Coordination of Independent Distributed Generation and Controllable Load

Coordination of Independent Distributed Generation and Controllable Load José Alberto da Cunha Barros Dissertation submitted to the Faculty of Engineering of University of Porto in partial fulfilment of the requirements for the degree of Doctor of Philosophy Supervisor: Prof. Hélder Filipe Duarte Leite Lecturer at the Department of Electrical and Computer Engineering Faculty of Engineering, University of Porto Co-supervisor: Prof. Nick Jenkins Professor at the Institute of Energy School of Engineering, Cardiff University United Kingdom February 2013 (Original Version) March 2014 (Reformulated Version) iii This work was financially supported by FCT – Fundação para a Ciência e Tecnologia de Portugal, under the grant SFRH/BD/43688/2008. v “I have nothing to offer but blood, toil, tears and sweat.” Winston Churchill vii Abstract The research carried out focuses on the way generators connect to distribution networks. Permission to connect a generator to the distribution system is generally obtained on the basis that the generator’s effect is limited and that the network voltages and currents remain acceptable at all times. This firm access connection policy limits the capacity of generation that can be connected. Generators may be allowed to connect to distribution networks above the limit defined by the firm access connection policy. When there is inadequate capacity in the system, the non-firm generators are generally constrained off on a “last-in, first-off” basis (the last to connect is the first to be affected). Only the order of connection of the generators is taken into account. Different costs of operation and ability to be dispatched are not considered. Thus, the firm access connection policy does not maximise the economic value of the generators. The coordination of independent distributed generators is formulated in this research to maximise the income received by the generators. The coordination schedules generators connected to the same circuit according to their different costs of operation and ability to be dispatched, without exceeding the power limit of the circuit. Additional income is obtained by the generators for the additional electricity sold and the substitution of expensive generators by cheaper ones. An income-sharing mechanism based on cooperative game theory to share the additional income is outlined. The objective is to provide the generators an economic incentive to be operated in a coordinated manner. Demand side flexibility can be used to maximise the production of the generators. The coordination of generators and controllable load is devised in this research to maximise the income of the generators. Controllable load is asked to shift its consumption to allow the generators to maximise their production. The additional income resultant of the coordination is allocated to the generators and the controllable load. A bargaining approach of game theory is used to determine this allocation. The controllable load receives part of the additional income to cover the increase of its electricity bill and to incentivise its coordination with the generators. This study is then extended to consider energy storage systems instead of controllable load, in coordination with non-dispatchable generators. A representative of the Portuguese distribution network is used to validate the coordination of independent distributed generators and the coordination of generators and controllable load. Four independent distributed generators and a load equivalent are connected to the network. A number of cases of wind power, price of electrical energy and load consumption are considered. Different costs of operation of the generators are analysed. Different levels of load flexibility and load capacity are evaluated. ix Resumo A investigação desenvolvida concentra-se na ligação de geradores às redes de distribuição. A permissão para ligar um gerador à rede de distribuição é geralmente obtida no pressuposto que o seu efeito é limitado e que as tensões e correntes na rede se mantêm aceitáveis em todas as circunstâncias. Esta política de acesso firme limita a capacidade de geração que pode ser ligada. Geradores podem obter autorização de ligação às redes de distribuição acima do limite definido pela política de acesso firme. Quando existe capacidade inadequada no sistema, os geradores sem acesso firme são geralmente restringidos segundo a regra “último a entrar, primeiro a sair”. Só a ordem de ligação à rede é tida em consideração. Diferentes custos de operação e capacidades de serem despachados não são considerados. Assim, a política de acesso firme não maximiza o valor económico dos geradores. A coordenação de produtores dispersos independentes é formulada nesta investigação para maximizar o rendimento recebido pelos geradores. A coordenação escalona geradores ligados no mesmo circuito de acordo com os seus diferentes custos de operação e capacidades de serem despachados, sem exceder o limite de potência do circuito. Rendimento adicional é obtido pelos geradores pela energia adicional vendida e pela substituição de geradores caros por geradores mais baratos. Um mecanismo de partilha de rendimentos, baseado na teoria dos jogos cooperativos, para partilhar o rendimento adicional é delineado. O objectivo é fornecer aos geradores um incentivo económico para a sua operação de forma coordenada. A flexibilidade da procura pode ser usada para maximizar a produção dos geradores. A coordenação de geradores e carga controlável é desenvolvida nesta investigação para maximizar o rendimento dos geradores. A carga controlável é chamada a transferir o seu consumo de forma a permitir aos geradores a maximização da sua produção. O rendimento adicional resultante da coordenação é alocado por geradores e carga controlável. Uma abordagem de negociação da teoria dos jogos é usada para determinar esta alocação. A carga controlável recebe parte do rendimento adicional para cobrir o aumento da sua conta da electricidade e para incentivar a sua coordenação com os geradores. Este estudo é em seguida estendido para incorporar sistemas de armazenamento de energia em vez de carga controlável, em coordenação com geradores não despacháveis. Uma secção da rede de distribuição portuguesa é usada para validar a coordenação de produtores dispersos independentes e a coordenação de geradores e carga controlável. Quatro produtores dispersos independentes e um equivalente de carga estão ligados à rede. Alguns casos de potência de vento, preço da energia eléctrica e consumo da carga são considerados. Diferentes custos de operação dos geradores são analisados. Diferentes níveis de flexibilidade e de capacidade da carga são avaliados. Table of Contents xvi References .................................................................................... 103 Appendix A - Cost-benefit analyses to determine the installed capacities of generators GenC and GenD ................................................................ 111 Appendix B - AC optimal power flow in the representative of the Portuguese MV distribution network ....................................................................... 117 Appendix C - Data of the selected period of operation ............................. 121 Appendix D - Output powers of the generators without and with the coordination of independent distributed generators ................................................. 125 Appendix E - Generation and consumption schedules without and with the coordination of distributed generators and controllable load .................... 137 xvii List of Figures Figure 2.1 – “Last-in, first-off” access ............................................................................. 15 Figure 2.2 – Pro-rata access ......................................................................................... 15 Figure 2.3 - One form of market-based access: capacity auction ............................................. 15 Figure 2.4 - The concept of virtual power plant ................................................................. 23 Figure 2.5 – Classification of demand-side integration implementations by timing requirements ........ 33 Figure 2.6 – Example of pricing schemes: a) time of use rates b) real-time pricing c) critical peak pricing .......................................................................................................................... 34 Figure 3.1 – 60 kV distribution network of Northeast Portugal ................................................. 39 Figure 3.2 – Distribution network below Valpaços substation (rural distribution network) ................ 40 Figure 3.3 - side, maximum load and generators not operating .............................................................. 42 Figure 3.4 - side, no load and generators operating at maximum output ................................................... 42 Figure 3.5 - Operation of the distribution network during 24 hours, with the generators producing and with a typical load curve ............................................................................................ 44 Figure 3.6 - Distribution network with the four generators (GenA and GenB are firm connected, GenC and GenD have no firm access rights) ............................................................................. 45 Figure 3.7 - Operation of the distribution network with the four generators in hour 23, with minimisation of the costs of producing active power (AC OPF) ................................................ 46 Figure 3.8 - Operation of the distribution network during 24 hours, with the four generators producing and with a typical load curve ....................................................................................... 47 Figure 4.1 - The Aggregator operating the coordination of distributed generators ......................... 52 Figure 4.2 – Two-busbar distribution network used to evaluate the coordination ........................... 57 Figure 4.3 - Three profiles of one day of price of electrical energy........................................... 59 Figure 4.4 - Three profiles of one day of wind power ........................................................... 59 Figure 4.5 - Two profiles of one day of load ...................................................................... 59 Figure 4.6 - Output powers of the generators without coordination (day 1) ................................. 61 Figure 4.7 - Output powers of the generators without coordination (day 4) ................................. 61 Figure 4.8 - Coordinated output powers of the generators (day 1) ............................................ 61 Figure 4.9 - Coordinated output powers of the generators (day 4) ............................................ 61 Figure 4.10 - Output powers of the generators without coordination (day 2) ............................... 62 Figure 4.11 - Output powers of the generators without coordination (day 5) ............................... 62 Figure 4.12 - Coordinated output powers of the generators (day 2) .......................................... 63 Figure 4.13 - Coordinated output powers of the generators (day 5) .......................................... 63 Figure 4.14 - Output powers of the generators on days 3 and 6 - no excess power observed in the distribution circuit .................................................................................................... 64 Figure 4.15 - Additional income obtained on each day with different costs of fuel of GenC .............. 64 Figure 4.16 - Coordinated output powers of the generators in point A ....................................... 65 Figure 4.17 - Output powers of the generators in point B ...................................................... 65 Figure 4.18 - Additional income obtained on the selected week of operation with different costs of fuel of GenC ................................................................................................................ 65 Figure 4.19 - Sharing of the additional income obtained on day 1 (66.87€) .................................. 66 List of Figures xviii Figure 4.20 - Sharing of the additional income obtained on day 2 (86.49€) .................................. 67 Figure 4.21 - Sharing of the additional income obtained on day 4 (162.84€) ................................ 67 Figure 4.22 - Sharing of the additional income obtained on day 5 (211.08€) ................................ 68 Figure 4.23 - Effect in the additional income of GenC of its reduction to allow GenD to produce, considering different technology coefficients .................................................................... 69 Figure 5.1 – Operation of the Aggregator with the integration of a controllable load in the coordination .......................................................................................................................... 72 Figure 5.2 – Inputs, parameters and outcomes of the Aggregator in the coordination of generators and controllable load ...................................................................................................... 72 Figure 5.3 - Price paid by the controllable load for buying electricity on days 1 and 4 .................... 76 Figure 5.4 - Price paid by the controllable load for buying electricity on days 2 and 5 .................... 76 Figure 5.5 - Price paid by the controllable load for buying electricity on days 3 and 6 .................... 77 Figure 5.6 - Consumption schedule of the controllable load with a ±10% fraction of load flexibility on day 1 (no coordination with the generators) ...................................................................... 77 Figure 5.7 - Coordinated output of the generators with a ±10% fraction of load flexibility on day 1 (without coordination with the controllable load) ............................................................... 78 Figure 5.8 - Consumption of the controllable load after the operation of the coordination of generators and controllable load, with a ±10% fraction of load flexibility on day 1 ...................................... 78 Figure 5.9 - Consumption schedule of the controllable load with a ±100% fraction of load flexibility on day 1 (no coordination with the generators) ...................................................................... 79 Figure 5.10 - Coordinated output of the generators with a ±100% fraction of load flexibility on day 1 (without coordination with the controllable load) ............................................................... 79 Figure 5.11 - Consumption of the controllable load after the operation of the coordination of generators and controllable load, with a ±100% fraction of load flexibility on day 1 .................................... 80 Figure 5.12 - Consumption schedule of the controllable load with a ±100% fraction of load flexibility on day 2 (no coordination with the generators) ...................................................................... 80 Figure 5.13 - Coordinated output of the generators with a ±100% fraction of load flexibility on day 1 (without coordination with the controllable load) ............................................................... 81 Figure 5.14 - Consumption of the controllable load after the operation of the coordination of generators and controllable load, with a ±100% fraction of load flexibility on day 2 .................................... 81 Figure 5.15 – Output powers of the generators after the coordination with the controllable load, with a ±100% fraction of load flexibility on day 2 ........................................................................ 81 Figure 5.16 – Additional income obtained with the coordination considering different fractions of controllable load and load capacities .............................................................................. 82 Figure 6.1 - The Aggregator operating the coordination of non-dispatchable generators and energy storage systems ....................................................................................................... 86 Figure 6.2 – Two-busbar distribution network used to evaluate the coordination ........................... 88 Figure 6.3 - Three profiles of one day of price of electrical energy ........................................... 89 Figure 6.4 - Three profiles of one day of wind power ........................................................... 89 Figure 6.5 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when GenB is connected last (day 1) ................................................................. 90 Figure 6.6 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when GenB is connected last (day 2) ................................................................. 90 List of Figures xix Figure 6.7 - Output powers of the generators and the energy storage system in “last in, first-off operation” when GenB is connected last (day 3) ................................................................ 90 Figure 6.8 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when ES connects last (day 1)......................................................................... 91 Figure 6.9 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when ES is connected last (day 2) .................................................................... 91 Figure 6.10 - Output powers of the generators and the energy storage system in coordination (day 1) . 91 Figure 6.11 - Output powers of the generators and the energy storage system in coordination (day 2) . 93 Figure 6.12 – connected last ........................................................................................................ 94 Figure 6.13 – ring one year when: i) GenB is connected last; ii) ES is connected last ........................................................................................................ 95 Figure 6.14 – when: i) GenB is connected last; ii) ES is connected last ....................................................... 96 Figure A1 - Wind speed average time series from a Portuguese wind farm (May 2010-May 2011) ....... 111 Figure A2 – Power curve of wind turbine Vestas V80 ........................................................... 111 Figure A3 – Cumulative wind power curve from May 2010 to May 2011 ...................................... 112 Figure A4 – Price of electrical energy of the Iberian Electricity Market (Portuguese side) during one year (May 2010 to May 2011) ............................................................................................. 112 Figure A5 – Net Present Value at the end of the investment with different ratings of GenC ............. 113 Figure A6 – Net Present Value at the end of the investment with different ratings of GenD ............. 115 Figure B1 - Distribution network below Valpaços substation .................................................. 117 xxi List of Tables Table 2.1 – Summary of the contributions to the integration of DG ........................................... 19 Table 2.2 – Marginal contributions of each player in a 3-player game ........................................ 30 Table 2.3 – Marginal contribution vectors of a 3-player game ................................................. 31 Table 2.4 - Applications of energy storage systems ............................................................. 32 Table 3.1 - Distribution substation loads and MV-connected distributed generation output, 20/12/2007 at 8.30 a.m. ........................................................................................................... 40 Table 4.1 – Parameters of the system ............................................................................. 58 Table 4.2 - Selected period of operation used for the evaluation of the coordination ..................... 59 Table 4.3 - Average price of electrical energy on each day of the selected period of operation ......... 59 Table 4.4 - Average wind power on each day of the selected day of operation ............................. 59 Table 4.5 - Average load on each day of the selected period of operation .................................. 59 Table 4.6 - Electrical energy produced and income received by each generator without and with coordination (day 1) .................................................................................................. 62 Table 4.7 - Electrical energy produced and income received by each generator without and with coordination (day 4) .................................................................................................. 62 Table 4.8 - Electrical energy produced and income received by each generator without and with coordination (day 2) .................................................................................................. 63 Table 4.9 - Electrical energy produced and income received by each generator with and without coordination (day 5) .................................................................................................. 64 Table 4.10 - Technology coefficients used in the income-sharing mechanism ............................... 66 Table 4.11 - Income received by each generator without coordination and with the income-sharing mechanism (day 1) ................................................................................................... 