火电厂机组负荷优化组合分配问题的研究
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摘要
本文针对火电厂负荷优化组合分配的特点,提出了以系统煤耗量为目标函数,包含负荷需求限制、单机输出功率上下限、机组最大允许启停次数、机组最小连续运行时间等约束条件的数学模型。通过对优化问题的研究,以优化算法为载体,来实现优化问题。首先,确定机组煤耗特性曲线,针对由于煤耗曲线可能出现微增率曲线非单调上升的现象,提出了用加权等式约束的最小二乘法建立机组煤耗特性曲线的方法。其次,分别对不同优化计算原理进行分析,对动态规划法和改进的遗传算法编制不同的优化计算程序,并对计算结果进行对比分析。算例结果表明,采用对初始解和遗传算子产生的解群进行可行性检查的遗传算法和等微增率法相结合的方法具有好的适应性和收敛性。
To meet the characters of optimizing unit commitment (UC), this paper choosestotal fuel-cost as the objective function, taking into account constraint function such asthe demand constraint, generation capacity limits, ramp rate limits, maximum allowablestart and stop times limits, the minimum uptime and downtime limits, unit and stop statelimits and etc. By optimization methods research, this paper gives an algorithm ofsolving UC. Firstly, as the incremental rate of fuel-cost curve might benon-monotonically increasing, a weighted least-square method is proposed to smooth thecurve. Secondly, various optimization principals are analyzed. Different methods areprogrammed such as dynamic programming and modified genetic algorithm (GA). Inaddition, the results are compared and analyzed. The illustrative example shows that, byfeasibility checking the original solutions and the solutions created by genetic operator,GA method combined with equal-incremental rate principal has good convergence andadaptability.
To meet the characters of optimizing unit commitment (UC), this paper choosestotal fuel-cost as the objective function, taking into account constraint function such asthe demand constraint, generation capacity limits, ramp rate limits, maximum allowablestart and stop times limits, the minimum uptime and downtime limits, unit and stop statelimits and etc. By optimization methods research, this paper gives an algorithm ofsolving UC. Firstly, as the incremental rate of fuel-cost curve might benon-monotonically increasing, a weighted least-square method is proposed to smooth thecurve. Secondly, various optimization principals are analyzed. Different methods areprogrammed such as dynamic programming and modified genetic algorithm (GA). Inaddition, the results are compared and analyzed. The illustrative example shows that, byfeasibility checking the original solutions and the solutions created by genetic operator,GA method combined with equal-incremental rate principal has good convergence andadaptability.
引文
[1] 陈浩勇,王锡凡.机组组合问题的优化方法综述(1).电力系统自动化,第 22 卷,第 4 期,1999,2,51-56
[2] 陈浩勇,王锡凡.机组组合问题的优化方法综述(2).电力系统自动化,第 22 卷,第 4 期,1999,3,51-56
[3] 周明,孙树栋.遗传算法原理及应用.北京:国防工业出版社,1996,6,第一 版
[4] 范从振.锅炉原理. 北京:水利电力出版社,1986,5 第一版
[5] 于良春.中国电力工业的改革与发展.中国工业经济,2000,4:53~57
[6] 马振华等.现代应用数学手册:运筹学与最优化理论卷.北京:清华大学出版 社,2003,11
[7] 刘严,谭忠富.动态规划法在机组负荷分配中的应用.现代电力,2002,4:76～ 80
[8] Sheble G B. Solution of the Unit Commitment Problem by the Method of Unit Periods.In:IEEE Trans on PWRS, 1996, 11(2).
[9] 解可新,韩立兴,林友联.最优化方法.天津:天津大学出版社,1997
[10] 王兴,刘广一,于尔铿.一种改进的火电厂煤耗特性曲线拟合方法.电网技术, Vol1.19 No.5 1995
[11] 翦天聪.汽轮机最优经济运行.北京:水利电力出版社,1989
[12] 蔡超豪,蔡元宇.机组优化组合的遗传算法.电网技术,1997,21(1):44~47
[13] Kazarlis, S.A.; Bakirtzis,A.G.;Petridis,V. A genetic algorithm solution to the unit commitment problem .In:IEEE Trans on Power Systems, Volume: 11 Ussue:1, Feb. 1996,83-92
[14] 洪钧.火电厂条调峰机组负荷分配优化的数学模型.中国电机工程学报,1990, 1
[15] Fung, C.C.; Chow, S.Y.; Wong, Solving the economic dispatch problem with an integrated parallel genetic algorithm. In:K.P. Power System Technology, 2000. Proceedings. Power Con 2000. International Conference on, Volume: 3, 2000, 1257-1262 vol.3.
