基于内点非线性规划的分散协调最优励磁控制研究
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摘要
电力系统是典型的大系统,有很多可控点或可控元件,且按地域分布。因此,无论是常规控制器,还是电力系统稳定器(PSS),或是最优励磁控制器等新型控制器,均是分散控制的。当然,从分散的角度来看,这无疑是我们所希望看到的。然而,这些分别依据各局部模型设计的控制器是很难相互协调的。那么,是否可以从全局出发,对整个系统进行全盘考虑,并进行综合设计呢?若回答是肯定的,则在这种情况下,各局部控制器就能使整个系统在统一指标下达到最优,换句话说,各局部控制器就能很好协调,以实现系统的最优性。当然,从整个电力系统出发,是很难找具有解析表达式的控制规律,使系统在所选性能指标下达到最优。然而,若换个角度,从非线性规划方面出发,问题就变得相对简单多了,这是因为:非线性规划方法,如:现代内点理论,能从整个系统出发,并确保系统在所选性能指标下达到最优。
鉴于此,本文旨在将非线性规划方法引入复杂电力系统的非线性控制研究中,从整个系统的角度出发,讨论电力系统的分散协调最优控制问题。首先,根据实际需要选取最优控制问题的二次性能指标,并将其转化为非线性规划问题的目标函数。其次,运用隐式积分方法,将控制系统的状态方程差分为等式约束,同时将控制量的上下限幅选取为不等式约束。最后运用现代内点法求解。可见,该设计是将最优控制问题转化为动态最优化问题进行求解。
以复杂电力系统励磁控制为例,提出了基于现代内点理论的分散协调最优励磁控制方法,在6机22节点系统上进行仿真,以验证提出方法的有效性。仿真结果表明:所提方法使系统各发电机具有良好的响应特性。
One of the most typical great systems is electrical power system. The great system has a general characteristic, all of them have so many control point or control component.
From the feedback signal of controllers, whatever electrical system general controller, PSS or optimal excitation controller etc new controller, which is developing in near twenty years, and all of them belongs to decenritralized control. No doubt, when we design controller, that point we wish to get. By all appearances, for all controllers which is designed parting by local model, that is so difficulty to considering coordinated. If we design control law of control component, consider across-the-board, synthesize design, make parting controller not only for them control object or local system, which control effect is optimal, also they can coordinated work, it also can ensure the system achieve the optimization under the chosen objective function. On the nonlinear programming, there are some full mature methods such as modern interior point method. They are widely applied in the various programming and get massive achievements.
This paper proposes a research for decenritralized coordinated optimal excitation control of an n-generator power system based on modern interior point nonlinear programming. The optimal control problem is transformed into nonlinear programming one. Modern interior point nonlinear programming method is applied to solve the nonlinear programming problem. The quadratic performance index of control system is chosen for actuality needs as the objective function. The state equations of control system are converted into numerical equivalent algebraic equations set by using the implicit trapezoidal method, and are involved in equality constrains set. The control quantity limits are used to be inequality constrains. The dynamic optimization problem is transformed as the static optimization one and the ideal to solve the nonlinear optimal control problem by using modern interior point nonlinear programming method is developed. For nonlinear control systems, the ideal is applicable universally. It also can ensure the system achieve the optimization under the chosen objective function.
For the power system excitation control system, based on modern interior point nonlinear programming method, an optimal power system excitation control design scheme is deduced. The results of simulation show that the scheme can coordinate the dynamic and the static performances of the n-generator power system effectively, and make it have a good output performance.
