基于卡尔曼滤波的电力系统动态状态估计算法研究
|
摘要
电力系统状态估计是电力系统调度、控制、安全评估等方面的基础，也是能量管理系统(EMS)的核心组成部分。动态状态估计通过状态预测能对电力系统进行安全评估，实现经济调度、预防控制等在线功能，重要性不言而喻，因此本文对基于扩展卡尔曼滤波的电力系统动态状态估计进行了分析研究。
本文首先通过对卡尔曼滤波算法的过程及计算公式的推导，阐述了电力系统模型下扩展卡尔曼滤波动态状态估计器的工作原理和实际应用中所面临的问题，并列举分析针对这些问题的几种改进算法。
在扩展卡尔曼滤波算法的基础上，本文提出一种自适应卡尔曼滤波原理的动态状态估计新算法，该算法通过采取增广最小二乘法来修正状态模型参数和指数加权法来估计时变噪声。这样，在利用量测数据进行状态估计的同时，来不断的对系统模型参数和噪声统计特性进行估计和修正以提高模型精确度，降低状态估计的误差。此外，本文算法还采取三次样条插值的数值分析方法，利用状态估计的历史数据来拟合状态函数，估计出状态转移矩阵的初值，以缩短状态估计周期和提高算法精确度；同时采取稀疏矩阵技术以减少算法的计算量。
仿真试验结果表明：本文算法不仅在电力系统正常状况下具有较好的预测、估计结果，而且在电力系统发生负荷突变和存在量测不良数据的异常情况下，也体现出良好的适应性。
Power system state estimation is not only the foundation of power system dispatch, control and security assessment, but also the core of Energy Management System. Through state prediction, dynamic state estimation is able to finish the security assessment in order to achieve economic dispatch, prevention control and other online functions. Therefore researches on power system dynamic state estimation based on extended Kalman filter were carried out
Along with the derivation of Kalman filter algorithm, the operating principle of extended Kalman filtering dynamic estimator in power system and the problems facing practical application were detailed. Then several improved algorithms were proposed.
On the basis of extended Kalman filter algorithm, a new dynamic state estimation algorithm based on adaptive Kalman filter was brought up. During the process of state estimation, recursive extended least square was introduced to update the parameters of state model, at the same time exponential weighted algorithm was put in use to estimate the statistical characteristic of time-varying noise. Thus the errors of state estimation could be reduced. What's more, cubic spline interpolation was proposed to fit the state function using historical state data. After that, the initial value of state transfer matrix could be estimated. All of that improvements together with sparse matrix technique contribute to the cut of calculation period and the increase of accuracy.
The simulation results show that with proposed algorithm, better prediction and estimate results could be got under normal condition in power system, further more when sudden changes or bad data were involved, this algorithm could still work with nice adaptability.
本文首先通过对卡尔曼滤波算法的过程及计算公式的推导，阐述了电力系统模型下扩展卡尔曼滤波动态状态估计器的工作原理和实际应用中所面临的问题，并列举分析针对这些问题的几种改进算法。
在扩展卡尔曼滤波算法的基础上，本文提出一种自适应卡尔曼滤波原理的动态状态估计新算法，该算法通过采取增广最小二乘法来修正状态模型参数和指数加权法来估计时变噪声。这样，在利用量测数据进行状态估计的同时，来不断的对系统模型参数和噪声统计特性进行估计和修正以提高模型精确度，降低状态估计的误差。此外，本文算法还采取三次样条插值的数值分析方法，利用状态估计的历史数据来拟合状态函数，估计出状态转移矩阵的初值，以缩短状态估计周期和提高算法精确度；同时采取稀疏矩阵技术以减少算法的计算量。
仿真试验结果表明：本文算法不仅在电力系统正常状况下具有较好的预测、估计结果，而且在电力系统发生负荷突变和存在量测不良数据的异常情况下，也体现出良好的适应性。
Power system state estimation is not only the foundation of power system dispatch, control and security assessment, but also the core of Energy Management System. Through state prediction, dynamic state estimation is able to finish the security assessment in order to achieve economic dispatch, prevention control and other online functions. Therefore researches on power system dynamic state estimation based on extended Kalman filter were carried out
Along with the derivation of Kalman filter algorithm, the operating principle of extended Kalman filtering dynamic estimator in power system and the problems facing practical application were detailed. Then several improved algorithms were proposed.
