Reliability assessment and energy storage solution for renewable energy integration

RELIABILITY ASSESSMENT AND ENERGY STORAGE SOLUTION FOR RENEWABLE ENERGY INTEGRATION SHU ZHEN A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Shu Zhen April 2014 Acknowledgements First and foremost, I would like to express my deep gratitude to my supervisor Dr. Panida Jitutitijaroen. She introduced me into this research community and provided valuable opportunities for me to develop professional skills. Her insightful guidance and advice have helped me successfully accomplish each milestone throughout the entire process from starting Ph.D. topic to finishing this thesis. Her constant encouragement, patience and support have made my Ph.D. experience productive and stimulating. Her enthusiasm and positive attitude have benefited me a lot in both academic record and personal life. I would like to give my best wishes to Dr. Panida Jirutitijaroen and her family. I am sincerely thankful to my thesis committee members for their time and constructive comments. I am also thankful to Dr. Chanan Singh and Dr. Armando Martins Leite da Silva for enlightening discussions and suggestions on my work. I gratefully acknowledge the financial support from National Research Foundation Clean Energy Program as well as academic assistance from Department of Electrical and Computer Engineering and National University of Singapore. I am grateful to my qualifying examiners Dr. Akshay Kumar Rathore and Dr. Chang Che Sau for their time and support in my work. I thank Mr. Seow Hung Cheng, Xiong Peng, Saranga, Bordin and all the other colleagues in the power systems laboratory; I also want to thank my friends Long Jian, Gu Qingyang, Gu Yisha and Cao Guopeng. I greatly cherish our friendships that have made my Ph.D. life much more enjoyable. i Most of all, I would like to thank my parents, Shu Jianrong and Wang Xuejin, as well as my grandparents. Without their unconditional love and care, I could not have made my journey this far. I also want to thank my best friend and husband, Tang Xinyi, who is always staying with me as a faithful supporter in good and bad times. ii TABLE OF CONTENTS ABSTRACT vii LIST OF TABLES viii LIST OF FIGURES . x LIST OF SYMBOLS . xii LIST OF ABBREVIATIONS . xviii CHAPTER I: INTRODUCTION 1.1 Background and Motivation 1.2 Objectives and Contributions 1.3 Thesis Outline CHAPTER II: NON-SEQUENTIAL SIMULATION METHODS FOR RELIABILITY ANALYSIS OF POWER SYSTEMS WITH RENEWABLE ENERGY SOURCES . 2.1 Introduction . 2.2 Incorporating Correlations among Load and Renewable Generations 12 2.3 Monte Carlo Random Sampling Methods . 13 2.4 2.5 2.6 2.3.1 Load Duration Method 13 2.3.2 Linear Regression Method 14 2.3.3 Joint Probability Method . 16 Proposed Latin Hypercube Sampling Methods . 16 2.4.1 Latin Hypercube Sampling with Load Duration . 20 2.4.2 Latin Hypercube Sampling with Linear Regression 20 2.4.3 Latin Hypercube Sampling with Joint Probability 20 2.4.4 Latin Hypercube Sampling with Rank Correlation . 21 Case Studies 23 2.5.1 ERCOT System . 24 2.5.2 IEEE RTS 29 Summary . 33 CHAPTER III: SEQUENTIAL SIMULATION METHODS FOR RELIABILITY ANALYSIS OF COMPOSITE POWER SYSTEMS 36 3.1 Introduction . 36 3.2 Classification of Sequential Simulation 40 3.2.1 Fixed Time Interval Method 41 3.2.2 Next Event Method 42 iii 3.3 Accelerated State Evaluation Approach 43 3.3.1 Algorithm 45 3.3.1.1 Calculation for Threshold Load Level . 45 3.3.1.2 Calculation for States of Loss of Load 46 3.3.2 Extension to Systems with Arbitrary Load Correlations . 48 3.4 Latin Hypercube Sampling Method for Sequential Simulation 49 3.5 Case Studies 51 3.5.1 3.5.1.1 Case – IEEE RTS . 