鉴于此,本文旨在将非线性规划方法引入复杂电力系统的非线性控制研究中,从整个系统的角度出发,讨论电力系统的分散协调最优控制问题。首先,根据实际需要选取最优控制问题的二次性能指标,并将其转化为非线性规划问题的目标函数。其次,运用隐式积分方法,将控制系统的状态方程差分为等式约束,同时将控制量的上下限幅选取为不等式约束。最后运用现代内点法求解。可见,该设计是将最优控制问题转化为动态最优化问题进行求解。
以复杂电力系统励磁控制为例,提出了基于现代内点理论的分散协调最优励磁控制方法,在6机22节点系统上进行仿真,以验证提出方法的有效性。仿真结果表明:所提方法使系统各发电机具有良好的响应特性。
One of the most typical great systems is electrical power system. The great system has a general characteristic, all of them have so many control point or control component.
From the feedback signal of controllers, whatever electrical system general controller, PSS or optimal excitation controller etc new controller, which is developing in near twenty years, and all of them belongs to decenritralized control. No doubt, when we design controller, that point we wish to get. By all appearances, for all controllers which is designed parting by local model, that is so difficulty to considering coordinated. If we design control law of control component, consider across-the-board, synthesize design, make parting controller not only for them control object or local system, which control effect is optimal, also they can coordinated work, it also can ensure the system achieve the optimization under the chosen objective function. On the nonlinear programming, there are some full mature methods such as modern interior point method. They are widely applied in the various programming and get massive achievements.
This paper proposes a research for decenritralized coordinated optimal excitation control of an n-generator power system based on modern interior point nonlinear programming. The optimal control problem is transformed into nonlinear programming one. Modern interior point nonlinear programming method is applied to solve the nonlinear programming problem. The quadratic performance index of control system is chosen for actuality needs as the objective function. The state equations of control system are converted into numerical equivalent algebraic equations set by using the implicit trapezoidal method, and are involved in equality constrains set. The control quantity limits are used to be inequality constrains. The dynamic optimization problem is transformed as the static optimization one and the ideal to solve the nonlinear optimal control problem by using modern interior point nonlinear programming method is developed. For nonlinear control systems, the ideal is applicable universally. It also can ensure the system achieve the optimization under the chosen objective function.
For the power system excitation control system, based on modern interior point nonlinear programming method, an optimal power system excitation control design scheme is deduced. The results of simulation show that the scheme can coordinate the dynamic and the static performances of the n-generator power system effectively, and make it have a good output performance.
引文
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[5]Q.Lu,Z.Xu,T.Mochizuki,Decentralized nonlinear optimal excitation control.IEEE Transaction on Power System,1996,11(4):1957-1962
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[9]谢新民,丁锋.自适应控制系统,北京:清华大学出版社,2002.
[10]Gao L.and Chert L.,A nonlinear control design for power systems,Automatica,1992,28(3):975-979.
[11]Tan Y.L.and Wang Y.Y.,Design of series and shunt coordinated design techniques,IEEE Transactions on Power Systems,1997,12(3):1374-1379.
[12]Tan Y.L.and Wang Y.Y.Nonlinear excitation and phase shifter controller for transient stability enhancement of power systems using adaptive control law.International Journal of Electrical Power & Energy Systems,1996,18(6):397-403.
[13]Tan Y.L.and Wang Y.Y.,Transient stabilization using adaptive excitation and dynamic brake control.Control Engineering Practice,1997,5(3):337-346.
[14]Tan Y.L.and Wang Y.Y.Augmentation of Transient stability using a super conducting coil and adaptive nonlinear control,IEEE Transactions on Power Systems,1998,13(2):361-366.
[15]Wang Y.Y.and Tan Y.L.Robust Nonlinear coordinated generator excitation and SVC control for power systems,International Journal of Electrical power & Energy Systems,2000,22(3):187-195.
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[23]Junyong Wu,Yokoyama A.Qiang Lu,Goto M.and Konishi H.Decentralized nonlinear ontrol of generators for enhancement of transient stability of large-scale interconnected power system.Proceedings PowerCon 2000.International Conference on Power System Technology.2000,1:7-12.
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[33]Zhishan Liang,Huangguang Zhang,Hongyue Wang and Hongzhan Nie.Holographic robust predictive control of synchronous machine excitation for power systems.IEEE PES.Conference Proceedings on 2000 Power Engineering Society Winter Meeting.2000,181-185.
