Planning and operations in fully renewable electric energy systems

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(1)UNIVERSIDAD DE CASTILLA-LA MANCHA. DEPARTAMENTO DE INGENIERÍA ELÉCTRICA, ELECTRÓNICA, AUTOMÁTICA Y COMUNICACIONES. PLANNING AND OPERATIONS IN FULLY RENEWABLE ELECTRIC ENERGY SYSTEMS. TESIS DOCTORAL. AUTOR: RUTH DOMÍNGUEZ MARTÍN DIRECTOR: ANTONIO J. CONEJO NAVARRO CO-DIRECTOR: MIGUEL CARRIÓN RUIZ-PEINADO. Toledo, Julio de 2015.

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(3) UNIVERSIDAD DE CASTILLA-LA MANCHA. DEPARTMENT OF ELECTRICAL ENGINEERING. PLANNING AND OPERATIONS IN FULLY RENEWABLE ELECTRIC ENERGY SYSTEMS. PhD THESIS. AUTHOR: RUTH DOMÍNGUEZ MARTÍN SUPERVISOR: ANTONIO J. CONEJO NAVARRO CO-SUPERVISOR: MIGUEL CARRIÓN RUIZ-PEINADO. Toledo, July 2015.

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(5) A mis padres y a mis hermanas.

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(7) “The ideal situation occurs when the things that we regard as beautiful are also regarded by other people as useful.” Donald Knuth.

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(9) Acknowledgements I would like to express my deepest acknowledgment to all those people and institutions who have supported and inspired me to accomplish this fascinating work. First of all, I would like to express my sincere admiration and gratitude to Professor Antonio J. Conejo for his expert guidance, his insightful comments, his time and dedication to this work, and for allowing me to envision how to develop an honest and fruitful research career. I also wish to thank Professor Antonio J. Conejo for his kindness, hospitality and gentleness during my stay in Columbus. Thanks for allowing me to have had that enriching experience, and for enabling me to work with people from all over the world. And secondly, I wish to express my profound gratitude to Professor Miguel Carrión for his technical support, his encouragement in moments of doubt, and for being an example of efficiency and kindness. Additionally, I wish to thank the Ministry of Education and the Ministry of Economy of Spain for their financial support through grant AP2012-0886 “Formación del Profesorado Universitario” and project DPI2012-31013. This has allowed me to spend part of my PhD studies at The Ohio State University in Columbus, Ohio, US. I would also like to thank Fundación Iberdrola for its financial support through grants “Ayudas a la Investigación en Energı́a y Medio Ambiente” during the first years of my studies. Thanks for trusting in our project. I wish to thank the Universidad de Castilla - La Mancha for allowing me to use its facilities. In addition, I really appreciate the support received from the professors and members of the Escuela de Ingenierı́a Industrial de Toledo. It has been a honour for me to be a member of the “capa baja” of the School. ix.

(10) x Thanks to my predecessors in this researching group for their help and advise, especially to Luis Baringo. A special mention to Gabriel and José Luis. Thanks to Gabriel for his friendship, his affection and his wonderful Mocha coffees. And thanks to José Luis for allowing me to stay in his lab and for the endless conversations, even though I know the risk I am running saying this. And thanks to Ismael for being the best shield against those endless conversations. I am indebted to the friends I made in Columbus. They made my stay there the most fruitful experience of my PhD studies. Especially, thanks to Chidozie for inspiring me and encouraging me to grow. My immense gratitude to the love and support of my family. Thanks to my parents for raising us in the morals of responsibility, effort, honesty and solidarity. Thanks to Rocı́o for having done this trip with me and for loving her chemical research. And thanks to my little Marı́a for reminding me that we should always try to change the world. Of course, thanks a lot to my girls, specially to the members of “El Trı́o Laralá”, Beatriz and Patricia. Thanks for your cheerfulness, your liveliness, your laughs and tears, your words and your company: thanks for sharing. And thanks to the 7-female engineers for feeding my engineering soul with their professional experience, and at the same time, for making me feel happy about my choice to live in the academic world.. “... Ası́ que acuérdense de mirar hacia las estrellas y no hacia sus pies. Intenten encontrarle un sentido a lo que ven y pregúntense por aquello que hace que exista el universo. Sean curiosos. Y por muy difı́cil que pueda parecerles la vida, siempre hay algo que pueden hacer y en lo que pueden tener éxito. Lo importante es que no se rindan.” Stephen Hawking.

(11) Contents Contents. xi. List of Figures. xvii. List of Tables. xxiii. Notation. xxviii. 1 Introduction 1.1. 1. Electricity Markets . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.1.1. Evolution . . . . . . . . . . . . . . . . . . . . . . . . . .. 1. 1.1.2. Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. 1.1.3. Structure . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. Renewable Energies . . . . . . . . . . . . . . . . . . . . . . . . .. 5. 1.2.1. General Overview . . . . . . . . . . . . . . . . . . . . . .. 5. 1.2.2. Wind Energy . . . . . . . . . . . . . . . . . . . . . . . .. 6. 1.2.3. Solar Energy . . . . . . . . . . . . . . . . . . . . . . . .. 6. 1.2.4. Biomass Energy . . . . . . . . . . . . . . . . . . . . . . .. 7. 1.3. Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . .. 8. 1.4. Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . .. 9. 1.4.1. Integration. 9. 1.4.2. Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 10. 1.4.3. Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. 1.4.4. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. 1.2. 1.5. . . . . . . . . . . . . . . . . . . . . . . . . .. Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 16 xi.

(12) xii. CONTENTS 1.6. Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 18. 2 Operation of a Fully Renewable Power System. 21. 2.1. Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. 2.2. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23. 2.3. Uncertainty Characterization and Decision-Making Process . . . 25. 2.4. Model Description. . . . . . . . . . . . . . . . . . . . . . . . . . 26. 2.4.1. Objective Function . . . . . . . . . . . . . . . . . . . . . 26. 2.4.2. Power Balance at the Day-Ahead Market . . . . . . . . . 28. 2.4.3. Power Balance at Real-Time Operation . . . . . . . . . . 28. 2.4.4. Modeling of CSP Plant Operation . . . . . . . . . . . . . 29. 2.4.5. Modeling of Biomass Unit Operation . . . . . . . . . . . 30. 2.4.6. Minimum Up/Down Times . . . . . . . . . . . . . . . . . 30. 2.4.7. Modeling of Wind Unit Operation . . . . . . . . . . . . . 31. 2.4.8. Modeling of Pumped-Storage Unit Operation . . . . . . 32. 2.4.9. Constraints Corresponding to the Transmission Network. 33. 2.4.10 Scheduled and Deployed Reserves . . . . . . . . . . . . . 33 2.5. Pricing Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 34. 2.6. Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . 36. 2.7. 2.8. 2.6.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36. 2.6.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39. Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.7.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44. 2.7.2. Results: Base Case . . . . . . . . . . . . . . . . . . . . . 51. 2.7.3. Results: Impact of the Generating System Flexibility . . 60. 2.7.4. Results: Impact of Variable Costs of Generating Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . 63. 2.7.5. Results: System Operation Across Seasons . . . . . . . . 64. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 67. 3 Two-Stage Stochastic-Programming Investment Model. 69. 3.1. Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70. 3.2. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.

