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电力能量流复杂性主要体现于其动态行为的实时性、非线性及不确定性等，网络动力学行为分析是关键. 本文在电力系统动力学平衡方程基础上，构建了系统势能与支路势能函数模型；通过提取扰动（或故障）后系统的能量信息，利用多尺度熵对扰动（或故障）后系统能量流演化过程进行了研究. 结果表明：1）稳定运行状态下系统复杂度较低，且随着故障持续时间的增加，系统故障后呈现出更高的复杂度；2）不稳定运行状态下，系统在小尺度时间上表现出更强的不确定性，而在大尺度时间上表现出相对更明显的规则性；3）临界稳定运行状态与临界不稳定运行状态下，故障后的系统复杂度在不同时间尺度上呈现出较明显的差异，这对动态过程中临界点的识别有着积极的参考价值. 本文研究揭示了电力能量流在物理动态过程中的演化机制，为电力系统动力学行为分析提供了新思路与新方法.Complexity of power system energy flow is mainly reflected in the features of dynamic behavior such as real-time, nonlinear, uncertainty, etc. The analysis of dynamics on network is a critical means. The potential energy function models of system and branches are established, which are based on power system dynamic equilibrium equation to extract the system energy information after the fault duration. And the complexity of the system energy flow evolution is analyzed by using the multi-scale entropy method. The analysis results show that the system complexity under steady operation is much low. In addition, the complexity of the fault system increases with the increase of fault duration. Moreover, the system complexity under unstable operation shows a strong uncertainty in a small time scale and obvious regularity in a large time scale. And the most important is that the system complexities of the critical stable state and the critical unstable state are clearly distinct in different time scales. Such a difference can be used as a positive reference to the identification of the critical point in the dynamic state. Research results reveal the evolution of power energy flow in physical dynamic process. This can provide new ideas and methods for analyzing the dynamics behavior of power system.
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Keywords:
- power system energy flow /
- dynamics on networks /
- multi-scale entropy /
- complexity analysis
[1] Arianos S, Bompard E, Carbone A, Xue F 2009 Chaos 19 013119
[2] Mei S W, Xue A C, Zhang X M 2008 Sci. China E 51 209
[3] Tang C K, Graham C E, El-Kady M, Alden R T H 1994 IEEE Trans. Power Syst. 9 031524
[4] Strogatz S H 2001 Nature 410 268
[5] Liu X, Liu T Q, Wang H, Li X Y 2010 Chin. Phys. B 19 070204
[6] Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军, 宁新宝, 邹鸣, 孙飙, 杨希 2008 物理学报 57 2805]
[7] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[8] Cao B, Xiang Y P, Lv X Q, Zeng M, Huang S S 2008 Chin. Phys. B 17 865
[9] Lake D E, Richman J S, Griffin M P, Moorman J R 2002 Am. J. Physiol. Regul. Integr. Comp. Physiol. 283 030789
[10] Richman J S, Moorman J R 2000 Am. J. Physiol. Heart Circ. Physiol. 278 2039
[11] Costa M, Peng C K, Goldberger A L, Jeffrey M H 2003 Physica A 330 53
[12] Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[13] Wang J, Ma Q L 2008 Chin. Phys. B 17 4424
[14] He L, Du L, Zhuang Y Q, Li W H, Chen J P 2008 Acta Phys. Sin. 57 6545 (in Chinese) [何亮, 杜磊, 庄奕琪, 李伟华, 陈建平 2008 物理学报 57 6545]
[15] Xiang Z T, Chen Y F, Li Y J, Xiong L 2014 Acta Phys. Sin. 63 038903 (in Chinese) [向郑涛, 陈宇峰, 李昱瑾, 熊励 2014 物理学报 63 038903]
[16] Ni Y X, Chen S S, Zhang B L 2002 Dynamic Power System Theory and Analysis (Beijing: Tsinghua University Press) pp135-215 (in Chinese) [倪以信, 陈寿孙, 张宝霖 2002 动态电力系统的理论和分析 (北京: 清华大学出版社) 第135–215页]