[34]常乃超,郭志忠.基于控制系统四元组形式的发电机非线性分散鲁棒控制.中国电机工程学报.2003,23(7):151-157.
[35]Zhu Chunlei,Zhou Rujing and Wang Y.Y.,A New Decentralized Nonlinear Voltage Controller for Muitimachine Power Systems.The Fourth International Conference on Control and Automation,2003,525-530.
[36]Wang Y,Guo G and Hill D.J.Robust decentralized nonlinear controller design for multi-machine power systems.Automatica.1997,33(9):1725-1733.
[37]Wang Y.Y.and Hill D.J.,Robust nonlinear coordinated control of power systems,Automatica,1996,64(4):611-618.
[38]蒋林,吴青华,基于扰动估计观测器的非线性分散控制,电力系统自动化,2001,25(3):30-36.
[39]Margaret H.Wright.The Interior-Point Revolution in Constrained Optimization,the First Pacific Rim Conference on Mathematics.Hong Kong:January 19-23,1998.
[40]J.A.Momoh.Interior Point Methods and Variants for OPF-A Tutorial,Department of Electrical Engineering.Howard University,Washington,D.C.2005,9.
[41]H.Wei,et al.An Interior Point Nonlinear Programming for Optimal Power Flow Problems with a Novel Data Structure.IEEE Trans on PWRS,1998,13(2):870-877.
[42]韦化,丁晓莺.基于现代内点理论的电压稳定临界点算法.中国电机工程学报,Vol.22,No.3,Mar.2001.
[43]H.Wei,et al.Large Scale Hydrothermal Optimal Power Flow Problems Based on Interior Point Nonlinear Programming.IEEE Trans on PWRS,2000,15(1):396-403.
[44]H.Wei,H.Sasaki,J.Kubokawa,et al.An Interior Point Method for Power System Weighted Nonlinear L1 Norm State Estimation.IEEE Transactions On Power Systems,1998,13(1):617-623.
[45]R.H.Byrd,J.C.Gilbert,and J.Nocedal.A trust region method based on interior point techniques for nonlinear programming.Mathematical Programming,2000,89:149-185.
[46]M.Ulbrieh,S.Ulbrieh and L.N.Vicente,A Globally Convergent Primal-Dual Interior-Point Filter Method for Nonlinear Programming,Technical Report TR00-12,Department of Computational and Applied Mathematics,Rice University,Main Street,Houston,USA,2000.
[47]Torres G L,Quintana V H.Optimal Power Flow by a Nonlinear Complementarity Method.IEEE Trans on Power Systems,2000,15(3):1028-1033.
[48]梅生伟.申铁龙.刘康志.现代鲁棒控制理论与应用.北京:清华大学出版社.2003.9
[49]谢小荣,韩英铎,崔文进,唐义良.多机电力系统中发电机励磁控制设计的数学模型分析.中国电机工程学报,Vol.29,No.9,Sep.2001
[50]Q.Lu,Y.Sun.Nonlinear-stabilizing control of multi-machine systems.IEEE Transactions on Power Systems.1989.4(1):236-241.
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[2]卢强.孙元章.电力系统非线性控制.北京:科学出版社,1993.1-2.
[3]韩英铎.王仲鸿.陈淮金.电力系统最优分散协调控制。北京:清华大学出版社,1996.
[4]John T.Betts.Practical Methods for Optimal Control Using Nonlinear Programming.Washington Boeing Company.2001.
[5]Q.Lu,Z.Xu,T.Mochizuki,Decentralized nonlinear optimal excitation control.IEEE Transaction on Power System,1996,11(4):1957-1962
[6]Brockett,R.W.Nonlinear systems and differential geometry.Proc.of IEEE,1976,64(1):61-72.
[7]Itkis,U.,Control systems of variable structure,Wiley,New York,1976.
