[1] 李文沅. 电力系统安全经济运行-模型与方法[M]. {重庆$:$ 重庆大学出版社, 1989.
[2] Knueven B, Ostrowski J, Watson J P. On mixed integer programming formulations for the unit commitment problem[J/OL]. http://www.optimization-online.org/DB FILE/2018/11/6930.pdf.
[3] Ackooij W V, Lopez I D, Antonio F, et al. Large-scale unit commitment under uncertainty:an updated literature survey[J]. Annals of Operations Research, 2018, 271(1):11-85.
[4] 潘珊珊, 祝宇楠, 简金宝. 带阀点效应水火联合调度问题的一种半定凸松弛求解法[J]. 运筹与管理, 2019(4):89-93.
[5] Baldwin C J, Dale K M, Dittrich R. F. A study of the economic shutdown of generating units in daily dispatch[J]. IEEE Transactions on Power Apparatus and Systems, 1960, 78(4):1272-1282.
[6] Lee F N. Short-term thermal unit commitment-a new method[J]. IEEE Transactions on Power Systems, 2002, 3(2):421-428.
[7] Moradi S, Khanmohammadi S, Hagh M T, et al. A semi-analytical noniterative primary approach based on priority list to solve unit commitment problem[J]. Energy, 2015, 88:244-259.
[8] Quan R, Jian J B, Yang L F. An improved priority list and neighborhood search method for unit commitment[J]. International Journal of Electrical Power & Energy Systems, 2015, 67:278-285.
[9] Petridis V, Kazarlis S, Bakirtzis A. Varying fitness functions in genetic algorithm constrained optimization:the cutting stock and unit commitment problems[J]. IEEE transactions on Systems, Man, and Cybernetics. Part B, Cybernetics:a Publication of the IEEE Systems, Man, and Cybernetics Society, 1998, 28(5):629-640.
[10] Storn R, Price K. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4):341-359.
[11] Kamboj V K, Bath S K, Dhillon J S. A novel hybrid DE-random search approach for unit commitment problem[J]. Neural Computing and Applications, 2015, 28(7).
[12] Victoire T A A, Jeyakumar A E. Unit commitment by a tabu-search-based hybrid-optimisation technique[J]. IEE Proceedings-Generation, Transmission and Distribution, 2005, 152(4):563-574.
[13] Victoire T A A, Jeyakumar A E. Unit commitment by a tabu-search-based hybrid-optimisation technique[J]. IEEE Proceedings-Generation, Transmission and Distribution, 2005, 152(4):563-574.
[14] Saber A Y, Senjyu T, Miyagi T, et al. Fuzzy unit commitment scheduling using absolutely stochastic simulated annealing[J]. IEEE Transactions on Power Systems, 2006, 21(2):955-964.
[15] Rajan C C A. Hydro-thermal unit commitment problem using simulated annealing embedded evolutionary programming approach[J]. International Journal of Electrical Power & Energy Systems, 2011, 33(4):939-946.
[16] Lowery P G. Generating unit commitment by dynamic programming[J]. IEEE Transactions on Power Apparatus & Systems, 1966, PAS-85(5):422-426.
[17] Pang C K, Sheblé G B, Albuyeh F. Evaluation of dynamic programming based methods and multiple area representation for thermal unit commitments[J]. IEEE Transactions on Power Apparatus and Systems, 1981, (3):1212-1218.
[18] Hobbs W J, Hermon G, Warner S, et al. An enhanced dynamic programming approach for unit commitment[J]. IEEE Transactions on Power systems, 1988, 3(3):1201-1205.
[19] Pereira M V F, Pinto L M V G. Multi-stage stochastic optimization applied to energy planning[J]. Mathematical Programming, 1991, 52(1-3):359-375.
[20] Zou J, Ahmed S, Xu A S. Multistage stochastic unit commitment using stochastic dual dynamic integer programming[J]. IEEE Transactions on Power Systems, 2018, 34(3):1814-1823.
[21] Kelley, Jr J E. The cutting-plane method for solving convex programs[J]. Journal of the Society for Industrial and Applied Mathematics, 1960, 8(4):703-712.
[22] Westerlund T, Pettersson F. An extended cutting plane method for solving convex MINLP problems[J]. Computers & Chemical Engineering, 1995, 19:131-136.
[23] 杨林峰, 简金宝, 郑海艳, 等. 求解UC问题的次超立方紧混合整数规划广义割平面法[J]. 中国电机工程学报, 2013, 33(01):99-108.
