基于分块信息矩阵的状态估计算法研究
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摘要
电力系统的发展对能量管理系统的自动化水平要求越来越高,电力系统状态估计是能量管理系统(EMS)的核心部分。而算法则是状态估计的核心,估计结果最优、计算速度快和内存使用少是对状态估计算法的基本要求。
论文首先介绍了电力系统状态估计的基本方法和研究现状,从加权最小二乘法(WLS)、抗差状态估计,到基于相角测量单元(PMU)的状态估计,对目前状态估计的方法进行了综述。经典WLS算法基于量测值服从正态分布,其优点是计算快速和操作简便,缺点是在恶劣条件下数值稳定性差。抗差估计理论建立在量测值符合数据实际分布模式的基础上,具备抗御粗差的能力。PUM的量测和SCADA原有量测构成混和量测系统一起用于状态估计,能提高网络的可观测性及状态估计的精度。
WLS法是多种估计方法的基础,研究基于这一方法概念的估计算法有重要的理论意义。借鉴WLS估计中带等式约束的正规方程法(NE/C)和Hachtel法数值稳定性更强的优点,将遥测量和虚拟量测合理分类,并采用分块和稀疏矩阵技术形成了一种计算速度快、数值稳定性好的状态估计改进算法。新算法消除了大量注入量测的存在和量测权值差距过大引起的病态条件,提高了估计质量。
用科学计算语言MATLAB编制了改进算法的计算程序,并进行了多种算法的对比模拟,对比结果说明算法了改进算法的有效性。对于大规模的电力系统而言,状态估计算法应当有新的突破。论文最后指出了要
进一步研究的课题。
The automation level of EMS (Energy Management System) should be improved with the development of future power systems. Correspondingly, we require EMS to control the system better. SE (State Estimation) is the pivotal part of EMS. Likewise, the algorithm is key element of SE. The algorithm should have great efficiency and speed as well as less demand for Memory.
Above all, the thesis introduces some basic methods and current status for SE of power systems. Several SE Methods in common use are summed up, including WLS (Weighted Least Squares), Robust Estimation theory and PMU (Phasor Measurement Unit) SE. Based on the the hypothesis that the measurements are normally distributed, the WLS method has the advantage of computational speed and implementation simplicity, on the other hand, it has the disadvantage of being numerically less stable. Based on the more actual probability distribution of the measurements, Robust Estimation is immune to bad data. Together with previous SCADA (Supervisory Control And Data Acquisition) syetem, PMU can enhance the observability and precision of SE.
WLS is the basic principle of various SE methods, thus it means a theoretical sense to do research for SE algorithms based on it. Considering the numerically more stable properties of Normal Equation with Constraints and Hachtel’s augmented matrix method for SE, all telemetered and virtual measurements are classified reasonably. Using blocked and sparse matrices technology, a new SE algorithm with computing speediness and numerical stability is proposed. The new algorithm can eliminate the ill condition and improve efficiency largely.
The computational validity of the proposed method is testified with MATLAB, a kind of scientific computation language. Also, the proposed method is compared with several variations of the WSL method.
As far as a large-scale power system is concerned, we must open up new SE methods to adapt to the development of future power systems. In the end, Areas for further research are indicated.
论文首先介绍了电力系统状态估计的基本方法和研究现状,从加权最小二乘法(WLS)、抗差状态估计,到基于相角测量单元(PMU)的状态估计,对目前状态估计的方法进行了综述。经典WLS算法基于量测值服从正态分布,其优点是计算快速和操作简便,缺点是在恶劣条件下数值稳定性差。抗差估计理论建立在量测值符合数据实际分布模式的基础上,具备抗御粗差的能力。PUM的量测和SCADA原有量测构成混和量测系统一起用于状态估计,能提高网络的可观测性及状态估计的精度。
WLS法是多种估计方法的基础,研究基于这一方法概念的估计算法有重要的理论意义。借鉴WLS估计中带等式约束的正规方程法(NE/C)和Hachtel法数值稳定性更强的优点,将遥测量和虚拟量测合理分类,并采用分块和稀疏矩阵技术形成了一种计算速度快、数值稳定性好的状态估计改进算法。新算法消除了大量注入量测的存在和量测权值差距过大引起的病态条件,提高了估计质量。
用科学计算语言MATLAB编制了改进算法的计算程序,并进行了多种算法的对比模拟,对比结果说明算法了改进算法的有效性。对于大规模的电力系统而言,状态估计算法应当有新的突破。论文最后指出了要
进一步研究的课题。
The automation level of EMS (Energy Management System) should be improved with the development of future power systems. Correspondingly, we require EMS to control the system better. SE (State Estimation) is the pivotal part of EMS. Likewise, the algorithm is key element of SE. The algorithm should have great efficiency and speed as well as less demand for Memory.
