电力系统稳定性的直接法分析
|
摘要
区域电网间的互联及电力市场的发展使得电力系统稳定问题日益严重,传统的电力系统稳定分析方法越来越不能满足现代电网的要求。为了能够可靠、快速地分析电力系统稳定性,需要探索研究新的稳定分析方法,也需要对已有的方法不断进行完善。论文对直接法在电力系统小扰动稳定和暂态稳定分析中的应用进行研究。主要成果如下：
将直接法引入电力系统小扰动稳定分析,主要解决了3个问题：(1)研究高阶系统李雅普诺夫方程的求解算法,分析对比了多种算法,重点剖析了matlab中的lyap命令所采用的算法,确认这一分解算法无论是可靠性和计算速度都可以基本满足电力系统小扰动稳定计算的要求；(2)从理论和算例上证明了直接法与特征值法在电力系统小扰动稳定性判定上的一致性,即李雅普诺夫方程解矩阵的定号性与系统特征根实部正负的一致性；(3)引入状态偏差平方积分指标对电力系统小扰动动态过程进行评价,并推导了计算功角偏差量平方积分指标的算式。应用该评价方法与特征值最小阻尼比评价方法相比较,发现在有的情况下二者不尽一致,状态偏差量平方积分指标较机电模式最小阻尼比能够更全面地评价系统的动态性能。
在电力系统暂态稳定方面,研究了稳定性的定性和定量分析两方面的问题：(1)将时域仿真法与直接法相结合的混合法用于暂态稳定定性判断,在仿真过程中根据系统功角状态量及暂态能量的变化特点给出积分终止的判据,可快速地终止仿真、完成系统稳定性的判断；(2)将混合法积分终止点提供的摇摆信息尝试应用于机组分群,基于EEAC法将多机系统最终等值为一个单机无穷大系统,再运用等面积定则计算系统的稳定度指标及故障临界切除时间,实现了系统稳定性的定量分析,算例表明了该方法的有效性。
Power system stability is becoming increasingly serious with connection of regional power grid and development of electricity market, traditional methods of power system stability can not meet the requirements of the modern power grid. In order to analyze power system stability reliably and quickly, new method of stability analysis need to be research, and the existing methods also need to continuously improve. Application of direct method in power system small signal stability and transient stability has been studied. Major results are as follow:
The direct method has been introduced to power system small signal stability, three problems has been solved:(1) method for solving the lyapunov equation of high order system has been studied, several methods has been analyzed and compared, algorithm of command lyap in matlab has been analyzed, this algorithm can meet the requirements of power system small signal stability reliability and rapidity; (2) consistency of direct method and eigenvalue method in stability judgment that between positive definite of lyapnov equation's solution and negative definite of the eigenvalue's real part has been proved from theory and examples; (3) square integral of state deviation indicators has been introduced to evaluate the dynamic process of power system small signal, the formula to calculate the square integral indicators of angle deviation has been derived. Comparison between this method and the minimum damping in eigenvalue method show that they were not consistent in some cases, the square integral indicators of the state deviation in direct method can evaluate the system dynamic performance more comprehensive than the electromechanical mode minimum damping ratio in eigenvalue method.
In power system transient stability, qualitative and quantitative analysis of transient stability has been studied:(1) hybrid method which combined simulation method and direct method has been used to judge transient stability, the termination criterion of integral has been given in the simulation process based on the change characteristics of the power-angle state variables and the transient energy, simulation can be terminated quickly to complete the judgment of system stability; (2) the swing information of termination points in hybrid method has been attempted to use in unit grouping, multi-machine system has been equivalence to a single infinite-bus system based on EEAC method, stability index and fault critical clearing time can be obtained by equal area criteria, quantitative analysis of system stability has been achieved, the example shows the effectiveness of the method.