[16] Maifeld,T.T.;Sheble,G.B. Genetic-based unit commitment algorithm .In:IEEE Trans on Power Systems, Volume:
[17] 于尔铿,韩放,谢开等.电力市场.北京:中国电力出版社,1998,2-50
[18] Baldwin C.J.,K.M. Dale, R.F.Dittrich. A study of economic shutdown of
generating units in daily dispatch .In:IEEE Tran. On PAS, 1960,78:1272~1284
[19] Narayan S. Rau. Optimal Dispatch of a System based on Offers and Bids A Mixed Integer LP Formulation [J].In:IEEE Trans. On Power System. 1999,PWRS-14 (1): 274-279
[20] 张文修,梁怡.遗传算法的数学基础.西安交通大学出版社,2000,5,9-45
[21] 孙艳丰,王众托.遗传算法在优化问题中的应用研究进展.控制和决策,1996, 11(4):425-431
[22] 汪峰,朱艺颖,白晓民.基于遗传算法的机组组合研究.电力系统自动化,2003, 27(6):36~41
[23] 云庆夏.进化算法.2000,5,第一版,北京:冶金工业出版社
[24] 曾鸣.电力市场理论及应用.北京:中国电力出版社, 2000
[25] 刘青松.改进遗传算法确定发电机组的优化组合.电网技术,1998,22(12), 31-38
[26] 刘继春,李兴源.电力市场中机组组合的智能算法.电力系统及其自动化学 报,2002,14(5):48~51
[27] 高山,单渊达.遗传算法搜索优化及其在机组启停中的应用.,中国电机工程 学报,2001,21(3),45-48
[28] J.G. Waight, A. Bose, G. B. Sheble. Generation Dispatch with Reserve Margin Constraints Using Linear Programming .In:IEEE Tran. On PAS, 1981, 100(1): 252~258
[29] A.L.Cohen, M.Yoshimuta. A Branch-and- for Unit Commitment .In:IEEE Tran. PAS,1983,PAS-102:444~451 Bound Algorithm
[30] W.L. Snyder,H.D.Powell Jr.,J.C.Rayburn. Dynamic Programming Approach to Unit Commitment .In:IEEE Transaction on Power Systems, 1987, 2(2): 239~350
[31] 韦柳涛,曾庆川,姜铁兵.启发式基因遗传算法及其在电力系统机组组合优化 中的应用.中国电机工程学报,1994,11(2):67272
[32] Pang C K,Sheble G B,Albuyeh F. Evalution of Dynamic Programming Based Methods and Multiple Area Representation for Thermal Unit Commitment .In: IEEE Trans on PAS, 1981, 100(3): 1212~1217
[33] 于尔铿.现代电力系统经济调度.北京:水利电力出版社,1986
[34] Dill T S, Edwin K W, Kochs H D. Integer Programming Approach to the Problem of Optimal Unit Commitment with Probabilistic Reserve Determination .In:IEEE Trans on PAS, 1978, 97(6): 2154~2166
[35] C.Wang, S.M. Shahidehpour. Optimal Generation Scheduling With Ramping Costs .In:IEEE Transaction on Power Systems 1995,10(1): 60~67
[36] 邢文训,谢金星.现代优化计算方法.北京:清华大学出版社,1999
[37] 郭斌,康松.火电厂各机组间负荷优化调度控制系统的研究.发电设备,2001, 6:26~30
[2] 陈浩勇,王锡凡.机组组合问题的优化方法综述(2).电力系统自动化,第 22 卷,第 4 期,1999,3,51-56
[3] 周明,孙树栋.遗传算法原理及应用.北京:国防工业出版社,1996,6,第一 版
[4] 范从振.锅炉原理. 北京:水利电力出版社,1986,5 第一版
[5] 于良春.中国电力工业的改革与发展.中国工业经济,2000,4:53~57
[6] 马振华等.现代应用数学手册:运筹学与最优化理论卷.北京:清华大学出版 社,2003,11
[7] 刘严,谭忠富.动态规划法在机组负荷分配中的应用.现代电力,2002,4:76～ 80
[8] Sheble G B. Solution of the Unit Commitment Problem by the Method of Unit Periods.In:IEEE Trans on PWRS, 1996, 11(2).