Above all, the thesis introduces some basic methods and current status for SE of power systems. Several SE Methods in common use are summed up, including WLS (Weighted Least Squares), Robust Estimation theory and PMU (Phasor Measurement Unit) SE. Based on the the hypothesis that the measurements are normally distributed, the WLS method has the advantage of computational speed and implementation simplicity, on the other hand, it has the disadvantage of being numerically less stable. Based on the more actual probability distribution of the measurements, Robust Estimation is immune to bad data. Together with previous SCADA (Supervisory Control And Data Acquisition) syetem, PMU can enhance the observability and precision of SE.
WLS is the basic principle of various SE methods, thus it means a theoretical sense to do research for SE algorithms based on it. Considering the numerically more stable properties of Normal Equation with Constraints and Hachtel’s augmented matrix method for SE, all telemetered and virtual measurements are classified reasonably. Using blocked and sparse matrices technology, a new SE algorithm with computing speediness and numerical stability is proposed. The new algorithm can eliminate the ill condition and improve efficiency largely.
The computational validity of the proposed method is testified with MATLAB, a kind of scientific computation language. Also, the proposed method is compared with several variations of the WSL method.
As far as a large-scale power system is concerned, we must open up new SE methods to adapt to the development of future power systems. In the end, Areas for further research are indicated.
引文
[1] 于尔铿.电力系统状态估计.北京:水利电力出版社,1985.
[2] 于尔铿,刘广一,周京阳,等.能量管理系统(EMS).北京:科学出版社,1998.
[3] Schweppe F C,Wildes J,Rom D B.Power System Static-State Estimation: Part Ⅰ-Ⅲ.IEEE Transactions on PAS,1970,89(1):120-135
[4] B.M.Zhang,S.Y.Wang,N.D.Xiang.A Linear Recursive Bad Data Identification Method With Real-Time Application To Power System State Estimation.IEEE Transactions on PWRS,1992,7(3):1378-1385
[5] HY.Horisberger,L C.Richard,C.Rossier.A Fast Decoupled Static-State Estimation for Electric Power System.IEEE Transactions on Power Apparatus and Systems,1976,95(1):208-215
[6] Monticelli A,Garcia A.Fast Decoupled State Estimator.IEEE Transactions on Power Systems,1990,5(2):556-564
[7] J.F.Dopazo,O.A.Klitin.State Calculation of Power System from Line Flow Measurements.IEEE Transactions on Power Systems,1970,89(7):1698-1708
[8] J.F.Doptao , O.A.Mitin . Implementation of the AEP Real-time Monitoring Systems.IEEE Transactions on Power Apparatus and Systems,1976,95(5):1618-1629
[9] L.Roy , T.A.Mohammed . Fast Super Decoupled State Estimator for Power Systems.IEEE Transactions on Power Systems,1997,12(4):1597-1603
[10] 李可文,张步涵,曲伟君.一种基于量测变换的快速解耦状态估计方法.华中理工大学学报,2000,28(2):61-63