On the basis of extended Kalman filter algorithm, a new dynamic state estimation algorithm based on adaptive Kalman filter was brought up. During the process of state estimation, recursive extended least square was introduced to update the parameters of state model, at the same time exponential weighted algorithm was put in use to estimate the statistical characteristic of time-varying noise. Thus the errors of state estimation could be reduced. What's more, cubic spline interpolation was proposed to fit the state function using historical state data. After that, the initial value of state transfer matrix could be estimated. All of that improvements together with sparse matrix technique contribute to the cut of calculation period and the increase of accuracy.
The simulation results show that with proposed algorithm, better prediction and estimate results could be got under normal condition in power system, further more when sudden changes or bad data were involved, this algorithm could still work with nice adaptability.
引文
[1] F C Schweppe, J Wilds. Power System static State Estimation, Part Ⅰ, Part Ⅱ and Part Ⅲ. IEEE Trans. on PAS, 1970, 89: 104-135.
[2] 于尔铿．电力系统状态估计．北京：水利电力出版社，1985．
[3] 秦永元，张洪钺，汪叔华．卡尔曼滤波与组合导航原理．西安：西北工业大学出版社，1998．
[4] 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．
[5] Wu F F. Power System State Estimation. A Survey Electrical Power&Energy Systems, 1990, 12(2).
[6] Baldick R, Clements K A, Pinjo-Dazigal Z, et al. Implementing Non-Quadratic Objective Functions for State Estimation and Bad Data Rejection. IEEE Transactions on Power Systems, 1997, 12(1).
[7] Celik M K, Abur All. A Robust WLAV State Estimator Using Transformations. IEEE Transactions on Power Systems, 1992, 7(1).
[8] Singh H, Alvarado F I, Liu W-H E. Constrained LAV State Estimation Using Penalty Functions. IEEE Transactions on Power Systems, 1997. 12(1).
[9] Mill L, Chenial M G, Rousseeuw P J. Robust State Estimation of Electric Power Systems. IEEE Transactions on Circuits and Systems:
[10] 黄彦全．电力系统状态估计若干问题的研究．西南交通大学，博士论文，2005．
[11] 刘辉乐．基于PMU的分布动态状态估计的研究．四川大学，硕士论文，2005．
[12] 李强，周京阳，于尔铿，等．基于向量量测的电力系统线性状态估计．电力系统自动化，2005，29(18)：24-28．
[13] Kamwa I, Grondin R. PMU configuration for system dynamic performance measurement inlarge, multiarea power systems. IEEE Trans. on Power Systems, 2002, 17(2): 385-394.
[14] 张伯明，王世缨，相年德．电力系统实时运行的状态估计和预报．中国电机工程学报，1991增刊：68-74．
[15] 张伯明，王世缨，相年德．电力系统动态估计不正常事件的处理．中国电 机工程学报，1993，13(3)：52-58．
[16] Debs A, Larson R. A Dynamic Estimator for Tracking the State of a Power System. IEEE Trans. on PAS, 1970, 89(7): 1670-1678.
[17] Masiello R D, Schweppc F C. A Tracking Static State Estimator. IEEE Trans. on PAS, 1971, 90(8): 1025-1033.
[18] Nishiya K, Takagi H, Hasegawa J, et al. Dynamic State Estimation for Electric Power Systems: Introduction of a Trand Factor and Detection of Innovation Processes. Trans. Inst. Electr. Eng. Jpn., 1976, 96(5): 497-504.
[19] Leite da silva A M, Do Coutto Filho M B, De Queiroz J F. State Forecasting in Electric Power Systems. IEE Proc.,1982,130(5): 237-244.
[20] Leita da Silva A M, Do Coutto Filho M B, Camera J M C. An Efficient Dynamic State Estimation Algorithm Including Bad Data Processing. IEEE Trans. on Power Systems, 1987, PWRS-2(4): 1050-1058.
