基于Markov理论的含风电电力系统随机建模及小干扰稳定性分析
|
摘要
随着风电并网规模的不断扩大,风能的波动性、间歇性导致电力系统的随机特性越来越突出,传统的确定性分析方法和基于常规随机微分方程的方法难以准确分析含风电电力系统的稳定性。在常规随机微分方程的基础上,引入Markov理论,建立了用于分析含风电电力系统随机小干扰稳定性的随机Markov动态模型。利用李雅普诺夫能量函数,结合M矩阵,提出含风电电力系统在多工况下随机均值和均方稳定的分析方法。该方法能克服常规随机微分方程分析方法无法分析系统在运行工况改变下的小干扰稳定性的缺点。仿真结果验证本文所提方法的有效性和正确性。
With continuous scale expansion of wind power integration, random characteristics of power system are more and more prominent due to volatility and intermittency of wind energy. Traditional deterministic analysis methods and stochastic differential equation methods are difficult to accurately analyze wind power system stability. In this paper, based on stochastic ordinary differential equations, Markov theory is utilized to establish a stochastic Markov dynamic model of wind power systems to analyze stochastic small signal stability. Then, based on the developed system model, Lyapunov energy function and M matrix are combined to present the analytical method of stochastic mean and mean square stability for wind power system under multiple operating conditions. Compared with conventional stochastic differential equation analysis method, the proposed method can overcome the shortcomings that small signal stability cannot be analyzed when system operating conditions change. Simulation results verify validity and correctness of the proposed method.
With continuous scale expansion of wind power integration, random characteristics of power system are more and more prominent due to volatility and intermittency of wind energy. Traditional deterministic analysis methods and stochastic differential equation methods are difficult to accurately analyze wind power system stability. In this paper, based on stochastic ordinary differential equations, Markov theory is utilized to establish a stochastic Markov dynamic model of wind power systems to analyze stochastic small signal stability. Then, based on the developed system model, Lyapunov energy function and M matrix are combined to present the analytical method of stochastic mean and mean square stability for wind power system under multiple operating conditions. Compared with conventional stochastic differential equation analysis method, the proposed method can overcome the shortcomings that small signal stability cannot be analyzed when system operating conditions change. Simulation results verify validity and correctness of the proposed method.
引文
[1]Milano F,Zarate-Minano R.A systematic method to model power systems as stochastic differential algebraic equations[J].IEEETransactions on Power Systems,2013,28(4):4537-4544.
[2]Wang K,Crow M L.Numerical simulation of stochastic differential algebraic equations for power system transient stability with random loads[C]//Power and Energy Society General Meeting.Detroit,MI:IEEE,2011:1-8.
[3]Qiu Y,Zhao J,Chiang H D.Effects of the stochastic load model on power system voltage stability based on bifurcation theory[C]//Transmission and Distribution Conference and Exposition.Chicago,USA:IEEE,2008:1-6.
[4]张建勇,鞠平,余一平,等.电力系统在高斯随机小激励下的响应及稳定性[J].中国科学:技术科学,2012,42(7):851-857.Zhang Jianyong,Ju Ping,Yu Yiping,et al.Response and stability ofpower system in Gauss small random excitation[J].China Science:Science and Technology,2012,42(7):851-857(in Chinese).
[5]刘咏飞,鞠平,薛禹胜,等.随机激励下电力系统特性的计算分析[J].电力系统自动化,2014,38(9):137-142.Liu Yongfei,Ju Ping,Xue Yusheng,et al.Calculation analysis on power system characteristics under random excitation[J].Automation of Electric Power Systems,2014,38(9):137-142(in Chinese).
[6]许纹碧,王杰.非线性电力系统随机小干扰稳定性分析[J].电网技术,2014,38(10):2735-2740.Xu Wenbi,Wang Jie.Stochastic small disturbance stability analysis of nonlinear power system[J].Power System Technology,2014,38(10):2735-2740(in Chinese).
[7]Parinya P,Sangswang A,Kirtikara K,et al.A study of impact of wind power to power system stability using stochastic stability index[C]//International Symposium on Circuits and Systems(ISCAS).Melbourne,Australia:IEEE,2014:2656-2659.
[8]周明,元博,张小平,等.基于SDE的含风电电力系统随机小干扰稳定分析[J].中国电机工程学报,2014,34(10):1575-1582.Zhou Ming,Yuan Bo,Zhang Xiaoping,et al.Stochastic small signal stability analysis of wind power integrated power systems based on stochastic differential equations[J].Proceedings of the CSEE,2014,34(10):1575-1582(in Chinese).
