FUZZY APPROACH TO OPTIMAL GENERATION SCHEDULING FOR GenCos IN COMPETITIVE ELECTRICITY MARKETS

A.F. Al-Ajlouni, H.Y. Yamin, W. Qassem, and S.M. Shahidehpour

References

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  25. [25] University of Washington, IEEE 118-bus system, available at the following web site: http://www.ee.washington.edu, 1996. 103 Appendix A: List of Symbols Ci(·) Quadratic cost function of unit i Cfi(·) Fuel consumption quadratic function of unit i Cei(·) Emission quadratic function of unit i DMT GenCo’s decision maker target ($) DR(i) Ramp down rate limit of unit i ¯E Upper limit on total emission allowance F(i, t) Profit of unit i at time t ¯F(i) Upper limit on total fuel consumption for unit i F(i) Lower limit on total fuel consumption for unit i MSR(i) Maximum sustain ramp rate of unit i(MW/min) N Number of unit in a GenCo P(i, t) Generation of unit i at time t Pg(i) Lower limit on generation of unit i ¯Pg(i) Upper limit on generation of unit i ¯P(t) Upper limit on GenCo’s desired total generation at time t Pmin(t) Minimum fuzzy GenCo’s desired demand at time t Pmax(t) Maximum fuzzy GenCo’s desired demand at time t R(i, t) Spinning reserve of unit i at time t ¯R(t) Upper limit on GenCo’s desired total spinning reserve at time t Rmin(t) Minimum fuzzy GenCo’s desired spinning reserve at time t Rmax(t) Maximum fuzzy GenCo’s desired spinning reserve at time t rs The probability that spinning reserve is called and generated S(i, t) Startup cost of unit i at time t T Hours in the study horizon (24 h in the day-ahead market) UR(i) Ramp up rate limit of unit i ρg(i, t) Forecasted market price for energy at bus i and time t ρs(i, t) Forecasted market price for spinning reserve at bus i and time t μx Fuzzy membership function for a parameter x μP Fuzzy membership function for the generated power P μR Fuzzy membership function for the spinning reserve R μmin _profit Fuzzy membership function for GenCo’s minimum profit μprofit Fuzzy membership function for GenCo’s optimal profit Appendix B: The IEEE 118-Bus System The IEEE 118-bus system one-line diagram is shown in Fig. B1. Figure B2 depicts forecasted bus energy prices for the 118-bus system at hour 18. The forecasted system demand and reserves are given in Table B1. Table B1 Forecasted System Demand and Spinning Reserves Hour Demand (MW) Spinning Reserve (MW) 1 3,308.8 165.4 2 3,054.2 152.7 3 2,884.6 144.2 4 2,799.7 140.0 5 2,794.9 139.7 6 2,797.3 139.9 7 2,799.7 140.0 8 2,969.4 148.5 9 3,393.6 169.7 10 3,733.0 186.6 11 3,817.8 190.9 12 3,860.2 193.0 13 3,817.8 190.9 14 3,733.0 186.6 15 3,690.5 184.5 16 3,690.5 184.5 17 3,860.2 193.0 18 4,242.0 212.1 19 4,199.6 210.0 20 4,114.7 205.7 21 3,987.5 199.4 22 3,902.6 195.1 23 3,690.5 184.5 24 3,436.0 171.8 104 Figure B1. IEEE118-bus system. Figure B2. Energy price profile for IEEE 118-bus system (at hour 18). 105 Appendix C: GenCos’ Generation Schedule Table C1 Total GenCos’ Generated Power and Spinning Reserves to be Sold in the Different Markets Hour Generated Power Spinning Reserve Quantity (MW) Membership Quantity (MW) Membership 1 2,415.3 0.978 81.3 0.968 2 2,165.3 0.957 76.4 0.943 3 1,977.0 0.880 71.2 0.875 4 1,885.5 0.841 69.4 0.833 5 1,875.5 0.824 65.0 0.820 6 1,880.2 0.840 65.0 0.831 7 1,894.1 0.845 69.9 0.836 8 2,074.0 0.915 73.5 0.908 9 2,503.0 0.976 85.7 0.969 10 2,633.4 0.985 94.5 0.981 11 2,818.2 1.000 97.6 1.000 12 2,960.0 1.000 98.6 1.000 13 2,916.7 1.000 101.5 1.000 14 2,833.0 1.000 94.4 1.000 15 2,789.1 0.992 94.2 0.998 16 2,790.5 0.993 94.5 0.999 17 2,959.6 1.000 97.4 1.000 18 3,319.5 1.000 104.6 1.000 19 3,299.0 1.000 105.8 1.000 20 3,214.2 1.000 101.3 1.000 21 3,087.0 1.000 98.6 1.000 22 3,002.2 1.000 96.2 1.000 23 2,790.2 0.990 94.6 0.998 24 2,536.1 0.979 87.4 0.971 106

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