基于正则化投影孪生支持向量机的电力系统暂态稳定评估
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摘要
提出一种基于正则化投影孪生支持向量机的暂态稳定评估方法。将基于传统支持向量机进行暂态稳定评估的高维二项式优化问题转化为两个低维二项式优化问题,并在投影孪生支持向量机的目标函数中引入正则项来改善评估稳定性。首先,构建由系统特征和投影能量函数特征组成的初始样本集,通过特征选择对初始特征进行压缩,获取可有效表征暂态稳定性的最优特征集。然后,基于正则化投影孪生支持向量机的思想将暂态稳定状态分成稳定类与不稳定类,寻找各稳定状态的最佳投影坐标轴,使稳定类投影到稳定类投影超平面上后尽可能地聚成簇,而不稳定类投影到稳定类投影超平面上后尽可能远离稳定类聚成的簇,降低暂态稳定评估的计算时间,同时借助遗传算法进行参数选择以提高准确率。最后,通过IEEE-145和南方电网算例的仿真分析,验证了所提方法的有效性和准确性。
A method is proposed to assess the power system transient stability using projection twin support vector machine with regularization(RPTSVM).The high dimensional binomial optimization problem of transient stability assessment(TSA)based on support vector machine is transformed into two low dimensional binomial optimization problems.The regularization term in the objective function of PTSVM is added to improve the stability of assessment.Firstly,agroup of classification features are extracted from the power system operation parameters to build the original features set,such as feature of power system and the feature of projection energy function.The approach of feature selection is employed to evaluate the classification capability of the original features.Secondly,the optimal feature set is determined to effectively reflect the transient stability of the power system.Then,the features set are divided into stable classes and unstable classes based on RPTSVM.The best projection axis for stable classes and unstable classes are found,so that the class of stable are projected onto the projection hyper-plane of stable class and then clustered as much as possible.While the class of unstable is projected onto the class of stable projection super-plane as far as possible away from the cluster of stable clusters.The computation time of the transient stability assessment is reduced.At the same time,the genetic algorithm is used for parameter optimization and the accuracy of transient evaluation methods is improved.Finally,the simulated results of classic IEEE 145-bus system and China Southern power grid demonstrate the feasibility and validity of the proposed method.
A method is proposed to assess the power system transient stability using projection twin support vector machine with regularization(RPTSVM).The high dimensional binomial optimization problem of transient stability assessment(TSA)based on support vector machine is transformed into two low dimensional binomial optimization problems.The regularization term in the objective function of PTSVM is added to improve the stability of assessment.Firstly,agroup of classification features are extracted from the power system operation parameters to build the original features set,such as feature of power system and the feature of projection energy function.The approach of feature selection is employed to evaluate the classification capability of the original features.Secondly,the optimal feature set is determined to effectively reflect the transient stability of the power system.Then,the features set are divided into stable classes and unstable classes based on RPTSVM.The best projection axis for stable classes and unstable classes are found,so that the class of stable are projected onto the projection hyper-plane of stable class and then clustered as much as possible.While the class of unstable is projected onto the class of stable projection super-plane as far as possible away from the cluster of stable clusters.The computation time of the transient stability assessment is reduced.At the same time,the genetic algorithm is used for parameter optimization and the accuracy of transient evaluation methods is improved.Finally,the simulated results of classic IEEE 145-bus system and China Southern power grid demonstrate the feasibility and validity of the proposed method.
引文
[1]田芳,周孝信,于之虹.基于支持向量机综合分类模型和关键样本集的电力系统暂态稳定评估[J].电力系统保护与控制,2017,45(22):1-8.TIAN Fang,ZHOU Xiaoxin,YU Zhihong.Power system transient stability assessment based on comprehensive SVMclassification model and key sample set[J].Power System Protection and Control,2017,45(22):1-8.
[2]姜涛,贾宏杰,姜懿郎,等.跨区互联电网热稳定安全域边界近似方法[J].电工技术学报,2016,31(8):134-146.JIANG Tao,JIA Hongjie,JIANG Yilang,et al.Approximating method of wide area thermal security region boundary in bulk power system[J].Transactions of China Electrotechnical Society,2016,31(8):134-146.