[9]苏展,徐谦,孙黎滢,等.含DFIG的电力系统随机建模及小干扰随机稳定分析[J].电网技术,2015,39(9):2404-2410.Su Zhan,Xu Qian,Sun Liying,et al.Stochastic modeling and small signal stability analysis of power systems including DFIG[J].Power System Technology,2015,39(9):2404-2410(in Chinese).
[10]李洪宇,鞠平,余一平,等.随机激励下电力系统有界波动域及域内概率解析分析方法[J].中国电机工程学报,2015,35(14):3561-3568.Li Hongyu,Ju Ping,Yu Yiping,et al.Bounded fluctuations region and analytic method of intra-region probability in power system under stochastic excitations[J].Proceedings of the CSEE,2015,35(14):3561-3568(in Chinese).
[11]Higham D J.An algorithmic introduction to numerical simulation of stochastic differential equations[J].SIAM Review,2001,43(3):525-546.
[12]黄通,王杰.基于改进EEAC法的随机复杂多机系统的暂态稳定性分析[J].电网技术,2017,41(4):1174-1180.Huang Tong,Wang Jie.Transient stability analysis of stochastic complex multi-machine system based on improved extended equalarea criteria[J].Power System Technology,2017,41(4):1174-1180(in Chinese).
[13]周海强,鞠平,薛禹胜,等.基于拟哈密顿理论的随机电力系统暂态稳定性分析[J].电力系统自动化,2016,40(19):9-14.Zhou Haiqiang,Ju Ping,Xue Yusheng,et al.Transient stability analysis of stochastic power system based on quasi-Hamiltonian system theory[J].Automation of Electric Power Systems,2016,40(19):9-14(in Chinese).
[14]蒋长江,刘俊勇,刘友波,等.计及风电随机激励的电力系统暂态稳定分析[J].电力自动化设备,2016,36(3):100-108:Jiang Changjiang,Liu Junyong,Liu Youbo,et al.Transient stability analysis of power system considering wind-power stochastic excitation[J].Electric Power Automation Equipment,2016,36(3):100-108(in Chinese).
[15]马静,高翔,李益楠,等.考虑风速随机特征的多工况电力系统稳定性分析[J].电力自动化设备,2016,36(8):26-32.Ma Jing,Gao Xiang,Li Yinan,et al.Stability analysis considering time-varying wind speed for power system with multiple operating conditions[J].Electric Power Automation Equipment,2016,36(8):26-32(in Chinese).
[16]陆丹,袁越,杨苏.基于马尔可夫链蒙特卡洛法的独立风光柴储微网运行风险评估[J].电网技术,2017,41(3):823-830.Lu Dan,Yuan Yue,Yang Su.Operation risk assessment of islanded wind-PV-diesel-storage microgrid based on Markov chain Monte Carlo method[J].Power System Technology,2017,41(3):823-830(in Chinese).
[17]蒋平,霍雨翀,张龙,等.基于改进一阶马尔可夫链的风速时间序列模型[J].电力系统自动化,2014,38(19):22-27.Jiang Ping,Huo Yuchong,Zhang Long,et al.A wind speed time series model based on advanced first-order Markov chain approach[J].Automation of Electric Power Systems,2014,38(19):22-27(in Chinese).
[18]马静,高翔,李益楠,等.考虑离散马尔可夫模型的多工况电力系统自适应控制策略[J].电网技术,2015,39(10):2856-2861.Ma Jing,Gao Xiang,Li Yinan,et al.Adaptive control strategy considering discrete Markov model for power system with multiple operating conditions[J].Power System Technology,2015,39(10):2856-2861(in Chinese).
[19]马静,高翔,李益楠,等.考虑连锁故障的多工况电力系统功角稳定性分析[J].中国电机工程学报,2016,36(14):3837-3844.Ma Jing,Gao Xiang,Li Yinan,et al.Angle stability analysis of multi-operation power system based on cascading failure[J].Proceedings of the CSEE,2016,36(14):3837-3844(in Chinese).
[20]王要策.马尔科夫切换型随机微分方程的数值稳定性[D].上海:东华大学,2011.
[21]Mao X,Yuan C.Stochastic differential equations with Markovian switching[M].London:Imperial College Press,2006:77-110.