[21] 刘辉乐，刘天琪．电力系统动态状态估计的研究现状和展望．电力自动化设备，2004，24(12)：73-77．
[22] Mandal J K, Sinha A K, Roy L. Incorporating Nonlinearities of Measurement Function in Power System Dynamic State Estimation. IEE Proc., 1995, 142(3): 289-296.
[23] Huang S J, Shih K R. Dynamic-state-estimation scheme including nonlinear measurement function considerations, IEE Proc., 2002, 149(6): 673-678.
[24] Jeu-Min Lin, Shyh-Jier Huang. Application of Sliding Surface-Enhanced Fuzzy Control for Dynamic State Estimation of A Power System. IEEE Trans. on Power Systems, 2003, 18(2): 570-577.
[25] Kuang-Rong Shih, Shyh-Jier Huang. Application of a Robust Algorithm for Dynamic State Estimation of a Power System. IEEE Trans. on Power Systems, 2002, 17(1): 141-147.
[26] G Durgaprasad, S S Thakur. Robust Dynamic State Estimation of Power Systems Based on M-estimation and Realistic Modeling of System Dynamics. IEEE Trans. on Power Systems, 1998, 13(4): 1331-1336.
[27] Sinha A K, Mandal J K. Dynamic State Estimation Using ANN based Bus Load Prediction. IEEE Trans. on Power Systems, 1999, 14(4): 1219-1225.
[28] A K Sinha, J K Mandal. Hierarchical Dynamic State Estimator Using ANN-based Dynamic load prediction, IEE Proc,1995,146(6): 541-549.
[29] 胡锡龙，强金龙，于尔铿，等．电力系统状态估计的快速正交变换算法．哈尔滨工业大学学报，1990，2(1)：65-70．
[30] 余贻鑫，王耀喻，陈德生，等．一种优越的电力系统状态估计方法—Hachtel方法及其实现．电力系统自动化，1993，5(17)：7-11．
[31] 于渤，梁一桥．最优步长因子法在电力系统状态估计计算中的应用．浙江大学学报(自然科学版)．1989，2(23)：268-275．
[32] 任先成，黄富春，樊丽丽，等．电力系统状态估计的快速分解法研究．太原理工大学学报，2002，33(5)：485-487．
[33] 刘浩，侯博渊．保留非线性的电力系统状态估计算法．山东建材学院学报，1991，2(5)：6-13．
[34] 韩富春，王娟娟．基于神经网络的电力系统状态估计．电力系统及其自动化学报，2002，14(6)：49-51．
[35] 周苏荃，柳悼．新息图法状态估计．继电器，2000，4(28)．
[36] 郭伟，单渊达．基于原—对偶内点算法的WLAV状态估计．电力系统自动化，1999，1(23)．
[37] 程浩忠，袁青山，汪一华，等．基于等效电流量测变换的电力系统状态估计方法．电力系统自动化，2000，7(25)：25-29．
[38] Bandler J W, Chen S H, Biernacki R M, et al. Power Nerwork Steady-State M-Robust Estimation and Observability. IEEE Conference Proceeding,2002,May: 415-418.
[39] Isabel M Ferreira, F P Maciel Barbosa. A Dynamic State Estimation Algorithm with Information Debugging. Electrotechnical Conference,1996.Melecon'1996,8th Mediterranean,1996,3(13-16): 1539-1542.
[40] Beides H M, Heydt G T. Dynamic State Estimation of Power System Harmonics Using Kalman Filter. IEEE Trans. on Power Systems, 2002, 17(1): 141-147.
[41] A Bahgat, M M F Sakr, A R EI-Shafei. Two Level Dynamic State Estimator for Electric Power Systems Based on Nonlinear Transformation. IEE Proc., 1989, 136(1): 15-23.
[42] Eli Brookner. Tracking and Kalman Filtering Made Easy. John Wiley&Sons Inc. 1998.