(13) CONTENTS. xiii. 3.3. Decision-Making Process and Uncertainty Characterization . . . 72. 3.4. Characterization of the Renewable Power Production . . . . . . 73. 3.5. Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74. 3.6. 3.7. 3.8. 3.5.1. Objective Function . . . . . . . . . . . . . . . . . . . . . 75. 3.5.2. Limits on the Power that Can Be Built . . . . . . . . . . 76. 3.5.3. Transmission Lines that Can Be Built . . . . . . . . . . . 76. 3.5.4. Limits on the Generated Power . . . . . . . . . . . . . . 77. 3.5.5. Power Balance. 3.5.6. Demand and Transmission Network Constraints . . . . . 78. . . . . . . . . . . . . . . . . . . . . . . . 78. Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78. 3.6.2. Case 1 Results: Uncongested Network. 3.6.3. Case 2 Results: Increment in Demand . . . . . . . . . . 83. 3.6.4. Case 3 Results: Congested Network . . . . . . . . . . . . 84. . . . . . . . . . . 81. Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.7.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85. 3.7.2. Generation of Operating Points . . . . . . . . . . . . . . 91. 3.7.3. Results: IEEE 118-Node System . . . . . . . . . . . . . . 94. 3.7.4. Results: Congested Network . . . . . . . . . . . . . . . . 99. 3.7.5. Results: Increasing Renewable Capacity . . . . . . . . . 102. 3.7.6. Results: Natural Gas Price . . . . . . . . . . . . . . . . . 106. 3.7.7. Results: IEEE 118+118-Node System . . . . . . . . . . . 114. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 116. 4 Multi-Stage Stochastic-Programming Investment Model. 119. 4.1. Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120. 4.2. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121. 4.3. Decision-Making Process . . . . . . . . . . . . . . . . . . . . . . 122. 4.4. Uncertainty Characterization. 4.5. Characterization of the Operating Conditions . . . . . . . . . . 125. 4.6. Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126. 4.7. Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.7.1. . . . . . . . . . . . . . . . . . . . 125. Objective Function . . . . . . . . . . . . . . . . . . . . . 127.

(14) xiv. CONTENTS. 4.8. 4.9. 4.7.2. Investment Constraints . . . . . . . . . . . . . . . . . . . 129. 4.7.3. Power Unit Constraints . . . . . . . . . . . . . . . . . . . 130. 4.7.4. Demand and Transmission Line Constraints . . . . . . . 131. 4.7.5. Power Balance. 4.7.6. Risk Management . . . . . . . . . . . . . . . . . . . . . . 131. . . . . . . . . . . . . . . . . . . . . . . . 131. Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . 132 4.8.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132. 4.8.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138. Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.9.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141. 4.9.2. Scenario Tree . . . . . . . . . . . . . . . . . . . . . . . . 146. 4.9.3. Results: Base Case . . . . . . . . . . . . . . . . . . . . . 149. 4.9.4. Results: No Nuclear Power . . . . . . . . . . . . . . . . . 151. 4.9.5. Results: No Greenhouse Gas Emissions . . . . . . . . . . 153. 4.9.6. Results: 100% Renewable . . . . . . . . . . . . . . . . . 154. 4.9.7. Results: Comparison of Results . . . . . . . . . . . . . . 155. 4.9.8. Increasing the Number of Stages . . . . . . . . . . . . . . 158. 4.10 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 158 5 Multi-Stage Investment Model: Linear Decision Rule Approach161 5.1. Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162. 5.2. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162. 5.3. Multi-Stage Problems Under Uncertainty . . . . . . . . . . . . . 163. 5.4. Uncertainty Characterization. 5.5. Decision-Making Process . . . . . . . . . . . . . . . . . . . . . . 165. 5.6. Solution Methodology: LDR Approach . . . . . . . . . . . . . . 166. . . . . . . . . . . . . . . . . . . . 164. 5.6.1. Decision Variables. . . . . . . . . . . . . . . . . . . . . . 167. 5.6.2. Uncertain Parameters. 5.6.3. Deterministic Parameters. 5.6.4. Uncertainty Bounds. . . . . . . . . . . . . . . . . . . . 168 . . . . . . . . . . . . . . . . . 169. . . . . . . . . . . . . . . . . . . . . 169. 5.7. Approximate Problem . . . . . . . . . . . . . . . . . . . . . . . 170. 5.8. Reformulation of the Approximate Problem . . . . . . . . . . . 170 5.8.1. Objective Function . . . . . . . . . . . . . . . . . . . . . 171.

(15) CONTENTS. xv. 5.8.2. Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 172. 5.8.3. Final Formulation . . . . . . . . . . . . . . . . . . . . . . 173. 5.9. Multi-Stage LDR Investment Model . . . . . . . . . . . . . . . . 173 5.9.1. Objective Function . . . . . . . . . . . . . . . . . . . . . 173. 5.9.2. Limits of Capacity that Can Be Built . . . . . . . . . . . 174. 5.9.3. Limits on the Generated Power . . . . . . . . . . . . . . 174. 5.9.4. Power Balance. 5.9.5. Demand and Transmission Network Constraints . . . . . 176. 5.9.6. Positive Variables . . . . . . . . . . . . . . . . . . . . . . 177. . . . . . . . . . . . . . . . . . . . . . . . 176. 5.10 Characterization of the Operating Conditions . . . . . . . . . . 178 5.11 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . 178 5.11.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 5.11.2 Uncertainty Characterization Through LDRs . . . . . . . 181 5.11.3 Stochastic Scenarios . . . . . . . . . . . . . . . . . . . . 183 5.11.4 Results: LDR Approach . . . . . . . . . . . . . . . . . . 185 5.11.5 Results: Comparison . . . . . . . . . . . . . . . . . . . . 187 5.12 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.12.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.12.2 Uncertainty Characterization . . . . . . . . . . . . . . . 194 5.12.3 Results: Computational Issues . . . . . . . . . . . . . . . 197 5.12.4 Results: Comparison Among Cases . . . . . . . . . . . . 198 5.13 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 202 6 Closure 6.1. 205. Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6.1.1. Operating a Fully Renewable Power System . . . . . . . 205. 6.1.2. Investment in Renewable Energies . . . . . . . . . . . . . 206. 6.2. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208. 6.3. Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209. 6.4. Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 211. A IEEE 24-Node System Data. 213. A.1 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.

(16) xvi. CONTENTS A.2 Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 A.3 Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . 215. B IEEE 118-Node System Data B.1 Network . . . . . . . . . . . B.2 Demand . . . . . . . . . . . B.3 Transmission Lines . . . . . B.4 118+118-Node System . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 217 . 217 . 219 . 220 . 226. Bibliography. 231. Index. 244.

(17) List of Figures 2.1. Fully renewable system: schematic of the considered network. . 25. 2.2. Fully renewable system example: network . . . . . . . . . . . . . 36. 2.3. Fully renewable system example: demand curve . . . . . . . . . 37. 2.4. Fully renewable system example: wind/solar scenarios . . . . . . 39. 2.5. Fully renewable system example: scheduled and generated power from the biomass unit . . . . . . . . . . . . . . . . . . . . . . . 40. 2.6. Fully renewable system example: power scheduled by the wind and CSP units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41. 2.7. Fully renewable system example: power generated and spilled by the wind unit in scenarios . . . . . . . . . . . . . . . . . . . . 41. 2.8. Fully renewable system example: power generated by the CSP plant in scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 42. 2.9. Fully renewable system example: system marginal cost at the day-ahead market and in real-time per scenario . . . . . . . . . 42. 2.10 Fully renewable system case study: typical demand curve during the summer in Texas. . . . . . . . . . . . . . . . . . . . . . . . . 48 2.11 Fully renewable system case study: final set of wind and solar scenarios at nodes 42 and 8, respectively. . . . . . . . . . . . . . 50 2.12 Fully renewable system case study: aggregated power and reserves scheduled by biomass units. . . . . . . . . . . . . . . . . . 51 2.13 Fully renewable system case study: hourly system marginal cost of the power system in the day-ahead market. . . . . . . . . . . 52 2.14 Fully renewable system case study: power generated by each technology in a high wind scenario. . . . . . . . . . . . . . . . . 53 xvii.