[3]姜涛,贾宏杰,李国庆,等.基于广域量测信息相关性的电力系统同调辨识[J].电工技术学报,2017,32(1):1-11.JIANG Tao,JIA Hongjie,LI Guoqing,et al.Cross-correlation coefficient-based coherency identification in bulk power system using wide-area measurements[J].Transactions of China Electrotechnical Society,2017,32(1):1-11.
[4]徐泰山,杜延菱,鲍颜红,等.在线暂态安全稳定评估的分类滚动故障筛选方法[J].电力系统自动化,2018,42(13):182-188.DOI:10.7500/AEPS20170602007.XU Taishan,DU Yanling,BAO Yanhong,et al.Aclassification rolling contingency screening method for online transient security and stability assessment[J].Automation of Electric Power Systems,2018,42(13):182-188.DOI:10.7500/AEPS20170602007.
[5]潘明帅,汪芳宗,宋墩文,等.基于广义向后差分方法的电力系统暂态稳定性快速数值计算方法[J].电力系统保护与控制,2018,46(1):9-15.PAN Mingshuai,WANG Fangzong,SONG Dunwen,et al.Fast power system transient stability simulations by generalized backward differentiation formulae[J].Power System Protection and Control,2018,46(1):9-15.
[6]陈厚合,王长江,姜涛,等.基于端口能量的含VSC-HVDC的交直流混合系统暂态稳定评估[J].电工技术学报,2018,33(3):498-511.CHEN Houhe,WANG Changjiang,JIANG Tao,et al.Transient stability assessment in hybrid AC/DC systems with VSC-HVDC via port energy[J].Transactions of China Electrotechnical Society,2018,33(3):498-511.
[7]陈乾,沈沉,刘锋.端口能量及其在风电系统暂态稳定分析中的应用[J].电力系统自动化,2015,39(15):9-16.DOI:10.7500/AEPS20140822002.CHEN Qian,SHEN Chen,LIU Feng.Port energy and its application to transient stability analysis of power systems with wind generation[J].Automation of Electric Power Systems,2015,39(15):9-16.DOI:10.7500/AEPS20140822002.
[8]魏少攀,杨明,韩学山,等.基于相轨迹MLE指标的暂态功角稳定在线辨识[J].电力系统自动化,2017,41(16):71-79.DOI:10.7500/AEPS20170105007.WEI Shaopan,YANG Ming,HAN Xueshan,et al.Online identification for transient angle stability based on MLE index of phase trajectory[J].Automation of Electric Power Systems,2017,41(16):71-79.DOI:10.7500/AEPS20170105007.
[9]姚德全,贾宏杰,赵帅.基于复合神经网络的电力系统暂态稳定评估和裕度预测[J].电力系统自动化,2013,37(20):41-46.YAO Dequan,JIA Hongjie,ZHAO Shuai.Power system transient stability assessment and stability margin prediction based on compound neural network[J].Automation of Electric Power Systems,2013,37(20):41-46.
[10]顾雪平,曹绍杰,张文勤.基于神经网络暂态稳定评估方法的一种新思路[J].中国电机工程学报,2000,20(4):77-82.GU Xueping,TSO Shiu-kit,ZHANG Wenqin.A new framework for transient stability assessment based on neural networks[J].Proceedings of the CSEE,2000,20(4):77-82.
[11]管霖,曹绍杰.基于人工智能的大系统分层在线暂态稳定评估[J].电力系统自动化,2000,24(2):22-26.GUAN Lin,TSO Shiu-kit.Combination of heuristic reasoning and ANN to realize online transient stability assessment in large scale power systems[J].Automation of Electric Power Systems,2000,24(2):22-26.
[12]赵天辉,王建学,马龙涛,等.基于非参数回归分析的工业负荷异常值识别与修正方法[J].电力系统自动化,2017,41(18):53-59.DOI:10.7500/AEPS20170118002.ZHAO Tianhui,WANG Jianxue,MA Longtao,et al.Outlier detection and correction method for industrial loads based on nonparametric regression analysis[J].Automation of Electric Power Systems,2017,41(18):53-59.DOI:10.7500/AEPS20170118002.
