多机系统全局相轨线的暂态稳定性分析
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摘要
为了进一步研究电力系统功角暂态稳定的结构特征,该文提出计及无穷远奇点的稳定域定性分析方法,给出相平面上全局相轨线(global phase portraits)的结构分布。首先,给出稳定域和无穷远奇点的理论基础,利用微分流形中子流形同胚变换的不变性,将系统状态轨线映射到Poincaré球面,借助微分方程定性理论求出系统无穷远奇点,分析系统轨线在无穷远处的形态。其次,根据同调性对多机电力系统进行分群与等值处理,通过分析闭轨线、鞍点分界线和无穷远奇点的稳定性,给出全局相平面上的暂态功角稳定域,讨论阻尼系数以及不同故障切除情况对稳定域边界的影响。最后,通过实验验证该方法在电力系统暂态功角稳定域分析中的有效性。
To investigate the structural characteristics of angle transient stability in power systems, a qualitative analysis technique including infinite singularities was proposed in this paper, focused on the stable boundary of the global phase portraits. Firstly, the basic concepts of the stability region and infinite singularities were introduced. The phase portrait was mapped to the Poincaré sphere and the infinite singularities of the differential algebraic equations were solved by the qualitative theory of differential equations and invariant submanifolds in the differential manifold. Secondly, the multi-machine power system was transformed into an equivalent model based on coherency characteristics of rotor angles. By analyzing the separatrix closed trajectories of saddle points and the infinity singularities, the stability region on the global phase plane was described in detail to discuss the influence of damping coefficient, and the stability region boundary under different fault conditions. Finally, the effectiveness of the proposed method in transient stability analysis was invalidated by simulation results.
To investigate the structural characteristics of angle transient stability in power systems, a qualitative analysis technique including infinite singularities was proposed in this paper, focused on the stable boundary of the global phase portraits. Firstly, the basic concepts of the stability region and infinite singularities were introduced. The phase portrait was mapped to the Poincaré sphere and the infinite singularities of the differential algebraic equations were solved by the qualitative theory of differential equations and invariant submanifolds in the differential manifold. Secondly, the multi-machine power system was transformed into an equivalent model based on coherency characteristics of rotor angles. By analyzing the separatrix closed trajectories of saddle points and the infinity singularities, the stability region on the global phase plane was described in detail to discuss the influence of damping coefficient, and the stability region boundary under different fault conditions. Finally, the effectiveness of the proposed method in transient stability analysis was invalidated by simulation results.
引文
[1]Bhui P,Senroy N.Real-time prediction and control of transient stability using transient energy function[J].IEEETransactions on Power Systems,2017,32(2):923-934.
[2]姜惠兰,吴玉璋,周照清,等.含双馈风力发电场的多机系统暂态功角稳定性分析方法[J].中国电机工程学报,2018,38(4):999-1005.Jiang Huilan,Wu Yuzhang,Zhou Zhaoqing,et al.Amethod to analyze the transient angle stability of multi-machine system with DFIG-based wind farm[J].Proceedings of the CSEE,2018,38(4):999-1005(in Chinese).
[3]岑炳成,唐飞,廖清芬,等.应用功角空间降维变换的相轨迹判别系统暂态稳定性[J].中国电机工程学报,2015,35(11):2726-2734.Cen Bingcheng,Tang Fei,Liao Qingfen,et al.Transient stability detection using phase trajectory obtained by dimension reduction transform of power angles[J].Proceedings of the CSEE,2015,35(11):2726-2734(in Chinese).
[4]顾卓远,汤涌,孙华东,等.一种基于转速差-功角差变化趋势的暂态功角稳定辨识方法[J].中国电机工程学报,2013,33(31):65-72.Gu Zhuoyuan,Tang Yong,Sun Huadong,et al.An identification method for power system transient angle stability based on the trend of rotor speed difference-rotor angle difference[J].Proceedings of the CSEE,2013,33(31):65-72(in Chinese).
[5]谢欢,张保会,于广亮,等.基于相轨迹凹凸性的电力系统暂态稳定性识别[J].中国电机工程学报,2006,26(5):38-42.Xie Huan,Zhang Baohui,Yu Guangliang,et al.Power system transient stability detection theory based on characteristic concave or convex of trajectory[J].Proceedings of the CSEE,2006,26(5):38-42(in Chinese).
