside the community microgrid, it can operate in islanded mode to provide an uninterruptible power supply for critical loads within the community by facilitating the self-regulation of local DERs. For this purpose, an extra line is added to form a meshed topology, shown as the dashed line in Figure 2. 4. Furthermore, a BESS is taken into consideration for further supporting the community microgrid islanding capability when a power outage occurs in the main grid [123]. The BESS will serve as a ‘virtual’ spinning reserve to quickly follow any sudden load changes and compensate instantaneous power mismatch without exceeding the frequency and voltage limits when the microgrid operates in an islanded mode. According to the ANSI 84.1-2006 Standards, under steady state conditions, the frequency must be within 59.3 Hz − 60.5 Hz and the voltage should not violate the range of 0.9 p.u. − 1.05 p.u. Besides, under the grid-connected mode of operation, the BESS can offer benefits like peak shaving and cost-effective operation.
33
Figure 2. 4 Single line diagram of a community microgrid
2.6
Summary With the retirement of the coal-fired power plant and government regulations,
DERs, particularly renewable generation, are expected to become more popular in the near future. In this chapter, a distribution system based typical community power network is displayed. Then, an LCOE based quantitative assessment and a QFD based qualitative evaluation are illustrated to compare variable types of DERs and select suitable ones for 34
the community network, cogitating the economic cost, environmental factors, customer requirements, government regulations, etc. With penetrations of DERs, the development of community microgrid within the distribution system is presented in Section 2.5. With the development of community microgrids, DERs can be better controlled and dispatched to power supply customers within the community. Although the suitable types of DERs have been determined, their power capacities are unknown yet. In the next chapter, the sizing scheme of dispatchable DERs will be elaborated.
35
CHAPTER 3: SIZING OF GENSETS AND BATTERY ENERGY STORAGE SYSTEM FOR ISLANDED COMMUNITY MICROGRID 3.1
Introduction When an extreme event happens, a resilient distribution system can be seamlessly
partitioned into several islanded community microgrids for uninterruptedly supplying important load centers. But, chapter one described the challenge of frequency response for islanded community microgrids. In addition, most of the renewable energy resources are non-dispatchable and have a negative influence on system inertia, since it is very difficult to exactly forecast and control their power generation. Loss of generation and scheduled maintenance will also affect systems performance. Furthermore, the load is stochastic and uncertain but needs to be power supplied uninterruptedly, particularly the critical portion. In order to guarantee the distribution system resilience, it is a necessity to have adequate reserve margin for unexpected events. Reserve margin is the difference between available capacity and peak demand, normalized by peak demand. It is expressed as a percentage to maintain reliable operation, meet unforeseen demand increases and ride through the unexpected loss of one generation. For example, a twenty percent reserve margin indicates that the electric system has excess capacity in the amount of one fifth of the expected peak demand. Even 36
though the concept is simple to understand, how to design it appropriately and costeffectively in planning horizon is not an easy thing. This stage reserve margin is also named as planning reserve margin (PRM). It has to identify whether the planning capacity is large enough to cover peak load demand, loss of one generation, and uncertainties from load and renewables. Besides, the expense should be the least when guaranteeing the availability of power supply. In this chapter, a gensets and BESS capacity planning is developed to ensure that the load will be power supplied at a certain level of system reliability in islanded community microgrids. The organization of this chapter is as follows. Reliability metrics are introduced in Section 3.2. Section 3.3 presents stochastic models of load and renewable energy resources. In Section 3.4, planning reserve margin and its impact on reliability metrics are illustrated. The sizing scheme of gensets and BESS is formulated in Section 3.5 to guarantee a reliable enough and cost-effective solution. Proposed optimization algorithm and validation with case studies are elaborated in Section 3.6 and Section 3.7. Finally, Section 3.8 summarizes the conclusions.
3.2
Reliability Metrics Distribution system reliability mainly relates to customer interruptions. In normal
operations, all electric facilities and customers are energized. Contingencies, like faults and open circuits, could disrupt normal conditions and result in power outages and customer interruptions. Reliability metrics are statistical data of power systems and are
37
widely used to evaluate systems characteristics in reliability [19]. The objective of this subsection is to review the commonly used reliability metrics in the United States [124]. 3.2.1
SAIDI SAIDI is the average outage duration for each customer, measuring how many
interruption hours a customer will experience in average within a year. It is expressed as follow [19], [124]. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 =
𝑆𝑆𝑆𝑆𝑆𝑆 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 ∑(𝑂𝑂𝑇𝑇𝑗𝑗 ∙ 𝑁𝑁𝑗𝑗 ) = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑁𝑁𝐶𝐶
(3.1)
where 𝑂𝑂𝑇𝑇𝑗𝑗 is the outage time in the area j within a year, 𝑁𝑁𝑗𝑗 is the number of interrupted customers in the area of j, and 𝑁𝑁𝐶𝐶 indicates the total number of customers.
With the decrease of interruption durations, SAIDI can be improved. In addition,
fewer interruptions could lead to a smaller value of SAIDI as well. Both two cases reflect the improvement in reliability, so SAIDI is able to correctly reflect system reliability. 3.2.2
SAIFI SAIFI is the average number of interruptions for each customer within a year. It is
expressed as follow [19], [124]. Similar to SAIDI, SAIFI will be reduced if the number of interruptions is decreased. Also, fewer interrupted customers could help drop down the value of SAIFI. Since reductions in the number of customer interruptions and interrupted customers reflect improvement in system reliability, SAIFI is also an indicator of system reliability. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 =
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 ∑(𝑁𝑁𝐼𝐼𝑗𝑗 ∙ 𝑁𝑁𝑗𝑗 ) = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑁𝑁𝐶𝐶
where 𝑁𝑁𝐼𝐼𝑗𝑗 is the number of interruptions in the area j within a year. 38
(3.2)
3.2.3
CAIDI CAIDI measures the average time each interruption lasts. Its expression is
presented below [19], [124]. It is equal to SAIDI divided by SAIFI. However, CAIDI can only reflect the reliability change when interruption happens. In other words, if the number of interruptions decreases to zero, CAIDI does not work, since its denominator is the number of interruptions. In addition, CAIDI can be improved by reducing the average duration of interruptions or increasing the number of shorter interruptions. So a smaller number in CAIDI may not be able to exactly indicate an improvement in reliability.
3.2.4
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = CAIFI
𝑆𝑆𝑆𝑆𝑆𝑆 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 ∑(𝑂𝑂𝑇𝑇𝑗𝑗 ∙ 𝑁𝑁𝑗𝑗 ) = 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 ∑(𝑁𝑁𝐼𝐼𝑗𝑗 ∙ 𝑁𝑁𝑗𝑗 )
(3.3)
CAIFI is the average number of interruptions for each interrupted customer, as presented below [19], [124]. In (3.4), CAIFI seems very similar to SAIFI. But there exists a difference in the denominator, causing a large impact. SAIFI can reach a value as low as zero, while the lowest value of CAIFI is one. Reducing a customer’s interruptions from a certain value to 1 will reduce CAIFI, while it will make CAIFI worse when the customer’s interruption is changed from 1 to 0, even though the reliability is improved all the way. Similarly, when more customers experienced a single interruption could improve CAIFI, but it might cause a deterioration of system reliability. Therefore, a CAIFI does not necessarily reflect system reliability correctly. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 =
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 ∑ 𝑁𝑁𝐼𝐼𝑗𝑗 ∙ 𝑁𝑁𝑗𝑗 = ∑ 𝑁𝑁𝑗𝑗 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 39
(3.4)
3.2.5
LOLP and LOLE Loss of load probability (LOLP) is employed in power systems reliability studies
to evaluate the probability that the load demand exceeds the available power supply [125], [126]. It is able to take into account the uncertainty in load demand and renewable generation by associating their stochastic distributions. If we say LOLP is the probability of a power deficit event, LOLE would be an average value of load interruptions during a long period. LOLE is often defined as the number of days of power supply insufficiency during one year or ten years. Regarding the definition, its unit is day(s)/year or day(s)/10year. No matter what the duration of the power shortage is, it would be counted as a single day outage as long as it happens within one day. Also, even if there are few times power interruptions in a day, only a single day power outage is counted. In North America, utilities and independent system operators (ISOs) often use LOLE as the criterion for PRM. In this dissertation, LOLE will also be employed as the reliability index for PRM of community microgrids.
3.3
Stochastic Models of Load and Renewable Energy Resources As the characteristics of zero fossil fuel consumption and no gas emission, PV
and WT are always allowed to reach the maximum power generation. However, because of their intermittent nature, the power generation is uncertain and fluctuating, resulting in less controllability and inaccurate prediction. In addition, the load demand cannot be forecasted precisely either. Mathematical models of load, PV, and WT are employed to mimic their stochastic natures [68], [127], [128]. 40
3.3.1
Stochastic Model of Load Demand Load demand is the summation of all end-users electricity usage. For each
consumer, the electricity usage behavior is distinct, uncertain and often affected by external conditions. Therefore, the load demand is changing all the time and hardly to be correctly predicted. At each time point, it can be seen as a stochastic variable following a normal distribution [127]. In Figure 3. 1, an annual commercial load profile and a single day sample are selected as examples. Generally speaking, load profile is quasi-periodic, which can be proved in Figure 3. 1. But it can be easily found that there is a difference between weekday and weekend. Also, seasons change has an influence on the level of electricity consumption. For example, in the summer, air conditioners are frequently used and heaters are often in use during winter, while this part of electricity energy can be mostly saved in spring and autumn. Besides, the load plotted in Figure 3. 1 is based on historical data and does not present any stochastic information. But for the reserve margin planning, the load demand should be estimated with consideration of its stochastic nature. Therefore, probability density function (PDF) of load demand is expressed in equation (3.5) following the normal distribution. Values of mean, μ, and variance, σ2 , can be calculated out based on historical load data.
41
(a) Commercial load profile on annual base
(b) Commercial load profile in a sample day during summer Figure 3. 1 Commercial Load Profile
𝑓𝑓𝑃𝑃𝑙𝑙 (𝑃𝑃𝑙𝑙 | 𝜇𝜇, 𝜎𝜎 2 ) =
1
√2 ∙ 𝜎𝜎 2 ∙ 𝜋𝜋
∙ 𝑒𝑒
(𝑃𝑃 −𝜇𝜇)2 − 𝑙𝑙 2 2∙𝜎𝜎
(3.5)
where, 𝑃𝑃𝑙𝑙 is the load demand, and 𝜇𝜇, 𝜎𝜎 2 are the mean value and variance of the normal distribution function.
42
3.3.2
Stochastic Model of PV Solar power is captured from the sunshine. It highly relies on the weather
condition and the surrounding environment. In Figure 3. 2, PV power output in a sample day is presented in per unit. It is fluctuating in the daytime and being zero before sunrise and after sunset. Because of the sunshine’s stochastic and fluctuating characters, its output prediction is hardly correct, having forecast errors.
Figure 3. 2 PV power output in a sample day during summer
According to statistical data, at each time point during the daytime, the solar irradiance is assumed to follow a beta distribution given by the following PDF [68], [128]: 𝑓𝑓𝑖𝑖𝑖𝑖 (𝑖𝑖𝑖𝑖; 𝑎𝑎, 𝑏𝑏) =
Г(𝑎𝑎 + 𝑏𝑏) 𝑖𝑖𝑖𝑖 𝑎𝑎−1 𝑖𝑖𝑖𝑖 𝑏𝑏−1 ∙� ∙ �1 − � � Г(𝑎𝑎) ∙ Г(𝑏𝑏) 𝑖𝑖𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 𝑖𝑖𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚
(3.6)
where, ir denotes the solar irradiance, and a, b are shape parameters of the Beta distribution function, Г denotes the gamma function. 43
Since the total active power 𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑖𝑖𝑖𝑖 ∙ 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑃𝑃𝑃𝑃 ∙ 𝜂𝜂𝑃𝑃𝑃𝑃 , the PDF of power available
from PV can be deduced as follows.
Г(𝑎𝑎 + 𝑏𝑏) 𝑃𝑃𝑃𝑃𝑃𝑃 𝑓𝑓𝑃𝑃𝑃𝑃𝑃𝑃 (𝑃𝑃𝑃𝑃𝑃𝑃 ; 𝑎𝑎, 𝑏𝑏) = ∙� � Г(𝑎𝑎) ∙ Г(𝑏𝑏) 𝑃𝑃𝑃𝑃𝑃𝑃_𝑚𝑚𝑚𝑚𝑚𝑚
where, 𝑃𝑃𝑃𝑃𝑃𝑃 is the PV output power. 3.3.3
𝑎𝑎−1
∙ �1 −
𝑃𝑃𝑃𝑃𝑃𝑃
𝑃𝑃𝑃𝑃𝑃𝑃_𝑚𝑚𝑚𝑚𝑚𝑚
�
𝑏𝑏−1
(3.7)
Stochastic Model of Wind
Similar to PV, wind turbine is widely used to capture wind energy and convert it to electric power, which largely depends on the weather conditions and the surrounding environment. Therefore, its power output is varying, as shown in Figure 3. 3.
Figure 3. 3 Wind turbine power output in a sample during summer
In addition, the forecast error of wind energy is also inevitable. According to statistical data, at each time point, wind speed is a stochastic number and assumed to follow Weibull distribution [68], [128]. 44
𝑓𝑓𝑣𝑣 (𝑣𝑣; 𝜏𝜏, 𝐾𝐾) =
𝐾𝐾 𝑣𝑣 𝐾𝐾−1 −�𝑣𝑣�𝐾𝐾 ∙� � ∙ 𝑒𝑒 𝜏𝜏 , 𝜏𝜏 𝜏𝜏 𝑣𝑣 𝐾𝐾
𝐹𝐹𝑣𝑣 (𝑣𝑣; 𝜏𝜏, 𝐾𝐾) = 1 − 𝑒𝑒 −�𝜏𝜏 �
𝑣𝑣 ≥ 0
(3.8)
(3.9)
where, 𝑣𝑣 is the wind speed, and τ, K indicate the shape parameters of Weibull distribution function.
For a typical wind turbine, it starts to generate power when wind speed is larger than the cut-in speed, 𝑉𝑉𝑖𝑖𝑖𝑖 , and the power output linearly increases as the wind speed goes
above from the cut-in speed, 𝑉𝑉𝑖𝑖𝑖𝑖 , to the rated speed, 𝑉𝑉𝑅𝑅 . When wind speed is between the
rated value and the cut-out speed, 𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 , power output is the rated power, 𝑃𝑃𝑅𝑅 . Otherwise, it does not generate power.