[24] Duran M A, Grossmann I E. An outer-approximation algorithm for a class of mixed-integer nonlinear programs[J]. Mathematical programming, 1986, 36(3):307-339.
[25] Han D L, Jian J B, Yang L F. Outer Approximation and Outer-Inner Approximation Approaches for Unit Commitment Problem[J]. IEEE Transactions on Power Systems, 2014, 29(2):505-513.
[26] Yang L F, Jian J B, Dong Z Y, et al. Multi-cuts outer approximation method for unit commitment[J]. IEEE Transactions on Power Systems, 2016, 32(2):1587-1588.
[27] Yang L F, Jian J B, Xu Y, et al. Multiple perspective-cuts outer approximation method for risk-averse operational planning of regional energy service providers[J]. IEEE Transactions on Industrial Informatics, 2017, 13(5):2606-2619.
[28] Niknam T, Khodaei A, Fallahi F. A new decomposition approach for the thermal unit commitment problem[J]. Applied Energy, 2009, 86(9):1667-1674.
[29] Naoum-Sawaya J, Elhedhli S. An interior-point Benders based branch-and-cut algorithm for mixed integer programs[J]. Annals of Operations Research, 2013, 210(1):33-55.
[30] 郑海艳, 简金宝, 全然, 等. 基于改进的Benders分解与透视割平面的UC算法[J]. 电力自动化设备, 2015, 35(1):133-138.
[31] Ruzic S, Rajakovic R. Optimal distance method for Lagrangian multipliers updating in shortterm hydro-thermal coordination[J]. IEEE Transactions on Power Systems, 1998, 13(4):1439-1444.
[32] Luenberger D G, Ye Y. Linear and Nonlinear Programming[M]. MA:Addison-wesley, 1984.
[33] 韦化, 吴阿琴, 白晓清. 一种求解UC问题的内点半定规划方法[J]. 中国电机工程学报, 2008, 28(1):35-40.
[34] 全然, 韦化, 简金宝. 求解大规模UC问题的二阶锥规划方法[J]. 中国电机工程学报, 2010, 30(25):101-107.
[35] Trespalacios F, Grossmann I. Review of mixed-Integer nonlinear and generalized disjunctive programming methods[J]. Chemie Ingenieur Technik, 2014, 86(7):991-1012.
[36] Günlük O, Linderoth J. Perspective reformulations of mixed integer nonlinear programs with indicator variables[J]. Mathematical Programming, 2010, 124(1-2):183-205.
[37] Wosely L. Integer Programming[M]. New York:Wiley, 1998.
[38] ILOG CPLEX Optimization Studio[EB/OL].[2020-02-01]. https://www.ibm.com/support/knowledgecenter/zh/SSSA5P 12.8.0/ilog.odms.cplex.help/refmatlabcplex/html/classCplex.html.
[39] Ott A L. Evolution of computing requirements in the PJM market:past and future[J]. IEEE Power and Energy Society General Meeting, 2010, 1:1-4.
[40] IBM ILOG CPLEX Optimization Studio[EB/OL].[2020-02-01]. https://www.ibm.com/prodUCts/ilog-cplex-optimization-studio
[41] GUROBI OPTIMIZATION[EB/OL].[2020-02-01]. https://www.gurobi.com.
[42] Mcdill M E, Braze J. Using the branch and bound algorithm to solve forest flanning problems with adjacency constraints[J]. Forest Science, 2001, 47(3):403-418.
[43] Schrijver A. Theory of Linear and Integer Programming[M]. New York:John Wiley & Sons, 1986.
[44] Carrión M, Arroyo J M. A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[J]. IEEE Transactions on Power Systems, 2006, 21(3):1371-1378
[45] Garver L L. Power generation scheduling by integer programming-development of theory[J]. Transactions of the American Institute of Electrical Engineers, Part III, power apparatus and systems, 1962, 81(3):730-734.
[46] Ostrowski J, Anjos M F, Vannelli A. Tight mixed integer linear programming formulations for the unit commitment problem[J]. IEEE Transactions on Power Systems, 2012, 27(1):39-46.
[47] Rajan D, Takrit S. Minimum up/down polytopes of the unit commitment problem with start-up costs[R]. IBM research report, 2005.
[48] Morales-Espana, Latorre J M, Ramos A. Tight and compact MILP formulation for the thermal unit commitment problem[J]. IEEE Transactions on Power Systems, 2013, 28(4):4897-4908.