[6]吴为,饶宏,洪潮,等.利用相平面轨迹特性的暂态稳定控制切机负效应的机理研究[J].中国电机工程学报,2016,36(17):4572-4579.Wu Wei,Rao Hong,Hong Chao,et al.Theoretical research on negative effect problems caused by generator tripping in transient stability control based on trajectory characteristic[J].Proceedings of the CSEE,2016,36(17):4572-4579(in Chinese).
[7]苏福,杨松浩,王怀远,等.电力系统暂态稳定时域仿真快速终止算法研究[J].中国电机工程学报,2017,37(15):4372-4378.Su Fu,Yang Songhao,Wang Huaiyuan,et al.Study on fast termination algorithm of time-domain simulation for power system transient stability[J].Proceedings of the CSEE,2017,37(15):4372-4378(in Chinese).
[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.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(in Chinese).
[9]周艳真,吴俊勇,于之虹,等.基于转子角轨迹簇特征的电力系统暂态稳定评估[J].电网技术,2016,40(5):1482-1487.Zhou Yanzhen,Wu Junyong,Yu Zhihong,et al.Power system transient stability assessment based on cluster features of rotor angle trajectories[J].Power System Technology,2016,40(5):1482-1487(in Chinese).
[10]罗恒,刘涤尘,史秋芸,等.基于暂态能量函数的核电机组接入电网暂态稳定性研究[J].电网技术,2013,37(1):119-125.Luo Heng,Liu Dichen,Shi Qiuyun,et al.Study on transient stability of nuclear power plant connected to power grid based on transient energy function[J].Power System Technology,2013,37(1):119-125(in Chinese).
[11]汪小明,刘涤尘,吴军,等.基于能量函数法的电网暂态稳定性分析[J].电网技术,2011,35(8):114-118.Wang Xiaoming,Liu Dichen,Wu Jun,et al.Energy function-based power system transient stability analysis[J].Power System Technology,2011,35(8):114-118(in Chinese).
[12]Chiang H D,Wu F F,Varaiya P P.A BCU method for direct analysis of power system transient stability[J].IEEETransactions on Power Systems,1994,9(3):1194-1208.
[13]Chu C C,Chiang H D.Boundary properties of the BCUmethod for power system transient stability assessment[C]//Proceedings of 2010 IEEE International Symposium on Circuits and Systems.Paris,France:IEEE:3453-3456.
[14]Theodoro E A R,Alberto L F C,Chiang H D.Energyguided time-domain simulation for critical clearing time reassessment in the TTS-CUEP/BCU method[C]//Proceedings of the 2014 IEEE PES General Meeting|Conference&Exposition.National Harbor,MD,USA:IEEE:1-5.
[15]Bosetti H,Khan S.Transient stability in oscillating multi-machine systems using Lyapunov vectors[J].IEEETransactions on Power Systems,2018,33(2):2078-2086.
[16]Oluic M,Ghandhari M,Berggren B.Methodology for rotor angle transient stability assessment in parameter space[J].IEEE Transactions on Power Systems,2017,32(2):1202-1211.
[17]马静,王上行,王彤,等.基于保护映射理论的电力系统小扰动稳定域计算方法[J].中国电机工程学报,2014,34(28):4897-4905.Ma Jing,Wang Shangxing,Wang Tong,et al.A power system Small Signal Stability Region(SSSR)calculation method based on the guardian map theory[J].Proceedings of the CSEE,2014,34(28):4897-4905(in Chinese).
[18]Chiang H D,Wang Tao.On the number and types of unstable equilibria in nonlinear dynamical systems with uniformly-bounded stability regions[J].IEEE Transactions on Automatic Control,2016,61(2):485-490.
[19]Martínez Y P,Vidal C.Classification of global phase portraits and bifurcation diagrams of Hamiltonian systems with rational potential[J].Journal of Differential Equations,2016,261(11):5923-5948.
[20]Amaral F M,Alberto L F C.Stability region bifurcations of nonlinear autonomous dynamical systems:Type-zero saddle-node bifurcations[J].International Journal of Robust and Nonlinear Control,2011,21(6):591-612.
[21]Wang Tao,Chiang H D.On the number of unstable equilibrium points on spatially-periodic stability boundary[J].IEEE Transactions on Automatic Control,2016,61(9):2553-2558.
[22]张芷芬.微分方程定性理论[M].北京:科学出版社,1985.Zhang Zhifen.Differential equation qualitative theory[M].Beijing:Science Press,1985(in Chinese).
[23]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002.Ni Yixin,Chen Shousun,Zhang Baolin.Theory and analysis of dynamic power system[M].Beijing:Tsinghua University Press,2002(in Chinese).