[43] 敬喜．卡尔曼滤波及其应用基础．北京：国防工业出版社，1973．
[44] 文成林，周东华．多尺度估计理论及其应用．北京：清华大学出版社， 2002．
[45] 李明干．基于卡尔曼滤波的神经网络学习算法及其在短期负荷预测中的应用．华中科技大学，硕士论文，2004．
[46] 夏沛璋，朱征桃．最优估计及其应用．北京：科学出版社，1984．
[47] 付梦印，邓志红，张继伟．Kalman滤波理论及其在导航系统中的应用．北京：科学出版社，2003．
[48] 邓自立．最优滤波理论及其应用—现代时间序列分析方法．哈尔滨：哈尔滨工业大学出版社，2000．
[49] 史忠利．最优估计的计算方法．北京：科学出版社，2001．
[50] 毛玉华，马照彦，关信，等．电力系统自适应卡尔曼滤波状态估计．东北电力学院学报，1995，15(2)：20-26．
[51] 孙红星，李德仁．非线性系统中卡尔曼滤波的一种新线性化方法．武汉大学学报(信息科学报)，2004，29(4)：346-348．
[52] 何致远．基于RELS方法的控制系统参数和结构辨识仿真．杭州应用工程技术学院学报，2000，12(2)：29-32．
[53] 何延超．基于ARMA模型在线辨识器的线性系统建模方法．西安航空技术高等专科学校学报，2004，22(5)：47-49．
[54] 邓自立，郭一新．现代时间序列分析及其应用．北京：知识出版社，1989．
[55] 王晓陵．系统建模与参数估计．哈尔滨：哈尔滨工程大学出版社，2003．
[56] 邓自立，杜洪越．带有色观测噪声的ARMA模型参数估计的三段方法．科学技术与工程，2003，1(3)．
[57] T Yoshimura, T Soeda. A Technique for Compensating the Filter Performance by a Fictitious Noise. Trans.ASME.Ser.G, Journal of Dynamic Systems, Measurement and Control, 1978, 100(2).
[58] 范文兵，张素贞．带未知时变噪声的非线性系统卡尔曼滤波器算法研究．华东理工大学学报，2003，29(3)：299-302．
[59] N K Sinha, A F W Tom. Adaptive State Estimation for Systems with Coroured Observation Noise. Int. J. Syst. Sci. 1978, 9(1): 31-43.
[60] 金一亲，陈越．数值方法．北京：机械工业出版社，2002．
[61] 陈文略，王子羊．三次样条插值在工程拟合中的应用．华中师范大学学报(自然科学版)，2004，38(4)：418-422．
[62] 高伯明，陈寿孙．高等电力网络分析．北京：清华大学出版社，1996．
[63] 孟昭军，薛禹胜，罗国麟．稀疏向量法的证明．电力系统自动化，2005， 29(16)：3-5．
[2] 于尔铿．电力系统状态估计．北京：水利电力出版社，1985．
[3] 秦永元，张洪钺，汪叔华．卡尔曼滤波与组合导航原理．西安：西北工业大学出版社，1998．
[4] 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．
[5] Wu F F. Power System State Estimation. A Survey Electrical Power&Energy Systems, 1990, 12(2).
[6] Baldick R, Clements K A, Pinjo-Dazigal Z, et al. Implementing Non-Quadratic Objective Functions for State Estimation and Bad Data Rejection. IEEE Transactions on Power Systems, 1997, 12(1).
[7] Celik M K, Abur All. A Robust WLAV State Estimator Using Transformations. IEEE Transactions on Power Systems, 1992, 7(1).
[8] Singh H, Alvarado F I, Liu W-H E. Constrained LAV State Estimation Using Penalty Functions. IEEE Transactions on Power Systems, 1997. 12(1).
[9] Mill L, Chenial M G, Rousseeuw P J. Robust State Estimation of Electric Power Systems. IEEE Transactions on Circuits and Systems:
[10] 黄彦全．电力系统状态估计若干问题的研究．西南交通大学，博士论文，2005．
[11] 刘辉乐．基于PMU的分布动态状态估计的研究．四川大学，硕士论文，2005．
[12] 李强，周京阳，于尔铿，等．基于向量量测的电力系统线性状态估计．电力系统自动化，2005，29(18)：24-28．
[13] Kamwa I, Grondin R. PMU configuration for system dynamic performance measurement inlarge, multiarea power systems. IEEE Trans. on Power Systems, 2002, 17(2): 385-394.