53 3.5.1.2 Case – IEEE RTS with Stressed Transmission Network 56 3.5.1.3 Case – IEEE RTS with Single Generating Unit per Bus 59 3.5.2 3.6 Systems with Correlated Loads . 53 Systems without Fully Correlated Loads . 62 3.5.2.1 IEEE RTS with Modified Bus Loads 62 3.5.2.2 An Extreme Case . 65 Summary . 67 CHAPTER IV: OPTIMAL SIZING OF ENERGY STORAGE SYSTEM FOR GRID-CONNECTED RENEWABLE POWER PLANTS 69 4.1 Introduction . 69 4.2 Energy Storage System Modeling . 71 4.3 Problem Formulation . 74 4.4 4.5 4.6 4.3.1 Continuous Sizing Case . 75 4.3.2 Discrete Sizing Case 78 Solution Technique 78 4.4.1 Sample Average Approximation . 79 4.4.2 Scenario Generation 81 Case Studies 83 4.5.1 Base Case Results 84 4.5.2 Sensitivity Analysis . 86 Summary . 89 CHAPTER V: OPTIMAL OPERATION STRATEGY OF ENERGY STORAGE SYSTEM FOR GRID-CONNECTED RENEWABLE POWER PLANTS . 91 5.1 Introduction . 91 5.2 Problem Description 94 5.2.1 Background 94 iv 5.2.2 5.2.2.1 Decision Stages . 96 5.2.2.2 State Variables . 97 5.2.2.3 Decision Variables . 97 5.2.3 5.4 5.5 5.6 Stochastic Dynamic Programming Applied to Storage Operation 97 5.2.3.1 State Transition Function 97 5.2.3.2 Objective Function 98 5.2.3.3 Constraints . 100 5.2.3.4 Initial Value Function 101 5.2.4 5.3 Stochastic Dynamic Programming Framework . 94 Challenges of Stochastic Dynamic Programming Approach 101 5.2.4.1 Closed-form Solutions . 101 5.2.4.2 Dimensionality 102 Solution Approach using Objective Function Approximation 103 5.3.1 Procedure I - Feasible States Identification . 104 5.3.2 Procedure II - Sub-problems Computation 105 Solution Validation and Comparison 107 5.4.1 Validating Objective Function Approximation with State Enumeration . 107 5.4.2 Comparing Stochastic Dynamic Programming Model to Other Models . 108 5.4.2.1 Stochastic Dynamic Programming Model . 110 5.4.2.2 Deterministic Model 111 5.4.2.3 Perfect Information Model 111 5.4.2.4 Heuristic Operating Rule-based Model . 111 5.4.2.5 Look-ahead Optimization Model . 112 Case Studies 113 5.5.1 Result Validation of Stochastic Dynamic Programming Approach 114 5.5.2 Optimal Operation Strategy . 116 5.5.3 Comparison of Simulation Results for Different Models 119 5.5.3.1 Profit Expectations 119 5.5.3.2 Profit Distributions 121 5.5.3.3 Operation Trajectories . 122 5.5.3.4 Discussion 125 Summary . 126 CHAPTER VI: ENERGY STORAGE SYSTEMS APPLIED FOR ANCILLARY SERVICES AND RENEWABLE UTILIZATION ENHANCEMENT 129 v 6.1 Operation of Coupling Energy Storage System with Wind Power Plants to Provide Ancillary Services . 129 6.2 6.1.1 Background 129 6.1.2 Problem Formulation . 131 6.1.3 Computational Results . 136 6.1.4 Summary 142 Operation of Energy Storage System for Renewable Utilization Enhancement . 144 6.2.1 Background 144 6.2.2 Problem Description 146 6.2.2.1 Stochastic Dynamic Programming Framework . 148 6.2.2.2 Stochastic Dynamic Programming Applied to Storage Operation 149 6.2.3 Case Studies . 152 6.2.3.1 Results from Stochastic Dynamic Programming Model . 153 6.2.3.2 Result Comparison of Proposed Model and Other Models . 156 6.2.4 Summary 159 CHAPTER VII: CONCLUSIONS 161 7.1 Summary and Contributions 161 7.2 Conclusions . 162 7.3 Future Research Directions . 166 BIBLIOGRAPHY . 168 LIST OF PUBLICATIONS . 194 APPENDIX A: DATA OF IEEE RELIABILITY TEST SYSTEMS . 