[24]戴晨松,薛峰,薛禹胜.受扰轨迹的分群研究[J].电力系统自动化,2000,24(1):13-16.Dai Chensong,Xue Feng,Xue Yusheng.Classification of disturbed trajectories[J].Automation of Electric Power Systems,2000,24(1):13-16(in Chinese).
[25]薛峰,丁纯,薛禹胜.数值积分自动终止的算法及其工程应用[J].电力系统自动化,2001,25(20):9-13.Xue Feng,Ding Chun,Xue Yusheng.Early termination algorithm for transient stability analysis[J].Automation of Electric Power Systems,2001,25(20):9-13(in Chinese).
[26]滕林,李万顺,李贵存,等.一种基于摇摆曲线的电力系统同调机群识别新方法[J].电力自动化设备,2002,22(4):18-20.Teng Lin,Li Wanshun,Li Guicun,et al.A new method of coherency identification to disturbed generators based on its swing curves[J].Electric Power Automation Equipment,2002,22(4):18-20(in Chinese).
[27]刘笙,陈陈.电力系统暂态稳定的能量函数分析[M].北京:科学出版社,2014.Liu Sheng,Chen Chen.Energy function analysis of power system transient stability[M].Beijing:Science Press,2014(in Chinese).
[28]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 equal-area criteria[J].Power System Technology,2017,41(4):1174-1180(in Chinese).
[2]姜惠兰,吴玉璋,周照清,等.含双馈风力发电场的多机系统暂态功角稳定性分析方法[J].中国电机工程学报,2018,38(4):999-1005.Jiang Huilan,Wu Yuzhang,Zhou Zhaoqing,et al.Amethod to analyze the transient angle stability of multi-machine system with DFIG-based wind farm[J].Proceedings of the CSEE,2018,38(4):999-1005(in Chinese).
[3]岑炳成,唐飞,廖清芬,等.应用功角空间降维变换的相轨迹判别系统暂态稳定性[J].中国电机工程学报,2015,35(11):2726-2734.Cen Bingcheng,Tang Fei,Liao Qingfen,et al.Transient stability detection using phase trajectory obtained by dimension reduction transform of power angles[J].Proceedings of the CSEE,2015,35(11):2726-2734(in Chinese).
[4]顾卓远,汤涌,孙华东,等.一种基于转速差-功角差变化趋势的暂态功角稳定辨识方法[J].中国电机工程学报,2013,33(31):65-72.Gu Zhuoyuan,Tang Yong,Sun Huadong,et al.An identification method for power system transient angle stability based on the trend of rotor speed difference-rotor angle difference[J].Proceedings of the CSEE,2013,33(31):65-72(in Chinese).
[5]谢欢,张保会,于广亮,等.基于相轨迹凹凸性的电力系统暂态稳定性识别[J].中国电机工程学报,2006,26(5):38-42.Xie Huan,Zhang Baohui,Yu Guangliang,et al.Power system transient stability detection theory based on characteristic concave or convex of trajectory[J].Proceedings of the CSEE,2006,26(5):38-42(in Chinese).
[6]吴为,饶宏,洪潮,等.利用相平面轨迹特性的暂态稳定控制切机负效应的机理研究[J].中国电机工程学报,2016,36(17):4572-4579.Wu Wei,Rao Hong,Hong Chao,et al.Theoretical research on negative effect problems caused by generator tripping in transient stability control based on trajectory characteristic[J].Proceedings of the CSEE,2016,36(17):4572-4579(in Chinese).
[7]苏福,杨松浩,王怀远,等.电力系统暂态稳定时域仿真快速终止算法研究[J].中国电机工程学报,2017,37(15):4372-4378.Su Fu,Yang Songhao,Wang Huaiyuan,et al.Study on fast termination algorithm of time-domain simulation for power system transient stability[J].Proceedings of the CSEE,2017,37(15):4372-4378(in Chinese).
[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.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(in Chinese).
[9]周艳真,吴俊勇,于之虹,等.基于转子角轨迹簇特征的电力系统暂态稳定评估[J].电网技术,2016,40(5):1482-1487.Zhou Yanzhen,Wu Junyong,Yu Zhihong,et al.Power system transient stability assessment based on cluster features of rotor angle trajectories[J].Power System Technology,2016,40(5):1482-1487(in Chinese).
[10]罗恒,刘涤尘,史秋芸,等.基于暂态能量函数的核电机组接入电网暂态稳定性研究[J].电网技术,2013,37(1):119-125.Luo Heng,Liu Dichen,Shi Qiuyun,et al.Study on transient stability of nuclear power plant connected to power grid based on transient energy function[J].Power System Technology,2013,37(1):119-125(in Chinese).
