基于临界转变理论的电力系统电压稳定分析与预警
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摘要
针对电力系统中面临的电压稳定问题,提出一种基于临界转变理论的电压失稳评估与预警方法。通过数学推导,证明了系统在接近电压失稳的过程中,系统的非线性度不断增强,系统变量由于随机扰动导致与稳态量的偏差离散度逐渐增大,外在表现为系统变量方差的单调增大。同时,推导出系统变量方差与驱动参数之间的标度律关系。实际应用时,利用实测数据对标度律进行简单的非线性拟合,即可快速估算出电压失稳点,为调度人员提供辅助决策信息。该文还分析所提方法与传统特征分析法的一致性。在2机3节点仿真系统中的仿真结果验证了提出方法的有效性。在没有详细系统模型或模型参数不准确时,常规基于模型的方法适用性有限。而该文提出的方法基于量测数据,能时刻跟踪系统当前状态,具有广阔的应用前景。
In order to address the long-term voltage instability problems in power systems, this paper proposed a voltage stability assessment and prediction method based on the critical transition theory. In this paper, it is proven rigorously that as the system approaches the collapse point, the system nonlinearity will dominate so that the variance of the deviation will increase dramatically. In addition, this paper has derived the relationship between the variance and the bifurcation parameter to make the collapse point forecasting possible. This paper has also found the consistency between the proposed method and the largely used eigen-analysis method. The simulation results on a two machines three buses and a ten machines thirty-nine buses power system model have verified the derivation. The method is totally based on measured data so that it is relatively quick and has the potential to be implemented in real world applications since the real power system model is unavailable or the parameter is inaccurate.
In order to address the long-term voltage instability problems in power systems, this paper proposed a voltage stability assessment and prediction method based on the critical transition theory. In this paper, it is proven rigorously that as the system approaches the collapse point, the system nonlinearity will dominate so that the variance of the deviation will increase dramatically. In addition, this paper has derived the relationship between the variance and the bifurcation parameter to make the collapse point forecasting possible. This paper has also found the consistency between the proposed method and the largely used eigen-analysis method. The simulation results on a two machines three buses and a ten machines thirty-nine buses power system model have verified the derivation. The method is totally based on measured data so that it is relatively quick and has the potential to be implemented in real world applications since the real power system model is unavailable or the parameter is inaccurate.
引文
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[15]陈磊,闵勇.发电机无功极限诱导分岔的机理分析及预防策略[J].中国电机工程学报,2008,28(12):14-19.Chen Lei,Min Yong.Mechanism analysis and preventive measures investigation of generator reactive power limit induced bifurcation[J].Proceedings of the CSEE,2008,28(12):6-10(in Chinese).
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[17]Veraart A J,Faassen E J,Dakos V,et al.Recovery rates reflect distance to a tipping point in a living system[J].Nature,2012,481(7381):357-361.
[18]Dakos V,van Nes E H,Donangelo R,et al.Spatial correlation as leading indicator of catastrophic shifts[J].Theoretical Ecology,2010,3(3):163-174.
[19]Dakos V,Scheffer M,van Nes E H,et al.Slowing down as an early warning signal for abrupt climate change[J].Proceedings of the National Academy of Sciences of the United States of America,2008,105(38):14308-14312.
[20]Kuehn C.A mathematical framework for critical transitions:bifurcations,fast-slow systems and stochastic dynamics[J].Physica D:Nonlinear Phenomena,2011,240(12):1020-1035.
[21]Kuehn C.A mathematical framework for critical transitions:normal forms,variance and applications[J].Journal of Nonlinear Science,2013,23(3):457-510.
[22]Venkatasubramanian V,Schattler H,Zaborszky J.Local bifurcations and feasibility regions in differentialalgebraic systems[J].IEEE Transactions on Automatic Control,1995,40(14):1992-2013.
[23]Berglund N,Gentz B.Noise-induced phenomena in slow-fast dynamical systems[M].New York:Springer,2006:89,190.
[24]Gardiner C W.Handbook of stochastic methods for physics,chemistry and the natural sciences[M].Heidelberg:Springer,1983:106.
[25]Higham D J.An algorithmic introduction to numerical simulation of stochastic differential equations[J].SIAMReview,2001,43(5):525-546.
[2]Van Cutsem T,Vournas C.Voltage stability of electric power systems[M].New York:Springer,1998:3-268.
[3]Sinha A,Hazarika D.Comparative study of voltage stability indices in a power system[J].International Journal of Electrical Power&Energy Systems,2000,22(8):589-596.