[11] R.E.Larson,W.F.Tinney,J.Peachon,L.P.Hadu,et al.State Estimation in Power Systems.IEEE Transactions on Power Apparatus and Systems,1970,89(1):345-363
[12] A.S.Debs,R.E.Larson.Dynamic Estimation of Tracking the State of a Power SystemStatic.IEEE Transactions on Power Apparatus and Systems,1970,89(2):1670-1678
[13] Seidu K,Mukai H.Parallel Multi-area State Estimation.IEEE Transactions on Power Apparatus and Systems,1985,104(5):1026-1034
[14] Falcao D M,Wu F F,Muphy L.Parallel and Distributed State Estimation.IEEE Tansactions on Power Systems,1995,10(2):724-730
[15] Abur A,Tapaciya P.Parallel State Estimation Using Multi-processor.Electrical Power System Research,1990,18(l):67-79
[16] 李碧君,薛禹胜,顾锦汶,等.电力系统状态估计问题的研究现状和展望.电力系统自动化,1998,22(11):53-60
[17] R.Baldick,K.A.Ciements,Z.Pinjo-Dzigal,et al.Implementing Nonquadratic Objective Functions for State Estimation and Bad Data Rejection.IEEE Transactions on Power Systems,1997,12(1):376-382
[18] Mehemt K.Celik , Ali Abur . A Robust WLAV State Estimator Using Transformations.IEEE Transactions on Power Systems,1992,7(1):106-113
[19] H.Singh,F.L.Alvarado,W-H E.liu.Constrained LAV State Estimation Using Penalty Functions.IEEE Transactions on Power Systems,1997,12(1):383-388
[20] Lamine Mili,Michael G.Chenial,Peter J.Rousseeuw.Robust State Estimation of Electric Power Systems.IEEE Transactions on Circuits and Systems-1: Fundamental Theory And Applications,1994,41(5):349-358
[21] L.Mili,V.Phaniraj,P.J.Rousseeuw.Least Median of Squares Estimation in Power Systems.IEEE Transactions on Power Systems,1991,6(2):511-523
[22] L.Mili,M.G.Cheniae,N.S.Vichare,et al.Algorithms for Least Median of Squares State Estimation of Power Systems.Proceedings of the 35th Midwest Symposium on Circuits and Systems,1992,2:1276-1283
[23] A.Bose,K.A.Clements.Real-Time Modeling of Power Networks.Proceedings of the IEEE,1987,75(12):1607-1622
[24] Lars Holten,Anders Gjesvik,Svere Anm,et al.Comparison of Different MethodsFor State Estimation.IEEE Transactions on Power Systems,1988,3(4):1798-1806
[25] 刘浩,侯博渊.保留非线性的快速 P-Q 分解状态估计法.电力系统自动化,1995,9(4):14-18
[26] 余贻鑫,王耀瑜,陈德生,等.一种优越的电力系统状态估计方法.电力系统自动化,1993,17(5):7-11
[27] 谭学清,李光熹,熊曼丽.直角坐标形式混合法状态估计.电力系统自动化,1997,21(12):44-47
[28] Narasimham Vempati,Ilya W.Slutsker,Willian F.Tinney.Enhancements To Givens For Power System State Estimation.IEEE Transactions on Power Systems,1991,6(2):842-849
[29] A.Simoes.Costa,V.H.Quintana.An Orthogonal Row Processing Algorithm For Sequential State Estimation.IEEE Transactions on Power Apparatus and Systems,1981,100(8):3791-3800
[30] Narasimham Vempati,Ilya W.Slutsker,William F.Tinney.Orthogonal Sparse Vector Methods.IEEE Transactions on Power Systems,1992,7(2):926-932
[31] Robert A M Van Amerongen.On the exact incorporation of virtual measurements in orthogonal-transformation based state estimation procedures.Electrical Power & Energy Systems,1991,13(3):167-174
