本論文提出一個混合型演算法，其結合了廣義乘子法（Generalized Multiplier Method）、隨機可行方向法（Random Feasible Directions Algorithm）與擬牛頓法（Quasi-Newton Method）三者的優點，用於求解電力系統中具有大規模非線性混合整數規劃的機組排程問題。
經濟調度問題於機組排程運算中扮演著很重要的角色，因為各時段每個組合的發電成本皆由經濟調度求得，以找出最佳的機組預定排程。本論文將使用過濾隱枚舉法（Filtering Constraint Implicit Enumeration Algorithm）搭配選擇規則策略來進行求解，以避免在搜尋時陷入區域解或是不可行解區間，並加快演算法求解的精確度和速度；其中，選擇規則策略將以具有過濾條件的隱枚舉法與進階優先順序法（Advanced Priority List Method）共同建立。
本論文模擬三種不同的案例，分別為IEEE-10台機組、獨立型再生能源發電系統短期調度，以及台灣電力系統的經濟調度。其中，一旦龍門電廠商轉後系統備轉容量需求、安全和穩定度的改變，必須將充裕的備轉容量分散至各不同的機組上，並對現有的機組重新調度以符合經濟成本和安全性。而各項研究結果的驗證，均在實際的電力系統完成，可提供台灣電力公司作為調度與規劃的參考。

This dissertation proposed a hybrid approach of combining the algorithm of Random Feasible Directions with a Generalized Multiplier Method and a Quasi-Newton Method (RFD-GMQN) developed for solving the unit commitment (UC) problems that exist in the large-scale nonlinear mixed integer programming of a power system.
Economic dispatch (ED) problems play an important role in UC problems. Because the generation cost of every combination is calculated by the ED in each hour in order to find the best UC. This dissertation used the Filtering Constraint Implicit Enumeration Algorithm (FCIEA) with rule-based selection strategy to improve the accuracy and computer operation time and prevent from falling into local or infeasible solutions while resolving the UC. In addition, the rule-based selection strategy was established on both the FCIEA and the advanced priority list method (APLM).
Three case studies were simulated in this dissertation: IEEE-10 units, a short-term dispatch of an autonomous renewable energy generation system, and an unit commitment of the Taiwan power system. Once the Lungmen nuclear power plant is commercially operated, critical concerns, such as the change of spinning reserve demand, the safety, the reliability, and the policy of dispatching ample spinning reserves to different units, will force a re-dispatch of the current units to meet economic costs and security. All of the results obtained in this study were tested under a practical power system. The results can provide Taipower Company a guideline for dispatch and scheduling.

[1] 台灣電力股份有限公司：http://taipower.eki.com.tw/。
[2] Wood, A. J. and B. F. Wollenberg, Power Generation Operation and Control, 2nd ed., John Willey & Sons, Inc., New York (1996).
[3] Senjyu , T., K. Shimabukuro , K. Uezato and T. Funabashi, “A Fast Technique for Unit Commitment Problem by Extended Priority List,” IEEE Trans. On Power Systems, Vol. 18, No. 2, pp. 882-888 (2003).
[4] Lee, F. N., “The Application of Commitment Utilization Factor (CUF) to Thermal Unit Commitment,” IEEE Trans. On Power Systems, Vol. 6, No. 2, pp. 691-698 (1991).
[5] Sheble’, G. B. and G. N. Fahd, “Unit Commitment Literature Synopsis,” IEEE Trans. On Power Systems, Vol. 9, No. 1, pp. 128-135 (1994).
[6] Olsen, K. A. and B. Indredavik, “A Proofreading Tool using Brute Force Techniques,” IEEE Potentials, Vol. 30, No. 4, pp.18-22 (2011).
[7] Romero, R. and A. Monticelli, “A Zero-One Implicit Enumeration Method for Optimizing Investments in Transmission Expansion Planning,” IEEE Trans. on Power Systems, Vol. 9, No. 3, pp.1385-1391 (1994).
[8] Merlin, A. and P. Sandrin, “A New Method for Unit Commitment At Electricite De France,” IEEE Trans. On PAS, Vol. 102, No.5, pp. 1218-1215 (1983).
[9] Hobbs, W. J., G. H. S. Warner and G. B. Sheble’, “An Enhanced Dynamic Programming Approach for Unit Commitment,” IEEE Trans. on Power Systems, Vol. 3, No. 3, pp.1201-1205 (1988).
[10] Finardi, E. C. and E. L. da Silva, “Solving the Hydro Unit
115
Commitment Problem via Dual Decomposition and Sequential Quadratic Programming,” IEEE Trans. on Power Systems, Vol. 21, No. 2, pp.835-844 (2006).
[11] Cohen, A. I. and M. Yoshimura, “A Branch-and-Bound Algorithm for Unit Commitment,” IEEE Trans. on Apparatus and Systems, Vol. PAS-102, No. 2, pp.444-451 (1983).