196 APPENDIX B: SOLUTIONS OF HOUR-BY-HOUR OPTIMAL OPERATION OF ENERGY STORAGE SYSTEM 201 vi ABSTRACT Integration of large-scale renewable energy sources brings new challenges to power system operation due to their high intermittency. This thesis aims to address two main issues arising from renewable energy integration, namely, how to efficiently assess system reliability, and how to optimally utilize energy storage systems. Simulation methods based on Latin Hypercube sampling are proposed for reliability analysis of power systems with renewable energy sources. They are able to explicitly incorporate the correlations among time-varying system load and renewable generation in order to achieve accurate reliability indices. Moreover, accelerated state evaluation methods are proposed for composite system reliability analysis. They can accommodate a computational challenge related to repeatedly calculating optimal power flow problems. Their main advantage over conventional approaches is that the computing efficiency is greatly improved without affecting solution accuracy. Energy storage systems (ESS) are commonly applied to manage the variability of renewable generation. This thesis has developed some solutions to the optimal utilization of ESS in large-scale grid-connected renewable power plants. A stochastic programming model is proposed to determine the optimal size for ESS considering a trade-off between investment cost and operational return. A stochastic dynamic programming framework is then proposed to provide ESS optimal operation policy. The proposed framework allows ESS operation to be highly adaptive to uncertainties in renewable production and can serve as a guideline for real-time renewable energy management with ESS. vii LIST OF TABLES Table 2.1 Reliability Indices from MC Sequential Sampling Methods (ERCOT) 27 Table 2.2 Reliability Indices from MC Random Sampling Methods (ERCOT) . 27 Table 2.3 Percentage Errors from MC Random Sampling Methods (ERCOT) 28 Table 2.4 Reliability Indices from LHS Methods (ERCOT) . 28 Table 2.5 Percentage Errors from LHS Methods (ERCOT) 28 Table 2.6 Reliability Indices from MC Sequential Sampling Methods (IEEE RTS) 31 Table 2.7 Reliability Indices from MC Random Sampling Methods (IEEE RTS) 31 Table 2.8 Percentage Errors from MC Random Sampling Methods (IEEE RTS) . 32 Table 2.9 Reliability Indices from LHS Methods (IEEE RTS) . 32 Table 2.10 Percentage Errors from LHS Methods (IEEE RTS) 32 Table 3.1 Indices from Sequential Simulation without Accelerated State Evaluation for IEEE RTS (δ of 0.01) 54 Table 3.2 Indices from Next Event Methods for IEEE RTS (δ of 0.05) 55 Table 3.3 Indices from Next Event Methods for IEEE MRTS (δ of 0.05) . 57 Table 3.4 Indices from Next Event Methods for IEEE MRTS with More Reliable Generation Equipment (δ of 0.05) 58 Table 3.5 Indices from Next Event Methods for IEEE RTS: Case (δ of 0.05) . 60 Table 3.6 Indices for IEEE RTS without Fully Correlated Loads (δ of 0.05) . 63 Table 3.7 Parameters of a Four-bus System 65 Table 4.1 Characteristic Comparison of CAES and PHS 72 Table 4.2 Characteristics of CAES 83 Table 4.3 Estimates and Approximate Solutions in Continuous Sizing Case 85 Table 4.4 Estimates and Approximate Solutions in Discrete Sizing Case . 86 Table 5.1 Results without ESS and Results with ESS Using SDP .115 Table 5.2 Results from SDP with State Enumeration Method .116 Table 5.3 Results from SDP with OFA Method 116 Table 5.4 Sample of Optimal Operations in Winter .118 Table 5.5 Simulation Results using Solutions of Various Models . 120 viii [140] P. 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Batu, “Day-night weather-based economic power dispatch,” IEEE Transactions on Power Systems, vol. 17, no. 2, pp. 469-475, May. 2002. [170] K. K. Kariu i, and R. N. Allan, “Evaluation of reliability worth and value of lost load,” IEE Proceedings-Generation, Transmission and Distributions, vol. 143, no. 2, pp. 171-180, Mar. 1996. 