[13]孙宏斌,王康,张伯明,等.采用线性决策树的暂态稳定规则提取[J].中国电机工程学报,2011,31(34):61-67.SUN Hongbin,WANG Kang,ZHANG Boming,et al.Rule extraction in transient stability study using linear decision trees[J].Proceedings of the CSEE,2011,31(34):61-67.
[14]李扬,顾雪平.基于改进最大相关最小冗余判据的暂态稳定评估特征选择[J].中国电机工程学报,2013,33(34):179-186.LI Yang,GU Xueping.Feature selection for transient stability assessment based on improved maximal relevance and minimal redundancy criterion[J].Proceedings of the CSEE,2013,33(34):179-186.
[15]陈厚合,王长江,姜涛,等.基于投影能量函数和Pin-SVM的电力系统暂态稳定评估[J].电工技术学报,2017,32(11):67-76.CHEN Houhe,WANG Changjiang,JIANG Tao,et al.Transient stability assessment in bulk power grid using projection energy function and support vector machine with pinball loss[J].Transactions of China Electrotechnical Society,2017,32(11):67-76.
[16]CHEN Xiaobo,YANG Jian,YE Qiaolin,et al.Recursive projection twin support vector machine via within-class variance minimization[J].Pattern Recognition,2011,44(10):2643-2655.
[17]YANG Jian,YANG Jianyu.Why can LDA be performed in PCA transformed space?[J].Pattern Recognition,2003,36(2):563-566.
[18]FARMER R G.Transient stability test systems for direct stability methods[J].IEEE Transactions on Power Systems,1992,7(1):37-43.
[19]戴远航,陈磊,张玮灵,等.基于多支持向量机综合的电力系统暂态稳定评估[J].中国电机工程学报,2016,36(5):1173-1180.DAI Yuanhang,CHEN Lei,ZHANG Weiling,et al.Power system transient stability assessment based on multi-support vector machines[J].Proceedings of the CSEE,2016,36(5):1173-1180.
[20]吴琼,杨以涵,刘文颖.基于最小二乘支持向量机的电力系统暂态稳定在线预测[J].中国电机工程学报,2007,27(25):38-43.WU Qiong,YANG Yihan,LIU Wenying.Electric power system transient stability on-line prediction based on least squares support vector machine[J].Proceedings of the CSEE,2007,27(25):38-43.
[21]HUANG X L,SHI L,SUYKENS J A K.Support vector machine classifier with pinball loss[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2014,36(5):984-997.
[22]HE M,ZHANG J,VITTAL V.Robust online dynamic security assessment using adaptive ensemble decision-tree learning[J].IEEE Transactions on Power Systems,2013,28(4):4089-4098.
[23]王英涛,张道农,谢晓冬,等.电力系统实时动态监测系统传输规约[J].电网技术,2007,31(13):81-85.WANG Yingtao,ZHANG Daonong,XIE Xiaodong,et al.Study on transmission protocol for real-time dynamic monitoring system of power systems[J].Power System Technology,2007,31(13):81-85.
[24]李立毅,唐勇斌,刘家曦,等.多种群遗传算法在无铁心永磁直线同步电机优化设计中的应用[J].中国电机工程学报,2013,33(15):69-77.LI Liyi,TANG Yongbin,LIU Jiaxi,et al.Application of the multiple population genetic algorithm in optimum design of aircore permanent magnet linear synchronous motors[J].Proceedings of the CSEE,2013,33(15):69-77.
[25]姜涛,黄河,贾宏杰,等.基于投影寻踪最佳方向的同调机群识别方法[J].中国电机工程学报,2015,35(2):359-367.JIANG Tao,HUANG He,JIA Hongjie,et al.Coherency identification through projection pursuit[J].Proceedings of the CSEE,2015,35(2):359-367.