67 Table 4.12 - Income received by each generator without coordination and with the income-sharing mechanism (day 2) ................................................................................................... 67 Table 4.13 - Income received by each generator without coordination and with the income-sharing mechanism (day 4) ................................................................................................... 68 Table 4.14 - Income received by each generator without coordination and with the income-sharing mechanism (day 5) ................................................................................................... 68 Table 5.1 – Additional income obtained with the coordination, with a ±10% fraction of load flexibility on day 1 .................................................................................................................... 78 Table 5.2 - Additional income obtained with the coordination, with a ±10% fraction of load flexibility on days 2 to 6 ............................................................................................................. 78 Table 5.3 - Additional income obtained with the coordination of generators and controllable load, with a ±100% fraction of load flexibility on day 1 ...................................................................... 80 Table 5.4 - Additional income obtained with the coordination of generators and controllable load, with a ±100% fraction of load flexibility on day 2 ...................................................................... 82 Table 5.5 - Additional income obtained with the coordination of generators and controllable load, with a ±100% fraction of load flexibility on days 4 to 6 ............................................................... 82 Table 5.6 – Income received by each generator considering a ±100% fraction of load flexibility on day 1, considering: “last-in, first-off” operation; coordination of distributed generators; coordination of generators and controllable load ................................................................................... 83 List of Tables xxii Table 5.7 - Income received by each generator considering a ±100% fraction of load flexibility on day 2, considering: “last-in, first-off” operation; coordination of distributed generators; coordination of generators and controllable load ................................................................................... 84 Table 6.1 - Parameters of the system ............................................................................. 88 Table 6.2 - Selected period of operation used for the evaluation of the coordination ..................... 89 Table 6.3 - Electrical energy produced and income of each generator and energy storage system with coordination and in “last-in, first-off” operation (day 1) ....................................................... 92 Table 6.4 - Electrical energy produced and income of each generator and energy storage system with coordination and in “last-in, first-off” operation (day 2) ....................................................... 92 Table 6.5 - Income received by each generator and energy storage system as determined by Eqs. (6.13) and (6.14) when GenB is connected last (day 1) ................................................................. 94 Table 6.6 - Income received by each generator and energy storage system as determined by Equations (6.13) and (6.14) when ES is connected last (day 1) ................................................ 94 Table 6.7 - Income received by each generator and energy storage system as determined by Equations (6.13) and (6.14) when GenB is connected last (day 2) ............................................. 95 Table 6.8 - Income received by each generator and energy storage system as determined by Equations (6.13) and (6.14) when ES is connected last (day 2) ................................................ 95 Table 6.9 - Income received by each generator and energy storage system with coordination and in “last-in, first-off” operation during the year of operation considered ........................................ 95 Table A1 – Parameters of the generators ......................................................................... 112 Table A2 – Parameters for the cost/benefit analysis of the rating of GenC ................................. 113 Table A3 – Production of GenC and respective income generated during the year of operation ......... 113 Table A4 – Parameters for the cost/benefit analysis of the rating of GenD ................................. 114 Table A5 – Production of GenD and respective income generated during the year of operation ......... 115 Table B1 – Operating limits of the generators in the AC OPF .................................................. 117 Table C1 – Values of price of electrical energy, wind power and load consumption on day 1 ............ 121 Table C2 – Values of price of electrical energy, wind power and load consumption on day 2 ............ 122 Table C3 – Values of price of electrical energy, wind power and load consumption on day 3 ............ 122 Table C4 – Values of price of electrical energy, wind power and load consumption on day 4 ............ 123 Table C5 – Values of price of electrical energy, wind power and load consumption on day 5 ............ 123 Table C6 – Values of price of electrical energy, wind power and load consumption on day 6 ............ 124 Table D1 - Output powers of the generators without coordination on day 1 ................................ 126 Table D2 - Output powers of the generators with coordination on day 1 .................................... 127 Table D3 - Output powers of the generators without coordination on day 2 ................................ 128 Table D4 - Output powers of the generators with coordination on day 2 .................................... 129 Table D5 - Output powers of the generators without coordination on day 3 ................................ 130 Table D6 - Output powers of the generators without coordination on day 4 ................................ 131 Table D7 - Output powers of the generators with coordination on day 4 .................................... 132 Table D8 - Output powers of the generators without coordination on day 5 ................................ 133 Table D9 - Output powers of the generators with coordination on day 5 .................................... 134 Table D10 - Output powers of the generators without coordination on day 6 .............................. 135 Table E1 - Output powers of the generators and the controllable load without coordination on day 1 (±10% load flexibility) ............................................................................................... 139 List of Tables xxiii Table E2 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 1 (±10% load flexibility) ................. 140 Table E3 - Output powers of the generators and the controllable load with coordination on day 1 (±10% load flexibility)....................................................................................................... 141 Table E4 - Output powers of the generators and the controllable load without coordination on day 2 (±10% load flexibility) ............................................................................................... 142 Table E5 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 2 (±10% load flexibility) ................. 143 Table E6 - Output powers of the generators and the controllable load without coordination on day 3 (±10% load flexibility) ............................................................................................... 144 Table E7 - Output powers of the generators and the controllable load without coordination on day 4 (±10% load flexibility) ............................................................................................... 145 Table E8 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 4 (±10% load flexibility) ................. 146 Table E9 - Output powers of the generators and the controllable load with coordination on day 4 (±10% load flexibility)....................................................................................................... 147 Table E10 - Output powers of the generators and the controllable load without coordination on day 5 (±10% load flexibility) ............................................................................................... 148 Table E11 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 5 (±10% load flexibility) ................. 149 Table E12 - Output powers of the generators and the controllable load without coordination on day 6 (±10% load flexibility) ............................................................................................... 150 Table E13 - Output powers of the generators and the controllable load without coordination on day 1 (±100% load flexibility).............................................................................................. 151 Table E14 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 1 (±100% load flexibility) ............... 152 Table E15 - Output powers of the generators and the controllable load with coordination on day 1 (±10% load flexibility)....................................................................................................... 153 Table E16 - Output powers of the generators and the controllable load without coordination on day 2 (±100% load flexibility).............................................................................................. 154 Table E17 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 2 (±100% load flexibility) ............... 155 Table E18 - Output powers of the generators and the controllable load with coordination on day 2 (±100% load flexibility).............................................................................................. 156 Table E19 - Output powers of the generators and the controllable load without coordination on day 3 (±100% load flexibility).............................................................................................. 157 Table E20 - Output powers of the generators and the controllable load without coordination on day 4 (±100% load flexibility).............................................................................................. 158 Table E21 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 1 (±100% load flexibility) ............... 159 Table E22 - Output powers of the generators and the controllable load with coordination on day 1 (±10% load flexibility)....................................................................................................... 160 Table E23 - Output powers of the generators and the controllable load without coordination on day 5 (±100% load flexibility).............................................................................................. 161 List of Tables xxiv Table E24 - Output powers of the generators and the controllable load (coordination of distributed generators, no coordination with the controllable load) on day 5 (±100% load flexibility) ............... 162 Table E25 - Output powers of the generators and the controllable load with coordination on day 5 (±100% load flexibility) .............................................................................................. 163 Table E26 - Output powers of the generators and the controllable load without coordination on day 6 (±100% load flexibility) .............................................................................................. 164 xxv List of Abbreviations and Acronyms AC – Alternate current AHP - Analytic hierarchy process CHP – Combined heat and power CIGRE - Conseil International des Grands Réseaux Électriques (in French), International Council on Large Electric Systems CO2 – Carbon dioxide DG – Distributed generation DNO – Distribution network operator DSI – Demand-side integration EU – European Union FACTS – Flexible AC transmission system FENIX – Flexible Electricity Network to Integrate the eXpected ‘energy evolution’ HV – High voltage LMP – Locational marginal pricing MV – Medium voltage OPF – Optimal power flow PFSF – Power flow sensitivity factors p.u. – per unit OFGEM – Office of Gas and Electricity Markets TNO – Transmission Network Operator TU-game – Cooperative game with transferable utility UK – United Kingdom USA – United States of America VAT – Value added tax VPP – Virtual power plant Chapter 1 - Introduction 6 against the non-coordinated operation of generators and controllable load is provided. Economic incentives to generators and controllable load for operating in a coordinated manner are quantified. Chapter 6 The coordination of independent non-dispatchable generators and energy storage systems is presented. Energy storage systems are asked to change their schedule to allow generators to maximise their production. The operation of the Aggregator considering the connection of energy storage systems is described. Additional income is obtained from the coordination for the additional energy produced. This additional income is allocated to the generators and the energy storage systems using a bargaining approach of game theory. The coordination is evaluated on a two-busbar distribution network with two generators and an energy storage system connected. The evaluation is performed using a set of extreme cases of price of electrical energy and wind power. The impact on the additional income of different orders of connection to the network is analysed. Comparison against the non-coordinated operation of generators and energy storage systems is provided. Economic incentives to generators and energy storage system for operating in a coordinated manner are quantified. Then, the evaluation is extended to a year of operation to assess the impact on the additional income of different installed capacities of the energy storage system. Chapter 7 The contribution of this research is presented. Conclusions are drawn, addressing: i) the limitations of the firm access connection policy; ii) the coordination of independent distributed generators; iii) the coordination of generators and controllable load; iv) the coordination of non-dispatchable generators and energy storage systems. Suggestions for extending the work carried out in this research are provided. Appendices In Appendix A are presented the cost-benefit analyses behind the determination of the ratings of generators connected without firm access rights. In Appendix B are provided details of the AC optimal power flow (OPF) carried out in the representative of the Portuguese MV distribution network introduced in Chapter 3. Details of the six days of operation used to validate the coordination of independent distributed generators and the coordination of distributed generators and controllable load are given in Appendix C. Results of the implementation of the coordination of independent distributed generators to each of the six days of operation are provided in Appendix D. Results of the implementation of the coordination of distributed generators and controllable load to each of the six days of operation are provided in Appendix E. Chapter 1 - Introduction 7 1.7 - Publications during the research Directly related with the research J. A. Barros, H. Leite, "Coordinating Independent Non-Dispatchable Generation and Energy Storage Systems," International Journal of Electrical Power & Energy Systems, accepted for future publication in April 2014. J. A. Barros, H. Leite and N. Jenkins, “Coordinating Independent Distributed Generators”, in 3rd IEEE PES Innovative Smart Grid Technologies Conference, 2012 ISGT Europe, Berlin, 14 – 17 October 2012. J. Barros and H. Leite, “Feed-In Tariffs for Wind Energy in Portugal: Current Status and Prospective Future”, in 11th International Conference on Electrical Power Quality and Utilization, IEEE EPQU 2011, Lisbon, 17 – 19 October 2011. Collateral work J. Carvalhosa, J. Barros, H. Leite, A. Barbosa, P. Pereira and P. Alves, “Technical and Economic Impacts of the 2010's Grid Code Requirements for Wind Energy in Portugal”, in 11th International Conference on Electrical Power Quality and Utilization, IEEE EPQU 2011, Lisbon, 17 – 19 October 2011. H. Leite, J. Barros, V. Miranda and R. Fiteiro, “Application of a Methodology based on the Evolutionary Particle Swarm Optimization to Protection Coordination”, in 21st International Conference and Exhibition on Electricity Distribution, CIRED 2011, Frankfurt, 6 – 9 June 2011. H. Leite, J. Barros, and V. Miranda, "The Evolutionary Algorithm EPSO to Coordinate Directional Overcurrent Relays," in 10th International Conference on Developments in Power System Protection, IET DPSP 2010, Manchester, 29 March – 1 April 2010. H. Leite, J. Barros, and V. Miranda, "Evolutionary Algorithm EPSO Helping Doubly Fed Induction Generator with Ride-Through-Fault," in International Conference on Power Systems, IEEE PowerTech 2009, Bucharest, 28 June – 2 July 2009. 8 Chapter 2 - Background and literature review 2.1 - Introduction An overview of the challenges to the connection of distributed generation is given in this chapter. Contributions to facilitate the integration of increased amounts of distributed generation are reviewed. Particular attention is paid to the coordination of independent distributed generation. Game theory is presented as a tool to encourage independent generators to be coordinated. The potential of demand-side integration to allow the integration of additional amounts of distributed generation is analysed. 2.2 - Integration of Distributed Generation Distribution networks were traditionally designed to accept bulk power from the transmission network and to distribute it to consumers. Power flows were considered to be unidirectional, from the higher to the lower voltage levels. However, with increasing penetration of distributed generation (DG) power flows may become reversed. DG is operated on a must-run basis due to environmental, commercial and political drivers [2-4]. Increasing levels of “fit-and-forget” connection of DG are expected in distribution networks. The challenges introduced by the “fit-and-forget” connection of generation are identified in section 2.2.1. Contributions to integrate DG are covered in sections 2.2.2 and 2.3. 2.2.1 - Challenges to the connection of additional amounts of distributed generation Concerns with the “fit-and-forget” connection of DG include [6, 7]:  voltage regulation;  thermal limits of lines and transformers;  effect on network losses;  behaviour of DG in the case of network perturbations (“survival” to voltage dips);  higher need of balancing and reserve services;  increased harmonic distortion;  network protection issues: o modifications in network short-circuit levels; o modifications in fault current profiles; o impact on fault location and clearing practices; Many DG schemes are connected in rural zones (with low demand). There are voltage constraints that limit the amount of DG capacity that can be connected [8]. Traditional line drop compensation techniques lose their effectiveness with the connection of DG. Chapter 2 – Background and Literature Review 9 The value of losses in each node depends of the penetration level of DG. Typically, losses decrease with low DG penetration levels. However, after a certain penetration level they start to increase [9]. Many DG schemes are based on intermittent energy sources (e.g., wind and photovoltaic). The massive connection of these DG schemes introduces an increased demand for balancing and reserve provision services from the transmission networks [10]. A methodology to identify the appropriate level of reserves and their cost in a power system with high penetration of wind power is presented in [11]. Performance metrics are used to clarify conflicting economic effects of wind power penetration: fuel cost reduction and reserve cost increase. It is reported that reserve costs vary significantly due to wind power uncertainty. Thus, the “fit-and-forget” connection of further DG will be technically limited in the near future. The installed capacity of new DG schemes will be limited by this firm access connection policy. The amount of energy exported will be constrained. On the point of view of network operators, quality of supply may be affected. An increase in network operation costs is expected. Therefore, the value of DG may be reduced if no changes are made to the planning and operation of distribution networks. Network reinforcement programmes are underway in many countries to allow the massive connection of DG [12]. However, in other countries regulation and economic reasons are likely to prevent network reinforcement to be effective in the timely connection of greater amounts of generation. For instance, in Great Britain energy regulator OFGEM only allows for generator-driven investment when there is contracted generation requiring connection [13]. Thus, Distribution and Transmission Network Operators (DNOs and TNOs, respectively) in Great Britain cannot invest ahead of need under the current regulatory framework. In addition, there is currently a “£200/kW installed” cost cap on socialised investment in any upgrade to the distribution network. This means that large upgrades to DNO’s assets to connect generation, which might benefit the DNO and the customers in the long term, should be financed in great part by the generator [13]. This is likely to impact the economic return of prospective generation projects at distribution level and deter the connection of new generation. On the other hand, contributions are being presented to integrate DG without considering such reinforcements. These contributions aim to mitigate the issues related with the “fit-and-forget” connection of DG and allow the integration of additional generation capacity [14-16]. 