基于支持向量机的静态电压稳定评估
|
摘要
在现代大型电力系统中,电压崩溃已经成为威胁电力系统安全运行的重要问题之一。为了预防电压崩溃,需要评估系统运行状态到电压稳定临界点的距离。
临界点的计算可以提供电压稳定裕度的重要信息,但是,在电压稳定临界点处,潮流方程雅可比矩阵奇异,常规潮流方程难以求解。为克服这个困难,采用了连续潮流法,通过追踪PV曲线来获取临界点。但对于高维电力系统,这种方法计算速度较慢,难以满足实时电压稳定评估的要求。为减少评估时间,应用快速且可靠的评估技术是很重要的。
支持向量机是新一代的机器学习算法,以统计学习理论作为其理论基础,其训练等价于解决一个二次规划问题,采用结构风险最小化原则,具有预测能力强、全局最优及收敛速度快等显著特点。因此,本文提出了一种基于支持向量机的静态电压稳定评估方法,并建立了电压稳定评估的支持向量机模型。从测试结果看,支持向量机模型经过训练后可以实时地根据系统运行状态估算系统的电压稳定临界点。该方法充分发挥支持向量机在解决高维、非线性和有限样本问题方面体现出的优势,保证了电压稳定评估模型的泛化能力,具有较快的评估速度和较高的预测精度。将支持向量机模型与BP人工神经网络模型进行了比较,结果证明,利用支持向量机模型进行电压稳定临界点预测比利用人工神经网络模型具有更高的拟合精度。
为了降低输入空间的维数,本文提出用主成分分析对数据进行特征提取,将提取出的包含样本数据信息的主元送入支持向量机进行训练。这样既结合了主成分分析的特征提取能力,又利用了支持向量机良好的非线性函数逼近能力。通过实际算例分析,验证了该方法在保证预测精度的同时可有效降低输入空间的维数。
Voltage collapse has become one of the most important problems which have threatened the operation safety of electric power systems. It is necessary to evaluate the distance between the operation state and the voltage critical point in order to escape from the voltage collapse.
By means of calculating the critical point, the loading margin to voltage collapse can be determined. But at the critical point, the Jacobian matrix of conventional power flow equations becomes singular. The continuation power flow method of getting the critical point by tracing the PV curve has been applied to overcome this difficulty. The calculation speed of this method is slow for power systems with high dimension, so it is difficult to realize real-time voltage stability assessment. The application of a faster and more reliable evaluation technique is very important to shorten the evaluation time.
Support vector machine(SVM), a method based on statistics learning theory, is a machine learning algorithm of the new era. It equals to solving a quadratic programming problem in the principle of minimum structural risk. This algorithm is featured with strong forecasting ability, global optimization and fast speed of approaching, etc. Hence a method of model construction which based on SVM is presented for the power system static voltage stability assessment, and a SVM model for voltage stability assessment is established in this dissertation. Basing on the operation state, the critical point can be estimated by the model being trained according to the test results. This method takes full advantage of SVM's ability to solve the problems with high dimension, nonlinear and small sample. Hence, with quicker assessment speed and higher forecast precision, better generalization ability is guaranteed. Compared with ANN model, it can be seen that SVM model has higher precision.
In this dissertation, the features of the data set are extracted by using principle component analysis to reduce the input dimension. Then the principle component containing the information of sample data is sent to support vector machine for training. This proposal combines the feature extraction ability of principle component analysis together with the excellent nonlinear function approaching ability of support vector machine. The empirical results show that with high forecast precision, the input dimension can be reduced by this method.