𝑣𝑣 − 𝑉𝑉𝑖𝑖𝑖𝑖 ⎧𝑃𝑃𝑅𝑅 ∙ 𝑉𝑉𝑅𝑅 − 𝑉𝑉𝑖𝑖𝑖𝑖 ⎪ 𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 (𝑣𝑣) = 𝑃𝑃𝑅𝑅 ⎨ ⎪ ⎩ 0
𝑉𝑉𝑖𝑖𝑖𝑖 ≤ 𝑣𝑣 ≤ 𝑉𝑉𝑅𝑅
𝑉𝑉𝑅𝑅 ≤ 𝑣𝑣 ≤ 𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜
(3.10)
𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
where, 𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 (𝑣𝑣) is the WT output power at wind speed 𝑣𝑣.
Then the PDF of power available from a wind turbine is presented below. ⎧ ⎪ ⎪ ⎪
𝐹𝐹1
𝑃𝑃𝑤𝑤𝑤𝑤𝑛𝑛𝑛𝑛 = 0
𝑉𝑉𝑅𝑅 − 𝑉𝑉𝑖𝑖𝑖𝑖 𝐾𝐾 𝑣𝑣̅ 𝐾𝐾−1 −�𝑣𝑣��𝐾𝐾 ∙ ∙� � ∙ 𝑒𝑒 𝜏𝜏 𝑓𝑓𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 (𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 ; 𝜏𝜏, 𝐾𝐾) = 𝜏𝜏 𝜏𝜏 ⎨ 𝑃𝑃𝑅𝑅 ⎪ ⎪ ⎪ 𝐹𝐹2 ⎩ 45
0 < 𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 < 𝑃𝑃𝑅𝑅 𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = 𝑃𝑃𝑅𝑅
(3.11)
where, 𝐹𝐹1 = 1 − [𝐹𝐹𝑣𝑣 (𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 ; 𝜏𝜏, 𝐾𝐾) − 𝐹𝐹𝑣𝑣 (𝑉𝑉𝑖𝑖𝑖𝑖 ; 𝜏𝜏, 𝐾𝐾)]; 𝐹𝐹2 = 𝐹𝐹𝑣𝑣 (𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 ; 𝜏𝜏, 𝐾𝐾) − 𝐹𝐹𝑣𝑣 (𝑉𝑉𝑅𝑅 ; 𝜏𝜏, 𝐾𝐾); 𝑣𝑣̅ = 𝑉𝑉𝑖𝑖𝑖𝑖 + (𝑉𝑉𝑅𝑅 − 𝑉𝑉𝑖𝑖𝑖𝑖 ) ∙
3.3.4
Net Load Profile
𝑃𝑃𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 (𝑣𝑣) ; 𝑃𝑃𝑅𝑅
With the help of historical data, the power capacity planning for gensets and BESS could cover all year round conditions. But, the uncertainties of PV, WT and load demand lead to the uncertain net load, equal to the power mismatch between renewable supply and load demand, and make historical information inadequate. Therefore, this section employs historical data based stochastic models to further mimic net load behaviors and improve the sizing performance for gensets and BESS. In addition, selecting representative weekdays and weekends in four seasons is able to save computation time without compromising accuracy. The net load profile, 𝑃𝑃𝑛𝑛𝑛𝑛 (𝑡𝑡), at each
moment, can be expressed as load demand, Ʃ𝑃𝑃𝑙𝑙 (𝑡𝑡) , minus PV and WT output, �Ʃ𝑃𝑃𝑃𝑃𝑃𝑃 (𝑡𝑡) + Ʃ𝑃𝑃𝑊𝑊𝑊𝑊 (𝑡𝑡)�.
𝑃𝑃𝑛𝑛𝑛𝑛 (𝑡𝑡) = Ʃ𝑃𝑃𝑙𝑙 (𝑡𝑡) − �Ʃ𝑃𝑃𝑃𝑃𝑃𝑃 (𝑡𝑡) + Ʃ𝑃𝑃𝑊𝑊𝑊𝑊 (𝑡𝑡)�
3.4
(3.12)
Planning Reserve Margin Unexpected net load changes could cause system instability, overloading, and
even power outages. In order to ensure a reliable community microgrid, it is a necessity to have adequate reserve margin. In previous sections, reliability metrics and the 46
uncertainty of net load are presented. A suitable reserve margin could be estimated by reaching the required values of reliability metrics. In this section, the concept of PRM is introduced. Besides, the relationship between reliability metrics and the PRM is investigated as well. 3.4.1
Planning Reserve Margin Reserve margin measures the difference between the maximum available power
supply and the expected peak load [129], [130]. 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 =
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
(3.13)
Since it is very difficult to accurately forecast future electricity usage, generation
loss and power generation from renewable energy resources, PRM is employed to maintain systems reliability [131], [132]. It is a key metric that measures the flexibility to meet customer demands and the ability to handle the loss of one or more system components. The calculation of PRM is coupled with probabilistic analysis to identify the resource adequacy and find out whether the planning capacity is large enough to cover peak load demand, loss of one generation unit, and also uncertainties from load and renewables, as expressed in (3.14). But, with penetrations of renewable generation units, there come some extra challenges because of their uncertainty. For example, should the capacity planning for gensets and BESS take renewable forecasted generation into consideration or not? If yes, is it better to count a portion of renewable generation? These questions will be explored in the following sections.
47
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 ∙ (1 + 𝑃𝑃𝑃𝑃𝑃𝑃)
(3.14)
= Peak Load + Largest Dispatchable Generation Unit + Uncertainties
where,
3.4.2
𝑃𝑃𝑃𝑃𝑃𝑃 =
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 + 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
Impact of PRM on Reliability Metrics
Reliability based resource adequacy is not readily observable. For example, one cannot quickly evaluate the system reliability, like LOLE and SAIFI, by simply taking a look at the reserve margin. But based on the probabilistic analysis and Monte Carlo simulation, the general relation between PRM and reliability metrics can be plotted out. In this section, situations like unexpected load changes, renewable generation intermittency and loss of one generation are covered. Power outages caused by external conditions, like bad weather, grounding fault, and distribution line disconnection are out of scope, since they cannot be improved by PRM. But these will be covered in the next two chapters with protective relay coordination and distribution system restoration. SAIFI and LOLE are plotted below to illustrate their trends with the increase of PRM. In Figure 3. 4, it is a curve of LOLE versus PRM. It shows that the expectation of load interruptions goes down with the increase of reserve margin. In other words, it indicates that a system is more reliable when the portion of planning reserve margin is larger. The curve of SAIFI versus PRM is presented in Figure 3. 5. The system average interruption frequency is also decreasing with the increase of PRM, although the tendency is not exactly the same as that in Figure 3. 4. In both Figure 3. 4 and Figure 3. 5, the capacity of the largest dispatchable generation unit is assumed as 10% of total 48
generation capacity. In order to investigate the impact of the largest dispatchable generator capacity on the reliability curves, cases with different ratios of the largest dispatchable generation unit to total capacity are investigated. Results are presented in Figure 3. 6 and Figure 3. 7. Figure 3. 6 displays the LOLE vs. PRM curves with different proportions of the largest dispatchable generation unit (PLG). Also, curves of SAIFI vs. PRM are presented in Figure 3. 7. Both figures reflect that, when the largest dispatchable generation unit takes up a larger portion of total generation capacity, the system reliability is worse, needing a larger PRM to achieve the same level of reliability.
Figure 3. 4 Curve of LOLE vs. planning reserve margin when the largest dispatchable generation unit is 10% of total available generation
49
Figure 3. 5 Curve of SAIFI vs. planning reserve margin when the largest dispatchable generation unit is 10% of total available generation
PLG = 50% PLG = 45% PLG = 40% PLG = 35% PLG = 30% PLG = 25% PLG = 20% PLG = 15% PLG = 10% PLG = 5%
Figure 3. 6 Curves of LOLE vs. planning reserve margin with different proportions of the largest dispatchable generation unit
50
PLG = 50% PLG = 45% PLG = 40% PLG = 35% PLG = 30% PLG = 25% PLG = 20% PLG = 15% PLG = 10% PLG = 5%
Figure 3. 7 Curves of SAIFI vs. planning reserve margin with different proportions of the largest dispatchable generation unit
3.5
Sizing of Gensets and BESS Renewable energy resources are considered as negative load and sized based on
customers needs, which is out of the scope of this dissertation. So the power capacities of renewable energy resources, like PV and WT, are determined first per customers requirements. The sizing of gensets and BESS will be processed then. The purpose of this chapter is to solve the problem of gensets and BESS sizing for reliable community microgrids and resilient distribution systems. As described in the previous section, a larger reserve margin could lead to a more reliable system. However, more reserve margin will also result in lower efficiency and higher cost, since reserve margin indicates the difference between available power supply and peak load demand. In other words, when the total generation capacity is larger, the operation efficiency could be lower with more reserve margin, resulting in higher capital cost, O&M cost and 51
fuel cost. So, there is a tradeoff between cost and resilience. In addition, the loss of largest dispatchable generation unit is needed to be covered by the planning reserve margin to obey the “N-1” criterion. Therefore, the number of natural gas gensets, if we assume each has the same capacity, or the largest dispatchable generation unit will affect the final value of PRM and should be finalized together with the PRM. In this dissertation, the gensets and BESS sizing problem has two objectives (i) to ensure the required level of reliability for community microgrids, and meanwhile (ii) to minimize the annualized total cost. Based on the discussion, system reliability is the primary goal of the sizing problem. But, to carry out the capacity planning of gensets and BESS, the cost is an inevitable topic, especially when there is a tradeoff between system reliability and cost. Therefore, this dissertation sets the total cost minimization as the objective and system reliability requirement as a constraint. In order to achieve the minimized cost, the reliability of the whole system has to be satisfied first. So the sizing problem is formulated as follows. Minimize 𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 (𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝑜𝑜𝑜𝑜𝑜𝑜 )
(3.15)
𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 (𝑡𝑡) ≥ 𝑃𝑃𝑙𝑙 (𝑡𝑡)
(3.16)
subject to
where,
𝑃𝑃𝑃𝑃𝑃𝑃 =
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 ≤ 𝐿𝐿𝐿𝐿𝐿𝐿𝐸𝐸𝑡𝑡ℎ𝑟𝑟
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 ≤ 𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 52
(3.17) (3.18)
𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝐶𝐶𝑃𝑃𝑃𝑃 + 𝐶𝐶𝑊𝑊𝑊𝑊 + 𝐶𝐶𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 + 𝐶𝐶𝑁𝑁𝑁𝑁 (𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ) + 𝐶𝐶𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 )
(3.19)
𝐶𝐶 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂ℎ𝑡𝑡 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝐶𝐶
(3.21)
𝐶𝐶 𝑂𝑂&𝑀𝑀 = 𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑂𝑂&𝑀𝑀 + 𝐶𝐶 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑂𝑂&𝑀𝑀
(3.23)
𝐶𝐶 = 𝐶𝐶 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + 𝐶𝐶 𝑂𝑂&𝑀𝑀 (+𝐶𝐶 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 ) (−𝐶𝐶 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 ) 𝐶𝐶𝐶𝐶𝐶𝐶 =
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
𝐶𝐶𝑁𝑁𝑁𝑁 𝑜𝑜𝑜𝑜
= 𝐹𝐹 ∙ � �
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
𝐶𝐶𝑁𝑁𝑁𝑁
𝑁𝑁𝑁𝑁
𝑟𝑟 ∙ (1 + 𝑟𝑟)𝑦𝑦 × 100 (%/𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦) (1 + 𝑟𝑟)𝑦𝑦 − 1
∑𝑖𝑖 𝑃𝑃𝑁𝑁𝑁𝑁 [𝑖𝑖] ∙ 𝑇𝑇 � ∙ 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 ∙ 𝐿𝐿𝐿𝐿 𝜂𝜂[𝑖𝑖]
𝐶𝐶 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑃𝑃𝑃𝑃𝑃𝑃 ∙ � �� 𝑃𝑃𝑟𝑟𝑟𝑟 [𝑖𝑖] ∙ 𝑇𝑇� 𝑟𝑟𝑟𝑟
𝑖𝑖
(3.22)
($/𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦)
= 𝐹𝐹 ∙ 𝑃𝑃𝑅𝑅 ∙ 8760 ℎ/𝑦𝑦𝑦𝑦 ∙ 𝐶𝐶𝐶𝐶 ∙ 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 ∙ 𝐿𝐿𝐿𝐿 (𝑓𝑓𝑓𝑓𝑓𝑓 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑔𝑔𝑔𝑔𝑔𝑔 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔)
(3.20)
($/𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦)
($/𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦)
(3.24)
(3.25)
where, 𝐶𝐶𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 (𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ) is the total annualized cost with the cutoff frequency, 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 , 𝑃𝑃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 is the total capacity of DERs.
As indicated in (3.15) − (3.18), the problem of sizing gensets and BESS is to
minimize the total cost with the satisfaction of load demand and system reliability. In (3.16), it expresses the necessity to plan adequate power supply. The system reliability requirement is expressed in (3.17). 𝐿𝐿𝐿𝐿𝐿𝐿𝐸𝐸𝑡𝑡ℎ𝑟𝑟 is the threshold value. When LOLE is
smaller than this value, system reliability is guaranteed. Furthermore, based on the discussion in previous section, LOLE will also be affected by the PRM and the PLG. So,
the PLG should be less than PRM, as expressed in (3.18). Otherwise, the system 53
reliability cannot be satisfied, since the customer interruption is a sure event when the largest dispatchable generator is off-line. This is also well supported by Figure 3. 6 and Figure 3. 7. The total annualized cost in (3.19) includes all DERs costs. Regarding natural gas gensets and BESS, their costs are highly dependent on the cutoff frequency, 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 .
For each type of DER, the annualized cost consists of annualized capital investment, annual O&M cost, annual fuel cost and the tax credit in a year, as presented in (3.20). Brackets indicate that fuel cost only applies to fossil fuel based generation units and only renewable energy generation has tax credit as payback. Each DER’s annualized capital cost is calculated using (3.21). The calculation of CRF is expressed in (3.22). DER’s lifetime and discount rate are counted into the calculation of CRF and annualized capital cost. The discount rate refers to the interest rate used in DCF analysis to set the present value of future cash flows. Besides annualized capital cost, the O&M cost is calculated in (3.23), including fixed part and variable portion. The fixed O&M cost depends on the power rating of each DER, while the variable one is determined by the real operation and related to the energy output energy. The fuel cost of natural gas gensets is calculated by (3.24). It is assumed that all natural gas gensets share the load evenly; and therefore, their operational efficiencies are the same. However, this can be changed for specific applications when necessary. For renewable electricity production, the tax credit payback is expressed in (3.25). This problem illustrates a way to size gensets and BESS with the satisfaction of system reliability and achievement of the minimum annualized cost. In the next section, the proposed algorithm for solving this problem will be elaborated.