将直接法引入电力系统小扰动稳定分析,主要解决了3个问题：(1)研究高阶系统李雅普诺夫方程的求解算法,分析对比了多种算法,重点剖析了matlab中的lyap命令所采用的算法,确认这一分解算法无论是可靠性和计算速度都可以基本满足电力系统小扰动稳定计算的要求；(2)从理论和算例上证明了直接法与特征值法在电力系统小扰动稳定性判定上的一致性,即李雅普诺夫方程解矩阵的定号性与系统特征根实部正负的一致性；(3)引入状态偏差平方积分指标对电力系统小扰动动态过程进行评价,并推导了计算功角偏差量平方积分指标的算式。应用该评价方法与特征值最小阻尼比评价方法相比较,发现在有的情况下二者不尽一致,状态偏差量平方积分指标较机电模式最小阻尼比能够更全面地评价系统的动态性能。
在电力系统暂态稳定方面,研究了稳定性的定性和定量分析两方面的问题：(1)将时域仿真法与直接法相结合的混合法用于暂态稳定定性判断,在仿真过程中根据系统功角状态量及暂态能量的变化特点给出积分终止的判据,可快速地终止仿真、完成系统稳定性的判断；(2)将混合法积分终止点提供的摇摆信息尝试应用于机组分群,基于EEAC法将多机系统最终等值为一个单机无穷大系统,再运用等面积定则计算系统的稳定度指标及故障临界切除时间,实现了系统稳定性的定量分析,算例表明了该方法的有效性。
Power system stability is becoming increasingly serious with connection of regional power grid and development of electricity market, traditional methods of power system stability can not meet the requirements of the modern power grid. In order to analyze power system stability reliably and quickly, new method of stability analysis need to be research, and the existing methods also need to continuously improve. Application of direct method in power system small signal stability and transient stability has been studied. Major results are as follow:
The direct method has been introduced to power system small signal stability, three problems has been solved:(1) method for solving the lyapunov equation of high order system has been studied, several methods has been analyzed and compared, algorithm of command lyap in matlab has been analyzed, this algorithm can meet the requirements of power system small signal stability reliability and rapidity; (2) consistency of direct method and eigenvalue method in stability judgment that between positive definite of lyapnov equation's solution and negative definite of the eigenvalue's real part has been proved from theory and examples; (3) square integral of state deviation indicators has been introduced to evaluate the dynamic process of power system small signal, the formula to calculate the square integral indicators of angle deviation has been derived. Comparison between this method and the minimum damping in eigenvalue method show that they were not consistent in some cases, the square integral indicators of the state deviation in direct method can evaluate the system dynamic performance more comprehensive than the electromechanical mode minimum damping ratio in eigenvalue method.
In power system transient stability, qualitative and quantitative analysis of transient stability has been studied:(1) hybrid method which combined simulation method and direct method has been used to judge transient stability, the termination criterion of integral has been given in the simulation process based on the change characteristics of the power-angle state variables and the transient energy, simulation can be terminated quickly to complete the judgment of system stability; (2) the swing information of termination points in hybrid method has been attempted to use in unit grouping, multi-machine system has been equivalence to a single infinite-bus system based on EEAC method, stability index and fault critical clearing time can be obtained by equal area criteria, quantitative analysis of system stability has been achieved, the example shows the effectiveness of the method.
引文
[1]郑宝森,郭日彩.中国互联电网的发展[J].电网技术,2003,27(2)：1-3
[2]曾德文.全国电力系统联网的基本格局及其分析[J].中国电力,1999,932(10):29-33