(18) xviii. LIST OF FIGURES. 2.15 Fully renewable system case study: power generated by each technology in a low wind scenario. . . . . . . . . . . . . . . . . . 54 2.16 Fully renewable system case study: power spillage for CSP and wind units in high/low wind scenarios. . . . . . . . . . . . . . . 54 2.17 Fully renewable system case study: hourly marginal cost of the power system in real-time operation in high/low-wind scenarios.. 55. 2.18 Fully renewable system case study: utilization factor of each generating technology. . . . . . . . . . . . . . . . . . . . . . . . 56 2.19 Fully renewable system case study: TES management for a CSP plant in a particular scenario. . . . . . . . . . . . . . . . . . . . 57 2.20 Fully renewable system case study: TES management for a CSP plant in a high solar scenario. . . . . . . . . . . . . . . . . . . . 57 2.21 Fully renewable system case study: distribution of expected hourly profits for each technology. . . . . . . . . . . . . . . . . . 59 2.22 Fully renewable system case study: comparison of the hourly marginal cost of the system in the day-ahead market in cases A, B and C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.23 Fully renewable system case study: comparison of the nonscheduled reserve deployed by biomass units in a low wind scenario and cases A, B and C. . . . . . . . . . . . . . . . . . . . . 61 2.24 Fully renewable system case study: aggregated demand, down scheduled reserve and unserved demand in the case without 6 TESs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.25 Fully renewable system case study: comparison of the average power spillage by wind and CSP units in the base and lower wind-cost case. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.26 Fully renewable system case study: aggregated forecasted demand in a representative day per season. . . . . . . . . . . . . . 64 2.27 Fully renewable system case study: final set of wind and solar scenarios at nodes 42 and 8, respectively, in winter. . . . . . . . 65 2.28 Fully renewable system case study: final set of wind and solar scenarios at nodes 42 and 8, respectively, in spring. . . . . . . . 65.

(19) LIST OF FIGURES. xix. 2.29 Fully renewable system case study: final set of wind and solar scenarios at nodes 42 and 8, respectively, in fall. . . . . . . . . . 66 3.1. Two-stage investment model: scenario tree . . . . . . . . . . . . 73. 3.2. Two-stage investment model example: network . . . . . . . . . . 79. 3.3. Two-stage investment model example: resulting network in case 3 85. 3.4. Two-stage investment model case study: demand level at zone 3 & wind power availability in each location and each season (200 operating points). . . . . . . . . . . . . . . . . . . . . . . . 92. 3.5. Two-stage investment model case study: demand level at zone 3 & solar power availability in each season (200 operating points). 93. 3.6. Two-stage investment model case study: investment cost (renewable, thermal and transmission facilities) for every case. . . . 96. 3.7. Two-stage investment model case study: renewable power built per technology for every case. . . . . . . . . . . . . . . . . . . . 97. 3.8. Two-stage investment model case study: thermal power built per technology for every case. . . . . . . . . . . . . . . . . . . . 97. 3.9. Two-stage investment model case study: energy generated by renewable units in the BAU case. . . . . . . . . . . . . . . . . . 98. 3.10 Two-stage investment model case study: energy generated by renewable units in the 80% Renewable case. . . . . . . . . . . . 99 3.11 Two-stage investment model case study: renewable capacity built per technology with and without network congestion. . . . 101 3.12 Two-stage investment model case study: thermal capacity built per technology with and without network congestion. . . . . . . 101 3.13 Two-stage investment model case study: increasing renewable capacity, expected costs. . . . . . . . . . . . . . . . . . . . . . . 103 3.14 Two-stage investment model case study: increasing renewable capacity, investment and operating costs per technology. . . . . 104 3.15 Two-stage investment model case study: increasing renewable capacity, renewable and thermal capacity built. . . . . . . . . . 105.

(20) xx. LIST OF FIGURES 3.16 Two-stage investment model case study: expected total, investment and operating costs regarding the decrease in NGP in the BAU and 80% Renewable cases. . . . . . . . . . . . . . . . . . . 107 3.17 Two-stage investment model case study: renewable and thermal capacity built regarding the decrease in NGP for the BAU case. 108 3.18 Two-stage investment model case study: energy generated by renewable and thermal units regarding the decrease in NGP for the BAU case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.19 Two-stage investment model case study: renewable and thermal capacity built regarding the decrease in NGP for the 80% Renewable case. . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.20 Two-stage investment model case study: energy generated by renewable and thermal units regarding the decrease in NGP for the 80% Renewable case. . . . . . . . . . . . . . . . . . . . . . . 110 3.21 Two-stage investment model case study: expected total, investment and operating costs regarding the increase in NGP for the BAU and 80% Renewable cases. . . . . . . . . . . . . . . . . . . 111 3.22 Two-stage investment model case study: renewable and thermal capacity built regarding the increase in NGP for the BAU case. 112 3.23 Two-stage investment model case study: energy generated by renewable and thermal units regarding the increase in NGP for the BAU case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.24 Two-stage investment model case study: renewable and thermal capacity built regarding the increase in NGP for the 80% Renewable case. . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.25 Two-stage investment model case study: energy generated by renewable and thermal units regarding the increase in NGP for the 80% Renewable case. . . . . . . . . . . . . . . . . . . . . . . 113 4.1. Multi-stage investment model: scenario tree. . . . . . . . . . . . 124. 4.2. Multi-stage investment model: pmf and cdf of a discrete distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127. 4.3. Multi-stage investment model example: network . . . . . . . . . 133.

(21) LIST OF FIGURES. xxi. 4.4. Multi-stage investment model example: decision-making process. 135. 4.5. Multi-stage investment model example: expected cost vs. CVaR 138. 4.6. Multi-stage investment model case study: IEEE 24-node system 142. 4.7. Multi-stage investment model case study: wind/demand operating points for the 4 onshore wind units in the hot and cold seasons (150 operating points). . . . . . . . . . . . . . . . . . . 145. 4.8. Multi-stage investment model case study: solar/demand operating points for the hot and cold seasons (150 operating points). 145. 4.9. Multi-stage investment model case study: expected cost vs. CVaR for the base case. . . . . . . . . . . . . . . . . . . . . . . 149. 4.10 Multi-stage investment model case study: capacity built per technology in scenario 1 in the base case. . . . . . . . . . . . . . 150 4.11 Multi-stage investment model case study: capacity built per technology in scenario 10 in the base case. . . . . . . . . . . . . 151 4.12 Multi-stage investment model case study: expected cost vs. CVaR for the non-nuclear case. . . . . . . . . . . . . . . . . . . 152 4.13 Multi-stage investment model case study: expected cost vs. CVaR for the non-GHG case. . . . . . . . . . . . . . . . . . . . 154 4.14 Multi-stage investment model case study: expected cost vs. CVaR for the 100% renewable case. . . . . . . . . . . . . . . . . 155 4.15 Multi-stage investment model case study: comparison of the expected power built per technology. . . . . . . . . . . . . . . . 156 4.16 Multi-stage investment model case study: comparison of the expected capacity built and available. . . . . . . . . . . . . . . . 157 5.1. LDR example: network. . . . . . . . . . . . . . . . . . . . . . . 179. 5.2. LDR case study: decision-making process. . . . . . . . . . . . . 192. 5.3. LDR case study: evolution of the total expected demand in Texas.195. 5.4. LDR case study: total capacity built per technology in the considered situations for the base and 100% Renewable cases. . . . 199. 5.5. LDR case study: total capacity built per technology in the considered situations for the non-nuclear and non-GHG cases. . . . 200.

(22) xxii 5.6 5.7. LIST OF FIGURES LDR case study: capacity built per technology in each stage in the expected situation for the base and 100% Renewable cases. . 201 LDR case study: capacity built per technology in each stage in the expected situation for the non-nuclear and non-GHG cases. . 202. A.1 24-node system: schematic . . . . . . . . . . . . . . . . . . . . . 214 B.1 118-node system: schematic . . . . . B.2 118+118-node system: schematic . . B.3 118-node system: distribution of the case study of Chapter 3 . . . . . . .. . . . . . . . . . . . . . . . 218 . . . . . . . . . . . . . . . 228 generating units for the . . . . . . . . . . . . . . . 229.