[11]汪小明,刘涤尘,吴军,等.基于能量函数法的电网暂态稳定性分析[J].电网技术,2011,35(8):114-118.Wang Xiaoming,Liu Dichen,Wu Jun,et al.Energy function-based power system transient stability analysis[J].Power System Technology,2011,35(8):114-118(in Chinese).
[12]Chiang H D,Wu F F,Varaiya P P.A BCU method for direct analysis of power system transient stability[J].IEEETransactions on Power Systems,1994,9(3):1194-1208.
[13]Chu C C,Chiang H D.Boundary properties of the BCUmethod for power system transient stability assessment[C]//Proceedings of 2010 IEEE International Symposium on Circuits and Systems.Paris,France:IEEE:3453-3456.
[14]Theodoro E A R,Alberto L F C,Chiang H D.Energyguided time-domain simulation for critical clearing time reassessment in the TTS-CUEP/BCU method[C]//Proceedings of the 2014 IEEE PES General Meeting|Conference&Exposition.National Harbor,MD,USA:IEEE:1-5.
[15]Bosetti H,Khan S.Transient stability in oscillating multi-machine systems using Lyapunov vectors[J].IEEETransactions on Power Systems,2018,33(2):2078-2086.
[16]Oluic M,Ghandhari M,Berggren B.Methodology for rotor angle transient stability assessment in parameter space[J].IEEE Transactions on Power Systems,2017,32(2):1202-1211.
[17]马静,王上行,王彤,等.基于保护映射理论的电力系统小扰动稳定域计算方法[J].中国电机工程学报,2014,34(28):4897-4905.Ma Jing,Wang Shangxing,Wang Tong,et al.A power system Small Signal Stability Region(SSSR)calculation method based on the guardian map theory[J].Proceedings of the CSEE,2014,34(28):4897-4905(in Chinese).
[18]Chiang H D,Wang Tao.On the number and types of unstable equilibria in nonlinear dynamical systems with uniformly-bounded stability regions[J].IEEE Transactions on Automatic Control,2016,61(2):485-490.
[19]Martínez Y P,Vidal C.Classification of global phase portraits and bifurcation diagrams of Hamiltonian systems with rational potential[J].Journal of Differential Equations,2016,261(11):5923-5948.
[20]Amaral F M,Alberto L F C.Stability region bifurcations of nonlinear autonomous dynamical systems:Type-zero saddle-node bifurcations[J].International Journal of Robust and Nonlinear Control,2011,21(6):591-612.
[21]Wang Tao,Chiang H D.On the number of unstable equilibrium points on spatially-periodic stability boundary[J].IEEE Transactions on Automatic Control,2016,61(9):2553-2558.
[22]张芷芬.微分方程定性理论[M].北京:科学出版社,1985.Zhang Zhifen.Differential equation qualitative theory[M].Beijing:Science Press,1985(in Chinese).
[23]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002.Ni Yixin,Chen Shousun,Zhang Baolin.Theory and analysis of dynamic power system[M].Beijing:Tsinghua University Press,2002(in Chinese).
[24]戴晨松,薛峰,薛禹胜.受扰轨迹的分群研究[J].电力系统自动化,2000,24(1):13-16.Dai Chensong,Xue Feng,Xue Yusheng.Classification of disturbed trajectories[J].Automation of Electric Power Systems,2000,24(1):13-16(in Chinese).
[25]薛峰,丁纯,薛禹胜.数值积分自动终止的算法及其工程应用[J].电力系统自动化,2001,25(20):9-13.Xue Feng,Ding Chun,Xue Yusheng.Early termination algorithm for transient stability analysis[J].Automation of Electric Power Systems,2001,25(20):9-13(in Chinese).
[26]滕林,李万顺,李贵存,等.一种基于摇摆曲线的电力系统同调机群识别新方法[J].电力自动化设备,2002,22(4):18-20.Teng Lin,Li Wanshun,Li Guicun,et al.A new method of coherency identification to disturbed generators based on its swing curves[J].Electric Power Automation Equipment,2002,22(4):18-20(in Chinese).
[27]刘笙,陈陈.电力系统暂态稳定的能量函数分析[M].北京:科学出版社,2014.Liu Sheng,Chen Chen.Energy function analysis of power system transient stability[M].Beijing:Science Press,2014(in Chinese).
[28]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 equal-area criteria[J].Power System Technology,2017,41(4):1174-1180(in Chinese).
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