[12] Sasaki, H., M. Watanabe, J. Kubokawa, N. Yorino and R. Yokoyama, “A Solution Method of Unit Commitment by Artificial Neural Networks,” IEEE Trans. on Power Systems, Vol. 7, No. 3, pp.974-981 (1992).
[13] Saber, A. Y., T. Senjyu, T. Miyaqi, N. Urasaki and T. Funabashi, “Fuzzy Unit Commitment Scheduling Using Absolutely Stochastic Simulated Annealing,” IEEE Trans. on Power Systems, Vol. 21, No. 2, pp.955-964 (2006).
[14] Damousis, I. G., A. G. Bakirtzis and P. S. Dokopoulos, “A Solution to the Unit-Commitment Problem Using Integer-Coded Genetic Algorithm,” IEEE Trans. on Power Systems, Vol. 19, No. 2, pp.1165-1172 (2004).
[15] Ting, T. O., M. V. C. Rao and C. K. Loo, “A novel approach for unit commitment problem via an effective hybrid particle swarm optimization,” IEEE Trans. On Power Systems, Vol. 21, No. 1, pp. 411-418 (2006).
[16] Saadat, H. Power System Analysis, New York: McGraw-Hall (1999).
[17] Chen. P. H. and H. C. Chang, “Large-Scale Economic Dispatch by Genetic Algorithm,” IEEE Trans. on Power Systems, Vol. 10, No. 4, pp.1919-1926 (1995).
116
[18] Senjyu, T., H. Yamashiro, K. Uezato and T. Funabashi, “A Unit Commitment Problem by Genetic Algorithm Based on Unit Characteristic Classification,” in Proc. IEEE/Power Eng. Soc. Winter Meeting, Vol. 1, pp 58-63 (2002).
[19] Abookazemi, K. and M. W. Mustafa, “Unit Commitment Optimization using Improved Genetic Algorithm,” IEEE Bucharest Power Tech. Conference, pp.1-6 (2009).
[20] 陳俊隆，多區域發電量與備轉容量排程之研究，國立台灣科技大學博士論文，民國九十年。
[21] 李昌廷，應用基因演算法進行獨立電力系統短期發電排程，中原大學碩士論文，民國九十四年。
[22] 陳維德，應用免疫演算法最佳化火力機組調派，台北科技大學碩士論文，民國九十七年。
[23] Bakirtzis, A. G. and P. S. Dokopoulos, “Short Term Generation Scheduling in a Small Autonomous System with Unconventional Energy Sources,” IEEE Trans. on Power Systems, Vol. 3, No. 3, pp. 1230-1236 (1988).
[24] Hong, Y. Y., C. S. Chiu and C. T. Li, “KW Scheduling in an Autonomous System,” IEEE Power Tech., pp.1730-1735 (2007).
[25] De Broe, A. M., S. Drouilhet and V. Gevorgian, “A Peak Power Tracker for Small Wind Turbines in Battery Charging Applications,” IEEE Trans. on Energy Conver., Vol. 14, No. 4, pp. 1630-1635 (1999).
[26] 呂學德，以同時擾動隨機近似法進行風場永磁同步發電機之最大功率追蹤控制，中原大學碩士論文，民國九十五年。
[27] 包璿瑋，太陽光發電系統運轉性能評估，碩士論文，民國九十一年。
[28] 陳德聖，軟式切換電池充電器及檢測器之研製，國立台灣科技大學
117
碩士論文，民國八十九年。
[29] 經濟部能源局，取自於 http://www.cadiis.com.tw/energy/。
[30] Dieu, V. N. and W. Ongsakul, “Enhanced Augmented Lagrangian Hopfield Network for Unit Commitment,” IEE Proc.-Gener. Transm. Distrib., Vol. 153, No. 6, pp. 624-632 (2006).
[31] Koduru, P., Z. Dong, S. Das, S. M. Welch, J. L. Roe and E. Charbit, “A Multiobjective Evolutionary-Simplex Hybrid Approach for the Optimization of Differential Equation Models of Gene Networks,” IEEE Trans. on Evolutionary Computation, Vol. 12, No. 5, pp. 572-590 (2008).
[32] Padberg, M. W. and G. Rinaldi, “A branch-and-Cut Algorithm for The Resolution of Large-Scale Symmetric Traveling Salesman Problems,” SIAM Review 33, pp. 60-100 (1991).
[33] Garfinkel, R. S. and G. L. Nemhauser﹐ Integer Programming﹐John Wiley & Sons﹐Inc., New York (1972).
[34] Khandani, A. K., “Design of Turbo-Code Interleaver using Hungarian Method,” Electron. Lett., Vol. 34, No. 1, pp. 63-65 (1998).
[35] Hart, W. E., “Evolutionary Pattern Search Algorithms for Unconstrained and Linearly Constrained Optimization,” IEEE Trans. on Evolutionary Computation, Vol. 5, No. 4, pp. 388-397 (2001).