(23) List of Tables 2.1. Fully renewable system example: transmission line data for the 3-node network . . . . . . . . . . . . . . . . . . . . . . . . . . . 37. 2.2. Fully renewable system example: biomass unit technical data . . 38. 2.3. Fully renewable system example: CSP unit technical data . . . . 38. 2.4. Fully renewable system example: profits (k$) . . . . . . . . . . . 43. 2.5. Fully renewable system case study: installed capacity and peak demand in each zone (MW) . . . . . . . . . . . . . . . . . . . . 44. 2.6. Fully renewable system case study: capacity vs. demand ratio (p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44. 2.7. Fully renewable system case study: CSP plant technical data . . 45. 2.8. Fully renewable system case study: CSP plant locations, types and variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . 46. 2.9. Fully renewable system case study: wind unit data . . . . . . . 46. 2.10 Fully renewable system case study: biomass unit technical data. 47. 2.11 Fully renewable system case study: biomass unit locations and variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.12 Fully renewable system case study: pumped-storage unit technical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.13 Fully renewable system case study: average daily results for generating units . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.14 Fully renewable system case study: biomass reserve capacity . . 60 2.15 Fully renewable system case study: comparison of the expected daily profits (k$) . . . . . . . . . . . . . . . . . . . . . . . . . . 62 xxiii.

(24) xxiv. LIST OF TABLES. 2.16 Fully renewable system case study: total operating cost and expected daily profits of each technology across seasons (k$) . . 66 2.17 Fully renewable system case study: average daily production per technology across seasons (MWh) . . . . . . . . . . . . . . . 67 3.1. Two-stage investment model example: transmission line data for the 3-node network . . . . . . . . . . . . . . . . . . . . . . . 79. 3.2. Two-stage investment model example: investment and variable costs of generating units . . . . . . . . . . . . . . . . . . . . . . 79. 3.3. Two-stage investment model example: prospective line data for the 3-node network . . . . . . . . . . . . . . . . . . . . . . . . . 80. 3.4. Two-stage investment model example: capacity limit per technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80. 3.5. Two-stage investment model example: demand levels and wind/solar power availability (p.u.) . . . . . . . . . . . . . . . . . . . . . . 81. 3.6. Two-stage investment model example: expected total, investment and operating costs in case 1 (M$) . . . . . . . . . . . . . 82. 3.7. Two-stage investment model example: power built per technology in case 1 (MW) . . . . . . . . . . . . . . . . . . . . . . . . . 82. 3.8. Two-stage investment model example: power generated per technology and per operating point in each scenario in case 1 (MW). 3.9. 82. Two-stage investment model example: expected total, investment and operating costs in case 2 (M$) . . . . . . . . . . . . . 83. 3.10 Two-stage investment model example: power built per technology in case 2 (MW) . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.11 Two-stage investment model example: expected generated energy per technology in case 2 (GWh) . . . . . . . . . . . . . . . 84 3.12 Two-stage investment model example: expected total, investment and operating costs in case 3 (M$) . . . . . . . . . . . . . 84 3.13 Two-stage investment model example: power built per technology in case 3 (MW) . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.14 Two-stage investment model case study: investment and variable costs of thermal units . . . . . . . . . . . . . . . . . . . . . 86.

(25) LIST OF TABLES. xxv. 3.15 Two-stage investment model case study: investment and variable costs of onshore wind units . . . . . . . . . . . . . . . . . . 86 3.16 Two-stage investment model case study: investment and variable costs of offshore wind units . . . . . . . . . . . . . . . . . . 87 3.17 Two-stage investment model case study: investment and variable costs of CSP units . . . . . . . . . . . . . . . . . . . . . . . 87 3.18 Two-stage investment model case study: investment and variable costs of solar PV units . . . . . . . . . . . . . . . . . . . . 88 3.19 Two-stage investment model case study: investment and variable costs of biomass units . . . . . . . . . . . . . . . . . . . . . 88 3.20 Two-stage investment model case study: capacity limit per technology and per node . . . . . . . . . . . . . . . . . . . . . . . . 89 3.21 Two-stage investment model case study: prospective line data for the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.22 Two-stage investment model case study: expected investment, operating and total costs (M$) . . . . . . . . . . . . . . . . . . . 95 3.23 Two-stage investment model case study: capacity built (MW) . 95 3.24 Two-stage investment model case study: operating cost in each scenario (M$) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.25 Two-stage investment model case study: expected costs with and without network congestion . . . . . . . . . . . . . . . . . . 100 3.26 Two-stage investment model case study: capacity built with and without network congestion . . . . . . . . . . . . . . . . . . 100 3.27 Two-stage investment model case study: expected operating cost in the BAU case with and without network congestion . . . 102 3.28 Two-stage investment model case study: prospective line data for the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.29 Two-stage investment model case study: computing time . . . . 115 3.30 Two-stage investment model case study: expected investment, operating and total costs in the 118+118-node system (M$) . . 116 3.31 Two-stage investment model case study: capacity built in the 118+118-node system (MW) . . . . . . . . . . . . . . . . . . . . 116.

(26) xxvi. LIST OF TABLES. 4.1. Multi-stage investment model example: characteristics of the existing thermal units . . . . . . . . . . . . . . . . . . . . . . . . 132. 4.2. Multi-stage investment model example: characteristics of the candidate renewable units . . . . . . . . . . . . . . . . . . . . . 133. 4.3. Multi-stage investment model example: transmission line data for the 4-node network . . . . . . . . . . . . . . . . . . . . . . . 133. 4.4. Multi-stage investment model example: demand and cost factors for each scenario and stage and probability of each scenario (p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136. 4.5. Multi-stage investment model example: number of hours comprising each operating point, demand level and wind/solar power availability (p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . 137. 4.6. Multi-stage investment model example: expected cost and CVaR (M$) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138. 4.7. Multi-stage investment model example: total capacity built in each stage and scenario for the risk-neutral and risk-averse conditions (MW) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139. 4.8. Multi-stage investment model example: total capacity built per technology in each scenario for the risk-neutral condition (MW) 140. 4.9. Multi-stage investment model example: total capacity built per technology in each scenario for the risk-averse condition (MW) . 140. 4.10 Multi-stage investment model case study: characteristics of the thermal units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.11 Multi-stage investment model case study: characteristics of the prospective renewable units . . . . . . . . . . . . . . . . . . . . 143 4.12 Multi-stage investment model case study: demand and cost factors for each scenario and stage and probability of each scenario (p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.13 Multi-stage investment model case study: expected capacity built per technology in each stage for the risk-neutral and riskaverse conditions (MW) in the base case . . . . . . . . . . . . . 150.

(27) LIST OF TABLES. xxvii. 4.14 Multi-stage investment model case study: expected capacity built per technology in each stage for the risk-neutral and riskaverse conditions (MW) in the non-nuclear case . . . . . . . . . 152 4.15 Multi-stage investment model case study: expected capacity built per technology in each stage for the risk-neutral and riskaverse conditions (MW) in the non-GHG case . . . . . . . . . . 153 4.16 Multi-stage investment model case study: expected capacity built per technology in each stage for the risk-neutral and riskaverse conditions (MW) in the 100% renewable case . . . . . . . 155 4.17 Multi-stage investment model case study: comparison of results 156 4.18 Multi-stage investment model case study: number of variables and constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 5.1. LDR example: characteristics of the existing thermal units . . . 179. 5.2. LDR example: characteristics of the candidate renewable units . 180. 5.3. LDR example: transmission lines data for the 4-node network . 180. 5.4. LDR example: demand levels and wind/solar power availability (p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181. 5.5. LDR example: correlation parameters (p.u.) . . . . . . . . . . . 182. 5.6. LDR example: uncertainty levels (p.u.) . . . . . . . . . . . . . . 182. 5.7. LDR example: demand and cost factors for each scenario and stage (p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184. 5.8. LDR example: expected operating, investment and total expected cost (M$) . . . . . . . . . . . . . . . . . . . . . . . . . . 186. 5.9. LDR example: expected capacity built per technology in each stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186. 5.10 LDR example: total capacity built per technology and in total in each scenario (MW) . . . . . . . . . . . . . . . . . . . . . . . 187 5.11 LDR example: computing times . . . . . . . . . . . . . . . . . . 187 5.12 LDR example: expected operating, investment and total cost for the LDR and stochastic approaches (M$) . . . . . . . . . . . 188.