临界点的计算可以提供电压稳定裕度的重要信息,但是,在电压稳定临界点处,潮流方程雅可比矩阵奇异,常规潮流方程难以求解。为克服这个困难,采用了连续潮流法,通过追踪PV曲线来获取临界点。但对于高维电力系统,这种方法计算速度较慢,难以满足实时电压稳定评估的要求。为减少评估时间,应用快速且可靠的评估技术是很重要的。
支持向量机是新一代的机器学习算法,以统计学习理论作为其理论基础,其训练等价于解决一个二次规划问题,采用结构风险最小化原则,具有预测能力强、全局最优及收敛速度快等显著特点。因此,本文提出了一种基于支持向量机的静态电压稳定评估方法,并建立了电压稳定评估的支持向量机模型。从测试结果看,支持向量机模型经过训练后可以实时地根据系统运行状态估算系统的电压稳定临界点。该方法充分发挥支持向量机在解决高维、非线性和有限样本问题方面体现出的优势,保证了电压稳定评估模型的泛化能力,具有较快的评估速度和较高的预测精度。将支持向量机模型与BP人工神经网络模型进行了比较,结果证明,利用支持向量机模型进行电压稳定临界点预测比利用人工神经网络模型具有更高的拟合精度。
为了降低输入空间的维数,本文提出用主成分分析对数据进行特征提取,将提取出的包含样本数据信息的主元送入支持向量机进行训练。这样既结合了主成分分析的特征提取能力,又利用了支持向量机良好的非线性函数逼近能力。通过实际算例分析,验证了该方法在保证预测精度的同时可有效降低输入空间的维数。
Voltage collapse has become one of the most important problems which have threatened the operation safety of electric power systems. It is necessary to evaluate the distance between the operation state and the voltage critical point in order to escape from the voltage collapse.
By means of calculating the critical point, the loading margin to voltage collapse can be determined. But at the critical point, the Jacobian matrix of conventional power flow equations becomes singular. The continuation power flow method of getting the critical point by tracing the PV curve has been applied to overcome this difficulty. The calculation speed of this method is slow for power systems with high dimension, so it is difficult to realize real-time voltage stability assessment. The application of a faster and more reliable evaluation technique is very important to shorten the evaluation time.
Support vector machine(SVM), a method based on statistics learning theory, is a machine learning algorithm of the new era. It equals to solving a quadratic programming problem in the principle of minimum structural risk. This algorithm is featured with strong forecasting ability, global optimization and fast speed of approaching, etc. Hence a method of model construction which based on SVM is presented for the power system static voltage stability assessment, and a SVM model for voltage stability assessment is established in this dissertation. Basing on the operation state, the critical point can be estimated by the model being trained according to the test results. This method takes full advantage of SVM's ability to solve the problems with high dimension, nonlinear and small sample. Hence, with quicker assessment speed and higher forecast precision, better generalization ability is guaranteed. Compared with ANN model, it can be seen that SVM model has higher precision.
In this dissertation, the features of the data set are extracted by using principle component analysis to reduce the input dimension. Then the principle component containing the information of sample data is sent to support vector machine for training. This proposal combines the feature extraction ability of principle component analysis together with the excellent nonlinear function approaching ability of support vector machine. The empirical results show that with high forecast precision, the input dimension can be reduced by this method.
引文
[1]王梅义,吴竞昌,蒙定中.大电网系统技术(第二版)[M].北京:中国电力出版社,1995
[2]韩祯祥.电力系统稳定[M].北京:中国电力出版社,1995
[3]袁季修.电力系统安全稳定控制[M].北京:中国电力出版社,1996
[4]余贻鑫.电压稳定研究述评[J].电力系统自动化,1999,23(21):1-8
[5]IEEE/CIGRE joint task force on stability terms and definitions.Definition and classification of power system stability[J].IEEE Trans on Power Systems,2004,19(2):1387-1401
[6]国家电网公司.国家电网公司电力系统安全稳定计算规定[Z].北京:国家电网公司,2006
[7]Carson W.Taylor.电力系统电压稳定[M].王伟胜,译.北京:中国电力出版社,2002
[8]T.Van Cutsem,C.Vournas.电力系统电压稳定性[M].王奔,译.北京:电子工业出版社,2008
[9]C.Canizares.Voltage stability assessment:concepts,practices and tools[R].IEEE/PES Power System Stability Subcommittee,Final Document,2002
[10]徐泰山,薛禹胜,韩祯样.关于电力系统电压稳定性分析方法的综述[J].电力系统自动化,1996,20(5):62-67
[11]孙元章,杨志平,王志芳,卢强.ASVG非线性控制及其对电压稳定性改善的研究[J].电力系统自动化,1996,20(6):21-26
[12]孙元章,王志芳.OLTC仿真模型及其对电压无功稳定性的影响[J].电力系统自动化,1998,22(5):10-13
[13]彭志炜,胡国根,韩祯祥.应用分支理论研究电力系统电压稳定性[J].电力系统自动化,1997,21(2):42-45
[14]Abs S,Hamada N.Load flow convergence in the vicinity of a voltage stability limit[J].IEEE Trans on Power Apparatus and Systems,1978,97(6):1983-1993
[15]Cutsem T V.An approach to corrective control of voltage instability using simulation and sensitivity[J].IEEE Trans on Power Systems,1995,10(2):616-622.