[49] 邓俊, 韦化, 黎静华, 等. 一种含四类0-1变量的UC混合整数线性规划模型[J]. 中国电机工程学报, 2015, 35(11):2770-2778.
[50] Lee J, Leung J, Margot F. Min-up/min-down polytopes[J]. Discrete Optimization, 2004, 1(1):77-85.
[51] Rajan D, Takriti S. Minimum up/down polytopes of the unit commitment problem with startup costs[J]. IBM Corporation, 2010, 119(2):331-352.
[52] Damcı-Kurt P, Küçükyavuz S, Rajan D, et al. A polyhedral study of production ramping[J]. Mathematical Programming, 2016, 158(1-2):175-205.
[53] Pan K, Guan Y. A polyhedral study of the integrated minimum-up/-down time and ramping polytope[EB/OL].[2020-02-01]. https://arxiv.org/pdf/1604.02184.
[54] Guan Y, Pan K, Zhou K. Polynomial time algorithms and extended formulations for unit commitment problems[J]. IISE Transactions. 2018, 50(8):735-751.
[55] Tejada-Arango D A, Lumbreras S, Sanchez-Martin P, et al. Which unit-commitment formulation is best? A systematic comparison[J]. IEEE Transactions on Power Systems, DOI:10.1109/TPWRS.2019.2962024.
[56] Atakan S, Lulli G, Sen S. A state transition MIP formulation for the unit commitment problem[J]. IEEE Transactions on Power Systems, 2018, 33(1):736-748.
[57] Yang L F, Li W, Xu Y, et al. High-dimensional three-periods locally ideal MIP formulations for the UC problem[EB/OL].[2020-02-01]. https://arxiv.org/pdf/2004.07077.
[58] Yang L F, Jian J B, Wang Y Y, et al. Projected mixed integer programming formulations for unit commitment problem[J]. International Journal of Electrical Power & Energy Systems, 2015, 68:195-202.
[59] Yang L F, Zhang C, Jian J B, et al. A novel projected two-binary-variable formulation for unit commitment in power systems[J]. Applied Energy, 2017, 187:732-745.
[60] Report I C. Present practices in the economic operation of power systems[J]. IEEE Transactions on Power Apparatus and Systems, 1971, 90(4):1768-1775.
[61] Zhan J P, Wu Q H, Guo C X, et al. Economic dispatch with non-smooth objectives-Part II:dimensional steepest decline method[J]. IEEE Transactions on Power Systems, 2015, 30(2):722-733.
[62] Hemamalini S, Simon S P. Maclaurin, Series-based Lagrangian method for economic dispatch with valve-point effect[J]. IET Generation, Transmission & Distribution, 2009, 3(9):859-871.
[63] 袁晓辉, 袁艳斌, 王乘. 计及阀点效应的电力系统经济运行方法[J]. 电工技术学报, 2005, 20(6):92-96.
[64] Wang M Q, Gooi H B, Chen S X, et al. A mixed integer quadratic programming for dynamic economic dispatch with valve point effect[J]. IEEE Transactions on Power Systems, 2014, 29(5):2097-2106.
[65] Pan S S, Jian J B, Yang L F. A hybrid MILP and IPM approach for dynamic economic dispatch with valve-point effects[J]. International Journal of Electrical Power & Energy Systems, 2018, 97:290-298.
[66] Fuentes-Loyola R, Quintana V H. Medium-term hydrothermal coordination by semidefinite programming[J]. IEEE Transactions on Power Systems, 2003, 18(4):1515-1522.
[67] Zhu Y N, Jian J B, Wu J K, et al. Global optimization of non-convex hydro-thermal coordination based on semidefinite programming[J]. IEEE Transactions on Power Systems, 2013, 28(4):3720-3728.
[68] Jian J B, Pan S S, Yang L F. Solution for short-term hydrothermal scheduling with a logarithmic size mixed-integer linear programming formulation[J]. Energy, 2019, 171:770-784.
[69] Yang Z, Xie K, Yu J, et al. A general formulation of linear power flow models:basic theory and error analysis[J]. IEEE Transactions on Power Systems, 2019, 34(2):1315-1324.
[70] Ruiz J P, Liu C, Sun G, et al. Outer-approximation method for security constrained unit commitment[J]. IET Generation, Transmission & Distribution, 2013, 7(11):1210-1218.