[8]Drazenovie,B.,The invarianee condition in variable structure systems,Automatica,1969,5:287-295.
[9]谢新民,丁锋.自适应控制系统,北京:清华大学出版社,2002.
[10]Gao L.and Chert L.,A nonlinear control design for power systems,Automatica,1992,28(3):975-979.
[11]Tan Y.L.and Wang Y.Y.,Design of series and shunt coordinated design techniques,IEEE Transactions on Power Systems,1997,12(3):1374-1379.
[12]Tan Y.L.and Wang Y.Y.Nonlinear excitation and phase shifter controller for transient stability enhancement of power systems using adaptive control law.International Journal of Electrical Power & Energy Systems,1996,18(6):397-403.
[13]Tan Y.L.and Wang Y.Y.,Transient stabilization using adaptive excitation and dynamic brake control.Control Engineering Practice,1997,5(3):337-346.
[14]Tan Y.L.and Wang Y.Y.Augmentation of Transient stability using a super conducting coil and adaptive nonlinear control,IEEE Transactions on Power Systems,1998,13(2):361-366.
[15]Wang Y.Y.and Tan Y.L.Robust Nonlinear coordinated generator excitation and SVC control for power systems,International Journal of Electrical power & Energy Systems,2000,22(3):187-195.
[16]Chapman J.W.and Illic M.D.,Stabilizing a multimachine power system via decentralized feedback linearizing excitation control.IEEE Transactions on Power Systems,1993,8(3):830-839.
[17]King C.A.and Chapman J.W.,Feedback linearizing excitation control on a full-scale power system model,IEEE Transactions on Power Systems,1994,9(2):1102-1109.
[18]Cao Y.J.,Wu Q.H.,and Jiang L.,Nonlinear control of power system multi-mode oscillations,International Journal of Electrical Power and Energy Systems,1998,20(1):61-68.
[19]孙元章,杨志平,ASVG非线性控制方式的研究及其对暂态稳定性的改善,电力系统自动化,1996,20(11):17-22.
[20]深沉,孙元章,ASVG的非线性控制对改善电力系统阻尼特性的研究,电力系统自动化,1997,21(5):29-32.
[21]Kaprielian S.and Clements K.,Feedback stabilization for an AC/DC power system model,In Proceedings of the 29~(th)IEEE Conference on Decision and Control Honolulu Hawaii(USA),1990,3367-3372.
[22]Q.Lu,S.Mei,W.Hu,Y.H.Song,M.Goto and H.Konishi.Decentralised nonlinear H∞ excitation control based on regulation linearization.IEE Proceedings--Generation,Transmission &Distribution.2000,147(4):245-251.
[23]Junyong Wu,Yokoyama A.Qiang Lu,Goto M.and Konishi H.Decentralized nonlinear ontrol of generators for enhancement of transient stability of large-scale interconnected power system.Proceedings PowerCon 2000.International Conference on Power System Technology.2000,1:7-12.
[24]Deqiang Gan,Zhihua Qu and Hongzhi Cai.Muitimachine power system excitation control design via theories of feedack linearization control and nonlinear robust control.International Journal of Systems Science.2000,31(4):519-527.
[25]熊正美,陈准金.大电力系统的解耦及关联测量控制法.中国电机工程学报.1986,6(6):1-7.
[26]Mei S.Shen T.Hu W.Lu Q.and Sun L.Robust H∞ control of a Hamiltonian system with uncertainty and its application to a multi-machine power system.IEE Proceedings-Control Theory and Applications.2005,152(2):202-210.
[27]Sun Y.Z.,Li X.,Yan S.,Song Y.H.and Farsangi M.M.,Novel decentralized robust excitation control for power system stability improvement.Proceedings DRPT 2000 International Conference on Electric Utility Deregulation and Restructuring and Power Technologies.2000,443-448.
[28]Silj D.D.Large-scale systems,stability and structure.North-Holland,1978.