[16]Tamura Y,Mori H,Iwamoto S I.Relationship between voltage instability and multiple load flow solutions in electric power systems[J].IEEE Trans on Power Apparatus and Systems,1983,102(5):1115-1125
[17]Venikov V A,Stroev V A,et al.Estimation of electrical power system steady-state stability in load flow calculation[J].IEEE Trans on Power Apparatus and Systems,1975,94(3):1034-1041
[18]Tiranuchit A,Thomas R J.A posturing strategy against voltage instabilities in electric power systems[J].IEEE Trans on Power Systems,1988,3(1):87-93
[19]Gao B,Morison G K,Kundur P.Voltage stability evaluation using modal analysis[J].IEEE Trans on Power Systems,1992,7(4):1529-1542
[20]Lof P A,Smed T,et al.Fast calculation of a voltage stability index[J].IEEE Trans on Power Systems,1992,7(1):54-64
[21]Ajjarapu V,Christy C.The continuation power flow:a tool for steady state voltage stability analysis[J].IEEE Trans on Power Systems,1992,7(1):416-423
[22]Canizares C A,Alvarado F L.Point of collapse and continuation methods for large AC/DC systems[J].IEEE Trans on Power Systems,1993,8(1):1-8
[23]Irisarri G D,Wang X,Tong J,et al.Maximum loadability of power systems using interior point non-linear optimization method[J].IEEE Trans on Power Systems,1997,12(1):162-172
[24]韦化,丁晓莺.基于现代内点理论的电压稳定临界点算法[J].中国电机工程学报,2002,22(3):27-31
[25]M.La Scala,M.Trovato,F.Torelli.A neural network-based method for voltage security monitoring[J].IEEE Trans on Power Systems,1996,11(3):1332-1341
[26]周晓渊.电力系统电压稳定分析和控制研究[D].杭州:浙江大学,2006
[27]Vournas C D.Voltage stability and controllability indices for multimachine power system[J].IEEE Trans on Power Systems,1995,10(3):1183-1194
[28]包黎昕.电压稳定动态分析及预防电压崩溃的措施[D].武汉:华中科技大学,2000
[29]Noroozian M,Taylor C W.Benefits of SVC and STATCOM for electric utility application[C].Proceedings of IEEE PES Transm and Distrib Conference and Exposition.IEEE,2003:1143-1150.