2.2.2 - Contributions to the integration of distributed generation An overview of the contributions to allow the integration of additional generation capacity is provided as follows. Voltage coordination by voltage changing devices and DG  When a DG scheme is connected, its active power export reduces the power flow from the primary substation and so it reduces the voltage Chapter 2 – Background and Literature Review 10 drop along the feeder. If the power export from the DG is larger than the feeder load, the power flows from the DG to the primary substation and this causes a voltage rise between the primary substation and the generator [2];  Several publications address the coordination between on-load tap changers, capacitor and inductor banks, FACTS (flexible AC transmission systems) and DG (active and reactive power flow) towards the regulation of network voltage profiles [17-19];  By controlling distribution network voltage profiles it is possible to integrate increased capacity of DG. Provision of ancillary services by DG  Depending on their generation technology, DG schemes may supply several ancillary services to Distribution Network Operators (DNOs). The provision of ancillary services to DNOs by DG can lead to a more economically efficient power system [20];  These DNO ancillary services include power balance, local voltage and reactive power support, mitigation of losses, congestion management and black start (power system restoration after a fault) [21, 22];  More flexible operation of DG according to network price signals can save investment or delay network reinforcement [23];  Operation schemes for DG to mitigate fast voltage fluctuations, voltage dips and harmonic distortion are addressed in [24].  A global restoration procedure for a power system with the participation of DG is presented in [22]. The procedure allows DG schemes with black start capability to accelerate network re-energising, restoring clients faster than in the conventional procedure. The results obtained show an increased performance of the restoration procedure with the contribution of DG compared with the base case (where no DG is directly involved). No commercial mechanisms to reward this participation are presented;  Different levels of participation of DG in the provision of ancillary services can be found in Europe. In most European countries, there is little contribution of DG to network ancillary services [23]. Current contributions of DG are: to keep their power factors within certain ranges, and; through aggregators, to participate in the balancing market or provide reserves. New Regulatory frameworks / Grid Codes  The establishment of commercial arrangements between DNOs and DG to recognize the contribution of DG to network efficiency are being sought in some countries [23]: o Regulated payments to the owners of DG schemes (e.g. reflected in use-of-system tariff charges). o Bilateral contracts between DG and DNOs. Chapter 2 – Background and Literature Review 11 o Participation of DG in the markets: (i) energy balancing and reserve markets; and (ii) network related markets, such as local balancing, reactive power, congestion management and energy losses compensation;  The importance of shifting the current EU prohibition (European Directive 2003/54/EC) of DG ownership by DNOs is addressed in [25, 26];  This rule was designed to avoid that a DNO favours with a generation business within the same group. This may lead to a lack of integration between network and generation planning. The importance of allowing DNOs to deploy DG in well-defined circumstances is highlighted in [25]. These circumstances include: if deploying DG at specific network locations is more economically favourable than investing in network infrastructure; when overall network efficiency can be improved (e.g., by reducing losses) without altering market competitiveness. Other approach to consider the ownership of DG by DNOs is to adapt a USA regulatory approach that introduces an obligation for DNOs to acquire DG. This is put to DNOs as an alternative to network reinforcement [25].  The creation of carbon taxes is proposed as a form of promoting the integration of renewable DG [27]. A carbon tax addresses the carbon content of fuels used for energy production. Carbon taxes might increase the competitiveness of renewable DG when compared to conventional generation. However, this consideration depends on the price and market context of each country [27]. Modifications in the structure of electricity markets  The creation of wholesale electricity markets introduced a competitive framework for the appearance of new players in the electricity sector (as new generators and retailers). These markets appeared as a result of a deregulation process that aimed to [28]: - provide better incentives for controlling capital and operating costs of new and existing generating capacity; - encourage innovation in power supply technologies, and; - shift the risks of technology choice, construction cost and operating inefficiencies from consumers to suppliers.  Existing electricity markets have been operated in various arrangements, such as electricity pools or bilateral contracts. Electricity pools enable competition in generation as they allow a merit order on the dispatch of generation. They also facilitate the mechanisms to support competition in supply where customers can freely choose their supplier. On bilateral trading, customers have the opportunity to negotiate the best energy price from suppliers and generators without being constrained by any official price [28];  Alterations in the electricity market design to enable the integration of further amounts of wind power are presented in [29, 30]: o Creation of “faster markets” (intraday schedule of generators); Chapter 2 – Background and Literature Review 12  May reduce costs with reserves, forecasting and increase revenues for wind power producers as they are able to make more accurate bids; o Implementation of broader-area markets;  Cooperation between control areas to:  reduce the effect of wind intermittency;  stabilise prices within control areas, regulating power flows. o Widespread application of implicit auctioning to allocate cross-border power capacity [29];  To promote the efficient use of interconnectors of neighbouring countries:  by means of mechanisms such as market coupling and market splitting;  A market interface for the participation of DG in wholesale electricity markets is presented in [31]. DG is interfaced as an “Equivalent Power Producer” on a pool-based market. Changes to spot price computation and capacity payments are described. A mechanism to mitigate the volatility of spot prices due to the integration of DG is introduced. The market interface is evaluated on the Chilean electricity market. Islanded operation of distribution networks  Considering network islanding operation is allowed, DG may find attractive economic opportunities [32, 33]: o Important loads (e.g., large consumers) may be maintained in service by DG; o Financial penalties for DNOs due to consumer interruptions and network unavailability may be reduced; o DG may be able to continue to sell energy during islanding;  Maintaining in service important loads is addressed in a number of publications: o A load shedding optimisation problem is formulated in [34]. The objective is to minimise the cost of load shedding after a disturbance. The optimisation problem is non-linear. Load priorities are pre-set offline and do not vary with changes in network operating conditions; o A load shedding scheme based on a dynamic priority list is presented in [32]. The dynamic priority list is determined using the real-time decision making technique AHP (Analytic Hierarchy Process). Non-firm access to the networks  Network operators may allow the connection of generation without firm access rights – non-firm access to the networks [35-37];  Non-firm access to the networks is aimed to allow generation to be connected in advance of necessary reinforcement works to remove a network constraint (such as circuit capacity limits, static or dynamic as Chapter 2 – Background and Literature Review 13 presented in [38]). However, on occasions the output of the generators with non-firm access may need to be curtailed;  Non-firm access to the networks implies the usage of one or more of the following strategies when there is inadequate capacity in the system [39, 40]: o Power curtailment; o Coordinated Voltage Control; o Adaptive power factors for DG power plants; o Local reactive power compensation;  Power curtailment is generally associated with the partial or full reduction of the generator output in case of network constraints.  Contributions presenting power curtailment as a way to integrate further amounts of generation have been presented [36, 40-42];  Curtailment of active power to increase reactive power injection in distribution networks in proposed in [41, 42]. Results show that reactive power compensation increases the amount of generation that can be connected, especially in networks with a high reactance to resistance ratio. Active power curtailment reduces the income of the generators;  An online AC Optimal Power Flow algorithm to manage the power flows of DG when network voltage or current limits are exceeded is presented in [40]. “Last-in, first-off” power curtailment is included in the formulation.  Financial and technical impacts of the connection of further amounts of DG considering different connection policies are demonstrated in [36]. Three connection policies are considered: firm connection policy, non-firm connection policy and the “first firm then non-firm” connection policy. Five sections of the 38 kV distribution network of Ireland are used to evaluate the potential benefits of each connection policy. An optimisation procedure is presented with the objective of maximising the energy delivered per unit of investment. Capital, operation, maintenance, connection, reserve and cycling costs are considered. Significant differences in DG scheduling are reported along a year depending on the connection policy. Differences are observed also in cycling costs, emission benefits and fuel usage. The non-firm connection policy presents a greater net benefit for the case study and optimisation methodology described.  The commercial rules for allocating curtailed capacity supported by active management solutions have been designated as “Principles of Access” (POAs), following a paper from Currie et al. [43]. Such active management solutions adjust the amount and frequency of curtailment in order to provide system reliability, minimise social costs and attract DG investment. These Principles of Access are expected to promote [44, 45]: o Cost effectiveness - for both generators and distribution network operators; Chapter 2 – Background and Literature Review 14 o Network efficiency - maximise the amount of generation that can be economically connected in any constrained zone and promote efficient network operation; o Certainty - provide each generator with certainty as to the long term level of curtailment; o Simplicity - methodology should be easy to implement and understand; o Fairness - be equitable in its allocation of curtailment costs between generators;  Different Principles of Access (POAs) establish differently physical curtailment and financial payment rules. The way curtailment is allocated will influence the distribution of risks among parties (DNOs, generators and consumers);  The following Principles of Access are being trialled and implemented internationally to regulate the access to distribution network capacity when non-firm access is permitted [43, 44, 46]: o Last-in, first-off (LIFO): generators are given a specific order for being curtailed (normally based on the date of application for connection or date of connection). The last on the list (based on the ranking) is the first to be disconnected under a network constraint. o Pro Rata, equal percentage basis or shared percentage: curtailment is equally allocated between all generators that contribute to the constraint. The amount of curtailment can be computed as a percentage of available capacity, installed capacity, or other ratio. o Market-based approaches: generators bid for curtailment by offering a price based on market mechanisms.  Figures 2.1 to 2.3 illustrate these Principles of Access. Only generators without firm access rights are shown. The dotted line in Figures 2.1 and 2.2 refers to a generic capacity factor below which the generators are not willing to accept further curtailment. This is related to the savings made by the generators for connecting without firm access rights (and therefore not paying for network reinforcements to obtain firm access rights). Chapter 2 – Background and Literature Review 15 Figure 2.1 – “Last-in, first-off” access (based on [44]) Figure 2.2 – Pro-rata access (based on [44]) Figure 2.3 - One form of market-based access: capacity auction (based on [44]) These Principles of Access are described with more detail as follows.  Last-in, first-off (LIFO) access The “last-in, first-off” (LIFO) approach prioritises the access of generators to the networks on the basis of their order of connection. It aims to ensure that no generator can be adversely affected by the arrival of new generators. Therefore, the latest generator to connect (having non-firm access rights) is the first to be curtailed. LIFO offers a simple and transparent allocation. In addition, it does not need major technological changes in order to be applied [43]. However, this option does not necessarily incentivise nor support the connection of new and more efficient generation. This is due to the fact that the new generation is taken Chapter 2 – Background and Literature Review 22 have near real-time operation. No commercial arrangements are considered to promote the coordinated operation of the generators. Real-time thermal constraint management using DG is addressed in [55]. The output powers of DG are set with the objective of minimising the power curtailment required to meet static network current limits. Two techniques are evaluated: a constraint programming algorithm and a current tracing algorithm. The constraint programming algorithm consists in “shaping” the desired solution using a backtrack approach. The solution obtained satisfies the order of connection of the generators and load flow constraints. The current tracing algorithm is an upstream search procedure that tracks the usage of the constrained line by each DG scheme. Based on the tracing obtained, the output power of each DG scheme is set in proportion until line thermal limits are met. This algorithm does not consider the order of connection of the generators. Both techniques are applied to a distribution network. Computational times are suitable for real-time implementation. The current tracing algorithm presents a smaller amount of power curtailed and a faster performance. An optimal power flow algorithm is introduced in [56] as an alternative to the constraint programming-based and current tracing algorithms described in [55]. The optimal power flow algorithm considers the order of connection of the generators. The coordination of the output powers of DG when network congestion occurs is detailed in [57]. Three possible strategies based on the evaluation of network power flow sensitivity factors (PFSFs) are presented. PFSFs measure the change in network voltages and angles with marginal changes in the injection of active and reactive power. PFSFs are used to evaluate the impact of power injection in each busbar to network congestion. Variable thermal ratings are considered for the transmission/distribution lines. Thermal state estimation is used in areas where no real-time thermal rating control systems are available. The three strategies to schedule the generators are: “last-in, first-off” approach based on PFSFs; an equalitarian approach, that determines the schedule of the generators based on a weighted proportion of PFSFs; and a “technically most appropriate” approach, which ranks generators by their PFSFs and actuates when necessary according to that ranking. The three strategies are compared against “last-in, first-off” operation of the generators, considering static thermal limits of the lines. The comparison of strategies is performed considering the annual energy income, network losses and voltage profiles. Costs of real-time thermal rating equipment and communication facilities are considered. Reactive power is assumed to be constant during the year of simulation. The time step between measurements is 30 minutes. Net present values and profitability indexes of each strategy for each generator are presented. The control actions are implemented by a rule-based inference system. This system collects all information regarding power flows, meter data and constraint limits. The system also sets, at every time step, the commands to be sent to the DG Chapter 2 – Background and Literature Review 23 schemes. For computation efficiency, PFSFs are pre-calculated being collected in real-time from a look-up table. Results show an increase in the aggregated amount of energy produced using any of the three strategies. However, the authors stress the need to devise commercial arrangements to promote the use of the methodology. 2.3.3 - Market-driven coordination A virtual power plant (VPP) is an infrastructure that aggregates distributed energy resources (generation and demand) to address technical and commercial operation objectives, see Figure 2.4 [58]. Figure 2.4 - The concept of virtual power plant [58] The VPP is controlled centrally by an operator or aggregator. A review of the concepts of virtual power plant and virtual utility is presented in [59]. VPP is defined as a “new model of energy infrastructure which consists of integrating different kind of DG in an energy (electricity and heat) generation network controlled by a central energy management system” [59]. The FENIX project [58] was a European Union (EU) project to develop the concept of VPP. The aim was “to conceptualise, design and demonstrate a technical architecture and commercial framework for enabling DG to become the solution for the future cost efficient, secure and sustainable EU electricity supply system” [58]. The FENIX Project produced three main outcomes:  FENIX Box server, which serves to aggregate demand and generation and ensure their operation according the optimisation model;  Commercial VPP server, that schedules and provides energy optimisation functions for the DG;  Technical VPP in the distribution management system server, that validates the generation schedules taking into account network voltages and currents. A number of contributions address the mitigation of power imbalances of wind generation using the coordination of generation on a market environment [60-63]. A combined bidding and operating market strategy for Chapter 2 – Background and Literature Review 24 hydro and wind generation is presented in [62]. Hydro generation is used to minimise imbalance penalties of wind generation in day-ahead markets. The objective is to maximise the total income for selling electricity. The generators are owned by the same producer. The coordinated operation of wind and thermal generators to reduce the risk of wind imbalance penalties is presented in [63]. The objective function is to maximise the total expected income subject to the trading risk attitude of the owner of the generators. Generators are assumed to be owned by the same producer. Uncertainty of wind power outputs, energy prices and imbalance prices is considered. Traded energy volumes are lower with risk-averse bidding. This is because wind generators reduce their bids to avoid under-generation penalties and thermal generators do not produce to avoid periods of lower income. The utilisation of water storage to increase the penetration of wind generation is presented in [64]. Water storage is controlled to smooth wind power fluctuations and maximise the wind-hydro global income for selling active power. A day-ahead hourly discretised optimization algorithm sets the schedule of both wind generators and hydraulic pumping. Generators may be owned by the same producer. Inputs are the wind power forecast, the estimation of price of electricity and the boundaries of the desired aggregated power profile. Wind power forecast is a stochastic quantity given by two series of hourly values: wind power average values and its standard deviation magnitude. The forecasting error is incorporated in the model by means of a neuro-fuzzy methodology. The estimation of price of electricity is made considering the feed-in tariff system in Portugal. The boundaries of the desired aggregated power profile are set by the network operator. The methodology runs a number of Monte Carlo simulations to collect different cases of available wind power for the next operating day. The optimisation algorithm is then run for each case of available wind power. The optimal wind-hydro dispatch is a “band” of possible solutions. A day-ahead planning algorithm for a multi-reservoir hydro system coordinated with wind power is developed in [60]. The objective is to minimise wind energy curtailment. Wind and hydro generators are owned by different producers. Hydro generators have priority access to the network. Uncertainty of wind power outputs and market prices is considered. It is assumed that the hydro generators are paid for reducing power production to allow wind generators to produce. The price paid to the hydro generators for the coordination service is agreed beforehand by the generators. This price is based on average annual economic losses of the wind generators due to curtailment, based on historical data. Results show that both wind and hydro generators receive a greater income if they coordinate their output powers. Coordination of independent generators to maximise the income of the generators is presented in [61]. Wind and hydro generators are connected to different feeders but sharing the same grid connecting point. Wind generators are connected without firm access rights. The methodology is set on the Chapter 2 – Background and Literature Review 25 day-ahead market. The storage capacity of the hydro generation is used to define a joint power schedule for the next day of operation (24 market periods of one hour). Penalisations for over/underproduction of the generators are included. A seven-day time span is considered to account with basin management constraints. Uncertainties in both prices and wind speeds are incorporated. Results show an increase in global electricity selling revenues. The extra income obtained by the coordination is shared by the generators using the Shapley Value (game theory approach). Shapley Value is an approach for the allocation of gains obtained in coalition and recognises the contribution of each player to these gains. Each generator receives a greater income in comparison to what they would have received without coordination. The methodology is validated on the Swedish transmission network. 