54
3.6
Optimization Algorithm Based on the formulated problem in the last section, gensets are sized together
with BESS to share the net load and provide adequate reserve margin. The net load can be divided into two parts: a) component with large power that varies smoothly over a longer duration, and b) small but frequently fluctuating power component. Gensets could take the smooth (i.e., flat) power variation and the BESS can compensate the small and frequent changes. 𝑃𝑃𝑛𝑛𝑛𝑛 (𝑡𝑡) = Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 (𝑡𝑡) + 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑡𝑡)
(3.26)
Methods of DTFT and PSO are employed to find the optimal allocation between gensets and BESS to minimize annualized cost with the satisfaction of the system reliability requirement. As described in Section 3.4 and Section 3.5, loss of one generation should also be covered with planning reserve margin to obey “N-1” criterion. So the largest generation unit should be taken into consideration for the worst condition. This section studies two cases. It first presents the sizing scheme for a case with the assumption that natural gas gensets have the same power capacity and then shows the other case with the consideration of the largest dispatchable generator. In the second case, the assumption is that the number of natural gas gensets is pre-determined. The procedures for these two cases are explained as follows and also illustrated in Figure 3. 8 and Figure 3. 9. With the input of power capacities of PV and WT, the net load profile can be achieved based on stochastic models in (3.5) − (3.12). The method of DTFT is applied to obtain the spectrum of the net load. The frequency range of the spectrum is determined 55
by the sampling rate of the net load profile. Then a randomly initialized cut-off frequency divides the net load into two parts. The low-frequency part of the net load is assigned to gensets, while BESS takes care of the high-frequency power components. This is able to help lower the capital cost, since the BESS, in terms of power and energy, will not be oversized. Once the power share for gensets is achieved, based on the initial cut-off frequency, the inverse DTFT is employed to get the power share for gensets in time domain. However, the process of inverse DTFT may produce negative values. But the gensets cannot absorb power. So it is necessary to shift the negative portion to the BESS. Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑘𝑘] = �
Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑘𝑘], Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑘𝑘] ≥ 0 Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑘𝑘] < 0 0,
(3.27)
After making such an adjustment, the BESS power share can be determined by subtracting the power allocation of gensets from the net load. The next step is to size gensets and BESS. As shown in (3.28), the power capacity of gensets needs to meet the maximum power output and also include a reserve margin to withstand forecast errors and unexpected events. BESS is supposed to have the same efficiency in both charging and discharging. So the BESS power capacity is calculated in (3.29) and (3.30). It is discharging when 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] ≥ 0 , and charging when 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] < 0 . Furthermore, the
BESS capacity in energy is determined in (3.31) and (3.32). The change in stored energy from the original status to kth sample point is given by (3.31). Equation (3.32) presents the sizing for BESS energy capacity, where 𝑆𝑆𝑆𝑆𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑆𝑆𝑆𝑆𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 are predetermined maximum and minimum values of state of charge (SOC).
𝑛𝑛𝑛𝑛𝑛𝑛 Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 = 𝑚𝑚𝑚𝑚𝑚𝑚�Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑘𝑘]� /(1 − 𝑅𝑅𝑅𝑅)
56
(3.28)
𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] = �
𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝑆𝑆 [𝑘𝑘]/𝜂𝜂𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] ≥ 0 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] ∙ 𝜂𝜂𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] < 0
𝑛𝑛𝑛𝑛𝑛𝑛 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = 𝑚𝑚𝑚𝑚𝑚𝑚{|𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘]|} 𝑘𝑘
𝐸𝐸[𝑘𝑘] = �(𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑖𝑖] ∙ 𝑇𝑇) , 𝑖𝑖=0
𝑛𝑛𝑛𝑛𝑛𝑛 𝐸𝐸𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 =
𝑘𝑘 = 0, … , 𝑁𝑁𝑆𝑆
𝑚𝑚𝑚𝑚𝑚𝑚{𝐸𝐸[𝑘𝑘]} − 𝑚𝑚𝑚𝑚𝑚𝑚{𝐸𝐸[𝑘𝑘]} 𝑆𝑆𝑆𝑆𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑆𝑆𝑆𝑆𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚
(3.29) (3.30)
(3.31)
(3.32)
𝑛𝑛𝑛𝑛𝑛𝑛 where, Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 is the nominal power of gensets, Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑘𝑘] is the total power output of
gensets at sample point k, RM is the portion of reserve margin, 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 [𝑘𝑘] is the power 𝑛𝑛𝑛𝑛𝑛𝑛 output from BESS at sample point k, 𝜂𝜂𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 is the efficiency of BESS, 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 is the
nominal power of BESS, 𝐸𝐸[𝑘𝑘] is the energy difference of BESS from the beginning to
𝑛𝑛𝑛𝑛𝑛𝑛 is the nominal energy capacity of BESS. sample point k, and 𝐸𝐸𝐵𝐵𝐵𝐵𝑆𝑆𝑆𝑆
After the preliminary sizing, the power capacities of gensets and BESS are
achieved. Power share for natural gas gensets equals the subtraction between total power capacity in gensets and biomass genset power capacity. However, since the cut-off frequency was initialized randomly, this may not guarantee the optimal power capacity planning. Therefore, the PSO is used to determine the cut-off frequency to achieve the minimum annualized cost based on equations (3.19) − (3.25). This is because particle swarm optimization is a population based stochastic optimization technique developed by Dr. Eberhart and Dr. Kennedy in 1995 [133]. The system is initialized with a population of random solutions and searches for optima by updating iterations. The potential solutions, called particles, search through the problem space by following the current optimum particles. The search process will end at the global optimum solution. 57
In addition, the largest dispatchable generation unit has an impact on system reliability and reserve margin determination. Therefore, before the PSO, the power capacity of largest natural gas genset has to be determined. In Figure 3. 8, the assumption is that all natural gas gensets have the same capacity. The number of natural gas gensets is initialized as one. In each iteration, the number is increased by one until the natural gas genset is smaller than the biomass one. Besides, PSO is implemented in every round to achieve the optimal solution. After all iterations, the optimal solution will be found. So the number of natural gas gensets is the key variable in this case.
58
Input power capacities of PV, WT Calculate net load profile based on stochastic models Determine net load spectrum with DTFT
Initialize a cut-off frequency to separate the low frequency band for gensets
Inverse DTFT to determine the assigned power for gensets and BESS; Size gensets and BESS to achieve Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝐸𝐸𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 Initialize the number of natural gas gensets: 𝑁𝑁𝑁𝑁𝑁𝑁 = 1 Use PSO to find the optimal cut-off frequency to minimize annualized cost with satisfaction of LOLE
Less than the cost in previous iteration?
No
Yes Size gensets and BESS and update Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 , Ʃ𝑃𝑃𝑁𝑁𝑁𝑁 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝐸𝐸𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 Ʃ𝑃𝑃𝑁𝑁𝑁𝑁 ≤ 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 ? 𝑁𝑁𝑁𝑁𝑁𝑁 Yes
Output co-optimization capacity design results Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 , Ʃ𝑃𝑃𝑁𝑁𝑁𝑁 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝐸𝐸𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵
No
𝑁𝑁𝑁𝑁𝑁𝑁 = 𝑁𝑁𝑁𝑁𝑁𝑁 + 1
Figure 3. 8 Flowchart of gensets and BESS sizing with assumption of identical gensets 59
Except for this case, a solution to a general case is elaborated in Figure 3. 9. Different from Figure 3. 8, it only cares about the PLG. So the number of natural gas gensets is no more a key variable. Instead, the power capacity of the largest natural gas genset is the main variable. Before the PSO, the power capacity of largest natural gas genset has to be determined. In Figure 3. 9, the power capacity of the largest natural gas genset is initialized as the subtraction of peak load and biomass genset capacity. In each iteration, the power capacity of the largest natural gas genset is reduced by ∆𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶 until it
is smaller than the biomass one. Besides, PSO is implemented within each iteration to
achieve the optimal solution. After going through all possible iterations, the optimal solution will be finally found out.
60
Input power capacities of PV, WT
Calculate net load profile based on stochastic models Determine net load spectrum with DTFT
Initialize a cut-off frequency to separate the low frequency band for gensets Inverse DTFT to determine the assigned power for gensets and BESS; Size gensets and BESS to achieve Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝐸𝐸𝐵𝐵𝐸𝐸𝐸𝐸𝐸𝐸 Initialize the capacity of the largest natural gas genset 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔−𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑃𝑃𝑝𝑝𝑝𝑝 − 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 Use PSO to find the optimal cut-off frequency to minimize annualized cost with satisfaction of LOLE No Less than the cost in previous iteration? Yes Size gensets and BESS and update Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 , Ʃ𝑃𝑃𝑁𝑁𝑁𝑁 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝐸𝐸𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔−𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 ? Yes
Output co-optimization capacity design results Ʃ𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 , Ʃ𝑃𝑃𝑁𝑁𝑁𝑁 , 𝑃𝑃𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 , 𝐸𝐸𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵
No
𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔−𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑃𝑃𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔−𝑚𝑚𝑚𝑚𝑚𝑚 − ∆𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶
Figure 3. 9 Flowchart of gensets and BESS sizing in general 61
3.7
Case Studies and Sensitivity Analysis In this section, the proposed strategy for sizing gensets and BESS is implemented
and analyzed for a community microgrid development in the State of Ohio, USA. 3.7.1
Community Microgrid The selected community is a part of a distribution system for a village located in
Northwest Ohio. The community microgrid system is presented in Figure 2. 4. It has a 4 MW peak critical load. The load data was collected in each fifteen minutes and were provided by the local utility, AEP Ohio. Based on the data profile, the stochastic distribution of load model could be estimated. Figure 3. 10 shows the community representative load profiles on weekdays and weekends in four seasons. As observed in Figure 3. 10, the load on a weekday is much larger than that corresponding to the weekend. Therefore, the power capacity planned for weekdays is adequate for weekends. The efficiency of BESS system is 85% and the SOC limit is set as [50%, 100%]. Besides, the discount rate is 5% and the overall system lifetime is assumed as 20 years. In this case, the community microgrid contains a 3 MW PV system, 1 MW WT, and 0.5 MW biomass genset. With help of references in [134], [135], the seasonal representative data of global horizontal irradiance (GHI) and wind speed could be selected to form stochastic models of PV and WT. Table 3. 1 shows the capital costs, O&M costs and fuel costs of different DERs [136]–[138]. Besides, according to the U.S. Internal Revenue Service, the renewable electricity PTC for PV and WT is 23 $/MWh and biomass PTC is 12 $/MWh [111]. The annualized capital cost and O&M cost of sodium-sulfur (NaS) BESS, shown in Table 3. 2, are obtained from ES-Select tool [139] and references [140], [141]. 62
(a) Representative load profile in spring
(b) Representative load profile in summer Continued Figure 3. 10 Weekday and weekend representative load profile in four seasons
63
Figure 3. 10 continued
(c) Representative load profile in autumn
(d) Representative load profile in winter
64
Table 3. 1 Cost parameters of DERs
Cost
Capital Cost
O&M Cost ($/MW-year)
Fuel Cost ($/MWh)
PTC ($/MWh)
224,700
19,000
0
23
1,710,000
137,200
29,000
0
23
1,000,000
82,045
91,000
10
0
1,000,000
82,045
91,000
0
12
Total ($/MW)
Annualized ($/MW-year)
PV Panel
2,800,000
Wind Turbine Natural Gas Genset Biomass Genset
DER
Table 3. 2 Cost parameters of BESS BESS
Annualized Capital Cost Power ($/MW-year)
Annualized Capital Cost Energy ($/MWh)
O&M Cost ($/MW-year)
NaS
280,000
24,000
3000
3.7.2
Gensets and BESS Sizing for the Community Microgrid Reliability The proposed gensets and BESS sizing scheme is implemented in MATLAB.
Based on the knowledge of historical information, stochastic models of load demand and renewable generation could be built, and the net load profile could be obtained with equations (3.5)–(3.12). DTFT is employed to achieve the net load spectrum. Figure 3. 11 displays a weekday net load profile as an example. Because of the 15-minute sampling interval, the spectrum is within the range of [0, 0.56 mHz], as shown in Figure 3. 11(b). In Figure 3. 11(c), it presents that the cut-off frequency is able to divide the spectrum into two parts. The low-frequency portion (i.e., left side) is assigned to gensets and the highfrequency portion (i.e., right side) to the BESS. Then PSO is used to find the optimal cutoff frequency associated with the minimum annualized cost within the frequency range. 65
(a) Net load profile in time domain
(b) Net load spectrum Continued Figure 3. 11 Net load profile and its spectrum for a weekday in summer
66
Figure 3. 11 continued Cut-off Frequency Net Load BESS
Gensets
(c) Net load profile spectrum with cut-off frequency
In addition, since the loss of one generation needs to be covered in PRM for the sake of system resilience, the largest dispatchable generation unit should be under consideration. This section studies two cases: (1) all natural gas gensets are identical and have the same power capacity; (2) natural gas gensets are not all the same. In addition, with penetrations of renewable energy resources, their impacts on reserve margin planning and distribution systems resilience should not be neglected. However, because of the intermittent and non-dispatchable characteristics, how to conduct the reserve margin planning with consideration of renewable energy penetration is a challenge. Therefore, within each case, six situations (a) none renewable generation is considered; (b) 20% of renewable generation is counted; (c) 50% renewable generation is included; (d) 80% of renewable generation is counted; (d) 90% of renewable generation is counted; 67
(f) all renewable generation is considered are investigated and compared for selecting a reliable and meanwhile cost-effective strategy. In the first case, all natural gas gensets have the same capacities. Table 3. 3 − Table 3. 8 present the sizing results of gensets and BESS under the six different situations mentioned above. Figure 3. 12 − Figure 3. 17 plot the tendencies of annualized cost and gensets total power capacity with the increase of the number of natural gas gensets. In each situation, the annualized cost and gensets total capacity go down first with the increase of natural gas gensets, reach the minimum point and then climb up. The reason for later climbing up is because the natural gas genset is smaller than the biomass genset. So the loss of one generation is at most 0.5 MW. However, with the increase in the number of natural gas gensets, the probability of one generation loss keeps increasing. Therefore, there is a turning point for annualized cost and gensets total capacity when the number of natural gas gensets increases. Of course, the chance of one generation loss is not always keeping increasing, but the turning point happens when the number of natural gas gensets is beyond several hundred, which is not possible for a community microgrid. Table 3. 9 and Figure 3. 18 present the comparison of the minimum annualized cost and the minimum total capacity of gensets among the six situations. It can be found that if 80% renewable is counted in the planning, the cost is the minimum. In other words, if we keep 20% renewable energy margin, the net load will be handled in a more economic way. Besides, the situation with 90% renewable energy also has a lower minimum annualized cost than the situation of considering 100% renewable energy.