[9] 解可新,韩立兴,林友联.最优化方法.天津:天津大学出版社,1997
[10] 王兴,刘广一,于尔铿.一种改进的火电厂煤耗特性曲线拟合方法.电网技术, Vol1.19 No.5 1995
[11] 翦天聪.汽轮机最优经济运行.北京:水利电力出版社,1989
[12] 蔡超豪,蔡元宇.机组优化组合的遗传算法.电网技术,1997,21(1):44~47
[13] Kazarlis, S.A.; Bakirtzis,A.G.;Petridis,V. A genetic algorithm solution to the unit commitment problem .In:IEEE Trans on Power Systems, Volume: 11 Ussue:1, Feb. 1996,83-92
[14] 洪钧.火电厂条调峰机组负荷分配优化的数学模型.中国电机工程学报,1990, 1
[15] Fung, C.C.; Chow, S.Y.; Wong, Solving the economic dispatch problem with an integrated parallel genetic algorithm. In:K.P. Power System Technology, 2000. Proceedings. Power Con 2000. International Conference on, Volume: 3, 2000, 1257-1262 vol.3.
[16] Maifeld,T.T.;Sheble,G.B. Genetic-based unit commitment algorithm .In:IEEE Trans on Power Systems, Volume:
[17] 于尔铿,韩放,谢开等.电力市场.北京:中国电力出版社,1998,2-50
[18] Baldwin C.J.,K.M. Dale, R.F.Dittrich. A study of economic shutdown of
generating units in daily dispatch .In:IEEE Tran. On PAS, 1960,78:1272~1284
[19] Narayan S. Rau. Optimal Dispatch of a System based on Offers and Bids A Mixed Integer LP Formulation [J].In:IEEE Trans. On Power System. 1999,PWRS-14 (1): 274-279
[20] 张文修,梁怡.遗传算法的数学基础.西安交通大学出版社,2000,5,9-45
[21] 孙艳丰,王众托.遗传算法在优化问题中的应用研究进展.控制和决策,1996, 11(4):425-431
[22] 汪峰,朱艺颖,白晓民.基于遗传算法的机组组合研究.电力系统自动化,2003, 27(6):36~41
[23] 云庆夏.进化算法.2000,5,第一版,北京:冶金工业出版社
[24] 曾鸣.电力市场理论及应用.北京:中国电力出版社, 2000
[25] 刘青松.改进遗传算法确定发电机组的优化组合.电网技术,1998,22(12), 31-38
[26] 刘继春,李兴源.电力市场中机组组合的智能算法.电力系统及其自动化学 报,2002,14(5):48~51
[27] 高山,单渊达.遗传算法搜索优化及其在机组启停中的应用.,中国电机工程 学报,2001,21(3),45-48
[28] J.G. Waight, A. Bose, G. B. Sheble. Generation Dispatch with Reserve Margin Constraints Using Linear Programming .In:IEEE Tran. On PAS, 1981, 100(1): 252~258
[29] A.L.Cohen, M.Yoshimuta. A Branch-and- for Unit Commitment .In:IEEE Tran. PAS,1983,PAS-102:444~451 Bound Algorithm
[30] W.L. Snyder,H.D.Powell Jr.,J.C.Rayburn. Dynamic Programming Approach to Unit Commitment .In:IEEE Transaction on Power Systems, 1987, 2(2): 239~350
[31] 韦柳涛,曾庆川,姜铁兵.启发式基因遗传算法及其在电力系统机组组合优化 中的应用.中国电机工程学报,1994,11(2):67272
[32] Pang C K,Sheble G B,Albuyeh F. Evalution of Dynamic Programming Based Methods and Multiple Area Representation for Thermal Unit Commitment .In: IEEE Trans on PAS, 1981, 100(3): 1212~1217
[33] 于尔铿.现代电力系统经济调度.北京:水利电力出版社,1986
[34] Dill T S, Edwin K W, Kochs H D. Integer Programming Approach to the Problem of Optimal Unit Commitment with Probabilistic Reserve Determination .In:IEEE Trans on PAS, 1978, 97(6): 2154~2166
[35] C.Wang, S.M. Shahidehpour. Optimal Generation Scheduling With Ramping Costs .In:IEEE Transaction on Power Systems 1995,10(1): 60~67
[36] 邢文训,谢金星.现代优化计算方法.北京:清华大学出版社,1999
[37] 郭斌,康松.火电厂各机组间负荷优化调度控制系统的研究.发电设备,2001, 6:26~30
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