2.3.4 - Comments on the reviewed approaches of the coordination of independent generation The technical and economic benefits of coordinating generation are addressed in the “Planning and Economic Assessment” contributions reviewed. These contributions do not address the allocation of the benefits obtained to the generators. Limited details of the technical implementation of these methodologies are provided. “Network-operator driven” contributions envisage the improvement of network operation and are generally operated by network operators. These contributions do not deliver economic signals to promote the coordinated operation of DG. The coordination of DG is then a mandatory requirement of network operators. “Market-driven coordination” contributions aim to maximise the electricity produced and the income of DG. However, most contributions reviewed do not provide details on how to allocate the additional income obtained by the generators. Game theory provides tools to allocate the income originated by different players in a coalition. The application of game theory to the coordination of independent DG is addressed in section 2.4. 2.4 - Applicability of game theory to the coordination of independent generation Game theory deals with problems of conflict amongst interacting decision makers. It may be regarded as a generalisation of decision theory to include multiple decision makers [65, 66]. These decision makers are usually called “players”. Game theory can be classified in two major areas: non-cooperative and cooperative game theory. 2.4.1 - Non-cooperative and cooperative game theory Game Theory provides tools to study the non-cooperative interactions between participants (commonly designated as “players”) looking to Chapter 2 – Background and Literature Review 26 maximise their income. In a non-cooperative game, each player has a number of choices/strategies available and a set of returns (commonly designated as “payoffs”) corresponding to these strategies. Examples of these interactions are wholesale electricity markets, which are normally established on the assumption that participants do not cooperate. Non-cooperative games can be zero-sum games or nonzero-sum games [67]. In zero-sum games, gains of one player equal the losses of the other player(s). In nonzero-sum games, gains of one player do not equal the losses of the other player(s). A solution to non-cooperative games is the concept of Nash equilibrium. A Nash equilibrium exists if, for all players, one player’s strategy is the best response to the strategies of the other players [68]. Multiple Nash equilibria may exist for a given game. In non-cooperative game theory, the payoff of a player depends not only on the strategy chosen but also on the strategies adopted by the remaining players. In addition, the rules of the game, the strategies available and their associated payoffs are of common knowledge. Each player is assumed to act rationally to maximise its own payoff [65]. The solution of non-cooperative games is the set of strategies adopted by each player individually and their outcome [67]. Non-cooperative games are believed to promote competition, driving players to bid near their marginal costs as competition grows. Therefore market efficiency is increased and prices are reduced [65]. Cooperative game theory is a branch of Game Theory that focuses on how an amount obtained in a coalition should be divided equitably amongst players. Particulars such as how players behave and how coalitions are formed (e.g., order of entrance in the coalition) are not addressed. The various solutions proposed for cooperative games can be interpreted as alternative solutions to an allocation problem [65]. Coalitions are formed to allow players to benefit from economies of scale, increasing their payoffs when compared to individual operation [67, 69]. The solution of cooperative games refers to the “grand coalition”, i.e. the coalition of all players. Although being in a coalition, players ultimately aim to maximise their own income [65]. Cooperation in wholesale electricity markets is normally not accepted by regulators as it may lead to market distortions due to the reduction in the number of players and the increase of the relative weight of certain players. This may give market power to some players (e.g., by means of cartelisation), which would harm competition, reduce market efficiency and drive up prices for consumers [28, 70]. However, in cases where players share a scarce resource (e.g., a distribution circuit) or when players can obtain cost savings with economies of scale, cooperative game theory is reported to be an efficient way to promote efficiency in electricity networks [71-73]. Proposed applications of cooperative game theory to electricity markets include the reduction of network losses [71] and the reduction in transaction charges and costs of operation of generators [72, 73]. The allocation of the additional income obtained in coordination by independent generators connected to the same circuit can be formulated Chapter 2 – Background and Literature Review 27 using cooperative game theory. A branch of cooperative game theory, cooperative games with transferable utility, is presented in section 2.4.2. In a cooperative game with transferable utility it is assumed that the earnings of a group of players can be expressed by an amount of utility [68]. This amount of utility is transferred without loss to the players. 2.4.2 - Cooperative games with transferable utility A cooperative game with transferable utility (TU-game) is described by a pair ),( vN , where   nN ...,,2,1 is a finite set with n elements (players) and is the “characteristic function” [68]. A subset S of the player set N is called “coalition”. N is the grand coalition, i.e. the coalition of all players. The number of players in a coalition S is denoted by . The characteristic function assigns a “worth” to each coalition [74]. The worth of a coalition is the amount of utility (which can be expressed in monetary terms) to be allocated to the players [68]. If for all NTS , , being TS , )()()( TvSvTSv  then the cooperation has greater value than the sum of the value obtained by coalitions alone. The property described by condition (2.1) is known as superadditivity. A stronger notion than superadditivity is convexity (see condition (2.2)). )()()()( TvSvTSvTSv  The total payoff of the grand coalition should be allocated to the players so that their cooperation is incentivised. Let be the worth of the individual operation of player . An allocation is a vector   N n xxx  ...,, 1 , where is the payoff due to player . Allocations are efficient if the payoff is entirely distributed, i.e. ∑ . The payoff received by each player should be at least equal to the amount it would have received individually, i.e. ii vx  for all . This property is called individual rationality. Allocations that meet the efficiency and the individual rationality properties are called imputations. Thus, is the set of imputations of (see condition (2.3)).        Ni ii nNiivxNvxxvI )(),(|:)( 2.4.3 - Methods to solve cooperative games with transferable utility The solution to TU-games is an allocation or set of allocations admissible to all players. There are two groups of solution methods for TU-games [67, 68, 75, 76]: (a) subset methods (e.g.: the Core, Least Core, Bargaining Set, Weber Set, Selectope) and (b) one-point methods (e.g: Nucleolus and Prenucleolus, the Shapley value, τ-value). The solution method for a given game should be chosen according to the particulars of that game [69]. (2.1) (2.2) (2.3) Chapter 2 – Background and Literature Review 28 2.4.3.1 – Subset-based methods Subset methods provide a "range" of allocations that satisfy the players. This flexibility allows players to consider various solutions. Core of a Cooperative Game An imputation is an efficient allocation that satisfies individual rationality, see condition (2.3). By extending the property of individual rationality to coalitions, then for all non-empty coalitions S: NSSvx Si i   allfor ,)( The property described by condition (2.4) is called group rationality. The set of imputations (condition (2.3)) that fulfil group rationality (condition (2.4)) form the core [68]. Formally,         Si i Ni i nNSSvxNvxxvC ),( and),(|:)( Being the core of . The lower bound of the core is the baseline for all players: no player will have incentive to cooperate if it receives less than in individual operation. The upper bound of the core is the set of allocations that one player can request without harming the other players’ payoffs. The core can be empty or non-empty. Least Core Considering an imputation , the excess vector    Si i xSvxSe )(),( is regarded as the objection raised by a coalition against imputation (see equation (2.6)). Let )( 1xe be the largest excess of any coalition relative to , )( 2xe the second largest excess and so forth. The Least Core of a TU-game is the set of all imputations that minimise )( 1xe , i.e., that minimise the biggest complain of S [69]. 2.4.3.2 – One-point methods One-point methods aim to select one allocation that satisfies all players. Nucleous and Prenucleous Considering the definition of Least Core, let be the set of all in that minimises )( 2xe , be the set of all in that minimises )( 3xe , and so forth. This process will ultimately lead to a set consisting of a sole imputation , called the nucleolus. The nucleolus is the imputation that minimises the maximum complaint of all coalitions. Formally (see condition (2.7)) [68]:             Si i xSvvNu )(maxmin:)( This minimisation is subject to the constraints of the core (efficiency, individual and group rationality). (2.4) (2.5) (2.7) (2.6) Chapter 2 – Background and Literature Review 29 The prenucleolus is the efficient allocation that minimises the maximum complaint of all coalitions [66]. The prenucleolus does not guarantee the individual rationality property, which may lead to a solution outside the core. Shapley Value Consider to be the set of superadditive games with players. The Shapley Value is the unique value n NH )(:  that satisfies simultaneously the following four properties (equations 2.8 to 2.12) [76]: - Efficiency: for every supperadditive game )(NHv , )()( Nvv Ni i    - Symmetry: If two players and contribute by the same amount to all coalitions − for all   jiNS ,\ ,      jSviSv  ), then     vv ji   - Dummy Player: If the contribution of a player to any coalition is the same that player is able to achieve individually − for all S such that ,       ivSviSv  This means that player receives a payoff exactly equal to the amount that it is able to achieve individually. For any , if is a dummy player then   ivv i)(  - Additivity:  satisfies additivity if, for every superadditive game )(, NHwv      wvwv   )( Provided that the aforementioned properties are fulfilled, the Shapley value  for player , for all , is given by equation (2.13):             iNS iSviSv n sns v \ )( ! !1! :)(  and denote the number of elements of and , respectively. { } is defined as player ’s marginal contribution to coalition . Term means that players are randomly ordered and all permutations (i.e., orders of entrance in the coalition) have equal probability. Thus, the Shapley value of player is the average of player ’s marginal contribution to all coalitions, including the empty coalition. The marginal contributions of each player in a 3-player game (players , , ) is given in Table 2.2. If game is a convex game (see constraint (2.2)) then the Shapley Value is in the core. Computational effort required to obtain the Shapley Value increases significantly with the increase in the number of players. This is due to the increase in the number of permutations. (2.8) (2.11) (2.9) (2.10) (2.12) (2.13) Chapter 2 – Background and Literature Review 30 Table 2.2 – Marginal contributions of each player in a 3-player game Player Permutation { } { } 0! (3 - 0 - 1)!/3!= 0.33(3) ({ }) - () ( ) 1! (3 - 1 - 1)!/3!= 0.16(6) ({ , }) - ({ }) ( ) 1! (3 - 1 - 1)!/3!= 0.16(6) ({ , }) - ({ }) ( , ) 2! (3 - 2 - 1)!/3!= 0.33(3) ({ , , }) - ({ , }) { } 0.33(3) ({ }) - () ( ) 0.16(6) ({ , }) - ({ }) ( ) 0.16(6) ({ , }) - ({ }) ( , ) 0.33(3) ({ , , }) - ({ , }) { } 0.33(3) ({ }) - () ( ) 0.16(6) ({ , }) - ({ }) ( ) 0.16(6) ({ , }) - ({ }) ( , ) 0.33(3) ({ , , }) - ({ , }) τ-value The τ-value (or tau value) is the trade-off between two vectors: , the marginal contribution vector, and; , the minimum right vector [69]. For player , is given by equation (2.14):     iNvN=vvMi\:)(  is the marginal contribution of player to the grand coalition. It is the best payoff player can expect (see equation (2.15)).       max:)( ;          iS\jjS iSi vMSv=vm is the minimum right of player , if all other players in obtain their marginal contributions. To compute the τ-value, let τ be the imputation that fulfils ∑ , such that for some value . In a 3-player game, the 4-equation and 4-unknowns system necessary to obtain is given by equation (2.16). The values for m and M are obtained as shown in Table 2.3.                  )(),,( _-__ _-__ _-__ 321321 3333 2222 1111 Nvpppv boundlbounduboundl boundlbounduboundl boundlbounduboundl ppp ppp ppp     (2.14) (2.15) (2.16) Chapter 2 – Background and Literature Review 31 Table 2.3 – Marginal contribution vectors of a 3-player game Vector Player 1 – Player 1 – Player 1 – { } { } { } { } { } { } 2.4.4 - Application of game theory to electric power systems The strategic behaviour of electricity market participants and solutions to avoid market power are addressed in [77-82]. The allocation of network costs using cooperative game theory is addressed in [83, 84]. The allocation of transmission network losses is presented in [85]. A contribution to transmission congestion pricing is investigated in [86]. Cooperative game theory is used to compensate generators for congestion relief in [87]. The pricing of reactive power support is addressed in [88]. Demand-side integration strategies using game theory are described in [89, 90]. Game theory is used to encourage consumers to adopt the expected behaviour and obtain cost savings. The allocation of the benefits of firm energy bids of independent hydro generators is presented in [91]. The coordination of independent generators connected to the same network using cooperative game theory is presented in [61, 72]. The objective is to increase the income of the generators. 2.5 - Demand-side integration in distribution network operation Demand-side integration is a set of methodologies to use demand and local generation to support network operation/management and improve the quality of power supply [1]. The term “demand-side integration” is used by CIGRE to congregate different nomenclature such as demand-side management and demand response [5, 92]. Demand-side integration is expected to increase so as to limit the growth in demand and make better use of the networks. Also, the flexibility of demand is being presented to allow the integration of additional amounts of non-dispatchable generation [93, 94]. Demand-side integration is expected to allow [95, 96]:  Reduction of demand peaks;  Load shifting and valley filling;  Reduction in overall demand without reducing services (energy efficiency); The participation of the demand-side aims to promote [95, 96]:  Power system balancing in systems with high penetration of non-dispatchable generation;  Increase of the share of load supplied by low-carbon generation;  Provision of ancillary services by the demand;  Reduction in network operating costs;  Deferment of investments in transmission and distribution systems. 39 Chapter 3 - Connection of generation to distribution networks 3.1 - Introduction The connection and operation of distributed generators under the firm access connection policy is described. A representative of the distribution system of Northeast Portugal is used as an example. The connection of distributed generation without firm access rights is considered. The limitations of the firm access connection policy are then discussed. 3.2 - Modelling of the distribution system analysed The firm access connection policy is described using the distribution system of Northeast Portugal as an example, see Figure 3.1. A 60 kV distribution network is illustrated. There are fifteen distribution substations and three interconnections with the transmission network. Wind and hydro distributed generation is connected. Figure 3.1 – 60 kV distribution network of Northeast Portugal (source: [112]) Load consumption and distributed generation output at the medium voltage (MV) side of the distribution network is shown in Table 3.1. Values were obtained at 8.30 a.m. on 20/12/2007 [112]. Chapter 3 – Connection of generation to distribution networks 40 Table 3.1 - Distribution substation loads and MV-connected distributed generation output, 20/12/2007 at 8.30 a.m. (source: [112]) Wind DG (MVA) Hydro DG (MVA) Thermal DG (MVA) Load (MVA) Total DG (MVA) Generation Maximum injection Generation Maximum injection Generation Maximum injection Amarante 19.1 5.1 - - 0.0 0.6 5.1 5.2 Bragança 21.9 0.0 - - 0.0 4.2 - - Carneiro 2.8 0.0 0.0 1.5 - - - - Chaves 20.0 3.2 3.2 3.3 - - - - Mirandela 11.1 Without DG Morgade 3.6 2.5 2.5 3.0 - - - - M. Cavaleiros 14.2 1.7 1.7 2.0 - - - - Pinhão 10.0 Without DG Soutelo 8.4 8.0 8.0 8.0 - - - - Telheira 27.0 7.2 2.6 2.5 4.6 20.0 - - Valpaços 5.7 Without DG Varosa 36.3 41.5 41.2 39.4 0.3 13.0 Vidago 11.2 2.7 1.2 1.2 1.5 4.2 - - Vila da Ponte 10.1 Without DG Total 201.4 71.9 60.4 60.8 6.4 42.0 5.1 5.2 There is no distributed generation connected to the distribution substation indicated in Figure 3.1 (Valpaços), see Table 3.1. Valpaços distribution substation has a single 60kV/15kV transformer with 15 MVA of installed capacity. The MV network below Valpaços substation is shown in Figure 3.2. This MV network is a representative of a rural distribution network in Portugal. The short-circuit power behind Valpaços substation, , is provided in [112]. is the leakage reactance of the transformer. and are the base power and the base voltage of the distribution network, respectively. Total load consumption in Figure 3.2 is equal to the consumption mentioned in Table 3.1, i.e. 5.7 MVA. Loads are considered to operate with a fixed power factor of 0.95 (inductive). Figure 3.2 – Distribution network below Valpaços substation (rural distribution network) Chapter 3 – Connection of generation to distribution networks 41 3.3 - Operation of generators with firm access rights Generators get permission to connect to distribution networks in Portugal on the basis of power flow studies with the following conditions [113]: - Generators must be operating at their maximum power, with unity power factor; - The voltage magnitude in the busbar of connection should not change more than +0.02 p.u., with all loads equal to zero; - Line capacity limits and voltage magnitude limits ([0.9 p.u.; 1.1 p.u.]) must be observed in all busbars. Generators who fulfil these and other non-technical requirements are allowed to connect to the distribution network with firm access rights. To exemplify the connection of generation with firm access rights, two independent distributed generators are connected to the distribution network of Figure 3.2. Generator GenA connected first to the network (on busbar B3) and has an installed capacity of 10 MVA. Generator GenB connected later (on busbar B9) and has an installed capacity of 5 MVA. Both generators are connected with firm access rights. GenA is a non-dispatchable generator (wind generator) and GenB is a dispatchable generator (thermal generator). A dispatchable generator has the ability to produce and store according to the strategy of the producer. Non-dispatchable generators only produce electricity when their primary resource comes available and do not have ability to store their production. 