68
Table 3. 3 Results of gensets and BESS sizing without consideration of renewable energy in the first case Number of Natural Gas Gensets
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
1 2 3 4 5 6 7 8 9 10 11 12
527,630 507,530 497,580 491,700 487,830 485,120 483,620 483,950 484,230 484,490 484,720
6.1393 5.5662 5.2827 5.1149 5.0047 4.9273 4.8846 4.8939 4.9021 4.9094 4.9159
BESS Capacity Power Energy (MW) (MWh) 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839 0.8507 1.1839
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 12 Tendencies of annualized cost and gensets total capacity without consideration of renewable energy in the first case
69
Table 3. 4 Results of gensets and BESS sizing with consideration of 20% renewable energy in the first case Number of Natural Gas Gensets
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
1 2 3 4 5 6 7 8 9 10 11 12
507,040 490,610 482,580 477,900 474,890 472,810 473,110 473,680 474,180 474,630 475,030
5.5587 5.0902 4.8612 4.7279 4.6420 4.5829 4.5913 4.6076 4.6219 4.6346 4.6461
BESS Capacity Power Energy (MW) (MWh) 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581 0.8507 1.1581
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 13 Tendencies of annualized cost and gensets total capacity with consideration of 20% renewable energy in the first case
70
Table 3. 5 Results of gensets and BESS sizing with consideration of 50% renewable energy in the first case Number of Natural Gas Gensets
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
1 2 3 4 5 6 7 8 9 10 11 12
482,100 470,590 465,150 462,140 460,300 460,260 461,390 462,370 463,230 463,990 464,880
4.8968 4.5687 4.4138 4.3278 4.2755 4.2742 4.3065 4.3343 4.3588 4.3806 4.4003
BESS Capacity Power Energy (MW) (MWh) 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908 0.8507 0.9908
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 14 Tendencies of annualized cost and gensets total capacity with consideration of 50% renewable energy in the first case
71
Table 3. 6 Results of gensets and BESS sizing with consideration of 80% renewable energy in the first case Number of Natural Gas Gensets
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
1 2 3 4 5 6 7 8 9 10 11 12
468,100 460,630 457,350 455,730 454,900 456,370 457,970 459,360 460,570 461,660 462,630
4.4608 4.2479 4.1545 4.1082 4.0846 4.1265 4.1722 4.2116 4.2463 4.2772 4.3051
BESS Capacity Power Energy (MW) (MWh) 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 15 Tendencies of annualized cost and gensets total capacity with consideration of 80% renewable energy in the first case
72
Table 3. 7 Results of gensets and BESS sizing with consideration of 90% renewable energy in the first case Number of Natural Gas Gensets
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
1 2 3 4 5 6 7 8 9 10 11 12
471,440 465,010 462,330 461,130 460,620 461,610 463,490 465,120 466,550 467,830 468,980
4.5562 4.3728 4.2964 4.2621 4.2477 4.2758 4.3296 4.3760 4.4168 4.4532 4.4859
BESS Capacity Power Energy (MW) (MWh) 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410 0.8693 1.0410
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 16 Tendencies of annualized cost and gensets total capacity with consideration of 90% renewable energy in the first case
73
Table 3. 8 Results of gensets and BESS sizing with consideration of 100% renewable energy in the first case Number of Natural Gas Gensets
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
1 2 3 4 5 6 7 8 9 10 11 12
479,470 474,220 472,230 471,530 471,420 471,600 473,810 475,770 477,490 479,020 480,400
4.7356 4.5857 4.5291 4.5090 4.5058 4.5112 4.5742 4.6300 4.6789 4.7226 4.7618
BESS Capacity Power Energy (MW) (MWh) 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308 0.8955 1.0308
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 17 Tendencies of annualized cost and gensets total capacity with consideration of 100% renewable energy in the first case
74
Table 3. 9 Comparison of different situations in the first case
Situations
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
No Renewable 20% Renewable 50% Renewable 80% Renewable 90% Renewable 100% Renewable
483,620 472,810 460,260 454,900 460,620 471,420
4.8846 4.5829 4.2742 4.0846 4.2477 4.5058
BESS Capacity Number of Natural Gas Power Energy Gensets (MW) (MWh) 0.8507 1.1839 8 0.8507 1.1581 7 0.8507 0.9908 7 0.8693 1.0410 6 0.8693 1.0410 6 0.8955 1.0308 6
Figure 3. 18 Tendencies of minimum annualized cost and minimum gensets total capacity with counted portion of renewable energy
Different from the first case, the second case is more general. The number of natural gas gensets is not a key point anymore, but the power capacity of the largest dispatchable generation unit is the focus. Table 3. 10 − Table 3. 15 present results of gensets and BESS sizing in the six situations. Figure 3. 19 − Figure 3. 24 plot the 75
tendencies of annualized cost and gensets total capacity with the power capacity decrease of the largest natural gas genset. In each situation, the annualized cost and gensets total capacity go down first with the decrease of the largest natural gas genset capacity and then keep stable. This is because when the largest natural gas genset is larger than the 0.5 MW biomass genset, the gensets total capacity could be reduced by cutting down the power capacity of the largest natural gas genset. But when the largest natural gas genset goes below 0.5 MW, smaller than the biomass genset, the gensets total capacity will not be changed by decreasing the largest natural gas genset capacity. Therefore, the annualized cost and gensets total capacity become constant when the largest natural gas genset is smaller than the biomass genset. In addition, all six situations verify that when the largest natural gas genset has the same power capacity as biomass genset or even smaller power capacity, the annualized total cost is the minimum, so as the total capacity of gensets. But, with more gensets in smaller capacities, the needed manpower, construction area and other factors could be more. Also, the control strategy will become more complicated and the system inertia will be affected. Table 3. 16 and Figure 3. 25 present the comparison of the minimum annualized cost and the minimum total capacity of gensets among the six situations. It can be found that if 80% renewable is counted in the planning, the cost, and the gensets total capacity are the minimum. In other words, if we keep 20% renewable margin, the net load will be handled in a more economic way. Besides, the situation with 90% renewable also has lower minimum annualized cost and gensets capacity than 100% renewable situation. Therefore, both cases have the same
76
conclusion, with the consideration of 80% renewable generation, the cost is the least to achieve the reliability requirement of the community system.
Table 3. 10 Results of gensets and BESS sizing without consideration of renewable energy in the second case Largest Natural Gas Genset (MW) 4.00 2.00 1.00 0.90 0.80 0.70 0.60 0.55 0.53 0.51 0.50 0.45
BESS Capacity
Annualized Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
Power (MW)
Energy (MWh)
599,200 529,050 493,980 490,470 486,960 483,450 479,950 478,190 477,490 476,790 476,440 476,440
8.1799 6.1799 5.1799 5.0799 4.9799 4.8799 4.7799 4.7299 4.7099 4.6899 4.6799 4.6799
0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507
1.1839 1.1839 1.1839 1.1839 1.1839 1.1839 1.1839 1.1839 1.1839 1.1839 1.1839 1.1839
77
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 19 Tendencies of annualized cost and gensets total capacity without consideration of renewable energy in the second case
Table 3. 11 Results of gensets and BESS sizing with consideration of 20% renewable energy in the second case Largest Natural Gas Genset (MW) 4.00 2.00 1.00 0.90 0.80 0.70 0.60 0.55 0.53 0.51 0.50 0.45
BESS Capacity
Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
Power (MW)
Energy (MWh)
583,310 513,160 478,080 474,570 471,060 467,560 464,050 462,300 461,590 460,890 460,540 460,540
7.7330 5.7330 4.7330 4.6330 4.5330 4.4330 4.3330 4.2830 4.2630 4.2430 4.2330 4.2330
0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507
1.1581 1.1581 1.1581 1.1581 1.1581 1.1581 1.1581 1.1581 1.1581 1.1581 1.1581 1.1581
78
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 20 Tendencies of annualized cost and gensets total capacity with consideration of 20% renewable energy in the second case
Table 3. 12 Results of gensets and BESS sizing with consideration of 50% renewable energy in the second case Largest Natural Gas Genset (MW) 4.00 2.00 1.00 0.90 0.80 0.70 0.60 0.55 0.53 0.51 0.50 0.45
BESS Capacity
Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
Power (MW)
Energy (MWh)
562,610 492,460 457,380 453,870 450,370 446,860 443,350 441,600 440,900 440,190 439,840 439,840
7.1922 5.1922 4.1922 4.0922 3.9922 3.8922 3.7922 3.7422 3.7222 3.7022 3.6922 3.6922
0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507 0.8507
0.9908 0.9908 0.9908 0.9908 0.9908 0.9908 0.9908 0.9908 0.9908 0.9908 0.9908 0.9908
79
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 21 Tendencies of annualized cost and gensets total capacity with consideration of 50% renewable energy in the second case
Table 3. 13 Results of gensets and BESS sizing with consideration of 80% renewable energy in the second case Largest Natural Gas Genset (MW) 4.00 2.00 1.00 0.90 0.80 0.70 0.60 0.55 0.53 0.51 0.50 0.45
BESS Capacity
Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
Power (MW)
Energy (MWh)
550,210 480,060 444,990 441,480 437,970 434,460 430,960 429,200 428,500 427,800 427,450 427,450
6.8019 4.8019 3.8019 3.7019 3.6019 3.5019 3.4019 3.3519 3.3319 3.3119 3.3019 3.3019
0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693
1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410
80
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 22 Tendencies of annualized cost and gensets total capacity with consideration of 80% renewable energy in the second case
Table 3. 14 Results of gensets and BESS sizing with consideration of 90% renewable energy in the second case Largest Natural Gas Genset (MW) 4.00 2.00 1.00 0.90 0.80 0.70 0.60 0.55 0.53 0.51 0.50 0.45
BESS Capacity
Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
Power (MW)
Energy (MWh)
550,350 480,200 445,120 441,610 438,110 434,600 431,090 429,340 428,640 427,930 427,580 427,580
6.8058 4.8058 3.8058 3.7058 3.6058 3.5058 3.4058 3.3558 3.3358 3.3158 3.3058 3.3058
0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693 0.8693
1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410 1.0410
81
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 23 Tendencies of annualized cost and gensets total capacity with consideration of 90% renewable energy in the second case
Table 3. 15 Results of gensets and BESS sizing with consideration of 100% renewable energy in the second case Largest Natural Gas Genset (MW) 4.00 2.00 1.00 0.90 0.80 0.70 0.60 0.55 0.53 0.51 0.50 0.45
BESS Capacity
Total Cost ($/MW-year)
Gensets Power Capacity in Total (MW)
Power (MW)
Energy (MWh)
553,490 483,340 448,260 444,750 441,240 437,740 434,230 432,480 431,770 431,070 430,720 430,720
6.8457 4.8457 3.8457 3.7457 3.6457 3.5457 3.4457 3.3957 3.3757 3.3557 3.3457 3.3457
0.8955 0.8955 0.8955 0.8955 0.8955 0.8955 0.8955 0.8955 0.8955 0.8955 0.8955 0.8955
1.0308 1.0308 1.0308 1.0308 1.0308 1.0308 1.0308 1.0308 1.0308 1.0308 1.0308 1.0308
82
LOLE (day/year) 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Figure 3. 24 Tendencies of annualized cost and gensets total capacity with consideration of 100% renewable energy in the second case
Table 3. 16 Comparison of different situations in the second case
Situations
Gensets Power Capacity in Total (MW)
Power (MW)
No Renewable 20% Renewable 50% Renewable 80% Renewable 90% Renewable 100% Renewable
476,440 460,540 439,840 427,450 427,580 430,720
4.6799 4.2330 3.6922 3.3019 3.3058 3.3457
0.8507 0.8507 0.8507 0.8693 0.8693 0.8955
83
Largest Natural Gas Energy Genset (MWh) (MW) 1.1839 0.5 1.1581 0.5 0.9908 0.5 1.0410 0.5 1.0410 0.5 1.0308 0.5
BESS Capacity
Annualized Total Cost ($/MW-year)
Figure 3. 25 Tendencies of minimum annualized cost and minimum gensets total capacity with counted portion of renewable energy
3.8
Summary In this section, a sizing methodology of gensets and BESS for islanded
community microgrid is elaborated to ensure the operation reliability. The methodology is based on DTFT and PSO to find the optimal solution. Stochastic models of load and renewable energy resources are included to cover uncertainty factors. In addition, a reliability requirement, like LOLE, is embedded in the problem as a constraint. Therefore, the optimized solution guarantees the community microgrid reliability and distribution system resilience. At last but not the least, this section presents two case studies to provide guidance for the capacity planning of dispatchable units. The first one assumes that all natural gas gensets have the same power capacity, while the second case is more general and only cares about the largest natural gas genset. Results of both cases direct to the same optimal solution. 84
CHAPTER 4: MULTILAYERED PROTECTION STRATEGY FOR RESILIENT DISTRIBUTION SYSTEM 4.1
Introduction Existing distribution systems are mostly passive and radial networks with
unidirectional power flow. With the large integration of DERs and community microgrids, the power flow is becoming bi-directional. The fault current could also change largely. Also, it was shown in [72], [73] that the fault currents within distribution systems based community microgrids are much different in grid-connected and islanded modes. Thus, the existing conventional protection schemes are incapable of accurately detecting and isolating faults for DER integrated distribution systems. This chapter presents a multilayered protection scheme and validates it in a 69bus distribution system based community microgrid [142], [143]. This is because the community microgrid is formed within the distribution system by integrating DERs. It is a portion of the distribution system, having same distribution lines, same distribution feeders and same voltage levels. In addition, if we see community microgrids as controllable units, the distribution system with tie-lines can be considered as a “microgrid” with penetration of dispatchable “DERs”. Therefore, if a protection scheme works well
85
for a distribution system based community microgrid, it should be also applicable to the distribution system with minimum adjustments of relay settings. This chapter is organized as follows: Section 4.2 gives a brief description of the community microgrid within a 69-bus distribution system. Section 4.3 elaborates the proposed multilayered protection strategy and provides case studies to validate its effectiveness. At last, the summary is provided in Section 4.4.
4.2
Community Microgrid within 69-Bus Distribution System The goal of a community microgrid is to increase the energy efficiency and
distribution system resilience. Such a microgrid shall meet the prerequisites, like [25], [77], [121], [144]–[146]. But the penetration of DERs challenges the conventional protection schemes due to bi-directional power flow and level changes in fault currents through distribution feeders [69], [70], [77], [80], [82], [144], [145]. As shown in Figure 4. 1(b), a community microgrid system is integrated within the 69-bus distribution system. The typical loads in the community network include hospital, university, government, commercial area, industry, and a wastewater treatment plant. Furthermore, a NaS battery station is installed within the microgrid for the islanding support and peak shaving features. DERs are placed closer to the critical loads (cf., Figure 4. 1(a)). This means that whenever a fault occurs externally, the microgrid will isolate itself for uninterruptedly supporting critical loads with local DERs. For this purpose, an extra line, shown in blue, is added (cf., Figure 4. 1(b)) to ensure reliable power supply to the critical loads by forming a meshed loop network. 86
(a) Schematic diagram of the community microgrid Continued Figure 4. 1 Schematic diagram of (a) the community microgrid (b) the 69-bus distribution system with integration of the community microgrid. Note: An extra line (shown in blue) was added to the benchmark 69-bus distribution system to form a mesh network. 87
Figure 4. 1 continued
(b) Schematic diagram of the 69-bus distribution system with integration of the community microgrid. Note: An extra line (shown in blue) was added to the benchmark 69-bus distribution system to form a mesh network.