[14] 张伯明，王世缨，相年德．电力系统实时运行的状态估计和预报．中国电机工程学报，1991增刊：68-74．
[15] 张伯明，王世缨，相年德．电力系统动态估计不正常事件的处理．中国电 机工程学报，1993，13(3)：52-58．
[16] Debs A, Larson R. A Dynamic Estimator for Tracking the State of a Power System. IEEE Trans. on PAS, 1970, 89(7): 1670-1678.
[17] Masiello R D, Schweppc F C. A Tracking Static State Estimator. IEEE Trans. on PAS, 1971, 90(8): 1025-1033.
[18] Nishiya K, Takagi H, Hasegawa J, et al. Dynamic State Estimation for Electric Power Systems: Introduction of a Trand Factor and Detection of Innovation Processes. Trans. Inst. Electr. Eng. Jpn., 1976, 96(5): 497-504.
[19] Leite da silva A M, Do Coutto Filho M B, De Queiroz J F. State Forecasting in Electric Power Systems. IEE Proc.,1982,130(5): 237-244.
[20] Leita da Silva A M, Do Coutto Filho M B, Camera J M C. An Efficient Dynamic State Estimation Algorithm Including Bad Data Processing. IEEE Trans. on Power Systems, 1987, PWRS-2(4): 1050-1058.
[21] 刘辉乐，刘天琪．电力系统动态状态估计的研究现状和展望．电力自动化设备，2004，24(12)：73-77．
[22] Mandal J K, Sinha A K, Roy L. Incorporating Nonlinearities of Measurement Function in Power System Dynamic State Estimation. IEE Proc., 1995, 142(3): 289-296.
[23] Huang S J, Shih K R. Dynamic-state-estimation scheme including nonlinear measurement function considerations, IEE Proc., 2002, 149(6): 673-678.
[24] Jeu-Min Lin, Shyh-Jier Huang. Application of Sliding Surface-Enhanced Fuzzy Control for Dynamic State Estimation of A Power System. IEEE Trans. on Power Systems, 2003, 18(2): 570-577.
[25] Kuang-Rong Shih, Shyh-Jier Huang. Application of a Robust Algorithm for Dynamic State Estimation of a Power System. IEEE Trans. on Power Systems, 2002, 17(1): 141-147.
[26] G Durgaprasad, S S Thakur. Robust Dynamic State Estimation of Power Systems Based on M-estimation and Realistic Modeling of System Dynamics. IEEE Trans. on Power Systems, 1998, 13(4): 1331-1336.
[27] Sinha A K, Mandal J K. Dynamic State Estimation Using ANN based Bus Load Prediction. IEEE Trans. on Power Systems, 1999, 14(4): 1219-1225.
[28] A K Sinha, J K Mandal. Hierarchical Dynamic State Estimator Using ANN-based Dynamic load prediction, IEE Proc,1995,146(6): 541-549.
[29] 胡锡龙，强金龙，于尔铿，等．电力系统状态估计的快速正交变换算法．哈尔滨工业大学学报，1990，2(1)：65-70．
[30] 余贻鑫，王耀喻，陈德生，等．一种优越的电力系统状态估计方法—Hachtel方法及其实现．电力系统自动化，1993，5(17)：7-11．
[31] 于渤，梁一桥．最优步长因子法在电力系统状态估计计算中的应用．浙江大学学报(自然科学版)．1989，2(23)：268-275．
[32] 任先成，黄富春，樊丽丽，等．电力系统状态估计的快速分解法研究．太原理工大学学报，2002，33(5)：485-487．
[33] 刘浩，侯博渊．保留非线性的电力系统状态估计算法．山东建材学院学报，1991，2(5)：6-13．
[34] 韩富春，王娟娟．基于神经网络的电力系统状态估计．电力系统及其自动化学报，2002，14(6)：49-51．
[35] 周苏荃，柳悼．新息图法状态估计．继电器，2000，4(28)．
[36] 郭伟，单渊达．基于原—对偶内点算法的WLAV状态估计．电力系统自动化，1999，1(23)．
[37] 程浩忠，袁青山，汪一华，等．基于等效电流量测变换的电力系统状态估计方法．电力系统自动化，2000，7(25)：25-29．
[38] Bandler J W, Chen S H, Biernacki R M, et al. Power Nerwork Steady-State M-Robust Estimation and Observability. IEEE Conference Proceeding,2002,May: 415-418.