[4]Gubina F,Strmcnik B.Voltage collapse proximity index determination using voltage phasors approach[J].IEEETransactions on Power Systems,1995,10(2):788-793.
[5]Ajjarapu V,Christy C.The continuation power flow:a tool for steady state voltage stability analysis[J].IEEETransactions on Power Systems,1992,7(1):416-423.
[6]Xie Le,Chen Yang,Liao Huaiwei.Distributed online monitoring of quasi-static voltage collapse in multi-area power systems[J].IEEE Transaction on Power Systems,2012,27(4):2271-2279.
[7]Wen Xiaoyu,Ajjarapu V.Application of a novel eigenvalue trajectory tracing method to identify both oscillatory stability margin and damping margin[J].IEEETransactions on Power Systems,2006,21(2):817-824.
[8]Yang Dan,Ajjarapu V.Critical eigenvalues tracing for power system analysis via continuation of invariant subspaces and projected arnoldi method[J].IEEETransactions on Power Systems,2007,22(1):324-332.
[9]刘益青,陈超英,梁磊,等.电力系统电压稳定性的动态分析方法综述[J].电力系统及其自动化学报,2003,15(1):105-108.Liu Yiqing,Chen Chaoying,Liang Lei,et al.Review of dynamical analysis art of voltage stability in power systems[J].Proceedings of the EPSA,2003,15(1):105-108(in Chinese).
[10]徐泰山,鲍颜红,薛禹胜,等.中期电压稳定的快速仿真算法研究[J].电力系统自动化,2000,24(24):9-11.Xu Taishan,Bao Yanhong,Xue Yusheng,et al.A fast simulation method for mid-term voltage stability[J].Automation of Electric Power Systems,2000,24(24):9-11(in Chinese).
[11]Dobson I,Chiang H D.Towards a theory of voltage collapse in electric power systems[J].Systems&Control Letters,1989,13(3):253-262.
[12]Ajjarapu V,Lee B.Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system[J].IEEE Transactions on Power Systems,1992,7(1):424-431.
[13]Ca?izares C.Conditions for saddle-node bifurcations in AC/DC power systems[J].International Journal of Electrical Power&Energy Systems,1995,17(1):61-68.
[14]贾宏杰,余贻鑫,李鹏.电力系统环面分岔与混沌现象[J].中国电机工程学报,2002,22(8):6-10.Jia Hongjie,Yu Yixin,Li Peng.Torus bifurcation and chaos in power systems[J].Proceedings of the CSEE,2002,22(8):6-10(in Chinese).
[15]陈磊,闵勇.发电机无功极限诱导分岔的机理分析及预防策略[J].中国电机工程学报,2008,28(12):14-19.Chen Lei,Min Yong.Mechanism analysis and preventive measures investigation of generator reactive power limit induced bifurcation[J].Proceedings of the CSEE,2008,28(12):6-10(in Chinese).
[16]Scheffer M,Bascompte J,Brock W A,et al.Earlywarning signals for critical transitions[J].Nature,2009,461(7260):53-59.
[17]Veraart A J,Faassen E J,Dakos V,et al.Recovery rates reflect distance to a tipping point in a living system[J].Nature,2012,481(7381):357-361.
[18]Dakos V,van Nes E H,Donangelo R,et al.Spatial correlation as leading indicator of catastrophic shifts[J].Theoretical Ecology,2010,3(3):163-174.
[19]Dakos V,Scheffer M,van Nes E H,et al.Slowing down as an early warning signal for abrupt climate change[J].Proceedings of the National Academy of Sciences of the United States of America,2008,105(38):14308-14312.
[20]Kuehn C.A mathematical framework for critical transitions:bifurcations,fast-slow systems and stochastic dynamics[J].Physica D:Nonlinear Phenomena,2011,240(12):1020-1035.
[21]Kuehn C.A mathematical framework for critical transitions:normal forms,variance and applications[J].Journal of Nonlinear Science,2013,23(3):457-510.
[22]Venkatasubramanian V,Schattler H,Zaborszky J.Local bifurcations and feasibility regions in differentialalgebraic systems[J].IEEE Transactions on Automatic Control,1995,40(14):1992-2013.
[23]Berglund N,Gentz B.Noise-induced phenomena in slow-fast dynamical systems[M].New York:Springer,2006:89,190.
[24]Gardiner C W.Handbook of stochastic methods for physics,chemistry and the natural sciences[M].Heidelberg:Springer,1983:106.
[25]Higham D J.An algorithmic introduction to numerical simulation of stochastic differential equations[J].SIAMReview,2001,43(5):525-546.