3.3.1 - Limitation in the capacity that can be connected The operation of the distribution network is analysed considering two extreme power flow cases: - Case 1  Minimum MV-side voltage magnitudes: transformer operates at its highest tap on the HV side (1.06), loads are at their maximum value, generators do not operate; - Case 2  Maximum MV-side voltage magnitudes: transformer operates at its lowest tap on the HV side (0.94), no loads, generators operate at maximum output power with unity power factor; Figure 3.3 shows the operation of the distribution network in case 1. Power flows are indicated. In case 1 all network voltage and current limits are observed. As the generators are not operating, power flows from the HV to the MV side of the distribution network. Chapter 3 – Connection of generation to distribution networks 42 Figure 3.3 - Case 1  Operation of the distribution network with the highest transformer tap on the HV side, maximum load and generators not operating Figure 3.4 shows the operation of the distribution network in case 2. Figure 3.4 - Case 2  Operation of the distribution network with the lowest transformer tap on the HV side, no load and generators operating at maximum output In case 2 all network voltage and current limits are respected. Active power flows from the MV to the HV side, while reactive power flows in the opposite direction due to the reactive losses. If losses were not considered, power flowing through the substation transformer would reach the transformer capacity. This way, no further generation can connect with firm access rights. Chapter 3 – Connection of generation to distribution networks 43 3.3.2 - Technical possibility of connecting additional generation capacity The operation of the distribution network in case 2 (transformer operating at its lowest tap on the HV side, no loads, generators operating at maximum output power with unity power factor) is extended to 24 hours, see Figure 3.5. The time granularity considered is one hour. The consumption of all loads is represented by a typical winter consumption profile [114], with a fixed power factor of 0.95 (inductive). The total load consumption at 8.30 a.m. is 5.7 MVA, as indicated in Table 3.1. The maximum consumption of the loads during the 24 hours is 7.3 MVA. The production of GenA follows the availability of wind. GenB schedules its production according to the price of electrical energy shown in Figure 3.5. The price of electrical energy considered was obtained in [115]. Both generators receive their income according to this price of electrical energy (no feed-in tariff schemes are considered). GenB does not produce between hours 0 and 8 because its costs of operation are higher than the price of electrical energy. GenB produces reactive power between hours 9 to 21. In Portugal, MV-connected generators below 6 MW of installed capacity must produce an amount of reactive power equal to 30% of their active power produced on peak hours (from 8 a.m. to 10 p.m.) [113]. During the 24 hours of operation considered, the power flowing through the distribution transformer is significantly below the rated capacity. Additional electrical energy could be produced on the MV side of the distribution network if further generation capacity was connected. 3.4 - Connection of generators without firm access rights The connection of two other independent generators to the MV distribution network is considered (see Figure 3.6). Generator GenC connected to the network on busbar B8 and has an installed capacity of 4 MVA. Generator GenD connected last (on busbar B5) and has an installed capacity of 3 MVA. The installed capacities of generators GenC and GenD were obtained following cost-benefit analyses, available in Appendix A. GenC is a dispatchable generator (thermal generator) and GenD is a non-dispatchable generator (wind generator). Chapter 3 – Connection of generation to distribution networks 44 Figure 3.5 - Operation of the distribution network during 24 hours, with the generators producing and with a typical load curve 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 012345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW/MVar) hour of the day Active power (MW) Reactive power (MVar) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW) hour of the day Active power (MW) -10 -5 0 5 10 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW/MVar/MVA) hour of the day Active power (MW) Reactive power (MVar) Apparent power (MVA) Transformer thermal limit (MVA) 0 0,5 1 1,5 2 2,5 3 3,5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Consumption of L1 (MW/MVar/MVA) hour of the day Active power (MW) Reactive power (MVar) Apparent power (MVA) cos = 0.95 0 10 20 30 40 50 60 70 80 90 100 110 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 price (€/MWh) hour of the day Price of electrical energy Chapter 3 – Connection of generation to distribution networks 45 Figure 3.6 - Distribution network with the four generators (GenA and GenB are firm connected, GenC and GenD have no firm access rights) As the connection of further generation with firm access rights is not possible, both GenC and GenD agreed to connect without firm access rights. Generators connected without firm access rights are constrained off on a “last-in, first-off” basis when there is inadequate capacity in the export circuit. 3.4.1 - Minimum cost operation of the distribution network The distribution network of Figure 3.6 is operated with minimum cost if the generators with lower costs of operation are scheduled first. An AC optimal power flow (AC OPF) is run in the distribution network of Figure 3.6. The objective function is the minimisation of the costs of producing active power. Matlab-based package MATPOWER is used to run the AC OPF [116]. The distribution transformer tap is adjusted manually. Generation and load consumption data of hour 23 are considered (data shown in Figure 3.5). All generators are able to operate up to their rated powers and operate with unity power factor. GenA and GenD have no operation costs. The operation of GenB and GenC costs 35€ per MWh produced. Generators located upstream Valpaços substation are more expensive than GenB and GenC. The total load consumption is 6.04+j1.98 MVA. The results of the AC OPF are given in Figure 3.7. Full details of the AC OPF implementation are provided in Appendix B. The distribution network is operated with the minimum cost of 272.3€ in hour 23, that corresponds to the cost of operating generators GenB and GenC. GenA, GenC and GenD produce at full output power and GenB is constrained off to meet the transformer capacity limit. However, GenB was connected with firm access rights so it should not be curtailed. Therefore, the minimum cost schedule of the distribution network cannot be implemented due to the order of connection of the generators. Chapter 3 – Connection of generation to distribution networks 46 Figure 3.7 - Operation of the distribution network with the four generators in hour 23, with minimisation of the costs of producing active power (AC OPF) 3.4.2 - Operation of the generators connected without firm access rights The operation of the distribution network during 24 hours (as described in section 3.3.2) is updated to consider generators GenC and GenD. The time granularity considered is one hour. GenC schedules its production according to the price of electrical energy shown in Figure 3.8 (same as in Figure 3.5). GenC does not produce between hours 0 and 8 because its costs of operation are higher than the price of electrical energy. The production of GenD follows the availability of wind. Both GenC and GenD are required to produce an amount of reactive power equal to 30% of their active power produced between 8 a.m. and 10 p.m., as their installed capacity is below 6 MW. In hours 9, 13, 22 and 23, the production of the generators exceeds the capacity limit of the transformer. GenD is curtailed to meet this excess, see Figure 3.8. GenD is curtailed because it was the last generator to be connected. GenD only produces when wind comes available, so its curtailed power is lost. Comparing the operation in hour 23 of Figure 3.8 with the results of the AC OPF in hour 23 (given in Figure 3.7), the cost of operating the distribution network is 315€ while with the AC OPF is 273€. This difference corresponds to the additional cost of operating generators GenB and GenC at full output power. 47 Figure 3.8 - Operation of the distribution network during 24 hours, with the four generators producing and with a typical load curve 0 10 20 30 40 50 60 70 80 90 100 110 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 price (€/MWh) hour of the day 0 0,5 1 1,5 2 2,5 3 3,5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Consumption of L1 (MW/MVar/MVA) hour of the day -20 -15 -10 -5 0 5 10 15 012345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW/MVar/MVA) hour of the day 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW/MVar) hour of the day 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW/MVar) hour of the day 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW) hour of the day 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MW/MVar) hour of the day Price of electrical energy cos = 0.95 tap= 1.06 Active power (MW) Reactive power (MVar) Apparent power (MVA) Active power (MW) Active power (MW) Active power (MW) Reactive power (MVar) Reactive power (MVar) Active power (MW) Reactive power (MVar) Apparent power (MVA) Transformer thermal limit (MVA) Active power (MW) Reactive power (MVar) Curtailment Chapter 4 – Coordination of independent distributed generators 54 electrical energy. Generators connected with firm access rights would not have any incentive to provide their anticipated outputs to the Aggregator. Therefore, the income received by each generator is determined using a mechanism based on cooperative game theory. Generators are paid what they would receive in “last-in, first-off” operation (i.e., without coordination) plus a share of the additional income obtained in coordination. The income-sharing mechanism is detailed in section 4.3. 4.3 - Sharing the additional income obtained in coordination Additional income is obtained from the coordinated operation of the generators. This additional income is the result of: i) changing the output of the dispatchable generators (with higher costs of operation) to let the non-dispatchable generators operate; ii) asking the dispatchable generators to operate in hours of reduced output of the non-dispatchable generators (additional electricity production). The Aggregator allocates this additional income using a mechanism based on cooperative game theory. The amount of electrical energy produced and the type of each generator are considered. Each generator receives an allocation of the additional income in addition to the income they would have received in “last-in, first-off” operation. The income-sharing mechanism is explained in section 4.3.1. An assessment of the willingness of the dispatchable generators to participate in the coordination is presented in section 4.3.2. 4.3.1 - Income-sharing mechanism The coordination of distributed generators produces a system income (SINC) given by equation (4.11).         DISN dn H h hdn h DIS d H h h d h d h d h d hPρStartFuelPuρSINC _ 1_ 1 _ 1 1 The system income determined by equation (4.11) is greater than the sum of the income received by the generators in “last-in, first-off” operation. The difference between these two values is the additional income obtained in coordination,  (see equation (4.12)). LIFOSINCSINCδ_ Being:                  DISN dn H h hdn h DIS d H h h d h d h d hP_lifoρStart_lifoFuel_lifolifoPρLIFOSINC _ 1_ 1 _ 1 1 __ The suffix _lifo in equation (4.13) refers to the values of the variables in “last-in, first-off” operation. The Aggregator distributes the additional income considering the coordination as a cooperative game with transferable utility. The additional income is the worth of the coalition of all generators. The core of this cooperative game is the set of allocations that meet three criteria: (i) the additional income is entirely allocated; (ii) all generators receive a greater income in coordination in comparison to “last-in, first-off” operation; (iii) the (4.11) (4.12) (4.13) Chapter 4 – Coordination of independent distributed generators 55 coalition of all generators provides a greater income for any generator when compared to the income it would have received in a partial coalition (coalitions that do not include all generators). The generators are unable to form partial coalitions. This is because they would need to know the anticipated outputs of the generators outside the coalition and the estimation of load consumption to schedule their own production. Therefore, the criterion iii) is always met. Any allocation inside the core provides all generators an economic incentive to operate in coordination. The core of this cooperative game can be a large set of allocations. Each of these allocations gives different economic incentives to the generators. So, the Aggregator chooses a single allocation from the core using equation (4.14). This allocation is determined by weighting the amount of electrical energy produced and the type of each generator. Generators at distribution level normally apply for a connection on the basis of the availability of local primary resources. In order to maximise the economic return of their projects, generators seek the cheapest point of connection to the distribution network. This point of connection, determined by the network operator, is normally the closest possible to the generator’s site. Therefore, connection to other sections of the distribution network (if allowed by the network operator) to benefit from larger allocations of additional income is likely to affect the economic viability of the generators. The type of each generator is differentiated using dimensionless technology coefficients (coef), agreed beforehand by the generators. The coefficients are reported to the Aggregator before its first operation. These coefficients are not expected to be modified unless an agreement between the generators to periodically revise them has been made. The coefficients are likely to be based on the technology coefficients defined in existing subsidy regimes.                                              1 __,1,0 __, , _ 1_ _ 1 _ 1 _ 1_ 1 __ 1 1__ _ 1 _ 1_ 1 __ 1 1 DISN dn dn DIS dd dnd DIS d DISN dn H h hdndn H h h d h dd H h hdndn dn DIS d DISN dn H h hdndn H h h d h dd H h h d h dd d allocalloc DISNdnDISd,allocalloc DISNdn PcoefPucoef Pcoef alloc DISd PcoefPucoef Pucoef alloc The income that each generator receives in coordination is given in equation (4.15). Each generator receives an allocation of the additional income in addition to the income it would have received in “last-in, first-off” operation. (4.14) Chapter 4 – Coordination of independent distributed generators 56                      DISNdnδalloclifoPρincome DISdδallocStart_lifoFuel_lifolifoPρincome dn H h hdn h dn d H h h d h d h d h d __,_ ,_ _ 1__ 1 The modification of the coefficients alters the amount of additional income allocated to each generator. This affects the income received by each generator in coordination. However, regardless of the defined coefficients the allocations will still remain in the core. This means that the additional income originated is allocated in full and: - the generators increase their income in coordination when compared to individual operation (“last-in, first-off” operation); - the generators receive a greater income with the coalition of all generators than with partial coalitions; Thus, all generators have an economic incentive to be operated in a coordinated manner. 4.3.2 - Assessment of the willingness of the dispatchable generators to participate in the coordination The dispatchable generators are interested in participating in the coordination as long as their income continues to increase. Consider the case of a dispatchable generator d that reduces its production by one unit of electricity (i.e., 1 MWh) in period h to allow a non-dispatchable generator n_d to operate. The dispatchable generator is not able to schedule this unit of production in other period. Also, this decrease in production does not lead to an additional start-up cost. The alteration in the production of generators d and n_d is described by equation (4.16):        MWhPP MWhPP hdn new dn h d new d 1 1 __ new refers to the value of the variables after the alteration. The alteration given in equation (4.16) modifies the additional income as shown in equation (4.17).       fcMWhfcMWh newh d h d new   11 The additional income increases by the amount of the fuel cost of the dispatchable generator d with the alteration shown in equation (4.16). The dispatchable generator will only be interested to continue reducing its output to allow the non-dispatchable generator to produce if (see inequation (4.18)): newnew dd allocalloc   Developing inequation (4.18):   fc alloc alloc fc alloc alloc allocalloc new d d new d d newnew dd          1  (4.15) (4.16) (4.17) (4.18) (4.19) Chapter 4 – Coordination of independent distributed generators 57 The ratio ⁄ is greater than 1 at all times. When the relation described by inequation (4.19) is not met, the dispatchable generator d is no longer interested in continuing to reduce its production. 4.4 - Application of the coordination of generators to a twobusbar distribution network The coordination of independent distributed generators is evaluated on a two-busbar version of the distribution network introduced in Chapter 3. Four generators are connected to the distribution network: a non-dispatchable generator and a dispatchable generator connected with firm access rights; a dispatchable generator and a non-dispatchable generator connected without firm access rights. An equivalent of the local load is also connected to the distribution network. The evaluation is performed during a selected period of operation of 6 days. This period of operation represents a set of extreme cases of price of electrical energy, wind power and load consumption. The influence of the costs of operation of the dispatchable generator without firm access rights in the additional income is investigated. The allocation of the additional income obtained is reported. The willingness of the dispatchable generators to participate in the coordination is analysed. For this, different technology coefficients are considered. The results of the application of the coordination of generators to the two-busbar distribution network are discussed in the summary. 