[39] Isabel M Ferreira, F P Maciel Barbosa. A Dynamic State Estimation Algorithm with Information Debugging. Electrotechnical Conference,1996.Melecon'1996,8th Mediterranean,1996,3(13-16): 1539-1542.
[40] Beides H M, Heydt G T. Dynamic State Estimation of Power System Harmonics Using Kalman Filter. IEEE Trans. on Power Systems, 2002, 17(1): 141-147.
[41] A Bahgat, M M F Sakr, A R EI-Shafei. Two Level Dynamic State Estimator for Electric Power Systems Based on Nonlinear Transformation. IEE Proc., 1989, 136(1): 15-23.
[42] Eli Brookner. Tracking and Kalman Filtering Made Easy. John Wiley&Sons Inc. 1998.
[43] 敬喜．卡尔曼滤波及其应用基础．北京：国防工业出版社，1973．
[44] 文成林，周东华．多尺度估计理论及其应用．北京：清华大学出版社， 2002．
[45] 李明干．基于卡尔曼滤波的神经网络学习算法及其在短期负荷预测中的应用．华中科技大学，硕士论文，2004．
[46] 夏沛璋，朱征桃．最优估计及其应用．北京：科学出版社，1984．
[47] 付梦印，邓志红，张继伟．Kalman滤波理论及其在导航系统中的应用．北京：科学出版社，2003．
[48] 邓自立．最优滤波理论及其应用—现代时间序列分析方法．哈尔滨：哈尔滨工业大学出版社，2000．
[49] 史忠利．最优估计的计算方法．北京：科学出版社，2001．
[50] 毛玉华，马照彦，关信，等．电力系统自适应卡尔曼滤波状态估计．东北电力学院学报，1995，15(2)：20-26．
[51] 孙红星，李德仁．非线性系统中卡尔曼滤波的一种新线性化方法．武汉大学学报(信息科学报)，2004，29(4)：346-348．
[52] 何致远．基于RELS方法的控制系统参数和结构辨识仿真．杭州应用工程技术学院学报，2000，12(2)：29-32．
[53] 何延超．基于ARMA模型在线辨识器的线性系统建模方法．西安航空技术高等专科学校学报，2004，22(5)：47-49．
[54] 邓自立，郭一新．现代时间序列分析及其应用．北京：知识出版社，1989．
[55] 王晓陵．系统建模与参数估计．哈尔滨：哈尔滨工程大学出版社，2003．
[56] 邓自立，杜洪越．带有色观测噪声的ARMA模型参数估计的三段方法．科学技术与工程，2003，1(3)．
[57] T Yoshimura, T Soeda. A Technique for Compensating the Filter Performance by a Fictitious Noise. Trans.ASME.Ser.G, Journal of Dynamic Systems, Measurement and Control, 1978, 100(2).
[58] 范文兵，张素贞．带未知时变噪声的非线性系统卡尔曼滤波器算法研究．华东理工大学学报，2003，29(3)：299-302．
[59] N K Sinha, A F W Tom. Adaptive State Estimation for Systems with Coroured Observation Noise. Int. J. Syst. Sci. 1978, 9(1): 31-43.
[60] 金一亲，陈越．数值方法．北京：机械工业出版社，2002．
[61] 陈文略，王子羊．三次样条插值在工程拟合中的应用．华中师范大学学报(自然科学版)，2004，38(4)：418-422．
[62] 高伯明，陈寿孙．高等电力网络分析．北京：清华大学出版社，1996．
[63] 孟昭军，薛禹胜，罗国麟．稀疏向量法的证明．电力系统自动化，2005， 29(16)：3-5．