193 LIST OF PUBLICATIONS Journal Papers [1] Z. Shu and P. Jirutitijaroen, “Latin hypercube sampling techniques for power systems reliability analysis with renewable energy sources,” IEEE Transactions on Power Systems, vol. 26, no. 4, pp. 2066-2073, Nov. 2011. [2] Z. Shu and P. Jirutitijaroen, “Optimal operation strategy of energy storage system for grid-connected wind power plants,” IEEE Transactions on Sustainable Energy, vol. 5, no. 1, pp. 190-199, Jan. 2014. [3] Z. Shu, P. Jirutitijaroen, A. M. Leite da Silva, and C. Singh, “Accelerated state evaluation and Latin Hypercube sequential sampling for composite system reliability assessment,” IEEE Transactions on Power Systems, Dec. 2013, accepted for publication. Conference Papers [4] Z. Shu and P. Jirutitijaroen, “Optimal sizing of energy storage system for wind power plants,” IEEE Power and Energy Society General Meeting, San Diego, CA, USA, July 2012. [5] Z. Shu, P. Jirutitijaroen, and B. Bordeerath, “Reliability evaluation of composite power systems using sequential simulation with Latin Hypercube 194 sampling,” 18th Power System Computation Conference, Wroclaw, Poland, Aug. 2014. [6] Z. Shu and P. Jirutitijaroen, “Composite system reliability analysis using an accelerated state evaluation considering bus load correlation”, IEEE International Conference on Probabilistic Methods Applied to Power Systems, Durham, UK, July 2014. 195 APPENDIX A: DATA OF IEEE RELIABILITY TEST SYSTEMS The data of IEEE RTS79 is given in Tables A.1-A.6. In Tables A.1-A.4, load data is given in an order of annual peak, weekly peak, daily peak and hourly peak. Table A.5 and Table A.6 give data for generating units and transmission lines, respectively. For IEEE RTS96, its generation and load data (used in Chapter II) is almost the same as IEEE RTS79. Compared to IEEE RTS79, a main change of IEEE RTS96 is that the topology is expanded from one area to three identical areas merged by inter-area tie lines. Therefore, IEEE RTS96 can be represented by triplication of the components of IEEE RTS79. Table A.1 Bus Annual Peak Load Data for IEEE RTS79 Bus ID Load (MW) 108 97 180 74 71 136 125 171 175 Bus ID 10 13 14 15 16 18 19 20 Load (MW) 195 265 194 317 100 333 181 128 196 Table A.2 Weekly Peak Load in Percent of Annual Peak for IEEE RTS79 Week Peak Load Week Peak Load 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 86.2 90.0 87.8 83.4 88.0 84.1 83.2 80.6 74.0 73.7 71.5 72.7 70.4 75.0 72.1 80.0 75.4 83.7 87.0 88.0 85.6 81.1 90.0 88.7 89.6 86.1 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 75.5 81.6 80.1 88.0 72.2 77.6 80.0 72.9 72.6 70.5 78.0 69.5 72.4 72.4 74.3 74.4 80.0 88.1 88.5 90.9 94.0 89.0 94.2 97.0 100.0 95.2 197 Table A.3 Daily Peak Load in Percent of Weekly Peak for IEEE RTS79 Day Peak Load Monday Tuesday Wednesday Thursday Friday Saturday Sunday 93 100 98 96 94 77 75 Table A.4 Hourly Peak Load in Percent of Daily Peak for IEEE RTS79 Winter Weeks 1-8 & 44-52 Hour Weekday 12-1am 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-Noon Noon-1pm 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 67 63 60 59 59 60 74 86 95 96 96 95 95 95 93 94 99 100 100 96 91 83 73 63 Weekend 78 72 68 66 64 65 66 70 80 88 90 91 90 88 87 87 91 100 99 97 94 92 87 81 Summer Weeks 18-30 Weekday 64 60 58 56 56 58 64 76 87 95 99 100 99 100 100 97 96 96 93 92 92 93 87 72 Weekend 74 70 66 65 64 62 62 66 81 86 91 93 93 92 91 91 92 94 95 95 100 93 88 80 Spring/Fall Weeks 9-17 & 31-43 Weekday 63 62 60 58 59 65 72 85 95 99 100 99 93 92 90 88 90 92 96 98 96 90 80 70 Weekend 75 73 69 66 65 65 68 74 83 89 92 94 91 90 90 86 85 88 92 100 97 95 90 85 198 Table A.5 Generating Unit Data for IEEE RTS79 Unit Index Bus ID 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1 1 2 2 7 13 13 13 15 15 15 15 15 15 16 18 21 22 22 22 22 22 22 23 23 23 Unit Size (MW) 20 20 76 76 20 20 76 76 100 100 100 197 197 197 12 12 12 12 12 155 155 400 400 50 50 50 50 50 50 155 155 350 MTTF (h) 450 450 1960 1960 450 450 1960 