4.4.1 - Modelling of the two-busbar equivalent of the typical distribution network The two-busbar network used to evaluate the coordination of distributed generators is illustrated in Figure 4.2. Generators GenA and GenB are generators connected with firm access rights. GenA is a wind generator (non-dispatchable) and GenB is a thermal generator (dispatchable). GenC and GenD are generators connected without firm access rights. GenC is a thermal generator and GenD is a wind generator. The parameters of the system are given in Table 4.1. Figure 4.2 – Two-busbar distribution network used to evaluate the coordination GenA Chapter 4 – Coordination of independent distributed generators 58 Table 4.1 – Parameters of the system Parameter Value Unit Power limit of the distribution circuit (Scircuit) 15 MVA Minimum output power of GenA and GenD (S_minA, S_minD) 0 MVA Operating limits of GenB ([S_minB; S_maxB]) [2; 5] MVA Operating limits of GenC ([S_minC; S_maxC]) [1.6; 4] MVA Fuel costs of GenB and GenC (fcB, fcC) 35 €/MWh Start-up costs of GenB and GenC (suB, suC) 100 € Load capacity (L_MV) 7.3 MVA Power factor of L_MV 0.95 (ind) - Both active and reactive power flows are considered in the application of the coordination to the two-busbar equivalent of the distribution network. This is to reflect the requirement set in the Portuguese Grid Code with respect to reactive power export in generators below 6 MW of installed capacity. For such generators, reactive power export should be 30% of the active power exported during peak hours (8 a.m. to 10 p.m.) [113]. Therefore, the generators below 6 MW of installed capacity (GenB, GenC and GenD) are required to produce reactive power as follows [113]: Peak hours (hours 8 to 22) Reactive power output must be equal to 30% of the active power output (tan = 0.3); Off-peak hours (hours 23 to 7) Reactive power output must be equal to zero; Losses in the two-busbar equivalent are neglected. The distribution transformer is substituted by a lossless circuit (circuit B1-B2) with the same power capacity, Scircuit. The local load is represented by an equivalent load, L_MV. 4.4.2 - Description of the period of operation considered for evaluating the coordination of distributed generators The coordination of distributed generators is evaluated on a selected period of six days that represents a set of extreme cases of price of electrical energy, wind power and load consumption (see Tables 4.2 to 4.5 and Figures 4.3 to 4.5). Chapter 4 – Coordination of independent distributed generators 59 Table 4.2 - Selected period of operation used for the evaluation of the coordination Day Price of electrical energy Wind power Load Day 1 Large variation of price High wind power Winter load profile Day 2 Medium magnitude of price Medium wind power Winter load profile Day 3 High magnitude of price Low wind power Winter load profile Day 4 Large variation of price High wind power Summer load profile Day 5 Medium magnitude of price Medium wind power Summer load profile Day 6 High magnitude of price Low wind power Summer load profile Figure 4.3 - Three profiles of one day of price of electrical energy [120] Table 4.3 - Average price of electrical energy on each day of the selected period of operation Average price of electrical energy (€/MWh) Day 1, Day 4 Day 2, Day 5 Day 3, Day 6 38.20 41.92 47.75 Figure 4.4 - Three profiles of one day of wind power Table 4.4 - Average wind power on each day of the selected day of operation Average wind power (p.u.) Day 1, Day 4 Day 2, Day 5 Day 3, Day 6 0.89 0.54 0.29 Figure 4.5 - Two profiles of one day of load [114] Table 4.5 - Average load on each day of the selected period of operation Average load (p.u.) Days 1, 2 and 3 Days 4, 5 and 6 0.81 0.72 0 10 20 30 40 50 60 70 80 90 100 110 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 price (€/MWh) hour of the day Day 1, Day4 Day 2, Day 5 Day 3, Day 6 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Wind power (p.u.) hour of the day Day 1, Day 4 Day 2, Day 5 Day 3, Day 6 0,4 0,5 0,6 0,7 0,8 0,9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Load (p.u.) hour of the day Winter profile - Days 1, 2, 3 Summer profile - Days 4, 5, 6 Chapter 4 – Coordination of independent distributed generators 60 The wind power data was obtained from the wind speed data (10-minute average series) of a Portuguese wind farm. This wind speed data was applied to the power curve of the wind turbine Vestas V80 [121]. Price data was obtained from the Iberian Electricity Market (Portuguese side) [120]. Wind power and price data were not collected on the same days (there is no correlation between data). Load data corresponds to the average consumption profiles of a working day in Portugal from 2004 to 2007, provided by the Portuguese Energy Services Regulator [114]. The load profiles were normalised by the maximum value observed in the winter load profile. Tables with the values of wind power, price of electrical energy and load in each hour of the selected period of operation are given in Appendix C. 4.4.3 - Assessment of the coordination in the selected period of operation The following considerations are made for the evaluation of the coordination of distributed generators:  GenA and GenD follow wind power forecasts;  GenB and GenC predict their output following the given price of electrical energy;  GenB and GenC are able to operate at full output up to 16 hours;  Without coordination, the generators access to the network by their order of connection;  GenB and GenC have the same costs of operation. The costs of operation of GenA and GenD are nil. Therefore, the Aggregator uses weights ( ) to enforce the order of connection of the generators in the coordinated operation. Tables with the output powers of the generators in each day of operation, without and with coordination, are available in Appendix D. Day 1, Day 4 Without coordination Figures 4.6 and 4.7 show the output powers of the generators considering winter (day 1) and summer load profiles (day 4), respectively. GenB and GenC do not produce between hours 0 and 8, because the price of electrical energy is lower than their costs of operation. GenB and GenC produce at full output in the other hours. There is an excess of power in the distribution circuit on both days, indicated by the shaded areas in Figures 4.6 and 4.7. The Aggregator determines this excess by considering the anticipated outputs of the generators and the estimation of load consumption. The excess is met by GenD, as it was connected last to the network (“last-in, first-off” operation). Since GenD is a wind generator, its curtailed power is lost. Chapter 4 – Coordination of independent distributed generators 61 Figure 4.6 - Output powers of the generators without coordination (day 1) Figure 4.7 - Output powers of the generators without coordination (day 4) With coordination The Aggregator schedules GenD to produce up to its available power and reduces GenC to meet the circuit limit. GenC is scheduled because it is a dispatchable generator connected without firm access rights. GenC is not able to operate in other hours because the price of electrical energy is lower than its costs of operation. However, GenC is able to store its production and release it when more convenient. The coordination leads to an additional income due to the exchange of a generator with higher costs of operation by a cheaper one. Figures 4.8 and 4.9 show the coordinated output of the generators with the winter (day 1) and the summer load profiles (day 4), respectively. Figure 4.8 - Coordinated output powers of the generators (day 1) Figure 4.9 - Coordinated output powers of the generators (day 4) 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC GenD 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC GenD 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC GenD 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC GenD excess power excess power Reduced production Reduced production Chapter 4 – Coordination of independent distributed generators 62 In Tables 4.6 and 4.7 is presented the electrical energy produced and the income of each generator without and with coordination, respectively for day 1 and day 4. GenC produces less in day 4 when compared to day 1, as the amount of load consumption is lower. Table 4.6 - Electrical energy produced and income received by each generator without and with coordination (day 1) GenA GenB GenC GenD TOTAL WITHOUT COORDINATION Electrical energy produced (MWh) 212.50 72.27 57.79 61.25 403.81 Income received (€) 7511.63 1211.71 948.89 2153.94 11826.17 WITH COORDINATION Electrical energy produced (MWh) 212.50 72.27 55.88 63.16 403.81 Income received (€) 7511.63 1211.71 938.20 2231.45 11892.98 Table 4.7 - Electrical energy produced and income received by each generator without and with coordination (day 4) GenA GenB GenC GenD TOTAL WITHOUT COORDINATION Electrical energy produced (MWh) 212.50 72.27 57.79 58.50 401.06 Income received (€) 7511.63 1211.71 948.89 2039.11 11711.33 WITH COORDINATION Electrical energy produced (MWh) 212.50 72.27 53.13 63.16 401.06 Income received (€) 7511.63 1211.71 919.38 2231.45 11874.17 The coordination leads to an additional income of 66.81€ in day 1 and 162.84€ in day 4. The total amount of electricity produced is the same with and without coordination in both days. Day 2, Day 5 Without coordination Figures 4.10 and 4.11 show the output powers of the generators considering a winter load profile (day 2) and summer load profile (day 5), respectively. Figure 4.10 - Output powers of the generators without coordination (day 2) Figure 4.11 - Output powers of the generators without coordination (day 5) 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC excess power excess power Chapter 4 – Coordination of independent distributed generators 63 There is an excess of power in the distribution circuit in both days, indicated by the shaded areas in Figures 4.10 and 4.11. This excess is met by GenD, as in days 1 and 4. With coordination The Aggregator schedules GenD to produce up to its available power and GenC operates in other hours to avoid exceeding the circuit rating. Figures 4.12 and 4.13 show the coordinated output powers of the generators with the winter (day 2) and the summer load (day 5) profiles, respectively. Figure 4.12 - Coordinated output powers of the generators (day 2) Figure 4.13 - Coordinated output powers of the generators (day 5) The electrical energy produced and the income of each generator (without and with coordination) in days 2 and 5 is given in Tables 4.8 and 4.9, respectively. GenC has to schedule more production in day 5 when compared to day 2, as the amount of load consumption is lower. The electricity produced by GenC without and with coordination is slightly different in both days. This is due to the change of production from hours without reactive power production requirements to hours when that is required. The coordination of distributed generators leads to an additional income of 86.62€ in day 2 and 217.40€ in day 5. The additional income originated is due to the exchange of a generator with higher costs of operation by a cheaper one and the additional amount of electricity that was able to be produced. Table 4.8 - Electrical energy produced and income received by each generator without and with coordination (day 2) GenA GenB GenC GenD TOTAL WITHOUT COORDINATION Electrical energy produced (MWh) 129.50 78.43 62.78 47.49 318.20 Income received (€) 5556.48 643.95 515.28 1992.22 8707.93 WITH COORDINATION Electrical energy produced (MWh) 129.50 78.43 62.67 49.56 320.16 Income received (€) 5556.48 643.95 505.31 2088.68 8794.42 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC Reduced production Reduced production Scheduled production Reduced production Reduced production Scheduled production Chapter 4 – Coordination of independent distributed generators 70 The share of additional income received by each generator is added to what they would receive in “last-in first-off” operation (i.e., without coordination). Generators with firm access rights receive more and thus have an incentive to be operated in a coordinated manner. Generators without firm access rights are able to increase their income when compared to “lastin, first-off” operation. Therefore, considering different costs of operation and allocations of the additional income, all generators are able to improve the return of their projects when compared to the return they would have if “last-in, first-off” operation were in place. 71 Chapter 5 - Coordinating generators and controllable load 5.1 - Introduction The coordination of generators and controllable load aims to maximise the income of the generators. A controllable load has flexibility to shift at least part of its consumption. The Aggregator shifts the consumption of the controllable load to allow the generators to maximise their production. Additional income is obtained from: i) the additional energy that the generators are able to produce; ii) the change of production to hours with a higher price of electrical energy. The additional income is allocated to the generators and the controllable load. A bargaining approach of game theory is used to set this allocation. The coordination of generators and controllable load is evaluated considering different cases of load flexibility and capacity. 5.2 - Integration of a controllable load in the coordination The objective of the coordination of generators and controllable load is to maximise the income of the generators. In the coordination of independent distributed generators described in Chapter 4, load was considered not to be controllable. Thus, generators produced up to the limit of the distribution circuit and the load was considered to be determined. In the coordination of generators and controllable load, the controllable load is asked to shift its consumption to: i) allow generators to produce additional electricity; ii) allow generators to change their production to hours of higher price of electrical energy. The operation of the Aggregator in the coordination of generators and controllable load has two stages (see Figure 5.1):  first, generators are scheduled as if load was determined (as described in Chapter 4);  second, if the production of the generators is not maximised, the Aggregator operates the coordination of generators and controllable load. The additional income obtained is allocated so that both generators and the load have an economic incentive to be operated in a coordinated manner. 5.2.1 - Assumptions and limitations The coordination of generators and controllable load is formulated considering the following assumptions and limitations: • The controllable load is not owned by any of the generators; • Without coordination with the generators, the controllable load schedules its flexible consumption in the hours of lower price; • Only the energy component is considered in the price paid by the load for buying electricity. Transmission/distribution charges, VAT and other costs are not considered. Chapter 5 – Coordinating generators and controllable load 72 Figure 5.1 – Operation of the Aggregator with the integration of a controllable load in the coordination 5.2.2 - Operation of the Aggregator with the integration of the controllable load The Aggregator has an additional input and two additional parameters (marked with *) in the coordination of generators and controllable load, see Figure 5.2. Figure 5.2 – Inputs, parameters and outcomes of the Aggregator in the coordination of generators and controllable load The objective function maximises the income of the generators ( for the dispatchable generators and for the non-dispatchable generators) considering the cost of shifting the consumption of the controllable load, (see equations (5.1) to (5.4)). Chapter 5 – Coordinating generators and controllable load 73 Maximise the income of the generators considering the cost of shifting the load LCOSTDISNINCDISINCnewSINC _____max  Being:       DIS d H h h d h d h d h d hnewStartnewFuelnewPnewuρDISINC 1 1 _____      DISN dn H h hdn hnewPρDISNINC _ 1_ 1 _ ___      H h hhh LcoordnoSloadnewSloadLCOST 1 ____  The suffix updates the value of the variables introduced in Chapter 4 to the coordination of generators and controllable load. The decision variables are , , and . The new fuel and start-up costs of each dispatchable generator d are given in equations (5.5) and (5.6), respectively: h dd h d h dnewPfcnewunewFuel ___     1 __;0max_   h d h dd h dnewunewusunewStart Variable is the consumption schedule of the controllable load after the coordination with the generators.  L is the price paid by the controllable load for buying electricity. is the consumption schedule of the controllable load if there was no coordination with the generators. There are no weights in equation (5.1) to enforce the order of access to the network when the costs of operation of the generators are the same. When the costs of operation are the same, the Aggregator adjusts the generation schedule after the optimisation to enforce the order of connection of the generators. The maximisation presented in equation (5.1) is subject to the apparent power limit of the distribution circuit (constraint (5.7)), the reactive power requirements of the generators (equations (5.8) and (5.9)), the operating limits of the generators (constraints (5.10) and (5.11)), the amount of electrical energy that the dispatchable generators are able to produce (constraint (5.12)), the power factor of the controllable load (equation (5.13)), the upper and lower bounds of flexible consumption (constraints (5.14) and (5.15)) and the maintenance of the same amount of consumption before and after the coordination with the generators (equation (5.16)). Apparent power limit of the distribution circuit HhScircuit,newQloadnewQnewQnewPloadnewPnewP h DISN dn hdn DIS d h d h DISN dn hdn DIS d h d                   2 _ 1_ _ 1 2 _ 1_ _ 1 ______ Reactive power requirements of the generators        DISNdnHIi,newPnewQ DISdHIi,newPnewQ idn idn i d i d __,_tan_ ,_tan_ __   (5.7) (5.8) (5.1) (5.2) (5.3) (5.4) (5.5) (5.6) Chapter 5 – Coordinating generators and controllable load 74            DISNdnIHJjnewQ DISdIHJjnewQ jdn j d __,\,0_ ,\,0_ _ Operating limits of the generators Dispatchable generators HhDISd,SnewSS d h dd  ,max__min_ Non-dispatchable generators HhDISNdn,antSnewSS hdn hdndn  ,____min_ ___ Amount of electrical energy that the dispatchable generators can produce     DISdSTFullnewSnewu dd H h h d h d   ,0max___ 1 Power factor of the controllable load  cos hh SloadPload Upper and lower bounds of flexible consumption HhuboundSloadnewSloadlboundSload hhh  ,___          )_1(max;_min_ )_1(_ fractionflexSloadSloaduboundSload fractionflexSloadlboundSload hh hh Same consumption before and after the coordination   H h h H h hSloadnewSload 11 _ is the fraction of controllable load (value between 0 and 1) and is the capacity of the controllable load. 5.3 - Allocation of the additional income obtained with the coordination of generators and controllable load The coordination leads to an additional income when changing the production of the generators provides an income higher than the cost of changing the consumption of the load. The additional income obtained, , is given by equation (5.17). SINCnewSINCnew  __  is the income obtained with the coordination of generators and controllable load (equation (5.1)) and SINC is the income obtained with the coordination of distributed generators (equation (4.11)). The allocation of the additional income is made considering the coordination of generators and controllable load as a problem of Rubinstein bargaining [123]. Rubinstein bargaining is a non-cooperative game theory approach that addresses the negotiation between two players (in this case, the generators and the controllable load) that make alternating offers for sharing of a certain amount until one player accepts an offer. The offers made by each player are the allocation of the additional income . According to the Rubinstein bargaining model, the generators and the controllable load should share the additional income in equal parts (50% for each player) if: (5.11) (5.12) (5.10) (5.9) (5.13) (5.14) (5.15) (5.16) (5.17) Chapter 5 – Coordinating generators and controllable load 75 • There is no devaluation of the amount to be shared after each round of negotiation. The negotiation occurs for a limited amount of time; • No player has interest in deliberately delaying the negotiation. Both have equal interest in the success of it; • The bargaining power of the players is equal, because they do not share privileged information. The Aggregator collects the parameters and inputs of the system without disclosing them to any of the players. As the aforementioned conditions are met, the additional income received by the generators, , is given by equation (5.18):   newgen _5.0_   is the additional income obtained in the coordination of distributed generators, see equation (4.12). The new allocation of the additional income to each generator is given in equation (5.19).                                              1__ __,1_,_0 __, ___ _ _ , ___ __ _ _ 1_ _ 1 _ 1 _ 1_ 1 __ 1 1__ _ 1 _ 1_ 1 __ 1 1 DISN dn dn DIS dd dnd DIS d DISN dn H h hdndn H h h d h dd H h hdndn dn DIS d DISN dn H h hdndn H h h d h dd H h h d h dd d newallocnewalloc DISNdnDISd,newallocnewalloc DISNdn newPcoefnewPnewucoef newPcoef newalloc DISd newPcoefnewPnewucoef newPnewucoef newalloc The income received by the generators is given in equation (5.20), which is an update of equation (4.15) to include the terms and .                      DISNdngenδnewalloclifoPρnewincome DISdgenδnewallocStart_lifoFuel_lifolifoPρnewincome dn H h hdn h dn d H h h d h d h d h d __,____ ,____ _ 1__ 1 The income received by the controllable load after the coordination with the generators is given in equation (5.21).   newδLCOSTincomeL_5.0_  The first term in equation (5.21), , allows the load to cover the cost of changing its consumption. is given by equation (5.4). The second term, , represents the incentive of the load for its operation in a coordinated manner. 5.4 - Example of the coordination with a controllable load on the two-busbar distribution network The coordination of generators and controllable load is evaluated on the two-busbar distribution network introduced in Chapter 4. The load connected to the distribution network is now considered to have flexible consumption. Different fractions of controllable load and load capacities are evaluated. The (5.20) (5.19) (5.21) (5.18) Chapter 5 – Coordinating generators and controllable load 76 evaluation is performed on the same selected period of operation. This period of operation represents a set of extreme cases of price of electrical energy, wind power and load consumption. The additional income obtained is quantified and the incentives for both generators and the load are reported. 