[71] Deeb, N.I. Shahidehpour S M. Cross decomposition for multi-area optimal reactive power planning[J]. IEEE Trans on Power Systems, 1993, 8(4):1539-1544.
[72] Alguacil N, Conejo A J. Multiperiod optimal power flow using Benders decomposition[J]. IEEE Transactions on Power Systems, 2000, 15(1):196-201.
[73] Montoya O D, Gil-Gonzalez W, Garces A. Optimal power flow on DC microgrids:a quadratic convex approximation[J]. IEEE Transactions on Circuits and Systems II:Express Briefs, 2018:1018-1022.
[74] Zhang H, Heydt G T, Vittal V, et al. An improved network model for transmission expansion planning considering reactive power and network losses[J]. IEEE Transactions on Power Systems, 2013, 28(3):3471-3479.
[75] Akbari T, Tavakoli Bina M. Linear approximated formulation of AC optimal power flow using binary discretisation[J]. IET Generation, Transmission & Distribution, 2016, 10(5):1117-1123.
[76] Yang Z, Zhong H, Xia Q, et al. A novel network model for optimal power flow with reactive power and network losses[J]. Electric Power Systems Research, 2017, 144:63-71.
[77] Li Z, Yu J, Wu Q H. Approximate linear power flow using logarithmic transform of voltage magnitudes with reactive power and power loss consideration[J]. IEEE Transactions on Power Systems, 2017, 33(4):4593-4603.
[78] 张利, 赵建国, 韩学山.考虑网络安全约束的UC新算法[J].电网技术, 2006, 30(21):50-55.
[79] Shaw J. A direct method for security-constrained unit commitment[J]. IEEE Transactions on Power Systems, 1995, 10(3):1329-1342.
[80] 耿建, 徐帆, 姚建国, 等.求解安全约束UC问题的混合整数规划算法性能分析[J]. 电力系统自动化, 2009, 33(21):24-27.
[81] 简金宝, 杨林峰, 全然.基于改进多中心校正解耦内点法的动态最优潮流并行算法[J]. 电工技术学报, 2012, 27(6):232-241.
[82] 杨林峰, 简金宝, 韩道兰, 等.基于最优中心参数的多中心校正内点最优潮流算法[J]. 中国电机工程学报, 2012, 32(4):136-144.
[83] Wu Y C, Debs A S, Marsten R E.A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows[J].IEEE Transactions on Power Systems, 1994, 9(2):876-883.
[84] Mehrotra S.On the implementation of a primal-dual interior point method[J].SIAM Journal on Optimization, 1992, 2(4):575-601.
[85] Gondzio J.Multiple centrality corrections in a primal-dual method for linear programming[J].Computational Optimization and Applications, 1996, 6(2):137-15.
[86] 梁梓均, 林舜江, 刘明波. 一种求解交直流互联电网分布式最优潮流的同步ADMM方法[J]. 电力系统保护与控制, 2018, 46(23):34-42.
[87] Wang Y, Wu L, Wang S. A fully-decentralized consensus-based ADMM approach for DC-OPF with demand response[J]. IEEE Transactions on Smart Grid, 2017, 8(6):2637-2647.
[88] 文云峰, 郭创新, 郭剑波, 等. 多区互联电力系统的分散协调风险调度方法[J]. 中国电机工程学报, 2015(14).
[89] 汪超群, 韦化, 吴思缘, 等. 七种最优潮流分解协调算法的性能比较[J]. 电力系统自动化, 2016, 40(06):55-63.
[90] Yang L F, Luo J Y, Xu Y, et al. A distributed dual consensus ADMM based on partition for DC-DOPF with carbon emission trading[J]. IEEE Transactions on Industrial Informatics, DOI 10.1109/TII.2019.2937513.
[91] Li Z, Guo Q, Sun H, et al. Coordinated economic dispatch of coupled transmission and distribution systems using heterogeneous decomposition[J]. IEEE Transactions on Power Systems, 2016, 31(6):4817-4830.
[92] Kargarian A, Mohammadi J, Guo J, et al. Toward distributed/decentralized DC optimal power flow implementation in future electric power systems[J]. IEEE Transactions on Smart Grid, 2018, 9(4):2574-2594.
[93] 陆文甜, 刘明波, 林舜江, 等. 基于分布式内点法的多区域互联电力系统最优潮流分散式求解[J]. 中国电机工程学报, 2016, 36(24):6828-6837.