[32] 李响,刘玲群,郭志忠.抗差最小二乘法状态估计.继电器,2005,31(7):50-53
[33] 李碧君,薛禹胜,顾锦汶,等.抗差估计理论及其在电力系统中的应用.电力系统自动化,1999,23(1):57-60
[34] G.Durgaprasad,S.S.Thakur.Robust Dynamic State Estimation of Power Systems Based on M-Estimation and Realistic Modeling of System Dynamics . IEEE Transactions on Power Systems,1998,13(4):1331-1336
[35] 郭伟,单渊达.M 估计方法及其在电力系统状态估计中的应用.中国电机工程学报,2000,20(9):26-31
[36] 李碧君,薛禹胜,顾锦汶,等.基于权函数的电力系统状态估计算法.电力系统自动化,1999,23(8):32-42
[37] 张丽,韩富春,杨翠如.一种权函数状态估计新算法.太原理工大学学报,2004,35(2):146-148
[38] 李慧,杨明皓.一种处理杠杆量测的配电网抗差估计算法.电力系统自动化,2005,29(3):31-35
[39] 卢志刚,穆永民.GPS技术在实时相角测量中的应用.电力自动化设备,2000,20(6):20-22
[40] 郑相华,米增强,赵洪山,等.基于PMU 的状态估计的研究.继电器,2004,32(17):16-19
[41] 王勇,鞠平.部分节点引入相量测量的状态估计.河海大学学报(自然科学版),2004,32(3):316-319
[42] 王克英,穆钢,陈学允.计及PMU的状态估计精度分析及配置研究.中国电机工程学报,2001,21 (8):29-33
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[2] 于尔铿,刘广一,周京阳,等.能量管理系统(EMS).北京:科学出版社,1998.
[3] Schweppe F C,Wildes J,Rom D B.Power System Static-State Estimation: Part Ⅰ-Ⅲ.IEEE Transactions on PAS,1970,89(1):120-135
[4] B.M.Zhang,S.Y.Wang,N.D.Xiang.A Linear Recursive Bad Data Identification Method With Real-Time Application To Power System State Estimation.IEEE Transactions on PWRS,1992,7(3):1378-1385
[5] HY.Horisberger,L C.Richard,C.Rossier.A Fast Decoupled Static-State Estimation for Electric Power System.IEEE Transactions on Power Apparatus and Systems,1976,95(1):208-215
[6] Monticelli A,Garcia A.Fast Decoupled State Estimator.IEEE Transactions on Power Systems,1990,5(2):556-564
[7] J.F.Dopazo,O.A.Klitin.State Calculation of Power System from Line Flow Measurements.IEEE Transactions on Power Systems,1970,89(7):1698-1708
[8] J.F.Doptao , O.A.Mitin . Implementation of the AEP Real-time Monitoring Systems.IEEE Transactions on Power Apparatus and Systems,1976,95(5):1618-1629
[9] L.Roy , T.A.Mohammed . Fast Super Decoupled State Estimator for Power Systems.IEEE Transactions on Power Systems,1997,12(4):1597-1603
[10] 李可文,张步涵,曲伟君.一种基于量测变换的快速解耦状态估计方法.华中理工大学学报,2000,28(2):61-63
[11] R.E.Larson,W.F.Tinney,J.Peachon,L.P.Hadu,et al.State Estimation in Power Systems.IEEE Transactions on Power Apparatus and Systems,1970,89(1):345-363
[12] A.S.Debs,R.E.Larson.Dynamic Estimation of Tracking the State of a Power SystemStatic.IEEE Transactions on Power Apparatus and Systems,1970,89(2):1670-1678
[13] Seidu K,Mukai H.Parallel Multi-area State Estimation.IEEE Transactions on Power Apparatus and Systems,1985,104(5):1026-1034
[14] Falcao D M,Wu F F,Muphy L.Parallel and Distributed State Estimation.IEEE Tansactions on Power Systems,1995,10(2):724-730
[15] Abur A,Tapaciya P.Parallel State Estimation Using Multi-processor.Electrical Power System Research,1990,18(l):67-79
[16] 李碧君,薛禹胜,顾锦汶,等.电力系统状态估计问题的研究现状和展望.电力系统自动化,1998,22(11):53-60