(28) xxviii. LIST OF TABLES. 5.13 LDR example: comparison of the total capacity built per technology and in total in each scenario for the LDR and stochastic approaches (MW) . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 LDR example: comparison of the total cost in each scenario for the LDR and stochastic approaches . . . . . . . . . . . . . . . 5.15 LDR case study: characteristics of the thermal units . . . . . 5.16 LDR case study: characteristics of the prospective renewable units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.17 LDR case study: Tgoff in each case . . . . . . . . . . . . . . . . 5.18 LDR case study: correlation parameters (p.u.) . . . . . . . . . 5.19 LDR case study: expected values and uncertainty levels (p.u.) 5.20 LDR case study: vector ξ for each situation (p.u.) . . . . . . . 5.21 LDR case study: computing times . . . . . . . . . . . . . . . . 5.22 LDR case study: size of the problems . . . . . . . . . . . . . . 5.23 LDR case study: comparison of results . . . . . . . . . . . . .. . 189 . 190 . 192 . . . . . . . .. 193 194 196 196 197 197 198 199. A.1 24-node system: peak demand per node . . . . . . . . . . . . . . 215 A.2 24-node system: characteristics of the transmission lines . . . . 216 B.1 118-node system: peak demand per node . . . . . . . . . . . . . 219 B.2 118-node system: characteristics of the transmission lines . . . . 220 B.3 118+118-node system: data of the transmission lines connecting zones 1, 2 and 3 with zones 1’, 2’, and 3’ . . . . . . . . . . . . . 227.

(29) Notation The main symbols used in this thesis are described in this section for better understanding. Please, note that in the multi-stage investment model proposed in Chapter 4 the same variables and parameters as in Chapter 3 are used but just adding the index corresponding to the stage t.. Indices g. Index of generating units, running from 1 to NG. j. Index of demands, running from 1 to NJ. l. Index of transmission lines, running from 1 to NL. n. Index of system nodes, running from 1 to NN. o. Index of operating points, running from 1 to NO. q. Index of the seasons of the year: 1 for the cold season and 2 for the hot season. s. Index of scenarios, running from 1 to NS. t. Index of stages, running from 1 to NT. Constants and Parameters a. Capital recovery factor [p.u.] xxix.

(30) xxx. LIST OF TABLES Bl. Susceptance of transmission line l [p.u.]. CgG. Variable cost of generating unit g [$/MWh]. CgI. Investment cost of generating unit g [$/kW]. ClL. Investment cost of transmission line l [$]. D/U. Cg. Cost of deploying down/up reserve of biomass unit g [$/MWh]. CgNS. Cost of deploying non-scheduled reserve of biomass unit g [$/MWh]. SD/U. Cost of scheduling down/up reserve of biomass unit g [$/MW]. SD/U. Cost of scheduling down/up reserve of demand j [$/MW]. Cg Cj. CgStart−up Start-up cost of biomass unit g [$] C US. Cost of the unserved demand [$/MWh]. djo. Forecasted demand j in operating point o [MW]. D/Umax. Dj. Maximum down/up scheduled reserve of demand j (MW). Fgq. Capacity factor of CSP unit g in season q [p.u.]. PV Fgo. Normalized solar-power production of solar PV unit g in operating point o [p.u.]. W Fgo. Normalized wind-power production of wind unit g in operating point o [p.u.]. NoH. Number of hours comprising operating point o [h]. I Pmax,g. Maximum power that can be built of generating unit g [MW]. G Pmax,g. Capacity of generating unit g [MW]. G Pmin,g. Minimum power output of generating unit g [MW]. L Pmax,l. Capacity of transmission line l [MW].

(31) LIST OF TABLES. xxxi. S Pmax,g. Maximum power that can be scheduled in the day-ahead market by wind unit g [MW]. W Pgos. Available wind power for wind unit g in operating o and scenario s [MW]. QFgos. Thermal power generated by the SF of CSP plant g in operating point o and scenario s [MW-t]. FS/SEmax. Qg. Maximum thermal power transferred to and taken out from TES of CSP plant g [MW-t]. Smax/min. Qg. Upper and lower limits on the energy content in the TES of CSP plant g [MWh-t]. QSini g. Energy level in the TES of CSP plant g in the initial period [MWh-t]. U/Pmax. qg. D/Umax. Rg. Maximum turbining/pumping flow of pumped-storage unit g (Hm3 /h) Maximum down/up reserve that can be scheduled by biomass unit g [MW]. do/up. rampg. D/Umin. Down/up ramping limit of generating unit g [MW/h]. Tg. Minimum down/up time of generating unit g [h]. Tgoff. Stages the generating unit g remains working [year]. L/Uini. Vg. Initial volume of water in the lower/upper reservoir of pumpedstorage unit g [Hm3 ]. Lmax/min. Vg. Maximum/minimum level of the lower reservoir of pumpedstorage unit g [Hm3 ]. Umax/min. Vg. Maximum/minimum level of the upper reservoir of pumpedstorage unit g [Hm3 ].

(32) xxxii. LIST OF TABLES. η1. Conversion efficiency of the thermal power produced in the SF to electricity of CSP plants [p.u.]. η2. Loss efficiency of TES of CSP plants [p.u.]. λno. System marginal cost at scheduling stage [$/MWh]. λnos. System marginal cost at real-time operation [$/MWh]. πs. Probability of scenario s [p.u.]. P/T. σg. Conversion factor for pumping/turbining of pumped-storage unit g [MW/Hm3 /h]. Variables Operation Model SD/SU. Down/up reserve scheduled by demand j in operating point o [MW]. djos. RD/RU. Down/up reserve deployed by demand j in operating point o and scenario s [MW]. dUS jos. Power unserved for demand j in operating point o and scenario s [MW]. pG gos. Power generated by unit g in operating point o and scenario s [MW]. pSgo. Power scheduled by unit g in operating point o [MW]. pLlo. Power flow through transmission line l in operating point o [MW]. pLlos. Power flow through transmission line l in operating point o and scenario s [MW]. Djo.

(33) LIST OF TABLES. xxxiii. pPgos. Consumed power by pumped-storage unit g in operating point o and scenario s [MW]. pspill gos. Power spillage of generating unit g in operating point o and scenario s [MW]. QFE gos. Thermal power produced in the SF to produce electricity for CSP plant g in operating point o and scenario s [MW-t]. QFS gos. Thermal power produced in the SF and transferred to the TES of CSP plant g in operating point o and scenario s [MW-t]. QSgos. Thermal energy available in the TES of CSP plant g in operating point o and scenario s [MWh-t]. QSE gos. Thermal power of the TES used to produce electricity of CSP plant g in operating point o and scenario s [MW-t]. SD/SU. Rgo. D/U. Down/up reserve scheduled by biomass unit g in operating point o [MW]. rgos. Down/up reserve deployed by biomass unit g in operating point o and scenario s [MW]. NS rgos. Non-scheduled reserve deployed by biomass unit g in operating point o and scenario s [MW]. SUgo. Start-up cost of biomass unit g in operating point o [$]. Ugo. Binary variable that is equal to 1 if generating unit g is online in operating point o, and 0 otherwise. Ygo. Binary variable that is equal to 1 if generating unit g is started up in operating point o, and 0 otherwise. Zgo. Binary variable that is equal to 1 if generating unit g is shut down in operating point o, and 0 otherwise. S δno. Voltage angle at node n in operating point o [rad].