88
4.3
Multilayered Protection Strategy One of the major barriers to the development of distribution systems based
community microgrids is the coordination of protective relays in the existing distribution systems. The conventional protection strategies were originally designed for radial and passive distribution systems. Hence, the fault currents just flow one way downstream. However, with the penetration of DERs and development of community microgrids, the power flow is no longer unidirectional, and the fault current level is different. Moreover, the proposed meshed architecture for a community microgrid in the distribution system also affects the fault currents in terms of both magnitude and direction [17], [147], [148]. Therefore, the protective relays for distribution lines need to be redesigned for bidirectional power flow and sensitive to different levels of fault currents. For this reason, this paper proposes a multilayered microgrid protection strategy, which consists of the adaptive overcurrent protection, the differential protection, and backup protection. The communication system employs a combination of centralized and distributed approach. The multilayered protection, as the name implies, includes protection at both the grid layer and distribution layer. Moreover, it is carried out for various levels including PCC level, loop-feeder level, loop level, load-line level and load level. The proposed scheme also allows load shedding under severe conditions like the isolation during grid outages. Furthermore, the fault currents of gensets can be detected easily as compared with power electronics inverter based DERs. This is because an inverter based DER’s fault current is typically 1.2 to 2 times of its rated current, whereas the synchronous generator based 89
DER, like genset, can contribute at most 3 to 5 times the rated current under fault conditions [80]. Thus, with the integration of inverter based DERs, the fault detection is more challenging because of the limited fault current. 4.3.1
Grid Layer Protection In the grid-connected mode, the microgrid could be seen as a controllable “DER”,
acting as a load when extracts power from the grid or working as a generator when there is additional power. However, as the community microgrids integrated distribution systems could be affected by events happening on the grid side, the existing grid protection scheme is still needed. Furthermore, the distribution utility could establish contracts with consumers like industries, to guarantee uninterruptible power supply under worst conditions including generation/network outage. 4.3.2
Distribution and Microgrid Layer Protection To ensure the distribution system resilience, the proposed protection strategy in
distribution and microgrid layer is illustrated in Figure 4. 1 (a). Table 4. 1 presents the protection principle for each level. Previous works have often used either a centralized or a decentralized approach. However, the claims of which one is better are contentious. For example, a centralized approach is able to offer higher accuracy but with longer time delays for computation and communication, whereas a decentralized one uses only local information to give a faster response. Hence, a combination of the two, named as hybrid protection strategy, is used in this dissertation to integrate the advantages of both approaches. Table 4. 2 employs QFD to display a qualitative evaluation of the protection schemes. 90
Table 4. 1 Protection levels for distribution and microgrid layer Protection Level PCC Protection
Protection Strategy in both Grid-Connected and Islanded Modes In grid-connected mode: a. anti-islanding; b. intentional islanding; c. over-current protection for the bus faults; d. backup protection for the entire microgrid; In islanded mode: resynchronization and reconnection;
Loop-feeder Protection
a. Over-current protection with adaptive relay setting for the bus faults; b. Back-up protection for loop, load-line and load protection;
Loop Protection
a. Differential protection for faults within in the loop; b. Over-current protection as a back-up for differential protection and load-line protection;
Load-line Recloser
a. Over-current protection with adaptive relay setting for load-line faults; b. Back-up protection for load protection; c. Auto-reclosing;
Load and DER Over-current protection with adaptive relay setting only for load Protection faults. Bypass-line Protection
Backup power supply for the load when load-line is disconnected.
Table 4. 2 Qualitative evaluation of various approaches for protection Protection
Importance (1-5)
Centralized Protection
Accuracy
5
9
3
9
Reliability
5
9
3
9
Ease of Adoption
3
1
9
3
Response
4
3
9
9
Cost
2
-3
-1
-3
99
91
129
Requirement
Absolute Weight
91
Decentralized Hybrid Protection Protection
4.3.2.1 Adaptive Over Current Protection The adaptive over-current protection is employed for defending buses, load-lines, customers and DERs (cf., Figure 4. 1(a) and Table 4. 1). The pickup current calculation is presented below [80]. 𝐼𝐼𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑝𝑝 ∙ �(𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 ∙ 𝑂𝑂𝑂𝑂) + � 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 �
(4.1)
𝑚𝑚
where 𝐼𝐼𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 is the protective relay’s pickup current, 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 is the fault current from the
grid side, 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 is the fault current contributed by the mth DER, OM indicates the
operation mode whether the microgrid is grid-connected (1) or islanded mode (0) of operation, and p is a constant less than 1 to ensure the safety margin between pickup current and fault current. The calculations of 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 and 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 are different from [80], viz., 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 =
𝑉𝑉𝑇𝑇ℎ 𝑚𝑚𝑚𝑚𝑚𝑚 𝑍𝑍𝑇𝑇ℎ +
𝑍𝑍𝑓𝑓
(4.2)
𝑚𝑚𝑚𝑚𝑚𝑚 indicates the highest Thevenin impedance among values between the grid where 𝑍𝑍𝑇𝑇ℎ
and any point within the microgrid, 𝑉𝑉𝑇𝑇ℎ is the rms value of phase voltage at PCC, and 𝑍𝑍𝑓𝑓
is the fault impedance that is assumed to be a constant value based on empirical studies. Accordingly, 𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 is assumed to be a constant value, thus decreasing the
𝑚𝑚𝑚𝑚𝑚𝑚 computational complexity. The reason for using 𝑍𝑍𝑡𝑡ℎ in the above equation is to obtain
the relay pickup current as low as possible to achieve higher security without risking its dependability.
92
𝐼𝐼𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ∙
𝑉𝑉𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑍𝑍𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝑍𝑍𝑓𝑓
(4.3)
where Status indicates whether the mth DER is online (1) or not (0), 𝑉𝑉𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 denotes the output phase voltage of the mth DER in rms value, and 𝑍𝑍𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 indicates the impedance of
distribution line.
To realize the above algorithm, a central controller is needed to monitor the community microgrid topology and updates the status of each DER. Then the protective relays receive signals to adjust their settings. In Figure 4. 2, a single-line-to-ground (SLG) fault happened on bus 1, in Figure 4. 1(a), at 12 seconds and it was isolated by PCC, relay-C and relay-J in about 50 ms. Figure 4. 2 also indicates that the fault current is mainly contributed by the grid side, and only a small proportion is from DERs.
1
Χ
10
4
Fault occurred
IBus Fault (A)
0.5
0
Fault is cleared by relay-PCC, relay-C and relay-J
-0.5 11.9
12
12.1
12.2
12.3
12.4
12.5
Time (s)
(a) Fault current in grid-connected mode Continued Figure 4. 2 Fault current during a bus fault in grid-connected mode
93
Figure 4. 2 continued 1000 500
Irelay−C (A)
Relay-C reclosed
0
-500 -1000 11.9
12
12.1
12.2
12.3
12.4
12.5
Time (s)
(b) Fault current through relay-C in grid-connected mode
1000 Relay-J reclosed
Irelay−J (A)
500 0
-500 -1000 11.9
12
12.1
12.2
12.3
12.4
12.5
Time (s)
(c) Fault current through relay-J in grid-connected mode Continued
94
Figure 4. 2 continued 1
Χ
10
4
Relay-PCC reclosed
Irelay−PCC (A)
0.5 0
-0.5
-1 11.9
12
12.1
12.2
12.3
12.4
12.5
Time (s)
(d) Fault current through relay-PCC in grid-connected mode
4.3.2.2 Differential Protection Differential protection is another part of the proposed multilayered protection strategy. It is applied to protect loop-lines within the community microgrid and distribution lines of the distribution system by local communication between protective relays. This protection scheme is based on the theory of Kirchhoff's Current Law (KCL), which states that the summation of currents entering a node is always equal to the total currents exit the node. In normal operations, a loop-line could be seen as a node, so the current flowing into the line is equal to the current flowing out of the line. But, when a fault occurs within a loop-line, this inference becomes false. Therefore, it can help accurately detect a fault and immediately send a tripping signal without a significant time delay. A key prerequisite to guarantee the accuracy of the differential protection is synchronous measurement and comparison of signals. Since the distribution lines are not 95
as long as transmission lines in the power grid, the issue of asynchronous current measurement is less severe. Furthermore, the GPS synchronized clock could be employed to ensure synchronous measurement if the distribution line is extended to a long distance or the measurement accuracy is asked to be improved further. Figure 4. 3 and Figure 4. 4 illustrate results of a temporary SLG loop fault in grid-connected mode and islanded mode. The fault occurred at 10 seconds on the loop-line between relay-3 and relay-4 and lasted for 200 ms. It needs 40 ms for the communication between relays, and 20 ms for corresponding circuit breakers to trip the fault. Reclosers are adopted due to frequent SLG faults in medium voltage circuits. The dead time after first open is selected to be 300 ms, and this should be kept above the minimum permissible value for being consistent with deionization of fault arc. It is obvious from the figures that the fault current under the grid-connected condition is much larger than that in islanded operation. This is because of DER’s limited output power and there is no grid contribution in islanded mode. Besides, it should be noted that the differential protection scheme is also adequate to detect high impedance faults. This is because its performance does not get impacted by the magnitude of fault current [122].
96
2000
Irelay−3 (A)
Relay-3 reclosed
0
-2000 9.8
9.9
10
10.1 Time (s)
10.2
10.3
10.4
(a) Fault current through relay-3 in grid-connected mode
Χ
10
4
2
Irelay−4 (A)
Relay-4 reclosed 0
-2
-4 9.8
9.9
10
10.1
10.2 Time (s)
10.3
10.4
(b) Fault current through relay-4 in grid-connected mode Figure 4. 3 Fault current during a loop fault in grid-connected mode
97
10.5
500
Irelay−3 (A)
Relay-3 reclosed 0
-500 9.8
9.9
10
10.1 10.2 Time (s)
10.3
10.4
10.5
(a) Fault current through relay-3 in islanded mode
200
Irelay−4 (A)
Relay-4 reclosed 0
-200
9.8
9.9
10
10.1
10.2
10.3
10.4
10.5
Time (s)
(b) Fault current through relay-4 in islanded mode Figure 4. 4 Fault current during a loop fault in islanded mode
4.3.2.3 Backup Protection To provide enough reliability and resilience, backup protection of the community microgrid is definitely necessary. A procedure to ask for backup protection is suggested 98
in [82]. However, it requires an independent arrangement with an alternative mechanism. Hence, this dissertation exploits the adaptive overcurrent scheme to serve as the backup protection. For the protection of loop-lines and distribution lines, adaptive directional overcurrent protection is implemented as the backup. This is apart from the differential protection scheme, which is the primary protection. Therefore, if a fault happens and is not cleared within a specified time by the primary protection device, the backup protective relay will send a trip signal to the corresponding circuit breaker to isolate the fault. Two important issues need to be addressed in this process (i) adaptive directional over-current protection should not respond faster than the current differential protection, which means there should be a time delay set for the backup relay and keep them waiting for a while before the response, (ii) the circuit breaker located closest to the faulted section should be tripped earlier than others. To satisfy both requirements, the loop relay provides backup protection for the neighboring zone. For example, as shown in Figure 4. 1(a), relay-3 and relay-8 provide backup protection for the loop zone between relay-5 and relay-6. So the relay-3’s respond time should be longer than relay-5’s when a fault occurs between relay-5 and relay-6. Similarly, the trip time of relay-8 should not be shorter than that of relay-6 when a fault occurs between relay-5 and relay-6. 𝑇𝑇𝑇𝑇𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 + 𝑇𝑇𝑇𝑇𝐶𝐶𝐶𝐶 + 𝑇𝑇𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
(4.4)
where 𝑇𝑇𝑇𝑇𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 is the time delay for the backup protection, 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 is the time delay
from the communication system, 𝑇𝑇𝑇𝑇𝐶𝐶𝐶𝐶 is the time delay of circuit breaker operation, and 𝑇𝑇𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 is the marginal time delay to ensure the coordination time interval (CTI) 99
between primary protection and backup protection. In this particular case, communication delay is 40 ms, operation time of circuit breaker is 20 ms, and CTI is set to be 30 ms. Hence, the total tripping time delay of backup protection is 90 ms, besides the tripping time of the backup relay. Another concern is about the CTI of relays used for backup protection. When primary protection fails, the relay located nearest to the fault should respond first. For example, when a fault occurs between relay-3 and relay-4, relay-6 is required to act faster than relay-8. Therefore, tripping time delay for relay 8 should be 𝑇𝑇𝑇𝑇𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝑇𝑇𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 when a fault occurs between relay-3 and relay-4.
For load-line protection, the logic of backup protection is similar to the loop-line backup protection. When a fault happens on a load-line, the two loop relays in its proximity shall trip if the primary load-line protection fails. For example, as shown in Figure 4. 1(a), relay-7, relay-10 shall trip if relay e1 did not work when a fault occurred on load-line e. Using (4.4), the time delay of backup protection in this case is calculated as 100 ms. Coordination can be ensured by different time delay level as well. For load protection, the corresponding load-line protection acts as the backup protection; for example, in Figure 4. 1(a), relay e1 gives backup protection for the residential load. But, it should have proper settings for CTIs. Figure 4. 5 and Figure 4. 6 present a temporary SLG fault happened at 10 seconds on load-line e and display the failure of the relay-e1. Because of this, relay-7 and relay-10 acted as the backup for relay-e1 to isolate the fault. Similar to previous cases, the fault current in the grid-connected mode is much larger than that in the islanded operation. 100
Moreover, the genset output current is also larger in the grid-connected mode. This is because it is controlled to only support the critical loads in islanded mode as they are not rated to supply all the neighboring loads. Therefore, once the microgrid is operating in the islanded mode, non-critical loads will be shed for maintaining the reliability of power delivery to the critical loads.