[22]Anderson W J.Continuous-time Markov chains:an applicationsoriented approach[M].New Work:Springer,1991:901-904.
[23]彭虎,郭钰锋,王松岩,等.风电场风速分布特性的模式分析[J].电网技术,2010,34(9):206-210.Peng Hu,Guo Yufeng,Wang Songyan,et al.Pattern analysis on characteristics of wind speed distribution in wind farms[J].Power System Technology,2010,34(9):206-210(in Chinese).
[24]郝正航.双馈风电机组的暂态行为及其对电力系统稳定性影响[D].天津:天津大学,2011.
[25]张宝群,张伯明,吴文传.基于小干扰稳定的双馈感应电机电磁模型降阶分析[J].电力系统自动化,2010,34(10):51-55.Zhang Baoqun,Zhang Boming,Wu Wenchuan.Small signal based reduced electromagnetic model analysis of double fed induction generator[J].Automation of Electric Power Systems,2010,34(10):51-55(in Chinese).
[26]Wu F,Zhang X P,Godfrey K,et al.Modeling and control of wind turbine with doubly fed induction generator[C]//Power Systems Conference and Exposition.Atlanta,USA:IEEE,2006:1404-1409.
[2]Wang K,Crow M L.Numerical simulation of stochastic differential algebraic equations for power system transient stability with random loads[C]//Power and Energy Society General Meeting.Detroit,MI:IEEE,2011:1-8.
[3]Qiu Y,Zhao J,Chiang H D.Effects of the stochastic load model on power system voltage stability based on bifurcation theory[C]//Transmission and Distribution Conference and Exposition.Chicago,USA:IEEE,2008:1-6.
[4]张建勇,鞠平,余一平,等.电力系统在高斯随机小激励下的响应及稳定性[J].中国科学:技术科学,2012,42(7):851-857.Zhang Jianyong,Ju Ping,Yu Yiping,et al.Response and stability ofpower system in Gauss small random excitation[J].China Science:Science and Technology,2012,42(7):851-857(in Chinese).
[5]刘咏飞,鞠平,薛禹胜,等.随机激励下电力系统特性的计算分析[J].电力系统自动化,2014,38(9):137-142.Liu Yongfei,Ju Ping,Xue Yusheng,et al.Calculation analysis on power system characteristics under random excitation[J].Automation of Electric Power Systems,2014,38(9):137-142(in Chinese).
[6]许纹碧,王杰.非线性电力系统随机小干扰稳定性分析[J].电网技术,2014,38(10):2735-2740.Xu Wenbi,Wang Jie.Stochastic small disturbance stability analysis of nonlinear power system[J].Power System Technology,2014,38(10):2735-2740(in Chinese).
[7]Parinya P,Sangswang A,Kirtikara K,et al.A study of impact of wind power to power system stability using stochastic stability index[C]//International Symposium on Circuits and Systems(ISCAS).Melbourne,Australia:IEEE,2014:2656-2659.
[8]周明,元博,张小平,等.基于SDE的含风电电力系统随机小干扰稳定分析[J].中国电机工程学报,2014,34(10):1575-1582.Zhou Ming,Yuan Bo,Zhang Xiaoping,et al.Stochastic small signal stability analysis of wind power integrated power systems based on stochastic differential equations[J].Proceedings of the CSEE,2014,34(10):1575-1582(in Chinese).
[9]苏展,徐谦,孙黎滢,等.含DFIG的电力系统随机建模及小干扰随机稳定分析[J].电网技术,2015,39(9):2404-2410.Su Zhan,Xu Qian,Sun Liying,et al.Stochastic modeling and small signal stability analysis of power systems including DFIG[J].Power System Technology,2015,39(9):2404-2410(in Chinese).
[10]李洪宇,鞠平,余一平,等.随机激励下电力系统有界波动域及域内概率解析分析方法[J].中国电机工程学报,2015,35(14):3561-3568.Li Hongyu,Ju Ping,Yu Yiping,et al.Bounded fluctuations region and analytic method of intra-region probability in power system under stochastic excitations[J].Proceedings of the CSEE,2015,35(14):3561-3568(in Chinese).
[11]Higham D J.An algorithmic introduction to numerical simulation of stochastic differential equations[J].SIAM Review,2001,43(3):525-546.