[2]姜涛,贾宏杰,姜懿郎,等.跨区互联电网热稳定安全域边界近似方法[J].电工技术学报,2016,31(8):134-146.JIANG Tao,JIA Hongjie,JIANG Yilang,et al.Approximating method of wide area thermal security region boundary in bulk power system[J].Transactions of China Electrotechnical Society,2016,31(8):134-146.
[3]姜涛,贾宏杰,李国庆,等.基于广域量测信息相关性的电力系统同调辨识[J].电工技术学报,2017,32(1):1-11.JIANG Tao,JIA Hongjie,LI Guoqing,et al.Cross-correlation coefficient-based coherency identification in bulk power system using wide-area measurements[J].Transactions of China Electrotechnical Society,2017,32(1):1-11.
[4]徐泰山,杜延菱,鲍颜红,等.在线暂态安全稳定评估的分类滚动故障筛选方法[J].电力系统自动化,2018,42(13):182-188.DOI:10.7500/AEPS20170602007.XU Taishan,DU Yanling,BAO Yanhong,et al.Aclassification rolling contingency screening method for online transient security and stability assessment[J].Automation of Electric Power Systems,2018,42(13):182-188.DOI:10.7500/AEPS20170602007.
[5]潘明帅,汪芳宗,宋墩文,等.基于广义向后差分方法的电力系统暂态稳定性快速数值计算方法[J].电力系统保护与控制,2018,46(1):9-15.PAN Mingshuai,WANG Fangzong,SONG Dunwen,et al.Fast power system transient stability simulations by generalized backward differentiation formulae[J].Power System Protection and Control,2018,46(1):9-15.
[6]陈厚合,王长江,姜涛,等.基于端口能量的含VSC-HVDC的交直流混合系统暂态稳定评估[J].电工技术学报,2018,33(3):498-511.CHEN Houhe,WANG Changjiang,JIANG Tao,et al.Transient stability assessment in hybrid AC/DC systems with VSC-HVDC via port energy[J].Transactions of China Electrotechnical Society,2018,33(3):498-511.
[7]陈乾,沈沉,刘锋.端口能量及其在风电系统暂态稳定分析中的应用[J].电力系统自动化,2015,39(15):9-16.DOI:10.7500/AEPS20140822002.CHEN Qian,SHEN Chen,LIU Feng.Port energy and its application to transient stability analysis of power systems with wind generation[J].Automation of Electric Power Systems,2015,39(15):9-16.DOI:10.7500/AEPS20140822002.
[8]魏少攀,杨明,韩学山,等.基于相轨迹MLE指标的暂态功角稳定在线辨识[J].电力系统自动化,2017,41(16):71-79.DOI:10.7500/AEPS20170105007.WEI Shaopan,YANG Ming,HAN Xueshan,et al.Online identification for transient angle stability based on MLE index of phase trajectory[J].Automation of Electric Power Systems,2017,41(16):71-79.DOI:10.7500/AEPS20170105007.
[9]姚德全,贾宏杰,赵帅.基于复合神经网络的电力系统暂态稳定评估和裕度预测[J].电力系统自动化,2013,37(20):41-46.YAO Dequan,JIA Hongjie,ZHAO Shuai.Power system transient stability assessment and stability margin prediction based on compound neural network[J].Automation of Electric Power Systems,2013,37(20):41-46.
[10]顾雪平,曹绍杰,张文勤.基于神经网络暂态稳定评估方法的一种新思路[J].中国电机工程学报,2000,20(4):77-82.GU Xueping,TSO Shiu-kit,ZHANG Wenqin.A new framework for transient stability assessment based on neural networks[J].Proceedings of the CSEE,2000,20(4):77-82.
[11]管霖,曹绍杰.基于人工智能的大系统分层在线暂态稳定评估[J].电力系统自动化,2000,24(2):22-26.GUAN Lin,TSO Shiu-kit.Combination of heuristic reasoning and ANN to realize online transient stability assessment in large scale power systems[J].Automation of Electric Power Systems,2000,24(2):22-26.