[30]Zhu T X,Tso S K,Lo K L.An investigation into the OLTC effects on voltage collapse[J].IEEE Trans on Power Systems,2000,15(2):515-521
[31]周双喜,朱凌志,郭锡玖,等.电力系统电压稳定性及其控制[M].北京:中国电力出版社,2004
[32]Y H Song,H B Wan,A T Johns.Power system voltage stability assessment using a self-organizing neural network classifier[C].IEE Power System Control and Management,Conference Publication No.421,1996:171-175
[33]B Jeyasurya.Artificial neural network for on-line voltage stability assessment[C].IEEE Power Engineering Society Summer Meeting,2000:2014-2018
[34]付英,钟德成.自组织映射神经网络用于动态电压稳定分析的新方法[J].电力系统自动化,2000,24(1):27-31
[35]瓦普尼克.统计学习理论的本质[M].张学工,译.北京:清华大学出版社,2000
[36]许涛,贺仁睦,王鹏,等.基于统计学习理论的电力系统暂态稳定评估[J].中国电机工程学报,2003,23(11):51-55
[37]P Kundur.电力系统稳定与控制[M].周孝信,等译.北京:中国电力出版社,2002
[38]边肇祺,张学工,等.模式识别[M].北京:清华大学出版社,2000
[39]V.N.Vapnik.统计学习理论[M].许建华,张学工译.北京:电子工业出版社,2004
[40]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-42
[41]姜静清.最小二乘支持向量机算法及应用研究[D].长春:吉林大学,2007
[42]邓乃扬,田英杰.数据挖掘中的新方法—支持向量机[M].北京:科学出版社,2004
[43]程浩忠.电力系统电压崩溃的研究(上)[J].电力系统自动化,1995,19(11):59-61
[44]A.A.El-Keib,X.Ma.Application of Artificial Neural Networks in Voltage Stability Assessment[J].IEEE Trans on Power Systems,1995,10(4):1890-1896
[45]P.M.安德逊,A.A.佛阿德.电力系统的控制与稳定(第一卷)[M].北京:水利电力出版社,1979
[46]Power System Analysis Toolbox-PSAT Version 2.0.0,Federico Milano,Canada,2006
[47]常永吉.PSAT在电力系统稳定性仿真中的应用[J].电气应用,2008,27(14):61-64
[48]Chapelle O,Vapnik V.Choosing Multiple Parameters for Support Vector Machines[R].New York:AT&T Research Labs,2001
[49]吴宏晓,侯志俭.基于免疫支持向量机方法的电力系统短期负荷预测[J].电网技术,2004,28(23):47-51
[50]Chih-Wei Hsu,Chih-Chung Chang,Chih-Jen Lin.A Practical Guide to Support Vector Classification.[EB/OL]http://www.csie.ntu.edu.tw/～cjlin/papers/guide/guide.pdf
[51]Chih-Chung Chang,Chih-Jen Lin.LIBSVM:a Library for Support Vector Machines,2001.Software available at http://www.csie.ntu.edu.tw/～cjlin/libsvm.
[52]L.Chen,K.Tomsovic,A.Bose,R.Stuart.Estimating Reactive Margin for Determining Transfer Limits.IEEE Power Engineering Society Summer Meeting,Seatle.USA,July 2000
[53]Andrade.A.C,et al.Voltage stability assessment using a new FSQV method and artificial neural networks[C].Electrotechnical Conference,2006:1003-1006.MELECON 2006,IEEE Mediterranean
[54]韩力群.人工神经网络理论、设计及应用(第二版)[M].北京:化学工业出版社,2007
[55]高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社,2003
[56]陈允平,王旭蕊,韩宝亮.人工神经网络原理及其应用[M].北京:中国电力出版社,2002
[57]White H.Commentionist Nonparametric Regression:Multi Layer Feed Forward Networks Can Learn Arbitrary Mapping[J].Neural Networks,1990(3)
[58]张尧,宋文南.节点电压稳定临界状态和弱节点的确定[J].中国电机工程学报,1993,13(61:40-45
[59]赵广社,张希仁.基于主成分分析的支持向量机分类方法研究[J].计算机工程与应用,2004,37(3):37-39
[60]Mao,K.Z.Feature subset selection for support vector machines through discriminative function pruning analysis[J].IEEE Trans on Systems,Man and Cybernetics,Part B,2004,34(1):60-67
[61]梅长林,周家良.实用统计方法[M].北京:科学出版社,2002
[62]高惠璇.应用多元统计分析[M].北京:北京大学出版社,2005
[2]韩祯祥.电力系统稳定[M].北京:中国电力出版社,1995
[3]袁季修.电力系统安全稳定控制[M].北京:中国电力出版社,1996