[17] R.Baldick,K.A.Ciements,Z.Pinjo-Dzigal,et al.Implementing Nonquadratic Objective Functions for State Estimation and Bad Data Rejection.IEEE Transactions on Power Systems,1997,12(1):376-382
[18] Mehemt K.Celik , Ali Abur . A Robust WLAV State Estimator Using Transformations.IEEE Transactions on Power Systems,1992,7(1):106-113
[19] H.Singh,F.L.Alvarado,W-H E.liu.Constrained LAV State Estimation Using Penalty Functions.IEEE Transactions on Power Systems,1997,12(1):383-388
[20] Lamine Mili,Michael G.Chenial,Peter J.Rousseeuw.Robust State Estimation of Electric Power Systems.IEEE Transactions on Circuits and Systems-1: Fundamental Theory And Applications,1994,41(5):349-358
[21] L.Mili,V.Phaniraj,P.J.Rousseeuw.Least Median of Squares Estimation in Power Systems.IEEE Transactions on Power Systems,1991,6(2):511-523
[22] L.Mili,M.G.Cheniae,N.S.Vichare,et al.Algorithms for Least Median of Squares State Estimation of Power Systems.Proceedings of the 35th Midwest Symposium on Circuits and Systems,1992,2:1276-1283
[23] A.Bose,K.A.Clements.Real-Time Modeling of Power Networks.Proceedings of the IEEE,1987,75(12):1607-1622
[24] Lars Holten,Anders Gjesvik,Svere Anm,et al.Comparison of Different MethodsFor State Estimation.IEEE Transactions on Power Systems,1988,3(4):1798-1806
[25] 刘浩,侯博渊.保留非线性的快速 P-Q 分解状态估计法.电力系统自动化,1995,9(4):14-18
[26] 余贻鑫,王耀瑜,陈德生,等.一种优越的电力系统状态估计方法.电力系统自动化,1993,17(5):7-11
[27] 谭学清,李光熹,熊曼丽.直角坐标形式混合法状态估计.电力系统自动化,1997,21(12):44-47
[28] Narasimham Vempati,Ilya W.Slutsker,Willian F.Tinney.Enhancements To Givens For Power System State Estimation.IEEE Transactions on Power Systems,1991,6(2):842-849
[29] A.Simoes.Costa,V.H.Quintana.An Orthogonal Row Processing Algorithm For Sequential State Estimation.IEEE Transactions on Power Apparatus and Systems,1981,100(8):3791-3800
[30] Narasimham Vempati,Ilya W.Slutsker,William F.Tinney.Orthogonal Sparse Vector Methods.IEEE Transactions on Power Systems,1992,7(2):926-932
[31] Robert A M Van Amerongen.On the exact incorporation of virtual measurements in orthogonal-transformation based state estimation procedures.Electrical Power & Energy Systems,1991,13(3):167-174
[32] 李响,刘玲群,郭志忠.抗差最小二乘法状态估计.继电器,2005,31(7):50-53
[33] 李碧君,薛禹胜,顾锦汶,等.抗差估计理论及其在电力系统中的应用.电力系统自动化,1999,23(1):57-60
[34] G.Durgaprasad,S.S.Thakur.Robust Dynamic State Estimation of Power Systems Based on M-Estimation and Realistic Modeling of System Dynamics . IEEE Transactions on Power Systems,1998,13(4):1331-1336
[35] 郭伟,单渊达.M 估计方法及其在电力系统状态估计中的应用.中国电机工程学报,2000,20(9):26-31
[36] 李碧君,薛禹胜,顾锦汶,等.基于权函数的电力系统状态估计算法.电力系统自动化,1999,23(8):32-42
[37] 张丽,韩富春,杨翠如.一种权函数状态估计新算法.太原理工大学学报,2004,35(2):146-148
[38] 李慧,杨明皓.一种处理杠杆量测的配电网抗差估计算法.电力系统自动化,2005,29(3):31-35
[39] 卢志刚,穆永民.GPS技术在实时相角测量中的应用.电力自动化设备,2000,20(6):20-22
[40] 郑相华,米增强,赵洪山,等.基于PMU 的状态估计的研究.继电器,2004,32(17):16-19
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