[29]Calovic M.S.Automatic generation control,decentralized area-wise optimal solution.Electric Power System Research.1984,7:115-139.
[30]Ikeda M and Siljak D.D.Overlapping decomposition,expansions and contractions of dynamic systems.Large Scale Systems.1980,1:29-38.
[31]Hassan M.F.and Singh M.G.A hierarchical structure for computing near optimal decentralized control.IEEE Trans.on Power Systems.1978,SMC-8:575-579.
[32]Chapman J.W.,Ilic M.D.,and King C.A.,Stabilizing a multi-machine power system via decentralized feedback linearizing excitation control.IEEE Transactions on Power Systems.1993,8(3):830-839.
[33]Zhishan Liang,Huangguang Zhang,Hongyue Wang and Hongzhan Nie.Holographic robust predictive control of synchronous machine excitation for power systems.IEEE PES.Conference Proceedings on 2000 Power Engineering Society Winter Meeting.2000,181-185.
[34]常乃超,郭志忠.基于控制系统四元组形式的发电机非线性分散鲁棒控制.中国电机工程学报.2003,23(7):151-157.
[35]Zhu Chunlei,Zhou Rujing and Wang Y.Y.,A New Decentralized Nonlinear Voltage Controller for Muitimachine Power Systems.The Fourth International Conference on Control and Automation,2003,525-530.
[36]Wang Y,Guo G and Hill D.J.Robust decentralized nonlinear controller design for multi-machine power systems.Automatica.1997,33(9):1725-1733.
[37]Wang Y.Y.and Hill D.J.,Robust nonlinear coordinated control of power systems,Automatica,1996,64(4):611-618.
[38]蒋林,吴青华,基于扰动估计观测器的非线性分散控制,电力系统自动化,2001,25(3):30-36.
[39]Margaret H.Wright.The Interior-Point Revolution in Constrained Optimization,the First Pacific Rim Conference on Mathematics.Hong Kong:January 19-23,1998.
[40]J.A.Momoh.Interior Point Methods and Variants for OPF-A Tutorial,Department of Electrical Engineering.Howard University,Washington,D.C.2005,9.
[41]H.Wei,et al.An Interior Point Nonlinear Programming for Optimal Power Flow Problems with a Novel Data Structure.IEEE Trans on PWRS,1998,13(2):870-877.
[42]韦化,丁晓莺.基于现代内点理论的电压稳定临界点算法.中国电机工程学报,Vol.22,No.3,Mar.2001.
[43]H.Wei,et al.Large Scale Hydrothermal Optimal Power Flow Problems Based on Interior Point Nonlinear Programming.IEEE Trans on PWRS,2000,15(1):396-403.
[44]H.Wei,H.Sasaki,J.Kubokawa,et al.An Interior Point Method for Power System Weighted Nonlinear L1 Norm State Estimation.IEEE Transactions On Power Systems,1998,13(1):617-623.
[45]R.H.Byrd,J.C.Gilbert,and J.Nocedal.A trust region method based on interior point techniques for nonlinear programming.Mathematical Programming,2000,89:149-185.
[46]M.Ulbrieh,S.Ulbrieh and L.N.Vicente,A Globally Convergent Primal-Dual Interior-Point Filter Method for Nonlinear Programming,Technical Report TR00-12,Department of Computational and Applied Mathematics,Rice University,Main Street,Houston,USA,2000.
[47]Torres G L,Quintana V H.Optimal Power Flow by a Nonlinear Complementarity Method.IEEE Trans on Power Systems,2000,15(3):1028-1033.
[48]梅生伟.申铁龙.刘康志.现代鲁棒控制理论与应用.北京:清华大学出版社.2003.9
[49]谢小荣,韩英铎,崔文进,唐义良.多机电力系统中发电机励磁控制设计的数学模型分析.中国电机工程学报,Vol.29,No.9,Sep.2001
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