1960 1200 1200 1200 950 950 950 2940 2940 2940 2940 2940 960 960 1100 1100 1980 1980 1980 1980 1980 1980 960 960 1150 MTTR (h) 50 50 40 40 50 50 40 40 50 50 50 50 50 50 60 60 60 60 60 40 40 150 150 20 20 20 20 20 20 40 40 100 199 Table A.6 Transmission Line Data for IEEE RTS79 Unit From To Index Bus Bus 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 1 2 3 8 9 10 10 11 11 12 12 13 14 15 15 15 15 16 16 17 17 18 18 19 19 20 20 21 24 10 10 10 11 12 11 12 13 14 13 23 23 16 16 21 21 24 17 19 18 22 21 21 20 20 23 23 22 Impedance (100 MWA base) R (p.u.) X (p.u.) B (p.u.) Capacity (MW) 0.0026 0.0546 0.0218 0.0328 0.0497 0.0308 0.0023 0.0268 0.0228 0.0139 0.0159 0.0427 0.0427 0.0023 0.0023 0.0023 0.0023 0.0061 0.0054 0.0061 0.0124 0.0111 0.0050 0.0022 0.0063 0.0063 0.0067 0.0033 0.0030 0.0018 0.0135 0.0033 0.0033 0.0051 0.0051 0.0028 0.0028 0.0087 0.0139 0.2112 0.0845 0.1267 0.1920 0.1190 0.0839 0.1037 0.0883 0.0605 0.0614 0.1651 0.1651 0.0839 0.0839 0.0839 0.0839 0.0476 0.0418 0.0476 0.0966 0.0865 0.0389 0.0173 0.0490 0.0490 0.0519 0.0259 0.0231 0.0144 0.1053 0.0253 0.0253 0.0396 0.0396 0.0216 0.0216 0.0678 0.4611 0.0572 0.0229 0.0343 0.0520 0.0322 0.0281 0.0239 2.4590 0.0166 0.0447 0.0447 0 0 0.0999 0.0879 0.0999 0.2030 0.1818 0.0818 0.0364 0.1030 0.1030 0.1091 0.0545 0.0485 0.0303 0.2212 0.0545 0.0545 0.0833 0.0833 0.0455 0.0455 0.1424 175 175 175 175 175 175 400 175 175 175 175 175 175 400 400 400 400 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 Failure Rate (per yr) MTTR (h) 0.24 0.51 0.33 0.39 0.48 0.38 0.02 0.36 0.34 0.33 0.30 0.44 0.44 0.02 0.02 0.02 0.02 0.40 0.39 0.40 0.52 0.49 0.38 0.33 0.41 0.41 0.41 0.35 0.34 0.32 0.54 0.35 0.35 0.38 0.38 0.34 0.34 0.45 16 10 10 10 10 10 768 10 10 35 10 10 10 768 768 768 768 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 200 APPENDIX B: SOLUTIONS OF HOUR-BY-HOUR OPTIMAL OPERATION OF ENERGY STORAGE SYSTEM Optimal solutions obtained from stochastic dynamic programming model for winter days are summarized in Table B.1. Due to limited space, symbols are used to represent the decisions: “+” denotes “charge”, “0” denotes “idle”, “-” denotes “discharge”, and “d” denotes “discard power”. Corresponding to a certain hour (in each row) and wind/price level (in each column), optimal operation is dependent on ESS energy level “l” in comparison to some threshold conditions given in brackets. As stated in Chapter V, symbols “L”, “ ”, “H” denote low, medium and high levels, respectively; the term “N. A.” denotes a nonexistent scenario; “l” denotes ESS energy level in percent of its total energy capacity. 201 Table B.1 Solutions of Hour-by-hour Optimal Operation of Energy Storage System Wind Level Price Level L L L M M M H H H L M H L M H L M H Hr + + - + + - + + - Hr N. A. + - + + - + + - Hr + + + + + Hr + + + + Hr N. A. + + +(l[...]... thesis, the use of ESS is illustrated for applications of ancillary services and renewable utilization enhancement, respectively 1.2 Objectives and Contributions The objective of this thesis is to develop simulation tools for power system reliability analysis including renewable energy sources, and to provide energy storage system solutions for renewable energy integration The main contributions of... incorporated For power system reliability analysis with MC simulation, to ensure good solution accuracy, there is a need to properly model and incorporate the correlations among time-varying variables such as load demand and renewable generations [14] Typically for systems including wind and solar energy, both renewable generating capacities and load demand are heavily dependent on time and weather... cost of storage charging ($/MWh) Operation cost of storage discharging ($/MWh) Capital cost of