[12]黄通,王杰.基于改进EEAC法的随机复杂多机系统的暂态稳定性分析[J].电网技术,2017,41(4):1174-1180.Huang Tong,Wang Jie.Transient stability analysis of stochastic complex multi-machine system based on improved extended equalarea criteria[J].Power System Technology,2017,41(4):1174-1180(in Chinese).
[13]周海强,鞠平,薛禹胜,等.基于拟哈密顿理论的随机电力系统暂态稳定性分析[J].电力系统自动化,2016,40(19):9-14.Zhou Haiqiang,Ju Ping,Xue Yusheng,et al.Transient stability analysis of stochastic power system based on quasi-Hamiltonian system theory[J].Automation of Electric Power Systems,2016,40(19):9-14(in Chinese).
[14]蒋长江,刘俊勇,刘友波,等.计及风电随机激励的电力系统暂态稳定分析[J].电力自动化设备,2016,36(3):100-108:Jiang Changjiang,Liu Junyong,Liu Youbo,et al.Transient stability analysis of power system considering wind-power stochastic excitation[J].Electric Power Automation Equipment,2016,36(3):100-108(in Chinese).
[15]马静,高翔,李益楠,等.考虑风速随机特征的多工况电力系统稳定性分析[J].电力自动化设备,2016,36(8):26-32.Ma Jing,Gao Xiang,Li Yinan,et al.Stability analysis considering time-varying wind speed for power system with multiple operating conditions[J].Electric Power Automation Equipment,2016,36(8):26-32(in Chinese).
[16]陆丹,袁越,杨苏.基于马尔可夫链蒙特卡洛法的独立风光柴储微网运行风险评估[J].电网技术,2017,41(3):823-830.Lu Dan,Yuan Yue,Yang Su.Operation risk assessment of islanded wind-PV-diesel-storage microgrid based on Markov chain Monte Carlo method[J].Power System Technology,2017,41(3):823-830(in Chinese).
[17]蒋平,霍雨翀,张龙,等.基于改进一阶马尔可夫链的风速时间序列模型[J].电力系统自动化,2014,38(19):22-27.Jiang Ping,Huo Yuchong,Zhang Long,et al.A wind speed time series model based on advanced first-order Markov chain approach[J].Automation of Electric Power Systems,2014,38(19):22-27(in Chinese).
[18]马静,高翔,李益楠,等.考虑离散马尔可夫模型的多工况电力系统自适应控制策略[J].电网技术,2015,39(10):2856-2861.Ma Jing,Gao Xiang,Li Yinan,et al.Adaptive control strategy considering discrete Markov model for power system with multiple operating conditions[J].Power System Technology,2015,39(10):2856-2861(in Chinese).
[19]马静,高翔,李益楠,等.考虑连锁故障的多工况电力系统功角稳定性分析[J].中国电机工程学报,2016,36(14):3837-3844.Ma Jing,Gao Xiang,Li Yinan,et al.Angle stability analysis of multi-operation power system based on cascading failure[J].Proceedings of the CSEE,2016,36(14):3837-3844(in Chinese).
[20]王要策.马尔科夫切换型随机微分方程的数值稳定性[D].上海:东华大学,2011.
[21]Mao X,Yuan C.Stochastic differential equations with Markovian switching[M].London:Imperial College Press,2006:77-110.
[22]Anderson W J.Continuous-time Markov chains:an applicationsoriented approach[M].New Work:Springer,1991:901-904.
[23]彭虎,郭钰锋,王松岩,等.风电场风速分布特性的模式分析[J].电网技术,2010,34(9):206-210.Peng Hu,Guo Yufeng,Wang Songyan,et al.Pattern analysis on characteristics of wind speed distribution in wind farms[J].Power System Technology,2010,34(9):206-210(in Chinese).
[24]郝正航.双馈风电机组的暂态行为及其对电力系统稳定性影响[D].天津:天津大学,2011.
[25]张宝群,张伯明,吴文传.基于小干扰稳定的双馈感应电机电磁模型降阶分析[J].电力系统自动化,2010,34(10):51-55.Zhang Baoqun,Zhang Boming,Wu Wenchuan.Small signal based reduced electromagnetic model analysis of double fed induction generator[J].Automation of Electric Power Systems,2010,34(10):51-55(in Chinese).
[26]Wu F,Zhang X P,Godfrey K,et al.Modeling and control of wind turbine with doubly fed induction generator[C]//Power Systems Conference and Exposition.Atlanta,USA:IEEE,2006:1404-1409.