(34) xxxiv δnos. LIST OF TABLES Voltage angle at node n in operating point o and scenario s [rad]. Investment Models djos. Consumed power for demand j in operating point o and scenario s [MW]. dUS jos. Power unserved for demand j in operating point o and scenario s [MW]. pIg. Power built of generating unit g [MW]. pG gos. Power generated by unit g in operating point o and scenario s [MW]. pLlos. Power flow through transmission line l in operating point o and scenario s [MW]. ylL. Binary variable that is equal to 1 if prospective line l is built, and 0 otherwise. δnos. Voltage angle at node n in operating point o and scenario s [rad]. µs. Auxiliary variable of the CVaR in scenario s [$]. ρ. Auxiliary variable of the CVaR [$]. Sets NG (n). Set of generating units connected to node n. NJ (n). Set of demands connected to node n. ΩB. Set of biomass units. ΩCSP. Set of CSP units. ΩGHG. Set of thermal units emitting greenhouse gases.

(35) LIST OF TABLES ΩG1. Set of mature technologies. ΩG2. Set of immature technologies. ΩL. Set of existing transmission lines. ΩL+. Set of prospective transmission lines. ΩN. Set of nuclear power units. ΩP. Set of pumped-storage units. ΩPV. Set of solar PV units. ΩQ q. Set of operating points pertaining to season q. ΩRW. Set of renewable units. ΩTh. Set of thermal units. ΩW. Set of wind units. Acronyms ac. Alternating current. CSP. Concentrating solar power. dc. Direct current. GHG. Greenhouse gas. ISO. Independent system operator. LDR. Linear decision rule. CCGT. Combined cycle gas turbine. O&M. Operation and maintenance. PV. Photovoltaic. xxxv.

(36) xxxvi. LIST OF TABLES. SF. Solar field of a concentrating solar power plant. TES. Thermal energy storage.

(37) Chapter 1 Introduction mportant reasons lead us to think that future electric energy systems may be dominated by renewable energy sources. Global warming issues, air quality deterioration, the eventual increase in fossil fuel costs, security problems of nuclear power and the decrease in renewable investment costs are drivers for an increasing penetration of renewable energies. The aim of this dissertation is to provide models to enable a good integration of renewable power in electric energy systems.. I. In this chapter, we provide an introduction to the thesis work. First, we describe the agents participating in electricity markets and the general rules that govern these markets. Second, we present an overview of the main characteristics of renewable energies. Third, the thesis motivation is provided. Fourth, a literature review is carried out regarding the main topics involved in this dissertation. Finally, the objectives and the structure of the thesis are described.. 1.1 1.1.1. Electricity Markets Evolution. The electric power sector is in continuous evolution. This strategic sector has to adapt its structure to the upcoming economic, social and environmental conditions. 1.

(38) 2. 1. Introduction. After the Second World War, the electric sector was operated in a centralized way. In general, public institutions were responsible for the generation, transmission and supply of electricity. However, economical and technical problems appeared due to the lack of competitiveness. As a consequence, in the 80’s and 90’s the liberalization of the electricity sector started [47]. In the following decades, electricity markets were established in most countries. On the other hand, the electricity generation has been traditionally based on burning fossil fuels, which has lead to well-known environmental issues. Thus, renewable power technologies are increasingly introduced in power systems to mitigate these issues. This implies integrating large amounts of intermittent and non-dispatchable generation coming from renewable sources. However, electricity cannot be stored in large amounts, and must be consumed at the same time as it is produced. Then, the integration of renewable resources may require introducing relevant changes in the way electric energy systems are operated and planned.. 1.1.2. Agents. The agents that participate in electricity markets are producers, consumers, retailers and system operators [47]: • Dispatchable producers: These agents own generating units whose electricity production is controllable. They produce and sell electricity through electricity markets and directly to consumers. Their aim is to maximize their profits. • Non-dispatchable producers: These agents own generating units whose electricity production depends on a stochastic (intermittent and non-dispatchable) resource. They sell their electricity production directly to the markets and consumers, and in some cases they can receive subsidies for their electricity production. • Retailers:.

(39) 1.1. Electricity Markets. 3. They are intermediaries between producers and consumers. They buy electricity from producers to sell it to those consumers that do not participate in the markets. They seek to maximize their respective profits. • Consumers: They use the electricity generated by the producers. Large consumers can directly participate in the electricity markets. Small consumers do not usually participate in the markets, but buy energy from retailers. • Market Operator: The Market Operator (MO) is the entity in charge of the economical management of the electricity markets. It clears the markets and provides the final prices and the traded energy quantities. • Independent System Operator: The Independent System Operator (ISO) is responsible for the technical management of the electric energy system. It determines the technical constraints required to ensure supply. In some markets, the ISO incorporates the functions of the MO, being in charge of both the economical and technical management of the system.. 1.1.3. Structure. The electricity trading takes place in several market floors. They are generally organized in a pool and in a futures market [35]. • Pool: The pool comprises the day-ahead market, several intra-day markets known as adjustment markets, and the balancing or real-time market. In these markets, the producers provide their production offers while the retailers and consumers propose their consumption bids. Then, the MO clears the market and gives the final prices and the produced/consumed scheduled quantities..

(40) 4. 1. Introduction. Most of the energy is purchased in the day-ahead market. The day-ahead market is cleared once a day the previous day to the real-time operation. In this market, the transmission network can be considered or not. If it is not considered, the resulting price is the same for all producers and consumers. Otherwise, if transmission network is considered and congestion takes place, the prices are different throughout the network. Then, locational marginal prices (LMPs) are obtained in each node of the network. The adjustment markets are cleared several times during the day and correct the possible deviations between the consumptions and productions scheduled in the day-ahead market. These markets are specially relevant for non-dispatchable producers, since their predictions of the available power improve to the proximity to power delivery. The balancing or real-time market is the last market resource and takes place minutes prior to power delivery. • Futures market: In this market, medium and long term energy transactions between producers, retailers and consumers take place at stable prices, which stabilizes the profit/cost volatility of producers/consumers.. The introduction of large amounts of variable power may lead to modifications in the structure of the electricity markets. If non-dispatchable producers provide most of the demand necessities, adjustment markets may acquire more relevance. In this dissertation, we consider a pool-based electricity market for scheduling energy and reserves in a renewable-dominated power system. In this market both dispatchable and non-dispatchable producers participate, although most of the generating capacity corresponds to non-dispatchable technologies. Further, we also focus on the expansion steps required to integrate large amounts of non-dispatchable power in electric energy systems..

(41) 1.2. Renewable Energies. 1.2 1.2.1. 5. Renewable Energies General Overview. Renewable energies have progressively increased their presence in electric energy systems. Global warming, energy dependency from fossil fuels and security and social problems associated with nuclear energy have lead developed countries to exploit renewable resources. The main advantages of renewable energies are fivefold: • Their production depends on unlimited resources • The resources are available all over the planet • They represent an environmental sustainable solution • They contribute to the economic development of the region where they are located • They reduce the energy dependency from fossil fuels Nevertheless, renewable energies have also disadvantages, which are the stochasticity of the resource and the high investment costs of the different technologies. These drawbacks have been moderately reduced in the last years by improving the capacity factors of different technologies while reducing their investment costs. By the end of 2013, the total renewable capacity in the world was 560 GW, not including hydropower, and 1,560 GW including hydropower [101]. Due to the economic difficulties, the growth in the installed renewable capacity has decreased in 2013 with respect to previous years, specially in Europe and the US, [101]. However, predictions of energy agencies indicate that the renewable capacity in 2020 will be about twice that in 2013 and up to five times in 2050 [43, 50, 59]. The installed capacity of 560 GW of renewable capacity is comprised as follows: 318 GW corresponds to wind power, 139 GW to solar photovoltaic (PV) power, 88 GW to bio-power, 12 GW to geothermal power and 3.4 GW.