Χ
10
4
1
Irelay−e1 (A)
Relay-7 and relay-10 reclosed
0
-1 9.8
9.9
10
10.1 10.2 Time (s)
10.3
10.4
10.5
(a) Fault current through relay-e1 in grid-connected mode Continued Figure 4. 5 Load-line fault current with failure of relay-e1 in grid-connected mode
101
Figure 4. 5 continued 2000
Irelay−e3 (A)
1000 Relay-e3 reclosed
0
-1000 9.8
9.9
10
10.1
10.2 Time (s)
10.3
10.4
10.5
(b) Fault current through relay-e3 in grid-connected mode
1000 Fault self-healing
Irelay−e5 (A)
500 0
-500
-1000 9.8
Relay-e5 closed as bypass and relay-e4 open 9.9
10
Relay-e5 tripped and relay-e4 closed when relay-e3 reclosed 10.1
10.2 Time (s)
10.3
(c) Fault current through relay-e5 in grid-connected mode
102
10.4
10.5
1000
Irelay−e1 (A)
Relay-7 and relay-10 reclosed
0
-1000 9.8
9.9
10
10.1
10.2 Time (s)
10.3
10.4
10.5
10.4
10.5
(a) Fault current through relay-e1 in islanded mode
500
Irelay−e3 (A)
Relay-e3 reclosed
0
-500 9.8
9.9
10
10.1
10.2 Time (s)
10.3
(b) Fault current through relay-e3 in islanded mode Continued Figure 4. 6 Load-line fault current with the failure of relay-e1 in islanded mode
103
Figure 4. 6 continued
Fault self-healing
Irelay−e5 (A)
500
0
-500
9.8
Relay-e5 closed as bypass
9.9
10
Relay-e5 tripped when Relay-e3 reclosed 10.1 10.2 Time (s)
10.3
10.4
10.5
(c) Fault current through relay-e5
The settings of adaptive overcurrent protection relays need to be adjusted depending on the system operation. This information is processed in Central Processing Unit (CPU) and transmitted to each adaptive overcurrent relay as displayed in Figure 4. 7 (a). The protection scheme implemented in loop relays is presented in Figure 4. 7 (b). As discussed earlier, the current differential relay (87) provides the primary protection. The adaptive overcurrent relay (51) and directional relay (67) are able to backup for the differential protection. Figure 4. 7 (c) shows that for relays in PCC, loop feeder, load-line, and bypass-line, adaptive overcurrent protection scheme is employed for both primary and backup protection. A directional relay (67) is used with the overcurrent relay (51) to guarantee that only forward fault current from bus to transmission line can trip the circuit breaker. Table 4. 3 presents a comparison between the proposed multilayered protection strategy and existing schemes for community microgrids.
104
Update settings signal (CPU) Communication link Settings in relay (51) (a) Communication between CPU and adaptive overcurrent relay
Ix’ (from the other end)
87
Ix (from one end)
51
Trip circuit breaker
67 Vx (b) Loop Relay (x = a, b, c)
Ix (from one end) Vx
51 Trip circuit breaker
67
(c) PCC relay, loop feeder relay, load-line relay and bypass-line relay (x = a, b, c) Figure 4. 7 Protection scheme implementation
105
Table 4. 3 Comparison between existing and proposed protection schemes for community microgrids Protection Scheme Existing Schemes
Proposed Scheme
Fault Condition
Fault on the Bus
In grid-connected mode, with the grid current contribution, the existing overcurrent protection is It employs the adaptive able to detect and trip the circuit overcurrent protection, breaker at PCC. However, containing different relay ✘ because of penetrations of ✔ settings in gridDERs, a part of the fault current connected and islanded is contributed by downstream operation modes, as DERs and will not be detected shown in (1)-(3). without the adaptive overcurrent protection scheme. In islanded mode, the fault current level is lower than that in grid-connected mode. The ✘ existing overcurrent protection setting is not adequate for fault detection and interruption.
It employs the adaptive overcurrent protection, containing different relay ✔ settings in gridconnected and islanded operation modes, as shown in (1)-(3).
In grid-connected mode, with grid contribution, the overcurrent protection could detect and trip Differential protection is the upstream circuit breaker. utilized to detect and ✘ ✔ But, downstream DERs are also isolate fault feeding the fault with lower fault instantaneously. Fault on currents, which are hardly Transmission detected. Line In islanded mode, the fault Differential protection is current level is lower than that in utilized to detect and ✘ grid-connected mode, and it is ✔ isolate fault hardly detected by the existing instantaneously. overcurrent relay. Continued 106
Table 4. 3 continued
Fault on Load-line
It employs the adaptive In grid-connected mode, with the overcurrent protection, grid contribution, the existing containing different relay ✔ ✔ overcurrent protection could settings in griddetect and isolate the fault. connected and islanded operation modes. In islanded mode, the fault current level is lower than that in ✘ grid-connected mode. The existing overcurrent protection setting is inadequate.
It employs the adaptive overcurrent protection, containing different relay ✔ settings in gridconnected and islanded operation modes.
Fault Close to DERs
✘ No protection device for DERs
✔
High Impedance Fault
✘
Back-up Protection
Not capable of detecting fault ✘ currents from the downstream DERs
No specialized protection scheme
Unintentional ✘ No anti-islanding device Islanding
Over-current protection and DER self-protection
✔ Differential protection
✔
Neighboring relays can be backup for each other
An anti-islanding ✔ protective device (PD) at PCC
Note: ✔ denotes that the system is well protected; whereas ✘ means no satisfactory protective action takes place and therefore results in a system collapse.
4.4
Summary This section proposed a multilayered protection strategy for resilient distribution
systems and community microgrids with case studies in various fault scenarios. Furthermore, a comparison between the proposed protection strategy and existing schemes was also illustrated.
107
CHAPTER 5: MODIFIED VITERBI ALGORITHM BASED RESTORATION FOR RESILIENT DISTRIBUTION SYSTEM 5.1
Introduction Power system blackouts are rare but extreme events. Natural disasters and
overloading caused cascading failures are the two main causes of large blackouts in the United States. Climate change results in an increase of extreme weather events. In recent years, severe weather events are becoming more common and damaging grid systems more severely. In addition, as another main cause of power outages, power system overloading could trigger large blackout following cascading failures as witnessed in the 2003 northeast blackout [27]. Hence, it is necessary to incorporate resilience into the power systems [28]–[30]. In radial distribution systems, when a power outage happens, the downstream loads get interrupted after fault isolation. For estimating the cost of blackouts, the Lawrence Berkeley National Laboratory has many related reports, like [149]–[151], and a free web-based tool, the Interruption Cost Estimation (ICE) Calculator [152]. The main target for having a resilient distribution system is fast recovery after an extreme event. Therefore, an efficient restoration scheme is necessary for quickly restoring power to the un-faulted but unserved portions [153].
108
This chapter presents an innovative modified Viterbi algorithm to identify the optimal restoration plan for improving the resilience of the distribution system. Besides, an improved flexible switching pair operation is proposed to keep the radial topology of distribution systems. Various case studies are presented to verify the effectiveness of the proposed modified Viterbi algorithm for both single-fault and multi-fault conditions. The performance of the restoration scheme in the presence of distributed energy resources (DERs) and community microgrids is also investigated. The rest of this chapter is organized as follows. Section 5.2 displays a bi-level distribution system restoration optimization problem and the improved flexible switching pair operation. Section 5.3 elaborates the proposed modified Viterbi algorithm. Several case studies on 33-bus and 69-bus distribution systems are presented in Section 5.4, including the performance investigation of the integration of DERs and community microgrids. Finally, the conclusion is given in Section 5.5.
5.2
Problem Formulation
5.2.1
Bi-level Optimization Problem The distribution system restoration scheme has two objectives (i) to achieve
maximum load restoration, and (ii) to realize objective (i) in the shortest time. The primary objective is to maximize system restoration. In order to carry out the restoration plan, switching operations have to be undertaken either from the remote control room or by dispatching field crews. If the number of switching operations could be minimized meaning the time needed for system restoration is minimized for achieving maximal 109
load restoration, the restoration plan is an optimal solution. Therefore, the strategy for post-event distribution system restoration is formulated as an optimization problem with two hierarchical objectives and the primary objective must be always satisfied first and the secondary objective has the next preference. Primary Objective
Secondary Objective
subject to 𝑝𝑝
𝑝𝑝
𝑝𝑝
𝑝𝑝
𝑝𝑝
Maximize ∑𝑖𝑖∈𝐼𝐼𝐼𝐼 𝑆𝑆𝑖𝑖
(5.1)
Minimize 𝑁𝑁𝑆𝑆𝑆𝑆
(5.2)
𝑝𝑝
𝑝𝑝
𝑆𝑆𝑖𝑖 = 𝑃𝑃𝑖𝑖 + 𝑗𝑗𝑄𝑄𝑖𝑖 , 𝑖𝑖 ∈ 𝐵𝐵, 𝑝𝑝 ∈ 𝑋𝑋
(5.3)
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
𝑝𝑝𝑚𝑚
(5.4)
𝑄𝑄𝑖𝑖 = |𝑉𝑉𝑖𝑖 | � ��𝑉𝑉𝑗𝑗𝑚𝑚 � ∙ �𝐺𝐺𝑖𝑖𝑖𝑖 𝑠𝑠𝑠𝑠𝑠𝑠𝜃𝜃𝑖𝑖𝑖𝑖 − 𝐵𝐵𝑖𝑖𝑖𝑖 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃𝑖𝑖𝑖𝑖 �
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
𝑝𝑝𝑝𝑝
(5.5)
�𝐼𝐼𝑖𝑖𝑖𝑖 � ≤ �𝐼𝐼𝑖𝑖𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 �, 𝑖𝑖, 𝑗𝑗 ∈ 𝐵𝐵, 𝑝𝑝 ∈ 𝑋𝑋
(5.6)
𝑃𝑃𝑖𝑖 = |𝑉𝑉𝑖𝑖 | � ��𝑉𝑉𝑗𝑗𝑚𝑚 � ∙ �𝐺𝐺𝑖𝑖𝑖𝑖 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃𝑖𝑖𝑖𝑖 + 𝐵𝐵𝑖𝑖𝑖𝑖 𝑠𝑠𝑠𝑠𝑠𝑠𝜃𝜃𝑖𝑖𝑖𝑖 � 𝑗𝑗∈𝐵𝐵 𝑚𝑚
𝑗𝑗∈𝐵𝐵 𝑚𝑚 𝑝𝑝
𝑝𝑝
�𝑉𝑉𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 � ≤ �𝑉𝑉𝑖𝑖 � ≤ |𝑉𝑉𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 |, 𝑖𝑖 ∈ 𝐵𝐵, 𝑝𝑝 ∈ 𝑋𝑋
(5.7)
Maintaining radial network structure
(5.9)
𝑝𝑝
𝜃𝜃𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝜃𝜃𝑖𝑖 ≤ 𝜃𝜃𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑖𝑖 ∈ 𝐵𝐵, 𝑝𝑝 ∈ 𝑋𝑋
where
B
A set of buses in the distribution system
X
A set of phases {a, b, c}
IB
A set of isolated buses in the distribution system
110
(5.8)
𝑁𝑁𝑆𝑆𝑆𝑆
Number of switching pair operations
𝑃𝑃𝑖𝑖
Total real power (MW) of the load at bus i
𝑉𝑉𝑖𝑖
Phase voltage at bus i
𝜃𝜃𝑖𝑖
Phase voltage angle at bus i
𝑆𝑆𝑖𝑖
Total apparent power (MVA) of the load at bus i
𝑄𝑄𝑖𝑖
Total reactive power (MVAr) of the load at bus i
𝐼𝐼𝑖𝑖𝑖𝑖
Phase current between buses i and j
𝐺𝐺𝑖𝑖𝑖𝑖
Real component of the 3 × 3 admittance matrix of branch between bus i and bus j Reactive component of the 3 × 3 admittance matrix of branch between bus i and bus j Variable of bus number
𝐵𝐵𝑖𝑖𝑖𝑖
i, j
p, m
Phase variable As indicated in (5.1), the primary objective is to ensure the maximum system
restoration. The secondary objective expressed in (5.2) minimizes the switching operations during the process of system restoration. But, the secondary objective can only be met after satisfying the primary one. The power flow constraints in (5.3) − (5.5) express that the power supply of phase p at bus i should be equal to the corresponding load demand of phase p at bus i. The current and voltage limits are displayed in (5.6) and (5.7). Inequality constraint (5.8) presents the limit of voltage angle. The last constraint in (5.9) requires keeping the radial structure of the distribution system to make sure the existing protection schemes are still suitable. This requires a pair of switching operation, which consists of closing a tie-line switch and opening a switch in regular distribution lines. More details on avoiding mesh networks are presented in the next subsection. 111
Since maximum load restoration is the main target of the distribution system restoration plan, the primary objective in (5.1) can be embedded into constraints of the secondary objective in (5.2). The reason is the constraint must be satisfied first before the optimization of the objective function. In this way, the maximum load restoration will be always guaranteed no matter how the restoration plan is executed. Then the only objective of the modified problem is to minimize the number of switching pair operations with the requirement of maximum load restoration being one of its constraints. Thus, the distribution system restoration plan can be reformulated as a bi-level optimization problem: Objective
subject to
Minimize 𝑁𝑁𝑆𝑆𝑆𝑆 Maximize ∑𝑖𝑖∈𝐼𝐼𝐼𝐼 𝑆𝑆𝑖𝑖 (5.3) − (5.9)
The 33-bus distribution system, shown in Figure 5. 1, is employed for further illustrating this problem. Suppose that a fault occurred on the distribution line between bus 4 and bus 5. Once the fault is detected and isolated by the protective relays, the postfault restoration starts. Figure 5. 2 shows the load restoration and bus voltage distributions within the system. The load can be fully restored with just two switching pair operations. In addition, the largest bus voltage deviation is decreased to the minimum after three switching pair operations. All possible scenarios have been explored. For each set of switching pair operations, the best one is selected as the representative. 112
The selection is depending on the level of load restoration and the minimum bus voltage within the distribution system. Switching pairs used to obtain the results in Figure 5. 2 are shown in Table 5. 1. This is a case study for the single-fault condition. In a severe situation where an extreme event or a nature disaster can cause multiple faults, a more complex restoration plan is needed.