[4]余贻鑫.电压稳定研究述评[J].电力系统自动化,1999,23(21):1-8
[5]IEEE/CIGRE joint task force on stability terms and definitions.Definition and classification of power system stability[J].IEEE Trans on Power Systems,2004,19(2):1387-1401
[6]国家电网公司.国家电网公司电力系统安全稳定计算规定[Z].北京:国家电网公司,2006
[7]Carson W.Taylor.电力系统电压稳定[M].王伟胜,译.北京:中国电力出版社,2002
[8]T.Van Cutsem,C.Vournas.电力系统电压稳定性[M].王奔,译.北京:电子工业出版社,2008
[9]C.Canizares.Voltage stability assessment:concepts,practices and tools[R].IEEE/PES Power System Stability Subcommittee,Final Document,2002
[10]徐泰山,薛禹胜,韩祯样.关于电力系统电压稳定性分析方法的综述[J].电力系统自动化,1996,20(5):62-67
[11]孙元章,杨志平,王志芳,卢强.ASVG非线性控制及其对电压稳定性改善的研究[J].电力系统自动化,1996,20(6):21-26
[12]孙元章,王志芳.OLTC仿真模型及其对电压无功稳定性的影响[J].电力系统自动化,1998,22(5):10-13
[13]彭志炜,胡国根,韩祯祥.应用分支理论研究电力系统电压稳定性[J].电力系统自动化,1997,21(2):42-45
[14]Abs S,Hamada N.Load flow convergence in the vicinity of a voltage stability limit[J].IEEE Trans on Power Apparatus and Systems,1978,97(6):1983-1993
[15]Cutsem T V.An approach to corrective control of voltage instability using simulation and sensitivity[J].IEEE Trans on Power Systems,1995,10(2):616-622.
[16]Tamura Y,Mori H,Iwamoto S I.Relationship between voltage instability and multiple load flow solutions in electric power systems[J].IEEE Trans on Power Apparatus and Systems,1983,102(5):1115-1125
[17]Venikov V A,Stroev V A,et al.Estimation of electrical power system steady-state stability in load flow calculation[J].IEEE Trans on Power Apparatus and Systems,1975,94(3):1034-1041
[18]Tiranuchit A,Thomas R J.A posturing strategy against voltage instabilities in electric power systems[J].IEEE Trans on Power Systems,1988,3(1):87-93
[19]Gao B,Morison G K,Kundur P.Voltage stability evaluation using modal analysis[J].IEEE Trans on Power Systems,1992,7(4):1529-1542
[20]Lof P A,Smed T,et al.Fast calculation of a voltage stability index[J].IEEE Trans on Power Systems,1992,7(1):54-64
[21]Ajjarapu V,Christy C.The continuation power flow:a tool for steady state voltage stability analysis[J].IEEE Trans on Power Systems,1992,7(1):416-423
[22]Canizares C A,Alvarado F L.Point of collapse and continuation methods for large AC/DC systems[J].IEEE Trans on Power Systems,1993,8(1):1-8
[23]Irisarri G D,Wang X,Tong J,et al.Maximum loadability of power systems using interior point non-linear optimization method[J].IEEE Trans on Power Systems,1997,12(1):162-172
[24]韦化,丁晓莺.基于现代内点理论的电压稳定临界点算法[J].中国电机工程学报,2002,22(3):27-31
[25]M.La Scala,M.Trovato,F.Torelli.A neural network-based method for voltage security monitoring[J].IEEE Trans on Power Systems,1996,11(3):1332-1341
[26]周晓渊.电力系统电压稳定分析和控制研究[D].杭州:浙江大学,2006
[27]Vournas C D.Voltage stability and controllability indices for multimachine power system[J].IEEE Trans on Power Systems,1995,10(3):1183-1194
[28]包黎昕.电压稳定动态分析及预防电压崩溃的措施[D].武汉:华中科技大学,2000
[29]Noroozian M,Taylor C W.Benefits of SVC and STATCOM for electric utility application[C].Proceedings of IEEE PES Transm and Distrib Conference and Exposition.IEEE,2003:1143-1150.