5.4.1 - Description of the price paid by the controllable load for buying electricity The price paid by the controllable load for buying electricity is different from the price of electrical energy. In each day of the period of operation, the load pays for electricity the price of electrical energy plus a margin of 6%, which corresponds to the supplier’s net margin 1 (see Figures 5.3 to 5.5). Day 1, Day 4 Figure 5.3 - Price paid by the controllable load for buying electricity on days 1 and 4 Day 2, Day 5 Figure 5.4 - Price paid by the controllable load for buying electricity on days 2 and 5 1 Value obtained from Ofgem (UK) for electricity consumers, September 2012 (available online: https://www.ofgem.gov.uk/ofgem-publications/39751/electricity-and-gas-supply-market-indicators-5september-2012.pdf – last accessed on 04/12/2012) 0 15 30 45 60 75 90 105 012345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 Price paid by the load for electrical energy (€/MWh) hour of the day 0 15 30 45 60 75 90 105 120 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Price paid by the load for electrical energy (€/MWh) hour of the day + 6% than the price of electrical energy (supplier’s net margin) PRICE PAID BY THE LOAD PRICE OF ELECTRICAL ENERGY + 6% than the price of electrical energy (supplier’s net margin) PRICE PAID BY THE LOAD PRICE OF ELECTRICAL ENERGY Chapter 5 – Coordinating generators and controllable load 77 Day 3, Day 6 Figure 5.5 - Price paid by the controllable load for buying electricity on days 3 and 6 5.4.2 - Assessment on the selected period of operation The coordination is evaluated on the selected period of operation considering: • fractions of ±10% and ±100% load flexibility, considering a load capacity of 7.3 MVA with a power factor of 0.95; • fractions of ±10% and ±100% load flexibility considering different load capacities (from no load to two times the installed capacities of the generators connected without firm access rights, GenC and GenD). The generation and consumption schedules determined by the Aggregator in each day of operation are provided in Appendix E. Generation and consumption schedules without coordination are also given. 5.4.2.1 – Considering a ±10% fraction of load flexibility Day 1 Without coordination of generators and controllable load The controllable load schedules its flexible consumption in the hours of lower price. Considering the price for buying electricity shown in Figure 5.3, the controllable load schedules its consumption as illustrated in Figure 5.6. Figure 5.6 - Consumption schedule of the controllable load with a ±10% fraction of load flexibility on day 1 (no coordination with the generators) The Aggregator schedules the generators but GenC is unable to produce all its available production in hours 9, 12, 13 and 15 (see the shaded areas in 0 15 30 45 60 75 90 105 120 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Price paid by the load for electrical energy (€/MWh) hour of the day + 6% than the price of electrical energy (supplier’s net margin) PRICE PAID BY THE LOAD PRICE OF ELECTRICAL ENERGY consumption schedule of the controllable load without coordination with the generators , ±10% fraction of load flexibility consumption of the load without flexible consumption Chapter 5 – Coordinating generators and controllable load 78 Figure 5.7). This is because the distribution circuit limit was reached and GenC could not schedule its available production in hours 0 to 8. This is because the price of electrical energy then is lower than the operation costs of GenC. Figure 5.7 - Coordinated output of the generators with a ±10% fraction of load flexibility on day 1 (without coordination with the controllable load) With coordination of generators and controllable load The Aggregator operates the coordination by changing the consumption of the controllable load to allow GenC to produce, see Figure 5.8. GenC still does not produce all its available production because the load is already at its maximum consumption in hour 9. Figure 5.8 - Consumption of the controllable load after the operation of the coordination of generators and controllable load, with a ±10% fraction of load flexibility on day 1 The additional income obtained with the coordination, , considering a ±10% fraction of flexible consumption on day 1 is given in Table 5.1. Table 5.1 – Additional income obtained with the coordination, with a ±10% fraction of load flexibility on day 1 Income of the additional production of GenC (€) Increase of the electricity bill of the load, (€) Additional income (€) 18.34 5.90 12.44 Days 2 to 6 On days 2 to 6, the additional income obtained is given in Table 5.2. Table 5.2 - Additional income obtained with the coordination, with a ±10% fraction of load flexibility on days 2 to 6 Day Day 2 Day 3 Day 4 Day 5 Day 6 Additional income (€) 0 0 8.90 0 0 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC GenD Available production of GenC consumption schedule of the controllable load without coordination with the generators, ±10% fraction of load flexibility consumption of the load after the coordination of generators and a controllable load, Chapter 5 – Coordinating generators and controllable load 79 On all days except day 4, the production of the generators is maximised after the operation of the coordination of distributed generators. Therefore, the coordination of generators and controllable load is not operated in those days. 5.4.2.2 – Considering a ±100% fraction of load flexibility Day 1 Without coordination of generators and controllable load The controllable load schedules its flexible consumption in the hours of lower price. Considering the price for buying electricity shown in Figure 5.3, the load schedules its consumption as illustrated in Figure 5.9. Figure 5.9 - Consumption schedule of the controllable load with a ±100% fraction of load flexibility on day 1 (no coordination with the generators) The Aggregator schedules the generators, but GenB and GenC are unable to produce all their available production between hours 19 and 22 (see the shaded area in Figure 5.10). This is because the distribution circuit limit was reached and both GenB and GenC could not schedule their available production in hours 0 to 8. The price of electrical energy then is lower than the operation costs of GenB and GenC. Figure 5.10 - Coordinated output of the generators with a ±100% fraction of load flexibility on day 1 (without coordination with the controllable load) With coordination of generators and controllable load The Aggregator operates the coordination by changing the consumption of the controllable load to allow GenB and GenC to produce, see Figure 5.11. 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB GenC GenD consumption schedule of the controllable load without coordination with the generators, ±100% fraction of load flexibility consumption of the load without flexible consumption Available production of GenB and GenC Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 86 Related to the optimisation  The generators and energy storage systems are price takers;  The forecasts considered (available power of the non-dispatchable generators and price of electrical energy) are entirely reliable;  The non-dispatchable generators and the energy storage systems do not have costs of operation; 6.2.2 – Operation of the Aggregator The Aggregator uses the following parameters for the coordination (see Figure 6.1): the order of connection to the network; the distribution circuit power capacity limit; operating limits of the generators and energy storage systems; the energy capacity and maximum number of daily charge/discharge cycles of each storage system. Figure 6.1 - The Aggregator operating the coordination of non-dispatchable generators and energy storage systems The operation of the Aggregator is described as follows: (1) The Aggregator receives from the generators their anticipated outputs and the anticipated charge/discharge schedule from the energy storage systems. Generators make their projections based on power forecasts. Energy storage systems make their projections considering the prediction of the price of electrical energy; (2) The Aggregator assesses whether the circuit rating is exceeded by the anticipated outputs. If the limit is not exceeded, the Aggregator accepts the anticipated outputs and takes no further action. If the limit is exceeded, the Aggregator runs an optimisation algorithm to schedule the generators and the energy storage systems, as described in step (3). (3) The optimisation algorithm has an objective function (Equation (6.1)) to maximise the income of the generators for producing electricity (variable F). The decision variables are the active power outputs of the generators and the energy storage systems in each time step h of the optimisation. P is the active power output of the generators. St_dis is the energy discharged by each energy storage system stor. St_ch is the energy charged by each energy storage system stor. Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 87         systems storageEnergy 1 1 generators ledispatchabNon 1 1 __max               STOR stor H h h stor h stor h stor G g H h h g h gchStdisStρwPρwF The first term of Equation (6.1) is the income of the non-dispatchable generators and the second term is the income of the energy storage systems. g is the index of the non-dispatchable generators; G and STOR are the total number of generators and energy storage systems, respectively; w is a weight to enforce the order of access to the network and favour the production of the generators in detriment of the discharge of the energy storage systems; H is the time span of the optimisation; ρ is the price of electrical energy. The constraints of the optimisation algorithm are: power limit of the distribution circuit (constraint (6.2)); operating limits of the generators (constraint (6.3)) and energy storage systems (constraints (6.4) and (6.5)); energy capacity limit of the energy storage systems (constraint (6.6)); limits for discharging (constraint (6.7)); and no charging and discharging in the same time step (constraint (6.8)). The discharge of the energy storage systems (given in constraint (6.5)) is limited by the operation of the generators: the generators are scheduled first, up to their anticipated power outputs, ; then, the discharge of the energy storage systems is the minimum of the available capacity after scheduling the non-dispatchable generators and the maximum output power of the energy storage systems, . The maximization term max in constraint (6.5) prevents negative values in the discharge of the energy storage systems. Power limit of the distribution circuit   HhPcircuit,St_chSt_disP STOR stor h stor h stor G g h g   11 Operating limits of the generators HhGg,antPPP h g h gg  ,_ Operating limits of the energy storage systems HhSTORstor,StchStSt stor h stor stor  ,_ HhSTORstor,StStantPPcircuitdisStSt stor St stor G g h g h stor stor stor                        , ; ;_maxmin_ 1   Energy capacity limit of the energy storage systems STORstor,nCcapEdisSt storstor H h h stor    __ 1 Discharge does not exceed charging STORstor,chStdisSt H h h stor H h h stor    11 __ Charging and discharging not possible in the same time step STORstorHji,chStdisSt j stor i stor  ,0__ (6.1) (6.2) (6.3) (6.4) (6.5) (6.6) (6.7) (6.8) Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 88 P is the minimum output power of the non-dispatchable generator g; P_ant is the anticipated power output of g, based on the power forecast; St is the minimum output power of the energy storage system stor; is the maximum output power of stor; E_cap is the energy capacity limit of stor; nC is the maximum number of daily charge/discharge cycles of stor. (4) The outcome of the optimisation is the coordinated output of generators and energy storage systems that maximises the income of the generators and does not exceed the distribution circuit rating. 6.3 - Application of the coordination to a two-busbar distribution network The coordination is evaluated on a two-busbar distribution network with two generators and an energy storage system connected. The evaluation is performed using a set of extreme cases of price of electrical energy and wind power. The impact on the additional income of different orders of connection to the network is analysed. Then, the evaluation is extended to a year of operation to assess the impact on the additional income of different installed capacities of the energy storage system. Figure 6.2 – Two-busbar distribution network used to evaluate the coordination 6.3.1 - Modelling of the distribution network The two-busbar network used to evaluate the coordination is shown in Figure 6.2. Generator GenA is a wind generator connected with firm access rights. GenB is a wind generator connected without firm access rights. Energy storage system ES is connected without firm access rights. The installed capacities of the generators and energy storage system were determined following cost-benefit analyses. The parameters of the system are given in Table 6.1. Table 6.1 - Parameters of the system Parameter Value Unit Power limit of the distribution circuit (Pcircuit) 15 MW Minimum output power of GenA and GenB (PA, PB) 0 MW Minimum charge/discharge limit of ES (StES) 0 MW Maximum charge/discharge limit of ES ( ES) 4 MW Energy capacity of ES (E_capES) 5 [124] MWh Maximum number of daily charge/discharge cycles (nCES) 1 The weights w used on the objective function of the coordination are: ; ; . Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 89 Figure 6.3 - Three profiles of one day of price of electrical energy [120] Figure 6.4 - Three profiles of one day of wind power 6.3.2 - Description of the set of extreme cases of price and wind power The coordination is evaluated on a selected period of three days that represents extreme cases of price of electrical energy and wind power (see Table 6.2 and Figures 6.3 and 6.4). Price data was obtained from the Iberian Electricity Market (Portuguese side) [120]. The wind power data was obtained from the wind speed data (10-minute average series) of a Portuguese wind farm. This wind speed data was applied to the power curve of wind turbine Vestas V80 [121]. Price and wind power data were not collected on the same days (no correlation). Table 6.2 - Selected period of operation used for the evaluation of the coordination Day Price of electrical energy Wind power Day 1 Large variation of price High wind power Day 2 Medium magnitude of price Medium wind power Day 3 High magnitude of price Low wind power 6.3.3 – Distribution network operation with extreme cases of price and wind power “Last-in, first-off” and coordinated operation of the generators and energy storage system are presented as follows. Two different orders of connection to the network are considered: GenB is connected last; ES is connected last. 6.3.3.1 – “Last-in, first-off” operation GenB is connected last GenB is scheduled after GenA and ES have determined their anticipated outputs. Days 1 and 2 0 10 20 30 40 50 60 70 80 90 100 110 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 price (€/MWh) hour of the day Day 1 Day 2 Day 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Wind power (p.u.) hour of the day Day 1 Day 2 Day 3 Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 90 The output powers of the generators and the energy storage system in days 1 and 2 are shown in Figures 6.5 and 6.6, respectively. GenB is curtailed when the power limit of the distribution circuit is exceeded. Figure 6.5 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when GenB is connected last (day 1) Figure 6.6 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when GenB is connected last (day 2) Day 3 The output powers of the generators and the energy storage system in day 3 are shown in Figure 6.7. The distribution circuit limit is not exceeded. There is no energy curtailment. Figure 6.7 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when GenB is connected last (day 3) ES is connected last ES is scheduled after GenA and GenB have determined their anticipated outputs. Days 1 and 2 The output powers of the generators and the energy storage system in days 1 and 2 are shown in Figures 6.8 and 6.9, respectively. In day 2 (Figure 6.9) it is assumed that ES comes fully charged from the previous 24-hour period of operation. GenB is curtailed when the power limit of the distribution circuit is exceeded. -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB Energy curtailed from GenB (last-in, first-off) ES discharging ES charging GenA GenB ES discharging ES charging Energy curtailed from GenB (last-in, first-off) GenA GenB ES discharging ES charging Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 91 Day 3 The output powers of the generators and the energy storage system in day 3 are the same as shown in Figure 6.7. This is because the distribution circuit limit is not exceeded, as in the case when GenB is connected last. Figure 6.8 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when ES connects last (day 1) Figure 6.9 - Output powers of the generators and the energy storage system in “last-in, first-off operation” when ES is connected last (day 2) 6.3.3.2 – Coordinated operation of generators and energy storage systems The Aggregator schedules the charging of ES to hours when GenB is curtailed. Hours of higher price are selected first for charging. The discharging is set to hours of reduced output of GenA and GenB. This leads to an additional income, due to the additional electricity produced by GenB. Day 1 The output powers of the generators and the energy storage system in coordination in day 1 are shown in Figure 6.10. ES changes its charging from hours 3 and 4 to hours 12, 13 and 15. The new charging hours are the hours of higher price when GenB was curtailed in “last-in, first-off” operation. This allows GenB to produce more electricity and originates an additional income. Figure 6.10 - Output powers of the generators and the energy storage system in coordination (day 1) -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day GenA GenB ES discharging ES charging Energy curtailed from GenB (last-in, first-off) GenA Energy curtailed from GenB (last-in, first-off) GenB ES discharging ES charging GenA GenB Energy curtailed from GenB (last-in, first-off) ES discharging ES charging Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 92 The electrical energy produced and the income of each generator and energy storage system in coordination in day 1 are presented in Table 6.3. Comparison with “last-in, first-off” operation is provided. Table 6.3 - Electrical energy produced and income of each generator and energy storage system with coordination and in “last-in, first-off” operation (day 1) GenA GenB ES TOTAL WITH COORDINATION Electrical energy produced (MWh) 255 89.54 5 349.54 Income received (€) 9013 3645 238 12896 “LAST-IN, FIRSTOFF” OPERATION GenB is connected last Electrical energy produced (MWh) 255 86.76 5 346.76 Income received (€) 9013 3260 478 12751 ES is connected last Electrical energy produced (MWh) 255 88.36 5 348.36 Income received (€) 9013 3421 460 12894 Day 2 The output powers of the generators and the energy storage system in coordination in day 2 are shown in Fig. 6.11. The energy storage system changes its charging from hours 8 and 18 to hours 21 and 22. This is to allow GenB to produce in the hours of higher price when it was curtailed in “last-in, first-off” operation. The electrical energy produced and the income of each generator and energy storage system in coordination is presented in Table 6.4. It is again assumed that ES comes fully charged from the previous 24-hour period of operation. The negative income of ES in coordination means that the cost of charging is greater than the income received for the discharge. ES would have no income if it was paid according to its charge/discharge schedule in coordination. Thus, the income received by generators and energy storage system in coordination is determined using a bargaining mechanism of game theory. This gives both generators and energy storage systems an economic incentive to operate in a coordinated manner. Table 6.4 - Electrical energy produced and income of each generator and energy storage system with coordination and in “last-in, first-off” operation (day 2) GenA GenB ES TOTAL WITH COORDINATION Electrical energy produced (MWh) 155.4 73.7 5 234.1 Income received (€) 6668 3151 -21.31 9798 “LAST-IN, FIRSTOFF” OP. GenB is connected last Electrical energy produced (MWh) 155.4 63.7 5 224.1 Income received (€) 6668 2645 63 9376 ES is connected last Electrical energy produced (MWh) 155.4 68.7 5 229.1 Income received (€) 6668 2898 42 9608 6.4 - Allocation of additional income obtained in coordination The coordination of independent non-dispatchable generators and energy storage systems originates an income (INC) given by Equation (6.9).           STOR stor H h h stor h stor h G g H h h g hchStdisStρPρINC 1 11 1 __ (6.9) Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 93 Figure 6.11 - Output powers of the generators and the energy storage system in coordination (day 2) Income INC is greater than the income originated in “last-in, first-off” operation, INC_lifo (see Equation (6.10)).           