Figure 5. 1 33-bus distribution system
113
|3.72+j2.30| MVA
(a) Load restoration with number of switching pair operations
(b) Bus voltage distributions with number of switching pair operations Figure 5. 2 System restoration with number of switching pair operations
114
Table 5. 1 Best switching pair operations for the case shown in Figure 5. 1 Number of Switching Pair Operation
Best Switching Pair
Load Restoration
Maximum Bus Voltage Deviation
0
0%
100%
1
Close 25-29
5.3%
18%
2
Close 25-29 & 12-22 Open 6-7
100%
7.1%
3
Close 21-8 & 12-22 & 25-29 Open 11-12 & 28-29
100%
6.3%
100%
6.3%
100%
6.3%
4
5
5.2.2
Close 21-8 & 12-22 & 25-29 & 18-33 Open 11-12 & 28-29 & 32-33 Close 21-8 & 12-22 & 25-29 & 18-33 & 9-15 Open 9-10 & 14-15 & 17-18 & 28-29
Improved Flexible Switching Pair Operation Regarding a radially structured distribution system, after the fault isolation, the
downstream loads will be out-of-service. So the power delivery should be restored quickly by closing a tie-line switch to ensure a high resilience. However, this switching action may have an influence on the distribution system radial topology. Thus it needs switching pair operations to maintain the radial topology. A switching pair is a group comprising one tie-line switch and one line segment switch. Since a meshed loop could be formed by closing a tie-line switch, to maintain the radial nature, it should be broken by opening a line segment within this loop. For each switching pair operation, the tie-line switch is easy to choose, but selecting which line segment to open is very difficult. In 115
previous works [101], [105], strategies with and without fixed switching pair were studied. When the switching pair is preset, it may not be sufficient for various fault conditions. Severe challenges are observed in large systems. Therefore, the fixed switching pair is not a viable option for the resilient distribution system. It was also explained in references [101], [105] that if the switching pair is flexible, the restoration plan can cover all fault conditions while maintaining the radial network structure. However, when the search space is the whole system, it takes a very long processing time to find the global optimal solution. Moreover, the complexity increases with the growth of system size. Hence, in this chapter, an improved flexible switching pair strategy is developed to limit the search space within the loop that was formed by closing the tie-line switch after fault isolation instead of the whole system. Once a tie-line switch is chosen, finding the best switching pair is equivalent to finding the most suitable line segment to break the loop. The improved flexible switching pair operation is performed under two conditions (i) if the fault isolation is within the loop, no line segment switch needs to be opened when the tie-line switch closes, (ii) otherwise, a line segment within the loop needs to open when the tie-line switch closes. For condition (i), fault isolation is indeed opening a line segment. Hence, the condition (i) can be treated as a special case of general switching pair operation in condition (ii). Figure 5. 1 can be used for further explanation. After the fault isolation between bus 4 and bus 5, if the tie-line between buses 8 and 21 closes, there is no need to open any line segment. This is because the loop formed by buses 2-8 and 19-21 is already broken by the fault isolation. However, if any bus voltage 116
is lower than the minimum bus voltage limit, �𝑉𝑉𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 �, another tie-line closure is required to raise the minimum bus voltage. Under such circumstance, another distribution line
segment may need to be opened to maintain the radial network. For example, if the tieline between buses 25 and 29 is also closed as well, another loop is created with buses 2, 3, 6-8, 19-21 and 23-29. Under this condition, a line segment between these buses should be opened.
5.3
Modified Viterbi Algorithm for Distribution System Restoration
5.3.1
Viterbi Algorithm As mentioned previously, the goal of the distribution system restoration is to
maximize load restoration with the minimum number of switching operations. To this end, the restoration problem is becoming a deterministic finite-state problem, which is equivalent to finding the shortest path to the solution. In practice, the shortest path can be easily built in sequence via forward dynamic programming. Viterbi algorithm is one of the forward dynamic programming approaches for finding the most likely sequence of hidden states, which is called the Viterbi path, based on the observed events [154]. It lays out all the states at each stage, uses a cost metric to evaluate, and determines the best sequence from the beginning stage to the final stage. Figure 5. 3 illustrates the optimality principle of Viterbi algorithm. Given the observation set 𝑂𝑂� = {𝑂𝑂0 , 𝑂𝑂1 , … , 𝑂𝑂𝑛𝑛 }, the optimal sequence of states is 𝑆𝑆̅ = {𝑆𝑆𝑂𝑂 , 𝑆𝑆1 , … , 𝑆𝑆𝑛𝑛 }, having the shortest path. If the previous 𝑛𝑛 − 1 segments of the shortest path to state 𝑆𝑆𝑛𝑛 are not the shortest path to state 𝑆𝑆𝑛𝑛−1 at the stage 117
of 𝑛𝑛 − 1, then there must exist a shorter path to state 𝑆𝑆𝑛𝑛 [155]. Therefore, looking back from each state at one stage, only the shortest path to this state is maintained.
0 S0
1
…… S1
𝑛𝑛 − 1
shortest path Sn−1
𝑛𝑛 Sn
Figure 5. 3 Optimality principle of Viterbi algorithm
5.3.2
Modified Viterbi Algorithm for Distribution System Restoration Contrary to the conventional Viterbi algorithm, a modified Viterbi algorithm is
proposed for additional benefits in distribution systems. In the modified method, the load restoration, as an observed event in the conventional algorithm, is unknown until the execution of corresponding switching pair operation. Each state represents a set of switching pair operation(s), so the number of states at each stage is determined by the 𝑘𝑘 number of switching pair operations, 𝐶𝐶𝑚𝑚 , where m is the number of tie-line switches and
k indicates the number of switching pair operations. Moreover, the number of stages is
varying, and the ultimate stage depends on the extent of load restoration. If the load is fully restored by satisfying all constraints, no more switching is needed. The corresponding state is the selected switching operation for the post-event restoration. In addition, for distributions systems restoration, the minimum bus voltage is the cost metric. 118
In the proposed modified Viterbi algorithm, each state is a binary set and each binary digit indicates the status of a specific tie-line switch status 0 stands for open and 1 means closure. The total number of binary digits equals the total number of tie-line switches. This is because, in a radial distribution system, when a fault occurs, the downstream load is disconnected from the grid after the fault isolation. However, with the tie-line switch, power supply to the unserved load can be restored. Since the tie-line switch is normally open, the starting state is a set of zeros. Thereafter, with the switching pair operations, the load restoration extent and the minimum bus voltage can be estimated by carrying out power flow analysis. The state diagram of the modified Viterbi algorithm is illustrated in Figure 5. 4. To minimize the number of switching pair operations, the program ends once the load is fully restored after meeting constraints in (5.3) − (5.9). However, the exact number of switching pair operations is not known in advance. Therefore, in Figure 5. 4, the dashed ellipses indicate potential states. The beginning stage/state is a set of zeros. At stage one, one switching pair operation is implemented and each state has only single one. At stage two, two switching pair operations are applied, having two ones in each state. Then, at the kth stage, k switching pair operations are executed. Hence, k ones are present in every state. If there exist m tie-line switches, the number of states in the first stage is designated 1 2 𝑘𝑘 as 𝐶𝐶𝑚𝑚 . Likewise, it is 𝐶𝐶𝑚𝑚 in the second stage and 𝐶𝐶𝑚𝑚 in the kth stage. For each stage, the
power flow analysis is conducted for every state to check operational constraints (5.3) − (5.9).
119
Beginning Stage Zero switching pair operation (1 state)
Stage m-1 m-1 switching pair operations 𝑚𝑚−1 (𝑐𝑐𝑚𝑚 states)
[1 0 0 ⋯ 0 0]
[0 1 0 ⋯ 0 0]
⋯⋯
[0 0 0 ⋯ 0 1]
[1 1 0 ⋯ 0 0]
[1 0 1 ⋯ 0 0]
⋯⋯
[0 0 0 ⋯ 1 1]
⋯⋯
[0 1 1 ⋯ 1 1]
[1 1 1 ⋯ 1 0]
[1 1 1 ⋯ 0 1]
Stage m m switching pair operations 𝑚𝑚 (𝑐𝑐𝑚𝑚 state)
⋯ ⋯
⋯ ⋯
⋯ ⋯
Stage Two Two switching pair operations 2 (𝑐𝑐𝑚𝑚 states)
⋯⋯
⋯ ⋯
Stage One One switching pair operation 1 (𝑐𝑐𝑚𝑚 states)
Starting State [0 0 0 ⋯ 0 0]
[1 1 1 ⋯ 1 1]
Figure 5. 4 State diagram of the modified Viterbi algorithm
120
The flowchart in Figure 5. 5 further depicts the modified Viterbi algorithm based distribution system restoration scheme. At first, the number of switching pair is initialized, k=1, and the number of tie-line switches is updated. Switching states and feasible switching pair operations are generated. Then the power flow analysis is carried out to select the representative switching pair operation for each state. If the load can be fully restored, the switching pair operation is qualified. If over one switching pair operation could give the full load restoration, the one with highest minimum bus voltage is chosen for resilience. In case multiple possibilities satisfy the above criterion, the one with lowest power loss should be chosen. Otherwise, the choice could be made randomly since the highest minimum bus voltage and power losses are the same. If the load cannot be fully restored by existing switching operations, it goes to next iteration by including one more switching pair in the operation. At the end, if the full load restoration cannot be met after the closure of all available tie-line switches, the best switching pair operation is selected to achieve the maximum load recovery. As shown in the flowchart, when many switching options are available for maximal load restoration, the one with minimum switching is preferred. If no switching pair operation is implemented, it means no viable switching pair operation satisfies (5.3) − (5.9). Under this condition, to restore the maximal load, the load with the lowest bus voltage should be cut off to relieve the system, and then the modified Viterbi algorithm is employed again to find the best switching pair operation.
121
Starting State [0 0 ⋯ 0 0] Initialize the number of switching pair, k = 1, and update the number of tie-line switches, m;
𝑘𝑘 Generate switching states 𝐶𝐶𝑚𝑚 (k ones and (m-k) zeros)
Generate feasible switching pair operations for each switching state
k=k+1
Power flow analysis for each switching pair operation and filter out those that violate constraints (5.3) − (5.9) Yes Choose the best switching pair operation for each switching state
k < m? No
(check for each switching state) No Does any switching state provide total load restoration? Yes
Choose the switching state to provide the maximum load restoration
Choose the best switching state if there is over one qualified switching state
Implement the switching operation Figure 5. 5 Flowchart of modified Viterbi algorithm based distribution system restoration 122
5.4
Restoration Performance Investigation with the Integration of Community Microgrids In this section, benchmark distribution systems, like 33-bus distribution system
and 69-bus distribution system, are used for validating the modified Viterbi algorithm. In addition, the restoration of the 69-bus distribution system is further tested with the presence of DERs and community microgrid systems. The distribution system including load profile, network topology, and line impedances are programmed into a MATLAB .m file. Also, the modified Viterbi algorithm is coded in MATLAB. Besides, the power flow analysis is conducted using MATPOWER, which is a MATLAB power system package. 5.4.1
33-Bus Distribution System Restoration Figure 5. 1 shows a single-line diagram of the 33-bus distribution system [156],
[157]. It is operating at 12.66 kV and supplying a total load of 3.72 MW and 2.30 MVAr. As shown in Figure 5. 1 by black dotted lines, five tie-lines are included to support postfault system restoration. The allowable minimum voltage at any load bus is 0.9 p.u. and the maximum voltage is 1.05 p.u. Six scenarios are presented in Table 5. 2. The first two are single-fault conditions. In scenario 1, the distribution system is restored with two switching pair operations, closing tie-line switches 25-29 and 12-22 and opening line segment switch 6-7. The minimum bus voltage is 0.9262 p.u. In scenario 2, the system can be fully restored just by closing tie-line switch 12-22. Scenario 3 has two faults happened, so it needs to close tieline switches 25-29 and 8-21. No extra line segment needed to be opened because of the two fault isolations. Similarly, in scenario 4, having three fault isolations, only three tie123
line switches are needed to close to restore the system. However, in scenarios 5 and 6, there is an isolated bus, which is formed after the isolation of two neighboring faults. So the load at the isolated bus cannot be restored. Furthermore, the number of switching pairs is less than the number of faults. This is because the two neighboring faults and the isolated bus can be considered as one combined fault. In Figure 5. 6, the bus voltage distributions in different scenarios are presented for comparison. The normal situation is presented in Figure 5. 6 (a) and Figure 5. 6 (b) displays post-restoration bus voltage distributions in the six fault scenarios. In addition, in Figure 5. 6 (b), the voltage of isolated bus 6 is zero, indicated as less than 0.9 p.u, in scenario 5. The same condition applies to bus 26 in scenario 6.
Table 5. 2 Results of restoration for 33-bus distribution system Scenario
Fault Location
Switching Pair Operation
Load Restoration
Minimum In-Service Bus Voltage
1
4-5
Close 25-29 & 12-22 Open 6-7
100%
0.9262 p.u.
2
11-12
Close 12-22
100%
0.9322 p.u.
3
4-5 & 2728
Close 25-29 & 8-21
100%
0.9110 p.u.
4
4-5 & 1112 & 27-28
Close 9-15 & 8-21& 25-29
100%
0.9191 p.u.
5
5-6 & 6-7 & 6-26
Close 25-29 & 12-22
Load at bus 6 is unserved
0.9262 p.u.
6
13-14 & 15-16 & 626 & 26-27
Close 9-15 & 18-33 & 25-29
Load at bus 26 is unserved
0.9190 p.u.
124
(a) Bus voltage distribution in normal operation
(b) Bus voltage distributions after system restoration Figure 5. 6 Bus voltage distributions in 33-bus distribution system
5.4.2
69-Bus Distribution System Restoration The 69-bus distribution system is shown in Figure 5. 7 [142], [143]. It consists of
69 buses and 73 branches along with 5 normally open tie-lines. Its voltage is 12.66 kV, 125
and the total load is 3.80 MW and 2.69 MVAr. The acceptable voltage range is 0.9 p.u. to 1.05 p.u. without the consideration of voltage regulator.
Figure 5. 7 69-bus distribution system
Table 5. 3 shows six fault scenarios and the corresponding restoration plans. In scenario 1, the unserved load can be fully restored with two switching pair operations. In this situation, the four line segments between buses 55 and 59 are equivalent, since there is no load on buses 55, 56, 57 and 58. There will be no power flow to these buses no matter which line segment is disconnected and the bus voltage will not be affected. In 126
scenarios 2, 3 and 5, the loads are also fully restored. However, in scenario 4, bus 61 is isolated because no feasible solution exists. Therefore the lowest voltage bus, bus 61, is disconnected, and thereafter an optimal solution is found. In scenario 6, because of the neighboring faults, bus 12 is isolated, and the branch having buses 12, 68 and 69 is deenergized after fault isolation. Hence, the load on the three buses cannot be reenergized since no tie-line connects to this branch. The bus voltage distribution in a normal situation is presented in Figure 5. 8 (a) and Figure 5. 8 (b) displays post-restoration bus voltage distributions in the six fault scenarios. In scenarios 4 and 6, the isolated buses have zero voltage, indicated as less than 0.9 p.u. in Figure 5. 8 (b).
Table 5. 3 Results of restoration for 69-bus distribution system Fault Location
Switching Pair Operation
Load Restoration
Minimum In-Service Bus Voltage
1
5-6
Close 11-43 & 50-59 Open 55-56 (56-57 or 57-58 or 58-59)
100%
0.9349 p.u.
2
18-19
Close 13-21
100%
0.9092 p.u.