[30]Zhu T X,Tso S K,Lo K L.An investigation into the OLTC effects on voltage collapse[J].IEEE Trans on Power Systems,2000,15(2):515-521
[31]周双喜,朱凌志,郭锡玖,等.电力系统电压稳定性及其控制[M].北京:中国电力出版社,2004
[32]Y H Song,H B Wan,A T Johns.Power system voltage stability assessment using a self-organizing neural network classifier[C].IEE Power System Control and Management,Conference Publication No.421,1996:171-175
[33]B Jeyasurya.Artificial neural network for on-line voltage stability assessment[C].IEEE Power Engineering Society Summer Meeting,2000:2014-2018
[34]付英,钟德成.自组织映射神经网络用于动态电压稳定分析的新方法[J].电力系统自动化,2000,24(1):27-31
[35]瓦普尼克.统计学习理论的本质[M].张学工,译.北京:清华大学出版社,2000
[36]许涛,贺仁睦,王鹏,等.基于统计学习理论的电力系统暂态稳定评估[J].中国电机工程学报,2003,23(11):51-55
[37]P Kundur.电力系统稳定与控制[M].周孝信,等译.北京:中国电力出版社,2002
[38]边肇祺,张学工,等.模式识别[M].北京:清华大学出版社,2000
[39]V.N.Vapnik.统计学习理论[M].许建华,张学工译.北京:电子工业出版社,2004
[40]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1):32-42
[41]姜静清.最小二乘支持向量机算法及应用研究[D].长春:吉林大学,2007
[42]邓乃扬,田英杰.数据挖掘中的新方法—支持向量机[M].北京:科学出版社,2004
[43]程浩忠.电力系统电压崩溃的研究(上)[J].电力系统自动化,1995,19(11):59-61
[44]A.A.El-Keib,X.Ma.Application of Artificial Neural Networks in Voltage Stability Assessment[J].IEEE Trans on Power Systems,1995,10(4):1890-1896
[45]P.M.安德逊,A.A.佛阿德.电力系统的控制与稳定(第一卷)[M].北京:水利电力出版社,1979
[46]Power System Analysis Toolbox-PSAT Version 2.0.0,Federico Milano,Canada,2006
[47]常永吉.PSAT在电力系统稳定性仿真中的应用[J].电气应用,2008,27(14):61-64
[48]Chapelle O,Vapnik V.Choosing Multiple Parameters for Support Vector Machines[R].New York:AT&T Research Labs,2001
[49]吴宏晓,侯志俭.基于免疫支持向量机方法的电力系统短期负荷预测[J].电网技术,2004,28(23):47-51
[50]Chih-Wei Hsu,Chih-Chung Chang,Chih-Jen Lin.A Practical Guide to Support Vector Classification.[EB/OL]http://www.csie.ntu.edu.tw/～cjlin/papers/guide/guide.pdf
[51]Chih-Chung Chang,Chih-Jen Lin.LIBSVM:a Library for Support Vector Machines,2001.Software available at http://www.csie.ntu.edu.tw/～cjlin/libsvm.
[52]L.Chen,K.Tomsovic,A.Bose,R.Stuart.Estimating Reactive Margin for Determining Transfer Limits.IEEE Power Engineering Society Summer Meeting,Seatle.USA,July 2000
[53]Andrade.A.C,et al.Voltage stability assessment using a new FSQV method and artificial neural networks[C].Electrotechnical Conference,2006:1003-1006.MELECON 2006,IEEE Mediterranean
[54]韩力群.人工神经网络理论、设计及应用(第二版)[M].北京:化学工业出版社,2007
[55]高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社,2003
[56]陈允平,王旭蕊,韩宝亮.人工神经网络原理及其应用[M].北京:中国电力出版社,2002
[57]White H.Commentionist Nonparametric Regression:Multi Layer Feed Forward Networks Can Learn Arbitrary Mapping[J].Neural Networks,1990(3)
[58]张尧,宋文南.节点电压稳定临界状态和弱节点的确定[J].中国电机工程学报,1993,13(61:40-45
[59]赵广社,张希仁.基于主成分分析的支持向量机分类方法研究[J].计算机工程与应用,2004,37(3):37-39
[60]Mao,K.Z.Feature subset selection for support vector machines through discriminative function pruning analysis[J].IEEE Trans on Systems,Man and Cybernetics,Part B,2004,34(1):60-67
[61]梅长林,周家良.实用统计方法[M].北京:科学出版社,2002
[62]高惠璇.应用多元统计分析[M].北京:北京大学出版社,2005