(42) 6. 1. Introduction. to concentrating solar power (CSP), [101]. Excluding hydropower, China, US, Germany, Spain, Italy and India lead the list of countries with more renewable capacity. However, renewable technologies (not including hydropower) only supplied 4% of the global electric demand needs. Operating and planning models that recognize the specificities of renewables are much needed to efficiently integrate renewable power in energy systems.. 1.2.2. Wind Energy. Large amounts of wind power have been integrated in power systems worldwide in the last years [57, 101]. The maturity of the technology, the relatively low investment costs as compared to other renewable technologies [58], and the resource availability have lead to building high wind capacity in some parts of the world. Further, the technology improvements have resulted in higher capacity factors while decreasing investment costs [57]. The integration of wind power in electric energy systems has been relevant in countries like Spain or Denmark. For instance, in 2013 wind power supplied 21% of the electric demand in Spain, similarly as nuclear power [100]. In the same year, 33% of the annual demand in Denmark was supplied by wind power [5]. The projection of international agencies for the future development of wind technologies in the world establish that the wind installed capacity can reach 500 GW by 2018 [57].. 1.2.3. Solar Energy. Two solar technologies have been widely used in the last years: solar PV and CSP. The comparatively low investment cost of solar PV and the solar resource availability have lead to an extraordinary growth of the solar PV capacity in the last years [101]. In 2013, 39 GW of solar PV were built around the world. To increase the efficiency of this technology, energy storages such as electrochemical batteries are usually used for domestic energy procurement [113]. CSP plants can provide higher stable capability than other renewable plants because the only difference between CSP plants and conventional thermal.

(43) 1.2. Renewable Energies. 7. plants is the resource used to heat the transfer fluid. The connection to the grid of both power plants (conventional thermal and CSP) is via a steam turbine and a synchronous generator, which provides stable capability [73], [124]. This is not the case of other renewable sources, such as wind power. The high potential of solar resources in some geographic areas and the controllability of CSP plants through thermal energy storage (TES) systems and/or hybridization with other generation technologies such as biomass units, [93], or coal or combined cycle natural gas units, [94], place the solar energy as a key component in the future generation mix in countries with high solar resources. It is relevant to note the high dispatchability of a CSP plant that incorporates a molten salt TES, which involves low heat losses and high overall efficiency of the plant, [117]. Although investment and operation costs of TESs are still high, CSP plants such as Andasol I and II in Granada, Spain, have demonstrated the viability of the CSP technology, [3]. TESs eliminate transition periods without production due to the lack of solar resources (cloudy periods), allow displacing the production periods (by storing thermal energy from the solar field (SF) during periods of low prices and then delivering it during high price periods) and, finally, TESs also allow the extension of the whole production period. The main drawbacks of the CSP technologies are the availability of the solar resource, which is limited to specific areas of the planet, and the high investment costs.. 1.2.4. Biomass Energy. To meet the clean energy expectations in developed countries, it may be necessary to increase the use of biomass resources to produce electricity. In references [76] and [77] an overview of the main characteristics of the biomass resources and the conversion technologies is analyzed. The main drawbacks of biomass energy are the difficulty in harvesting and transporting the resources, and consequently the high cost involved, and the low efficiency in the energy conversion processes, [29]. However, renewable-dominated power systems with high generating capacity of non-dispatchable technologies require enough dispatchable capacity to assure supply security of the electric demand regarding.

(44) 8. 1. Introduction. the variability of renewable resources. Biomass units produce electricity using the same thermodynamic principles as thermal units, which provides stability and reliability to the system.. 1.3. Thesis Motivation. To avoid an increment of more than 2 degrees Celsius in the average global temperature of the planet Earth, the greenhouse gas (GHG) emissions must drastically decrease in the following years [54]. About 30% of the total GHG emissions comes from electricity generation. Emission reductions in this sector can be tackled by reducing the energy necessities, increasing the efficiency of generating technologies and integrating renewable energies in power systems. In this dissertation, we focus on the last action. Integrating large amounts of renewable production in electric energy systems constitutes an interesting challenge since the electricity production from wind and solar technologies depends on variable and uncertain resources. Power systems with high variable capacity are difficult to manage. This causes to increase the reserve needs, which are supplied by dispatchable units such as biomass or hydropower units. On the other hand, pumped-storage and CSP units can control their production since they have storage capacity. If available, these units provide stability to the system while representing an environmental friendly solution. The reliability of wind and solar predictions methods, the evolution of biofuels prices and the reserve needs of power systems will determine the production strategies of producers and the electricity prices. Within this framework, the following questions arise: • How a fully renewable system, involving variable and uncertain production sources, should be operated so that the energy supply quality is maintained? • How are scheduled productions/consumptions and prices affected if nondispatchable renewable sources dominate the system?.

(45) 1.4. Literature Review. 9. • How do scheduling outcomes change if storage facilities are available? • How does an appropriate level of flexibility facilitate the operation of the system? • How current thermal-based electric systems should evolve to become renewable-dominated or fully renewable? In this dissertation, we seek to answer these questions. To do so, we propose both operating and investment models whose main objective is to ease the integration of renewable energies in a power system.. 1.4 1.4.1. Literature Review Integration. In the last years, the presence of wind power facilities in electric energy systems has noticeably increased all over the world. The difficulty to predict the wind power availability has lead to numerous studies in different topics: • Forecasting models and modeling of prediction errors [44, 119, 123], • Scenario generation and scenario reduction techniques [17, 51, 71, 83], • Determination the reserve requirements in power systems with high wind capacity [27, 39, 81, 86, 90]. Additionally, several references propose models to efficiently generate offering curves for wind producers, [19, 82, 96]. These references present models based on stochastic programming which allow a wind power producer to offer efficaciously in an electricity pool, maximizing its expected profit while controlling the risk of profit variability. In [80], a complete proposal of operating models for electric energy systems with high penetration of renewable power is provided. The proposed operating models aim to efficiently integrate renewable power in electric energy systems, adopting in each case the point of view of the ISO, the non-dispatchable producers and the demand..

(46) 10. 1. Introduction. On the other hand, the technical literature pertaining to the operation of CSP plants is modest. The pioneering work reported in [111] analyzes the value of CSP plants and TES in various regions of the US and characterizes the profitability of CSP plants using a mixed-integer linear programming model, whose inputs come from a specialized software. The thermal power produced by the SF in each hour and the market prices are input data to the model. Using this information, [111] reports results from several studies to assess the profits obtained by a CSP plant with TES when participating in the pool, the impact on the profits of the optimization horizon and the impact of participating in reserve markets, among others. On the other hand, reference [40] proposes a model to build strategic offering curves for a CSP plant which incorporates a TES. The model is formulated as a mixed-integer linear stochastic programming problem, where the thermal power production from the SF and the market prices are considered as uncertain parameters. The uncertainty of the solar resource availability is modeled using robust optimization [24, 25], whereas the variability of market prices are represented via scenarios [26]. Since storage capacity is important in a renewable-based power system, several references consider storage system. References [116] and [89] propose scheduling strategies for a producer with storage capacity. Specifically, reference [116] defines a self-scheduling strategy for a producer that owns wind and pumped-storage units. This producer participates in the day-ahead and ancillary markets, and the uncertainty of wind power production is modeled through a neural network. Reference [89] considers a virtual power plant that comprises a stochastic source, a storage facility and a dispatchable unit. This virtual power plant sells and purchases electric energy in the day-ahead and balancing markets to maximize its profit. Stochastic programming is used to model the uncertainty of electricity prices and the stochastic production.. 1.4.2. Operations. References regarding the operation of fully renewable electric energy systems in the technical literature are scarce. However, a number of references regarding the operation of electric energy systems with high penetration of wind.