3
49-50
Close 50-59 & 27-65 Open 61-62
100%
0.9092 p.u.
4
60-61
Close 27-65 Open 61-62
Load at bus 61 is unserved
0.9407 p.u.
100%
0.9084 p.u.
Scenario
5
42-43 & 43Close 11-43 & 15-46 44
6
11-12 & 12Load at buses 12, 68 Close 13-21 & 15-46 13 & 15-16 and 69 is unserved
127
0.9142 p.u.
(a) Bus voltage distribution in normal operation
(b) Bus voltage distributions after system restoration Figure 5. 8 Bus voltage distributions in 69-bus distribution system
5.4.3
69-Bus Distribution System Restoration with Penetration of DERs In this case study, the impact of DERs penetration in the 69-bus distribution
system is investigated. DERs are assumed to be installed at heavily loaded buses to 128
reduce power losses and relieve the congestion on the distribution lines. In particular, they are assumed to be frequency-droop controlled voltage sources, and therefore the buses at which they are connected become PV buses. Placement of the DERs close to the critical loads will improve the distribution system resilience for unexpected events. Based on the load data [158], three DERs are installed at buses 50, 61 and 64 of the 69-bus distribution system, as shown in Figure 5. 9. The three buses totally deliver 48.83% real power and 49.24% reactive power of the load. The location and generation capacity of each DER is illustrated in Table 5. 4.
Figure 5. 9 69-bus distribution system with integration of DERs
129
Table 5. 4 Locations and generation capacities of DERs DER 1
DER 2
DER 3
Location
Bus 50
Bus 61
Bus 64
Power Capacity
0.5 MW
1 MW
0.3 MW
To study the influence of DERs penetration on 69-bus distribution system restoration, the analysis is carried out and results for the same fault conditions as before are listed in Table 5. 5. In this case, the switching pair operations are very different. For scenarios 1 − 3, only one switching pair operation is needed. Regarding scenarios 1 and 3, the switching time in this case is one-third of that in the case of the 69-bus distribution system. In scenario 4, bus 61 does not need to be isolated, because the DERs on bus 61 and bus 64 relieve the load burden and raises the minimum bus voltage. Besides, the restoration speed of the scenario 4 is much faster in this case, since the switching operation is only half of that in the case of the 69-bus distribution system. For scenarios 5 and 6, even though the switching pair operations are the same as before, the minimum bus voltage is lifted, thereby improving the performance of system restoration. In Figure 5. 10, the bus voltage distributions in the 69-bus system with the presence of DERs are presented. Through the comparison between Figure 5. 8 and Figure 5. 10, it is obvious that the minimum bus voltages are much improved with the integration of DERs.
130
Table 5. 5 Results of restoration for 69-bus distribution system with DER integration Scenario
Fault Location
Switching Pair Operation
Load Restoration
Minimum In-Service Bus Voltage
1
5-6
Close 11-43
100%
0.9194 p.u.
2
18-19
Close 13-21
100%
0.9580 p.u.
3
49-50
Close 50-59
100%
0.9574 p.u.
4
60-61
Close 27-65
100%
0.9043 p.u.
100%
0.9572 p.u.
5
42-43 & 43- Close 11-43 & 44 15-46
6
11-12 & 12- Close 13-21 & Load at buses 12, 68 13 & 15-16 15-46 and 69 is unserved
0.9626 p.u.
(a) Bus voltage distribution in normal operation Continued Figure 5. 10 Bus voltage distributions in DERs integrated 69-bus distribution system
131
Figure 5. 10 continued
(b) Bus voltage distributions after system restoration
5.4.4
69-Bus Distribution System Restoration with Community Microgrids In this subsection, the influence of community microgrid systems is explored.
Figure 5. 11 presents three community microgrid systems have local DERs to support neighboring loads shown in red dashed regions within the 69-bus distribution system. In community microgrid 1, a meshed topology is planned by adding an extra line, shown as the blue solid line between bus 28 and bus 35 (cf. Figure 5. 11). Community microgrid 2 has a radial backbone. It forms a meshed loop by closing the tie-line between bus 13 and bus 21, shown as a green solid line in Figure 5. 11. In addition, a third microgrid, community microgrid 3, with radial structure is also covered. It is assumed that the three microgrids are self-sufficient and can deliver power to local loads without support from the main grid. For this reason, the three community microgrid systems are equivalent to zero-load buses seen from the 69-bus distribution system side. Accordingly, the three 132
microgrids can offset 52.92% real power and 52.65% reactive power of the total load demand in the distribution system. The generation capacity of each community microgrid system is shown in Table 5. 6. In post-fault restoration, three scenarios are possible: (1) If a fault happens and gets isolated within the meshed loop of a community microgrid, no restoration action is needed because the meshed loop is broken into a radial structure after fault isolation and the load can still be supplied without any interruption. (2) If a fault occurs on the radial part of either community microgrid 2 or community microgrid 3, the power flow analysis should be carried out. In case any operational constraint is violated, a restoration plan is to be implemented. (3) If the fault happens outside the three community microgrids, the post-fault restoration plan is needed to recover unserved but un-faulted portion.
133
Community Microgrid 2
Community Microgrid 3 Community Microgrid 1
Figure 5. 11 69-bus distribution system with community microgrids.
Table 5. 6 Generation capacities of community microgrids
Power Capacity
Community Microgrid 1
Community Microgrid 2
Community Microgrid 3
MW
0.1
0.4
1.75
MVAr
0.07
0.24
1.12
Table 5. 7 shows the results of distribution system restoration with community microgrids. For scenarios 1, 3 and 5, although the switching pair operations are the same as the case with DERs integration, the system minimum in-service bus voltages are much 134
improved. In addition, compared with the case of the only 69-bus distribution system, the switching pair operations in scenarios 1 and 3 are much simplified, reducing two-thirds of switching and largely saving the operation time. For scenarios 2 and 4, no switching action is needed since the faults occur within microgrids and load can be uninterruptedly supported by local DERs after fault isolation. But in scenario 6, customers at buses 12, 68 and 69 cannot be restored either, since no tie-line is connected to the branch through buses 12, 68 and 69 and no local DERs or microgrids cover that place. Figure 5. 12 illustrates the bus voltage distributions in the 69-bus distribution system with community microgrids. After being compared with Figure 5. 8 and Figure 5. 10, Figure 5. 12 shows much improvement in the system minimum bus voltages.
Table 5. 7 Results of restoration for 69-bus distribution system with community microgrids Scenario Fault Location
Switching Pair Operation
Load Restoration
Minimum In-Service Bus Voltage
1
5-6
Close 11-43
100%
0.9762 p.u.
2
18-19
100%
0.9894 p.u.
3
49-50
Close 50-59
100%
0.9696 p.u.
4
60-61
100%
0.9894 p.u.
5
42-43 & 43-44
Close 11-43 & 15-46
100%
0.9860 p.u.
6
11-12 & 1213 & 15-16
Load isolated and unserved at buses 12, 68 and 69
0.9920 p.u.
135
(a) Bus voltage distribution in normal operation
(b) Bus voltage distributions after system restoration Figure 5. 12 Bus voltage distributions in 69-bus distribution system with the presence of community microgrids
136
5.5
Summary For improving the resilience of distribution system, an innovative modified
Viterbi algorithm based restoration strategy was proposed. It is formulated as a bi-level optimization problem to realize the maximum load restoration with least number of switching pair operations after fault isolation. An improved flexible switching pair operation was employed to keep the system radial architecture. Various case studies were presented to validate the proposed restoration scheme on both 33-bus distribution system and 69-bus distribution system. Both single fault and multi-fault conditions were taken into consideration. The power flow analysis and modified Viterbi algorithm have been implemented in MATLAB to achieve the optimal restoration plan. Furthermore, its effectiveness in the presence of DERs and microgrids was also investigated.
137
CHAPTER 6: CONCLUSIONS AND FUTURE WORK 6.1
Conclusions Because of climate change, severe weather events are happening more frequently
nowadays. They are causing serious damages to electrical facilities and large scale blackouts. Besides, the rapidly growing load demand is becoming one of the major causes of power outages. Therefore, a resilient distribution system with community microgrids is developed to ensure the capability of overcoming these rare but extreme events and the ability to bounce back from catastrophic incidents. The conclusions made in this dissertation are as follows: The power system of a typical community is studied for community microgrid development. Community microgrids are coordinated local grids served by one or more distribution substations and supported by local renewables and other distributed energy resources (DERs). For selection of different types of DERs, the metric of levelized cost of energy (LCOE) is used for quantitative assessment of power generation costs. This was used in conjunction with the qualitative functional deployment (QFD) tool that considers environmental factors, customer requirements, and government regulations, among others. Then the suitable DERs for community microgrids are finalized. Thus, distribution systems can be seamlessly partitioned into community microgrids during 138
extreme events. Such community microgrids are energy independent and can provide uninterruptible power supply to critical loads. To guarantee the reliable operation of community microgrids in the islanded mode, the planning reserve margin (PRM) is the key variable for ensuring resource adequacy. But, with the high penetration of renewable resources, uncertainties exist in power supply in addition to load demand. Therefore, mathematical models of load demand and renewable generation are estimated to mimic their stochastic characteristics. The probability analysis and Monte Carlo simulation are conducted to generate net load profile for the capacity planning of gensets and battery energy storage system (BESS). For the capacity planning, it not only needs to cover the peak net load but also has to keep enough planning reserve margin for net load uncertainties and loss of one generation. Also, the impact of PRM on system reliability is included. With a higher PRM, the system reliability is higher. However, there is a tradeoff between system reliability and the system cost. So the problem of capacity planning was formulated to minimize the cost with the satisfaction of reliability requirement. This was realized by adding constraints to ensure the system reliable operation before the cost minimization. The methods of DTFT and PSO were employed to find the optimal solution. In addition, sensitivity analysis was presented for providing guidance on the sizing of dispatchable generators various levels of renewable generation. After ensuring the reliable operation of islanded community microgrids, a multilayered protection strategy was proposed for a distribution system having community microgrids. This is very important because the existing grid protection logic 139
cannot deal with the challenges posed when power flow becomes bi-directional and fault current levels have been largely changed. A comparison between the proposed protection strategy and existing schemes was also included. By the action of the proposed protection scheme, faults are quickly detected and accurately isolated. In order to restore electricity to disrupted areas, a novel modified Viterbi algorithm is presented to find the optimal restoration plan and improve system resilience. The power restoration of the distribution system was formulated as a bi-level optimization problem to realize the maximum load restoration with least number of switching pair operations after fault isolation. An improved flexible switching pair operation was employed to keep the system radial architecture. Various case studies were presented to validate the proposed restoration scheme on both 33-bus and 69-bus distribution system. Both single fault and multi-fault conditions were considered. The power flow analysis and modified Viterbi algorithm have been implemented in MATLAB to achieve the optimal restoration plan. Furthermore, its effectiveness in the presence of DERs and microgrids was also investigated.
6.2
Contributions The contributions made in this dissertation are summarized below:
6.2.1
Community Microgrid Development in Distribution System •
DERs selection for community microgrids based on quantitative assessment and qualitative evaluation.
140
•
LCOE is employed to conduct a quantitative assessment of electricity generation cost for different types of DERs.
•
The method of QFD is used for qualitative evaluation of various types of DERs
by
considering
environment
factors,
customer
requirements,
government regulations, etc. •
Community microgrids are developed by integrating selected DERs within existing distribution systems.
6.2.2
Sizing of Gensets and Battery Energy Storage System for Islanded Community Microgrid •
Planning reserve margin is used to ensure reliable operation of islanded community microgrids by covering peak net load, uncertainties and loss of one generation.
•
The impact of planning reserve margin on system reliability is analyzed, including the influence of the largest dispatchable generation unit.
•
Sizing of gensets and BESS to fulfill the resource adequacy with the consideration of system reliability and cost minimization.
•
Methods of DTFT and PSO are employed to achieve the minimum cost while satisfying the system reliability constraints.
•
On the impact of renewable generation, sensitivity analysis is conducted to provide guidance for the sizing of dispatchable generators.
141
6.2.3
Multilayered Protection Strategy for Resilient Distribution System •
Developed protection schemes for community microgrid within the 69-bus distribution system.
•
Multilayered protection strategy, containing adaptive directional over current protection and differential protection, is proposed for resilient distribution system and verified for various fault scenarios.
•
A comparison between the proposed protection strategy and existing schemes is presented.
6.2.4
Modified Viterbi Algorithm based Restoration for Resilient Distribution System •
The distribution system restoration is formulated as a bi-level optimization problem to realize the maximum load restoration with least number of switching pair operations.
•
An improved flexible switching pair operation is employed to keep the distribution system with radial architecture.
•
A modified Viterbi algorithm is proposed to solve the bi-level optimization problem and find the optimal restoration plan.
•
The proposed restoration scheme is verified on the 33-bus distribution system and the 69-bus distribution system with scenarios of single fault and multifault.
•
In the presence of DERs and community microgrids, the proposed distribution system restoration is observed to give improved performance.
142
6.3
Future Work
6.3.1
Multiple Community Microgrids Reserve Margin Planning In this dissertation, the PRM is determined for each single community microgrid
to guarantee its own capability of riding through unexpected events. The strategy could help develop a resilient distribution system, but may not guarantee cost-effectiveness, even though the sizing scheme for gensets and BESS sets the cost minimization as the objective function. If the PRM can be conducted for multiple microgrids together without compromising system reliability and resilience, the total power capacity of DERs could be brought down and the system energy efficiency could be raised up. 6.3.2
Operation Reserve Margin for Resilient Distribution Systems with Community Microgrids Different from PRM, operation reserve margin is based on real-time operation,
reflecting system ability to meet unforeseen demand increase in operation stage. So counting operation reserve margin will better improve distribution systems resilience. In addition, because of DERs low inertia, system frequency response is a big problem. How to efficiently deploy different DERs to improve system stability is very important. 6.3.3
Resilient Distribution System Operation with Multiple Microgrids With the likelihood of higher deployment of microgrids in the near future, the
coordination between multiple microgrids is expected to result in greater benefits and energy savings. For example, a residential community consumes a lot of power at night, while a commercial or an industry has huge power consumption in the daytime. It would
143
be advantageous to find ways to optimize the operation among multiple community microgrids. 6.3.4
Resilience Metrics Development For the development of resilient distribution systems, various strategies, like
hardening system infrastructures, deployment of DERs, development of community microgrids and distribution automation, are well known. However, quantitative and riskbased metrics to assess and measure systems resilience need further research. Standardized definitions of resilience metrics are required for the planning and operation of distribution systems. Such metrics would be useful, as the context and criteria in decision-support processes or tools, to manage trade-offs and make decisions for policy, planning, investments, and operations.
144
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