storage energy capacity ($/MWh) Cost coefficient of storage energy capacity ($/MWh/day) Capital cost of storage power capacity ($/MW) Cost coefficient of storage power capacity ($/MW/day) Vector of peak loads of buses (MW) Initial storage level (MWh), in storage operation problem Energy capacity of storage. .. of energy at time ($/MWh) Real time price of reserve capacity for regulation up service at time ($/MWh) Real time price of reserve capacity for regulation down service at time ($/MWh) Ratio of generated energy to energy consumed from compressed air Ratio of used energy to reserved energy for regulation up Ratio of used energy to reserved energy for regulation down Sampled state of system load demand... services BESS Battery energy storage system CAES Compressed air energy storage CAISO California Independent System Operator DET Model Deterministic model ERCOT Electric Reliability Council of Texas ESS Energy storage system EUE Expected unserved energy F&D Frequency and duration FR Frequency regulation FTI Fixed time interval HO Model Heuristic operating ruled-based model IEEE RTS IEEE Reliability Test... operation and generation dispatch; these solutions are highly adaptive to the uncertainties from wind and load This policy can allow transmission system operators to effectively enhance their renewable integration and reduce total operation cost 1.3 Thesis Outline Chapter II presents new simulation methods for power system reliability analysis 7 in the context of recent developments in renewable energy integration. .. improvements for simulation approaches used for composite power system reliability assessment Chapter IV and Chapter V discuss optimization problems involving the utilization of energy storage system to manage intermittent renewable generation Specifically, Chapter IV discusses an optimal storage sizing problem based on a stochastic programming model, and Chapter V proposes an optimal operation strategy of storage. .. level (MW) Power capacity of storage (MW), in storage operation problem Probability of a scenario (realization) Unit size of storage energy capacity (MWh) Unit size of initial storage level (MWh) Unit size of storage power capacity (MW) Small threshold value defined as convergence criteria Energy conversion efficiency of storage charging Energy conversion efficiency of storage discharging Component... Proposal of simulation techniques for reliability analysis of power systems including renewable energy sources, with an emphasis on the fluctuations of system load and intermittent behaviors of renewable generation such as wind and solar The developed methods properly incorporate the correlations among time-varying load and renewable generations; they are able to achieve accurate reliability indices with good... capacity of storage (MWh), in storage sizing problem An integer indicating the number of energy capacity units, in storage sizing problem Energy level of storage at time Charging ( hour (MWh) ) or discharging ( ) energy of storage during (MWh) Vector of power flows in transmission lines (MW) Vector of bus generation capacities (MW) Scheduled conventional generation of unit Charging power of energy storage . RELIABILITY ASSESSMENT AND ENERGY STORAGE SOLUTION FOR RENEWABLE ENERGY INTEGRATION SHU ZHEN A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. Ratio of generated energy to energy consumed from compressed air.   Ratio of used energy to reserved energy for regulation up.   Ratio of used energy to reserved energy for regulation down address two main issues arising from renewable energy integration, namely, how to efficiently assess system reliability, and how to optimally utilize energy storage systems. Simulation methods