[36] Chen, H. Y. and S. M. Kang, “A New Circuit Optimization Technique for High Performance CMOS Circuits,” IEEE Trans. on Computer-Aided Design, Vol. 10, No. 5, pp.670-677 (1991).
[37] Lazarou, S., V. Vita and L. Ekonomou, “Application of Powell’s Optimisation Method for the Optimal Number of Wind Turbines in a Wind Farm,” IEE Sci. Meas. Technol., Vol. 5, No. 3, pp. 77-80 (2011).
118
[38] Kebriaei, H., B. N. Araabi and A. Rahimi-Kian, “Short-Term Load Forecasting With a New Nonsymmetric Penalty Function,” IEEE Trans. on Power Systems, Vol. 26, No. 4, pp.1817-1825 (2011).
[39] 趙繼俊，優化技術與Matlab優化工具箱，機械工業出版社 (2011)。
[40] 謝政，非線性最優化理論與方法，高等教育出版社 (2010)。
[41] Kuo, W., H. H. Lin, Z. Xu and W. Zhang, “Reliability Optimization with the Lagrange-Multiplier and Branch-and-Bound Technique,” IEEE Trans. on Reliability, Vol. 36, No. 5, pp.624-630 (1987).
[42] Theiler, J. and J. Alper, “On the Choice of Random Directions for Stochastic Approximation Algorithms,” IEEE Trans. on Automatic Control, Vol. 51, No. 3, pp. 476-481 (2006).
[43] Chang, Y. P., W. K. Tseng and T. F. Tsao, “Application of Combined Feasible-Direction Method and Genetic Algorithm to Optimal Planning of Harmonic Filters Considering Uncertainty Conditions,” IEE Proc.-Gener. Transm. Distrib., Vol. 152, No. 5, pp. 729-736 (2005).
[44] Leandro, D. S. C. and C. M. Viviana, “Particle Swarm Optimization with Quasi-Newton Local Search for Solving Economic Dispatch Problem,” IEEE International Conference on Systems, Man, and Cybernetics, Vol. 4, pp. 3109-3113 (2006).
[45] Levy, M. N., M. W. Trosset and R. R. Kincaid, “Quasi-Newton Methods for Stochastic Optimization,” Fourth International Symposium on Uncertainty Modeling and Analysis, pp. 304-309 (2003).
[46] Chen, C. L. and N. Chen, “Direct Search Method for Solving Economic Dispatch Problem Considering Transmission Capacity Constraints,” IEEE Trans. on Power Systems, Vol. 16, No. 4,
119
pp.764-769 (2001).
[47] Ongsakul, W. and N. Petcharaks, “Unit Commitment by Enhanced Adaptive Lagrangian Relaxation,” IEEE Trans. on Power Systems, Vol. 19, No. 1, pp.620-628 (2004).
[48] Ozturk, U. A., M. Mazumdar and B. A. Norman, “A Solution to the Stochastic Unit Commitment Problem Using Chance Constrained Programming,” IEEE Trans. on Power Systems, Vol. 19, No. 3, pp.1589-1598 (2004).
[49] Kazarlis, S. A., A. G. Bakirtzis and V. Petridis, “A Genetic Algorithm Solution to the Unit Commitment Problem,” IEEE Trans. on Power Systems, Vol. 11, No. 1, pp.83-92 (1996).
[50] Juste, K. A., H. Kita, E. Tanaka and J. Hasegawa, “An Evolutionary Programming Solution to the Unit Commitment Problem,” IEEE Trans. on Power Systems, Vol. 14, No.4, pp. 1452-1459 (1999).
[51] Cbeng, C. P., C.W. Liu and C.C. Liu, “Unit Commitment by Lagrangian Relaxation and Genetic Algorithms,” IEEE Trans. on Power Systems, Vol. 15, No. 2, pp. 707-714 (2000).
[52] 吳進忠，獨立電力系統合理備轉容量規劃與調度之研究，國立台灣科技大學電機工程系博士論文，民國九十二年七月。
[53] Senjyu, T., H. Yamashiro, K. Uezato and T. Funabashi, “A unit commitment problem by using genetic algorithm based on characteristic classification,” IEEE Proc.-Power Eng. Soc. Vol. 1, pp. 58-63. (2002).
[54] 台灣電力公司，電力調度規則彙編，民國九十六年。
[55] Hsu, Y. Y., J. D. Jien, C. C. Liang, K. K. Chen, T. S. Lai and T. E. Lee, “Operating Reserve and Reliability Analysis of the Taiwan Power System,” IEE Proc.-C, Vol. 137, No. 5, pp. 349-357 (1990).
[56] 嚴逸帆，龍門電廠商轉後台電系統合理備轉容量的規劃，國立台灣科技大學碩士論文，民國一百年。
[57] 經濟部，台灣電力公司729停電事故調查報告，行政院經濟部研究報告，台北，民國八十八年。
[58] 徐瑋佑，互聯電力系統中自動發電控制最佳化之研究，中原大學碩士論文，民國九十六年。