[17] Liu S, Wang J 1996 Energy Function Analysis of Power System Transient Stability (Shanghai: Shanghai Jiaotong University Press) pp2-5 (in Chinese) [刘笙, 汪静 1996 电力系统暂态稳定的能量函数分析 (上海: 上海交通大学出版社) 第2–5页]
[18] Fang D Z, Zhang Y, Song W N, Chung T S 1998 Proceedings of the CSEE 18 030200 (in Chinese) [房大中, 张尧, 宋文南, 钟德成 1998 中国电机工程学报 18 030200]
[19] Pai M A 1989 Energy Function Analysis for Power System Stability (USA: Kluwer Academic Publisher) pp26-33
[20] Padiyar K R, Krishna S 2006 IEEE Trans. Power Deliver. 21 46
[21] Liu Y B, Liu J Y, Wang M K, Yang J S 2011 Proceedings of the CSEE 31 130040 (in Chinese) [刘友波, 刘俊勇, 王明昆, 杨嘉湜 2011 中国电机工程学报 31 130040]
[22] Cai G W, Chan K W, Yuan W P, Mu G 2007 Int. J. Elec. Power 29 199
[23] Lin J K, Yang J, Li Y C, Zheng W H, Wang H L 2008 J. Tianjin Univ. 41 060660 (in Chinese) [林济铿, 杨静, 李杨春, 郑卫红, 王海林 2008 中国电机工程学报 41 060660]
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[1] Arianos S, Bompard E, Carbone A, Xue F 2009 Chaos 19 013119
[2] Mei S W, Xue A C, Zhang X M 2008 Sci. China E 51 209
[3] Tang C K, Graham C E, El-Kady M, Alden R T H 1994 IEEE Trans. Power Syst. 9 031524
[4] Strogatz S H 2001 Nature 410 268
[5] Liu X, Liu T Q, Wang H, Li X Y 2010 Chin. Phys. B 19 070204
[6] Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军, 宁新宝, 邹鸣, 孙飙, 杨希 2008 物理学报 57 2805]
[7] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[8] Cao B, Xiang Y P, Lv X Q, Zeng M, Huang S S 2008 Chin. Phys. B 17 865
[9] Lake D E, Richman J S, Griffin M P, Moorman J R 2002 Am. J. Physiol. Regul. Integr. Comp. Physiol. 283 030789
[10] Richman J S, Moorman J R 2000 Am. J. Physiol. Heart Circ. Physiol. 278 2039
[11] Costa M, Peng C K, Goldberger A L, Jeffrey M H 2003 Physica A 330 53
[12] Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[13] Wang J, Ma Q L 2008 Chin. Phys. B 17 4424
[14] He L, Du L, Zhuang Y Q, Li W H, Chen J P 2008 Acta Phys. Sin. 57 6545 (in Chinese) [何亮, 杜磊, 庄奕琪, 李伟华, 陈建平 2008 物理学报 57 6545]
[15] Xiang Z T, Chen Y F, Li Y J, Xiong L 2014 Acta Phys. Sin. 63 038903 (in Chinese) [向郑涛, 陈宇峰, 李昱瑾, 熊励 2014 物理学报 63 038903]
[16] Ni Y X, Chen S S, Zhang B L 2002 Dynamic Power System Theory and Analysis (Beijing: Tsinghua University Press) pp135-215 (in Chinese) [倪以信, 陈寿孙, 张宝霖 2002 动态电力系统的理论和分析 (北京: 清华大学出版社) 第135–215页]
[17] Liu S, Wang J 1996 Energy Function Analysis of Power System Transient Stability (Shanghai: Shanghai Jiaotong University Press) pp2-5 (in Chinese) [刘笙, 汪静 1996 电力系统暂态稳定的能量函数分析 (上海: 上海交通大学出版社) 第2–5页]
[18] Fang D Z, Zhang Y, Song W N, Chung T S 1998 Proceedings of the CSEE 18 030200 (in Chinese) [房大中, 张尧, 宋文南, 钟德成 1998 中国电机工程学报 18 030200]
[19] Pai M A 1989 Energy Function Analysis for Power System Stability (USA: Kluwer Academic Publisher) pp26-33
[20] Padiyar K R, Krishna S 2006 IEEE Trans. Power Deliver. 21 46
[21] Liu Y B, Liu J Y, Wang M K, Yang J S 2011 Proceedings of the CSEE 31 130040 (in Chinese) [刘友波, 刘俊勇, 王明昆, 杨嘉湜 2011 中国电机工程学报 31 130040]
[22] Cai G W, Chan K W, Yuan W P, Mu G 2007 Int. J. Elec. Power 29 199
[23] Lin J K, Yang J, Li Y C, Zheng W H, Wang H L 2008 J. Tianjin Univ. 41 060660 (in Chinese) [林济铿, 杨静, 李杨春, 郑卫红, 王海林 2008 中国电机工程学报 41 060660]
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