[12]赵天辉,王建学,马龙涛,等.基于非参数回归分析的工业负荷异常值识别与修正方法[J].电力系统自动化,2017,41(18):53-59.DOI:10.7500/AEPS20170118002.ZHAO Tianhui,WANG Jianxue,MA Longtao,et al.Outlier detection and correction method for industrial loads based on nonparametric regression analysis[J].Automation of Electric Power Systems,2017,41(18):53-59.DOI:10.7500/AEPS20170118002.
[13]孙宏斌,王康,张伯明,等.采用线性决策树的暂态稳定规则提取[J].中国电机工程学报,2011,31(34):61-67.SUN Hongbin,WANG Kang,ZHANG Boming,et al.Rule extraction in transient stability study using linear decision trees[J].Proceedings of the CSEE,2011,31(34):61-67.
[14]李扬,顾雪平.基于改进最大相关最小冗余判据的暂态稳定评估特征选择[J].中国电机工程学报,2013,33(34):179-186.LI Yang,GU Xueping.Feature selection for transient stability assessment based on improved maximal relevance and minimal redundancy criterion[J].Proceedings of the CSEE,2013,33(34):179-186.
[15]陈厚合,王长江,姜涛,等.基于投影能量函数和Pin-SVM的电力系统暂态稳定评估[J].电工技术学报,2017,32(11):67-76.CHEN Houhe,WANG Changjiang,JIANG Tao,et al.Transient stability assessment in bulk power grid using projection energy function and support vector machine with pinball loss[J].Transactions of China Electrotechnical Society,2017,32(11):67-76.
[16]CHEN Xiaobo,YANG Jian,YE Qiaolin,et al.Recursive projection twin support vector machine via within-class variance minimization[J].Pattern Recognition,2011,44(10):2643-2655.
[17]YANG Jian,YANG Jianyu.Why can LDA be performed in PCA transformed space?[J].Pattern Recognition,2003,36(2):563-566.
[18]FARMER R G.Transient stability test systems for direct stability methods[J].IEEE Transactions on Power Systems,1992,7(1):37-43.
[19]戴远航,陈磊,张玮灵,等.基于多支持向量机综合的电力系统暂态稳定评估[J].中国电机工程学报,2016,36(5):1173-1180.DAI Yuanhang,CHEN Lei,ZHANG Weiling,et al.Power system transient stability assessment based on multi-support vector machines[J].Proceedings of the CSEE,2016,36(5):1173-1180.
[20]吴琼,杨以涵,刘文颖.基于最小二乘支持向量机的电力系统暂态稳定在线预测[J].中国电机工程学报,2007,27(25):38-43.WU Qiong,YANG Yihan,LIU Wenying.Electric power system transient stability on-line prediction based on least squares support vector machine[J].Proceedings of the CSEE,2007,27(25):38-43.
[21]HUANG X L,SHI L,SUYKENS J A K.Support vector machine classifier with pinball loss[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2014,36(5):984-997.
[22]HE M,ZHANG J,VITTAL V.Robust online dynamic security assessment using adaptive ensemble decision-tree learning[J].IEEE Transactions on Power Systems,2013,28(4):4089-4098.
[23]王英涛,张道农,谢晓冬,等.电力系统实时动态监测系统传输规约[J].电网技术,2007,31(13):81-85.WANG Yingtao,ZHANG Daonong,XIE Xiaodong,et al.Study on transmission protocol for real-time dynamic monitoring system of power systems[J].Power System Technology,2007,31(13):81-85.
[24]李立毅,唐勇斌,刘家曦,等.多种群遗传算法在无铁心永磁直线同步电机优化设计中的应用[J].中国电机工程学报,2013,33(15):69-77.LI Liyi,TANG Yongbin,LIU Jiaxi,et al.Application of the multiple population genetic algorithm in optimum design of aircore permanent magnet linear synchronous motors[J].Proceedings of the CSEE,2013,33(15):69-77.
[25]姜涛,黄河,贾宏杰,等.基于投影寻踪最佳方向的同调机群识别方法[J].中国电机工程学报,2015,35(2):359-367.JIANG Tao,HUANG He,JIA Hongjie,et al.Coherency identification through projection pursuit[J].Proceedings of the CSEE,2015,35(2):359-367.
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