(47) 1.4. Literature Review. 11. power are available. As an example, reference [114] quantifies the reduction in total operating cost if stochastic optimization is used instead of deterministic optimization in power systems with high presence of stochastic generators. Reference [37] integrates numerical weather prediction methods in stochastic unit commitment and economic dispatch formulations via a computational framework that allows updating the wind power available more frequently and, therefore, the intra-day rescheduling of thermal units. Reference [78] proposes a stochastic mixed integer linear model that minimizes the expected system cost in Ireland, considering the load and the wind power production as stochastic inputs to the model. In an electric energy system in which most of the power supplied comes from non-dispatchable producers, reserve needs to increase. Therefore, it is most appropriate to co-optimize the schedules of energy and reserve. References [27, 79, 81, 91, 118, 126] are examples of market models that co-optimize energy and reserve. Reference [126] proposes a pricing scheme based on cooptimization in the real-time dispatch, in which prices are calculated in a decoupled manner. Reference [27] applies the stochastic security concept described in [28] to formulate a short-term electricity market-clearing problem with two uncertainty sources: wind power availability and errors in demand predictions. In reference [118], the problems associated with the volatility of wind power are addressed within a Benders’ framework by iterating a master unit commitment problem and subproblems that consider plausible wind power scenarios. Reference [81] proposes a stochastic programming marketclearing model to determine the optimal level and the costs of spinning and non-spinning reserves in a power system with high penetration of wind power. Reference [91] presents a two-stage stochastic unit commitment model to determine the reserve requirements in a power system with high presence of wind power and develops a method for generating and weighting wind power scenarios based on certain criteria that capture the typical behavior of wind. On the other hand, [79] develops a single-period network-constrained auction in an electricity pool with numerous wind producers, dispatching simultaneously energy and reserve. The proposed formulation allows deriving day-ahead and balancing energy prices..

(48) 12. 1.4.3. 1. Introduction. Planning. In the technical literature, there exits relevant works describing investment models in generating capacity in power systems. Most of these works adopt a static (only one investment decision) approach due to the high computational cost of multi-stage (multiple investment decisions) models. Recently, the capacity expansion problem has been framed within a market environment and also from the point of view of producers. We provide below relevant references tackling investment models from static and multi-stage perspectives. Static Approach Relevant references regarding the investment in generating and transmission capacity within a static framework are described below. Reference [13] proposes a two-stage mixed integer non-linear stochastic programming model for the transmission and generating capacity expansion, where the uncertainty associated to the demand, the capacity of transmission lines and the capacity factor of generating units is considered. References [105] and [106] present a market-based model to coordinate generation and transmission capacity expansion with a mechanism of incentives and payments for transmission and capacity agents. Reference [16] presents an investment model in wind power facilities within a market environment. A Benders decomposition technique is used to efficiently solve the proposed bi-level model [36]. As an extension of the previous model, reference [15] proposes a mathematical model that simultaneously considers wind power investment decisions and transmission reinforcements, within a market environment, where consumer payments are minimized. In both [15] and [16], the perspective of an electric company is adopted, whose objective is maximizing its profits. Reference [85] also focuses on the integration of wind power in the electric energy systems but from the ISO perspective. The aim of this paper is to determine the best wind locations and the optimal capacity to be built taking into account the investment cost of transmission facilities. On the other hand, references [64], [65] and [66] propose bi-level stochastic programming models to define the strategic investment decisions to be made by a power producer within a competitive market. The.

(49) 1.4. Literature Review. 13. uncertainty of the demand growth and the rivals behavior are represented. In reference [97], a three-level equilibrium model for the optimal transmission and capacity expansion is presented, considering uncertainty in demand and in wind and hydro power production. Reference [61] develops a bi-level programming model to jointly coordinate generation and transmission capacity investments within a competitive electricity market. Finally, reference [50] analyzes the operation of the electric energy system of the US in 2050 with a high penetration of renewable production. In this reference, several renewable integration case studies are analyzed and relevant suggestions are made to attain a better integration of renewable resources in the US.. Multi-Stage Investment Models Multi-stage decision-making problems in which the involved uncertainty is gradually disclosed as the decision-making process advances are frequent in practice [35]. From a modeling perspective, the mathematical formulation of these problems is challenging because it requires to model precisely the dynamic aspects of the decision-making process and the involved uncertainty. Traditionally, multi-stage decision-making problems under uncertainty have been formulated as multi-stage stochastic programming problems [26]. However, there are few references in the technical literature of multi-stage stochastic capacity planning models since the large dimension of these models usually lead to computational intractability. Reference [121] develops a bi-level generation capacity expansion model to maximize the profits of an electric company that participates in an oligopolistic market, where the investment decisions of competitors are uncertain. On the other hand, reference [18] proposes a multi-stage investment model for a wind power producer that aims to maximize its profit by selling its production in the market. The uncertainty of demand growth and investment cost of wind facilities is represented via scenarios. A risk measure is considered to control the profit variability. A Benders decomposition technique is applied to efficiently solve this problem..

(50) 14. 1.4.4. 1. Introduction. Methods. Methods to address operations and planning problems under uncertainty are briefly revised below. Stochastic Programming In real world, it is common to find decision-making problems in which some of the input data are uncertain (price of electricity, demand growth, investment costs, etc.). These uncertain parameters can usually be described through probabilistic distributions. Stochastic programming allows modeling decisionmaking problems by considering the probabilistic distributions of the uncertain parameters [35]. In some occasions, the solution provided by the equivalent deterministic problem which uses the expected values of the uncertain parameters does not offer the best outcomes. Thus, the stochastic programming problem provides the best solution to the decision-maker considering all possible values of the uncertain parameters. However, the main drawback of stochastic programming is the size of the resulting problem, which usually leads to computational intractability. The basics and mathematical fundamentals of stochastic programming can be found in [26, 38, 62, 63]. Stochastic programming relies on the knowledge of the probabilistic distribution of the uncertain parameters. Scenarios are used to represent the plausible values of uncertain parameters. Therefore, an adequate generation technique of scenario trees is important to achieve a good representation of the uncertain parameters [41,53,83]. Further, efficient scenario reduction techniques needed [42, 49, 51, 84]. On the other hand, significant works have been carried out to define appropriate risk measures to control the variability of the profits in decision-making problems under uncertainty [12, 75, 95, 104]. Decision Rules Approach The main disadvantage of multi-stage stochastic programming models is the growth of the size of the problem with the number of scenarios, making the problem computationally intractable. This fact is determinant when several decision points or stages are considered. Indeed, the number of constraints.

(51) 1.4. Literature Review. 15. in a multi-stage stochastic programming problem increases exponentially with the number of stages. For this reason, in those cases in which a large number of stages are needed, the usage of multi-stage stochastic programming models may not be adequate. In such situation, the decision rules approach [70] allows us to approximate multi-stage stochastic problems efficiently. Although the first steps on the use of decision rules to solve problems under uncertainty were made long time ago [46], the consideration of this technique has been received recently significant attention. Reference [21] uses the idea of establishing an affine relationship between the decision variables and the uncertain parameters under the framework of the robust optimization. References [33] and [110] analyze the potential of applying linear decision rules to solve complex decision-making models such as multi-stage stochastic problems. The use of the so-called decision rule approach results in a problem that approximates the initial one, since the space of optimal solutions is restricted to that in which optimization variables and the uncertain data are linearly related. Therefore, there is an error between the optimal solution of the initial problem and that of the approximate one. References [69] and [70] propose a methodology to measure this approximation error. Finally, references [102] and [120] apply the decision rule approach to problems concerning electric energy issues.. Robust Optimization In recent years, robust optimization has been used to solve optimization problems under uncertainty. Robust optimization allows mitigating two stochastic programming drawbacks, namely the need to generate scenarios, and derived from this, potential computational intractability [20, 22]. In a robust optimization approach, the uncertain parameters are kept within robust sets. The solutions are feasible for all values of the uncertain parameter, while the optimal solution results from considering the worst-possible situation. Regarding the operation of electric energy systems, references [23, 32, 125] apply robust optimization to solve the unit commitment problem. Reference [127] proposes a robust optimization model to dispatch energy and reserve in.