STOR stor H h h stor h stor h G g H h h g hlifochStlifodisStρlifoPρlifoINC 1 11 1 ______ Suffix _lifo in Equation (6.10) refers to “last-in, first-off” operation. The difference between INC and INC_lifo is the additional income obtained in coordination, , see Equation (6.11). This difference varies with the order of connection of the generators and energy storage systems in “last-in, first-off operation”. lifoINCINCδ_ The allocation of is made considering the coordination as a problem of Rubinstein bargaining [123], similarly as described in Chapter 5. In this case, the players are the sets of generators and energy storage systems. According to the Rubinstein bargaining model, the generators and energy storage systems share the additional income equally (50% for each player). The additional income to be allocated by the generators, , and the energy storage systems, , is then given by Equation (6.12):   5.0__ stgen 6.4.1 – Allocation amongst generators The part of received by each generator , , is determined in a similar manner as described in the coordination of independent distributed generators (Chapter 4, equation (4.14)), see equation (6.13).                      gen Gggen Pcoef Pcoef G gg G g H h h gg H h h gg g _ ,_ 1 1 1 1   6.4.2 – Allocation amongst energy storage systems The part of received by each energy storage system is calculated pro rata to the absolute amount of energy changed in coordination, see Equation (6.14). -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Power output (MVA) hour of the day (6.12) (6.11) (6.10) GenA GenB Energy curtailed from GenB (last-in, first-off) ES charging ES discharging (6.13) Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 94                               st st lifochStlifodisStchStdisSt lifochStlifodisStchStdisSt STOR stor stor STOR stor H h h stor h stor h stor h stor H h h stor h stor h stor h stor stor _ _ ______ ______ 1 1 1 1   6.5 - Sharing the additional income on the two-busbar distribution network example The coordination presented in section 6.3.3.2 originates an additional income in both days, as shown in Figure 6.12. The additional income is greater when GenB is connected last. This is because the amount of energy curtailed in “last-in, first-off” operation is greater than when ES is connected last. The additional income obtained in coordination is allocated as described by Equations (6.13) and (6.14) and added to what the generators and the energy storage system would receive in “last in, first-off” operation. GenA receives a greater income for communicating its anticipated output to the Aggregator. The income received by the generators and the energy storage system in days 1 and 2 is given in Tables 6.5 to 6.8. Comparison with “last-in, first-off” operation is provided. As both generators are wind generators, they have the same technology coefficient coef. Figure 6.12 – Additional income  obtained in days 1 and 2 when: i) GenB is connected last; ii) ES is connected last Day 1 Table 6.5 - Income received by each generator and energy storage system as determined by Eqs. (6.13) and (6.14) when GenB is connected last (day 1) INCOME RECEIVED (€) GenB is connected last GenA GenB ES TOTAL With coordination – Equations (6.13) and (6.14) 9066.65 3278.85 550.50 12896 “Last-in, first-off” operation 9013 3260 478 12751 Table 6.6 - Income received by each generator and energy storage system as determined by Equations (6.13) and (6.14) when ES is connected last (day 1) INCOME RECEIVED (€) ES is connected last GenA GenB ES TOTAL With coordination – Equations (6.13) and (6.14) 9013.74 3421.26 461 12896 “Last-in, first-off” operation 9013 3421 460 12894 145 422 2 190 0 50 100 150 200 250 300 350 400 450 Day 1 Day 2 Additional income obtained in corrdination (€) Day of operation GenB is connected last ES is connected last (6.14) Chapter 6 – Coordinating non-dispatchable generators and energy storage systems 95 Day 2 Table 6.7 - Income received by each generator and energy storage system as determined by Equations (6.13) and (6.14) when GenB is connected last (day 2) INCOME RECEIVED (€) GenB is connected last GenA GenB ES TOTAL With coordination – Equations (6.13) and (6.14) 6811.12 2712.88 274 9798 “Last-in, first-off” operation 6668 2645 63 9376 Table 6.8 - Income received by each generator and energy storage system as determined by Equations (6.13) and (6.14) when ES is connected last (day 2) INCOME RECEIVED (€) ES is connected last GenA GenB ES TOTAL With coordination – Equations (6.13) and (6.14) 6732.44 2928.56 137 9798 “Last-in, first-off” operation 6668 2898 42 9608 6.5.1 – Additional income obtained during one year of operation The coordination is operated during one year, in independent 24-hour periods with one hour time step. 6.5.1.1 – Impact of different orders of connection to the network The additional income  obtained in coordination during one year is presented in Figure 6.13. Wind power data from the same Portuguese wind farm is used. Price data used is obtained from the Iberian Electricity Market (Portuguese side) from May 2010 to April 2011 [125]. Figure 6.13 – Additional income  obtained during one year when: i) GenB is connected last; ii) ES is connected last The additional income obtained is greater when GenB is connected last. This is because of the greater amount of energy curtailed in “last-in, first-off” operation. In both orders of connection the coordination is operated approximately 25% of the year. The coordination is not operated in the rest of the year as the distribution circuit limit is not exceeded then. The income received by the generators and the energy storage system in the year of operation considered is given in Table 6.9. The additional income  during the year of operation is 18.03 k€ if GenB is connected last and 9.05 k€ if ES is connected last. 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These cost/benefit analyses have the following assumptions:  One year of operation of the generators is considered;  The generators schedule their production in periods of 24 hours;  Only the active power production of the generators is considered;  There is no load consumption;  Generator GenA produces according to the availability of wind. One year of wind speed average time series (10-minute average series) from a Portuguese wind farm is considered, see Figure A1. Data were collected from May 2010 to May 2011. Figure A1 - Wind speed average time series from a Portuguese wind farm (May 2010-May 2011) The power curve of wind turbine Vestas V80 (shown in Figure A2 [121]) is linearized to determine the wind power produced by GenA during the year of operation. Figure A2 – Power curve of wind turbine Vestas V80 The available wind power during the year of operation is shown in the cumulative wind power curve of Figure A3. 0 5 10 15 20 25 30 Wind sppeed (m/s) day of the year 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25,1 26 Power output (p.u.) Wind speed (m/s) Average= 6.69 m/s Appendix B – AC optimal power flow in the representative of the Portuguese MV distribution network 118 The following taps were manually tested for the transformer connected between busbars B1 and B2: {0.94; 0.96; 0.98; 1; 1.02; 1.04; 1.06}. The results of the AC OPF reported by MATPOWER are shown as follows. Power flows and busbar voltage data are presented. The objective function value is 558.4€. The cost of operation of the generators located upstream the Valpaços substation is . Then, the cost of operating generators GenA, GenB, GenC and GenD is . This minimum cost of operating the distribution network is obtained being the transformer tap equal to 1.06. Results of the AC OPF reported by MATPOWER ################################################################### MATPOWER Version 4.1, 14-Dec-2011 -- AC Optimal Power Flow MATLAB Interior Point Solver -- MIPS, Version 1.0, 07-Feb-2011 Converged! Converged in 0.15 seconds Objective Function Value = 558.4 €/hr ================================================================================ | System Summary | ================================================================================ How many? How much? P (MW) Q (MVAr) --------------------- ------------------- ------------- ----------------- Buses 10 Total Gen Capacity 222.0 -300.0 to 300.0 Generators 5 On-line Capacity 222.0 -300.0 to 300.0 Committed Gens 5 Generation (actual) 21.5 4.8 Loads 5 Load 21.0 2.0 Fixed 5 Fixed 21.0 2.0 Dispatchable 0 Dispatchable -0.0 of -0.0 0.0 Shunts 0 Shunt (inj) -0.0 0.0 Branches 10 Losses (I^2 * Z) 0.49 2.81 Transformers 1 Branch Charging (inj)  0.0 Inter-ties 0 Total Inter-tie Flow 0.0 0.0 Areas 1 Minimum Maximum ------------------------- ------------------------------- Voltage Magnitude 0.918 p.u. @ bus 6 1.000 p.u. @ bus 0 Voltage Angle 0.00 deg @ bus 0 12.05 deg @ bus 9 P Losses (I^2*R)  0.14 MW @ line 2-3 Q Losses (I^2*X)  1.35 MVAr @ line 1-2 Lambda P 35.00 €/MWh @ bus 9 339.54 €/MWh @ bus 0 Lambda Q 0.00 €/MWh @ bus 0 89.13 €/MWh @ bus 6 Appendix B – AC optimal power flow in the representative of the Portuguese MV distribution network 119 ================================================================================ | Bus Data | ================================================================================ Bus Voltage Generation Load Lambda(€/MVA-hr) # Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q ----- ------- -------- -------- -------- -------- -------- ------- ------- 0 1.000 0.000* 0.75 4.79 15.00 0.00 339.539 - 1 0.998 2.153 - - - - 333.865 3.056 2 0.921 7.232 - - - - 51.915 87.474 3 0.932 10.012 10.00 0.00 2.65 0.87 42.128 89.118 4 0.919 7.651 - - 1.16 0.38 50.690 88.396 5 0.922 8.290 3.00 0.00 - - 48.379 88.735 6 0.918 7.999 - - 0.85 0.28 49.547 89.126 7 0.927 8.639 - - 1.38 0.45 47.024 88.560 8 0.939 11.064 4.00 0.00 - - 38.421 89.066 9 0.944 12.047 3.78 0.00 - - 35.000 89.125 -------- -------- -------- -------- Total: 21.53 4.79 21.04 1.98 ================================================================================ | Branch Data | ================================================================================ Branch From To From Bus Injection To Bus Injection Loss (I^2 * Z) # Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr) ----- ----- ----- -------- -------- -------- -------- -------- -------- 1 0 1 -14.25 4.79 14.39 -4.25 0.137 0.55 2 1 2 -14.39 4.25 14.39 -2.89 0.000 1.35 3 2 3 -7.21 1.21 7.35 -0.87 0.141 0.34 4 2 4 -0.98 0.70 0.98 -0.69 0.003 0.01 5 2 7 -6.20 0.98 6.26 -0.84 0.062 0.15 6 4 5 -2.14 0.31 2.15 -0.29 0.010 0.02 7 5 6 0.85 0.29 -0.85 -0.28 0.002 0.01 8 7 8 -7.64 0.39 7.76 -0.06 0.112 0.32 9 8 9 -3.76 0.06 3.78 0.00 0.019 0.06 10 6 9 -0.00 0.00 0.00 -0.00 0.000 0.00 -------- -------- Total: 0.486 2.81 ################################################################### 121 Appendix C - Data of the selected period of operation Data of the selected period of operation used to evaluate the coordination of independent distributed generators and the coordination of generators and controllable load are presented as follows. Tables C1 to C6 show the values of price of electrical energy, wind power and load consumption for each hour of six days of operation. Price data was obtained from the Iberian Electricity Market (Portuguese side) [120]. Wind power data was obtained from the wind speed data (10 minute average series) of a Portuguese wind farm. This wind speed data was applied to the power curve of the wind turbine Vestas V80. Wind power and price data were not collected on the same days (there is no correlation between data). Load data corresponds to the average consumption profiles of a working day in Portugal from 2004 to 2007, provided by the Portuguese Energy Services Regulator [114]. The load profiles were normalised by the maximum value observed in the winter load profile. Day 1 – Large variation of price, high wind power, winter load profile Table C1 – Values of price of electrical energy, wind power and load consumption on day 1 Hour Price of electrical energy (€/MWh) Wind power (p.u. of rated power) Load consumption (p.u. of maximum consumption) 0 30 1 0.75 1 15.69 1 0.67 2 4.90 1 0.63 3 3 1 0.61 4 2 0.99 0.60 5 4 0.93 0.61 6 5.65 1 0.63 7 32.28 1 0.66 8 22 0.99 0.73 9 38.67 1 0.83 10 38.89 1 0.88 11 40.01 1 0.91 12 48.33 0.94 0.91 13 45.59 0.99 0.86 14 43.85 0.94 0.88 15 45.59 0.94 0.89 16 43.57 0.82 0.88 17 49.11 0.69 0.89 18 53.06 0.50 0.93 19 57.87 0.77 1 20 100 0.70 1 21 89 0.59 0.98 22 57.87 0.81 0.93 23 45.95 0.65 0.87 Appendix C – Data of the selected period of operation 122 Day 2 – Medium magnitude of price, medium wind power, winter load profile Table C2 – Values of price of electrical energy, wind power and load consumption on day 2 Hour Price of electrical energy (€/MWh) Wind power (p.u. of rated power) Load consumption (p.u. of maximum consumption) 0 47.48 0.65 0.75 1 44.82 0.78 0.67 2 43.38 0.82 0.63 3 43.13 0.56 0.61 4 43.10 0.48 0.60 5 42.80 0.70 0.61 6 39.14 0.73 0.63 7 38.02 0.31 0.66 8 37.90 0.42 0.73 9 40.45 0.19 0.83 10 43.10 0.10 0.88 11 41.45 0.10 0.91 12 40.82 0.07 0.91 13 41.16 0.15 0.86 14 40 0.24 0.88 15 39.07 0.57 0.89 16 38.20 0.74 0.88 17 38.20 0.47 0.89 18 37.90 0.59 0.93 19 38.73 0.45 1 20 42.15 0.83 1 21 48.98 1 0.98 22 51.68 1 0.93 23 44.48 1 0.87 Day 3 – High magnitude of price, low wind power, winter load profile Table C3 – Values of price of electrical energy, wind power and load consumption on day 3 Hour Price of electrical energy (€/MWh) Wind power (p.u. of rated power) Load consumption (p.u. of maximum consumption) 0 44.40 0.20 0.75 1 48.51 0.14 0.67 2 44.40 0.07 0.63 3 43.59 0.14 0.61 4 42.40 0.38 0.60 5 42.40 0.26 0.61 6 43.59 0.21 0.63 7 43.59 0.15 0.66 8 40.38 0.20 0.73 9 44.08 0.31 0.83 10 49.30 0.35 0.88 11 51.30 0.26 0.91 12 64.99 0.27 0.91 13 56.38 0.45 0.86 14 52.01 0.34 0.88 15 52.27 0.24 0.89 16 52.01 0.43 0.88 17 51.25 0.40 0.89 18 49.51 0.53 0.93 19 48.51 0.47 1 20 46.10 0.22 1 21 44.02 0.31 0.98 22 44.99 0.28 0.93 23 46.10 0.23 0.87 Appendix C – Data of the selected period of operation 123 Day 4 – Large variation of price, high wind power, summer load profile Table C4 – Values of price of electrical energy, wind power and load consumption on day 4 Hour Price of electrical energy (€/MWh) Wind power (p.u. of rated power) Load consumption (p.u. of maximum consumption) 0 30 1 0.66 1 15.69 1 0.62 2 4.90 1 0.58 3 3 1 0.56 4 2 0.99 0.54 5 4 0.93 0.55 6 5.65 1 0.56 7 32.28 1 0.58 8 22 0.99 0.65 9 38.67 1 0.76 10 38.89 1 0.80 11 40.01 1 0.82 12 48.33 0.94 0.84 13 45.59 0.99 0.80 14 43.85 0.94 0.81 15 45.59 0.94 0.80 16 43.57 0.82 0.80 17 49.11 0.69 0.78 18 53.06 0.50 0.77 19 57.87 0.77 0.77 20 100 0.70 0.80 21 89 0.59 0.82 22 57.87 0.81 0.80 23 45.95 0.65 0.75 Day 5 – Medium magnitude of price, medium wind power, summer load profile Table C5 – Values of price of electrical energy, wind power and load consumption on day 5 Hour Price of electrical energy (€/MWh) Wind power (p.u. of rated power) Load consumption (p.u. of maximum consumption) 0 47.48 0.65 0.66 1 44.82 0.78 0.62 2 43.38 0.82 0.58 3 43.13 0.56 0.56 4 43.10 0.48 0.54 5 42.80 0.70 0.55 6 39.14 0.73 0.56 7 38.02 0.31 0.58 8 37.90 0.42 0.65 9 40.45 0.19 0.76 10 43.10 0.10 0.80 11 41.45 0.10 0.82 12 40.82 0.07 0.84 13 41.16 0.15 0.80 14 40 0.24 0.81 15 39.07 0.57 0.80 16 38.20 0.74 0.80 17 38.20 0.47 0.78 18 37.90 0.59 0.77 19 38.73 0.45 0.77 20 42.15 0.83 0.80 21 48.98 1 0.82 22 51.68 1 0.80 23 44.48 1 0.75 Appendix C – Data of the selected period of operation 124 Day 6 – High magnitude of price, low wind power, summer load profile Table C6 – Values of price of electrical energy, wind power and load consumption on day 6 Hour Price of electrical energy (€/MWh) Wind power (p.u. of rated power) Load consumption (p.u. of maximum consumption) 0 44.40 0.20 0.66 1 48.51 0.14 0.62 2 44.40 0.07 0.58 3 43.59 0.14 0.56 4 42.40 0.38 0.54 5 42.40 0.26 0.55 6 43.59 0.21 0.56 7 43.59 0.15 0.58 8 40.38 0.20 0.65 9 44.08 0.31 0.76 10 49.30 0.35 0.80 11 51.30 0.26 0.82 12 64.99 0.27 0.84 13 56.38 0.45 0.80 14 52.01 0.34 0.81 15 52.27 0.24 0.80 16 52.01 0.43 0.80 17 51.25 0.40 0.78 18 49.51 0.53 0.77 19 48.51 0.47 0.77 20 46.10 0.22 0.80 21 44.02 0.31 0.82 22 44.99 0.28 0.80 23 46.10 0.23 0.75 125 Appendix D - Output powers of the generators without and with the coordination of independent distributed generators The output powers of the generators without and with the coordination of independent distributed generators for each day of the selected period of operation are presented as follows. Load consumption is also presented (columns “Load (MW)”, “Load (MVar)” and “Load (MVA)”). Column “Distr. Circuit (MVA)” shows the utilisation of the distribution circuit. The utilisation of the distribution circuit is presented in absolute value. Column “Circuit limit (MVA)” shows the distribution circuit limit. The output powers of GenD with asterisk (*) in Tables D1, D3, D6 and D8 refer to curtailed outputs. Appendix D – Output powers of the generators without and with the coordination of independent distributed generators 126 DAY 1 Without coordination Table D1 - Output powers of the generators without coordination on day 1 hour GenA (MW) GenA (MVar) GenA (MVA) GenB (MW) GenB (MVar) GenB (MVA) GenC (MW) GenC (MVar) GenC (MVA) GenD (MW) GenD (MVar) GenD (MVA) Load (MW) Load (MVar) Load (MVA) Distr. circuit (MVA) Circuit limit (MVA) 0 10 0 10 0 0 0 0 0 0 3 0 3 5.19 1.71 5.46 8 15 1 10 0 10 0 0 0 0 0 0 3 0 3 4.68 1.54 4.93 8.46 15 2 10 0 10 0 0 0 0 0 0 3 0 3 4.40 1.44 4.63 8.72 15 3 10 0 10 0 0 0 0 0 0 3 0 3 4.23 1.40 4.46 8.88 15 4 9.90 0 9.90 0 0 0 0 0 0 2.97 0 2.97 4.18 1.36 4.40 8.80 15 5 9.30 0 9.30 0 0 0 0 0 0 2.79 0 2.79 4.23 1.40 4.46 7.98 15 6 10 0 10 0 0 0 0 0 0 3 0 3 4.34 1.44 4.57 8.78 15 7 10 0 10 0 0 0 0 0 0 3 0 3 4.56 1.50 4.80 8.57 15 8 9.90 0 9.90 0 0 0 0 0 0 2.87 0.86 3 5.08 1.66 5.34 7.73 15 9 10 0 10 4.79 1.44 5 3.83 1.15 4 2.09 * 0.63 * 2.18 * 5.75 1.89 6.05 15.00 15 10 10 0 10 4.79 1.44 5 3.83 1.15 4 2.43 * 0.73 * 2.54 * 6.10 2.01 6.42 15.00 15 11 10 0 10 4.79 1.44 5 3.83 1.15 4 2.65 * 0.8 * 2.77 * 6.32 2.07 6.65 15.00 15 12 9.40 0 9.40 4.79 1.44 5 3.83 1.15 4 2.82 0.85 2.95 6.32 2.07 6.65 14.58 15 13 9.90 0 9.90 4.79 1.44 5 3.83 1.15 4 2.4 * 0.72 * 2.51 * 5.97 1.97 6.29 15.00 15 14 9.40 0 9.40 4.79 1.44 5 3.83 1.15 4 2.82 0.85 2.95 6.10 2.01 6.42 14.81 15 15 9.40 0 9.40 4.79 1.44 5 3.83 1.15 4 2.82 0.85 2.95 6.15 2.02 6.47 14.76 15 16 8.20 0 8.20 4.79 1.44 5 3.83 1.15 4 2.46 0.74 2.57 6.10 2.01 6.42 13.25 15 17 6.90 0 6.90 4.79 1.44 5 3.83 1.15 4 2.07 0.62 2.16 6.15 2.02 6.47 11.5 15 18 5 0 5 4.79 1.44 5 3.83 1.15 4 1.50 0.45 1.57 6.49 2.14 6.83 8.68 15 19 7.70 0 7.70 4.79 1.44 5 3.83 1.15 4 2.31 0.69 2.41 6.93 2.28 7.3 11.74 15 20 7 0 7 4.79 1.44 5 3.83 1.15 4 2.10 0.63 2.19 6.93 2.28 7.3 10.83 15 21 5.90 0 5.90 4.79 1.44 5 3.83 1.15 4 1.77 0.53 1.85 6.77 2.23 7.13 9.56 15 22 8.10 0 8.10 5 0 5 4 0 4 2.43 0 2.43 6.49 2.14 6.83 13.21 15 23 6.50 0 6.50 5 0 5 4 0 4 1.95 0 1.95 6.04 1.98 6.36 11.58 15 TOTAL 212.5 0 212.5 72.27 18.72 75 57.79 14.95 60 61.25 9.95 62.74 135.5 44.57 142.64 GenA GenB GenC GenD TOTAL INCOME (€) 7511.63 1211.71 948.89 2153.94 11826.17 Appendix D – Output powers of the generators without and with the coordination of independent distributed generators 127 With coordination Table D2 - Output powers of the generators with coordination on day 1 hour GenA (MW) GenA (MVar) GenA (MVA) GenB (MW) GenB (MVar) GenB (MVA) GenC (MW) GenC (MVar) GenC (MVA) GenD (MW) GenD (MVar) GenD (MVA) Load (MW) Load (MVar) Load (MVA) Distr. circuit (MVA) Circuit limit (MVA) 0 10 0 10 0 0 0 0 0 0 3 0 3 5.19 1.71 5.46 8 15 1 10 0 10 0 0 0 0 0 0 3 0 3 4.68 1.54 4.93 8.46 15 2 10 0 10 0 0 0 0 0 0 3 0 3 4.40 1.44 4.63 8.72 15 3 10 0 10 0 0 0 0 0 0 3 0 3 4.23 1.40 4.46 8.88 15 4 9.90 0 9.90 0 0 0 0 0 0 2.97 0 2.97 4.18 1.36 4.40 8.80 15 5 9.30 0 9.30 0 0 0 0 0 0 2.79 0 2.79 4.23 1.40 4.46 7.98 15 6 10 0 10 0 0 0 0 0 0 3 0 3 4.34 1.44 4.57 8.78 15 7 10 0 10 0 0 0 0 0 0 3 0 3 4.56 1.50 4.80 8.57 15 8 9.90 0 9.90 0 0 0 0 0 0 2.87 0.86 3 5.08 1.66 5.34 7.73 15 9 10 0 10 4.79 1.44 5 3.04 0.91 3.17 2.87 0.86 3 5.75 1.89 6.05 15.00 15 10 10 0 10 4.79 1.44 5 3.39 1.02 3.54 2.87 0.86 3 6.10 2.01 6.42 15.00 15 11 10 0 10 4.79 1.44 5 3.61 1.08 3.77 2.87 0.86 3 6.32 2.07 6.65 15.00 15 12 9.40 0 9.40 4.79 1.44 5 3.83 1.15 4 2.82 0.85 2.95 6.32 2.07 6.65 14.58 15 13 9.90 0 9.90 4.79 1.44 5 3.36 1.01 3.51 2.87 0.86 3 5.97 1.97 6.29 15.00 15 14 9.40 0 9.40 4.79 1.44 5 3.83 1.15 4 2.82 0.85 2.95 6.10 2.01 6.42 14.81 15 15 9.40 0 9.40 4.79 1.44 5 3.83 1.15 4 2.82 0.85 2.95 6.15 2.02 6.47 14.76 15 16 8.20 0 8.20 4.79 1.44 5 3.83 1.15 4 2.46 0.74 2.57 6.10 2.01 6.42 13.25 15 17 6.90 0 6.90 4.79 1.44 5 3.83 1.15 4 2.07 0.62 2.16 6.15 2.02 6.47 11.5 15 18 5 0 5 4.79 1.44 5 3.83 1.15 4 1.50 0.45 1.57 6.49 2.14 6.83 8.68 15 19 7.70 0 7.70 4.79 1.44 5 3.83 1.15 4 2.31 0.69 2.41 6.93 2.28 7.3 11.74 15 20 7 0 7 4.79 1.44 5 3.83 1.15 4 2.10 0.63 2.19 6.93 2.28 7.3 10.83 15 21 5.90 0 5.90 4.79 1.44 5 3.83 1.15 4 1.77 0.53 1.85 6.77 2.23 7.13 9.56 15 22 8.10 0 8.10 5 0 5 4 0 4 2.43 0 2.43 6.49 2.14 6.83 13.21 15 23 6.50 0 6.50 5 0 5 4 0 4 1.95 0 1.95 6.04 1.98 6.36 11.58 15 TOTAL 212.5 0 212.5 72.27 18.72 75 55.87 14.37 57.99 63.16 10.51 64.74 135.5 44.57 142.64 GenA GenB GenC GenD TOTAL INCOME BEFORE INCOME SHARING (€) 7511.63 1211.71 938.20 2231.45 11892.98 INCOME AFTER INCOME SHARING (€) 7539.80 1228.78 962.09 2162.31 11892.98