[3]周孝信.研究开发面向21世纪的电力系统技术[J].电网技术,1997,21(11)：11-15
[4]周小谦,丁功扬,郭日彩.三峡电力系统的形成和发展[J].电网技术,1998,22(3)：1-3,10
[5]丁功扬.三峡电站的特点、特性及其在系统中的地位和作用[J].电网技术,2000,24(8)：1-4
[6]胡学浩.美加联合电网大面积停电事故的反思和启示[J].电网技术,2003,27(9)：T2-T6
[7]周孝信,郑建超,沈国荣等.从美加东北部电网大面积停电事故中吸取教训[J].电网技术,2003,27(9)：T1
[8]王康,金宇清,甘德强等.电力系统小信号稳定分析与控制综述[J].电力自动化设备,2009,29(5)：10-19
[9]王锡凡,方万良,杜正春.现代电力系统分析[M].北京：科学出版社,2003
[10]徐光虎,苏寅生,孙衢等.基于特征值分析法的PSS最佳安装地点的确定[J].继电器,2004,32(8)：1-4
[11]罗国俊,徐显华,龙绍清等.广东-香港联网系统的低频振荡[J].中国电机工程学报,1986,6(1)：29-35
[12]王海风,陈珩,李乃湖等.多机电力系统中灵活交流输电稳定器安装地点和反馈信号选择的降阶模态分析法[J].中国电机工程学报,1998,18(6)：399-404
[13]律方成,王亚玲,杨以涵等TCSC阻尼系统低频振荡的控制策略分析[J].电力系统自动化,1998,22(7)：23-27
[14]Watkins D S. Forward stability and transmission of shifts in the QR algorithm[J]. SIAM,1995,16(2):469-487
[15]L.Rouco, I.J.Perez-Arriaga. Multi-area Analysis of Small Signal Stability in Large Electric Power System by SMA[J].IEEE Trans on PWRS,1993,8(3):1257-1265
[16]Byerly R T, Bennon R J, Sherman D E. Eigenvalue Analysis of Synchronizing Power Flow Oscillations in Large Electric Power System[J]. IEEE Trans on PAS,1982,101(9):3117-3134
[17]Naoyuki Uchida, Taiji Nagao. A New Eigen-Analysis Method of Steady-State Stability Studies for Large Power Systems:S Matrix Method[J].IEEE Trans. on PWRS, 1988,3(2):706-714
[18]谷寒雨,陈陈.一种新的大型电力系统低频机电模式计算方法[J].中国电机工程学报,2000,20(9)：50-54
[19]徐贤,万秋兰.低频振荡模式选择法的再改进[J].电力系统自动化,2003,27(17):23-25
[20]刘豹.现代控制理论(第2版)[M].北京：机械工业出版社,2000
[21]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
[22]余贻鑫,陈礼义.电力系统的安全性与稳定性[M].北京：科学出版社,1988
[23]Magnusson P.C. The Transient-energy Method of Calculating Stability[J]. T-AIEE,1947, 66(1):747-755
[24]Magnusson P.C. Transients in Coupled Inductance-Capacitance Circuits Analyzed in Terms of a Rolling-Ball Analogue[J]. T-AIEE.1950,69(2):1525-1530
[25]Ayllett P D. The Energy Integral Criterion of Transient Stability Limits of Power Systems[J]. Proceedings of Iee,1958,105(8):527-536
[26]Gless G E. Direct Method of Liapunov Applied to Transient Power System Stability[J]. IEEE Trans. PAS,1966,PAS-85(2):159-168
[27]El-Abiad A, Nagappan H K. Transient Stability Regions of Multimachine Power System[J]. IEEE Trans. PAS,1966, PAS-85(2):169-178
[28]Athay T, Podmore R, Virmani S. A Practical Method for the Direct Analysis of Transient Stability[J]. IEEE Trans. PAS,1979, PAS-98(2):573-584
[29]Kakimoto N, Ohsawa Y, Hayashi M. Transient Stability Analysis of Multimachine Power System with Field Flux Decays via Lyapunov's Direct Method[J], IEEE Trans.PAS, 1980,PAS-99(5):1819-1827
[30]Michel A N, Fouad A A, Vittal V Power System Transient Stability Using Individual Machine Energy Functions[J]. IEEE Trans.1983,30(5)266-276
[31]Chiang H D, Wu F F, Varaiya P P. Foundations of Direct Methods for Power System Transient Stability Analysis[J]. IEEE Trans.1987,34(2):160-173
[32]Chiang H D, Wu F F,Varaiya P P. Foundations of The Potential Energy Boundary Surface Method for Power System Transient Stability Analysis[J]. IEEE Trans.1988,35(6):712-718
[33]Chiang H D, Wu F F, Varaiya P P. A BCU method for direct analysis of power system transient stability [J]. IEEE Trans.1994,9(3):1194-1208
[34]Xue Y, Cutsem T V,Ribbens-Pavella V. A simple direct method for fast transient stability assessment of large power systems [J]. IEEE Trans.1988,3(2):400-412
[35]石恒初,严正.基于时域仿真的暂态稳定裕度研究现状分析[J].华东电力,2008.36(1)：76-80
[36]Xia Daozhi, heydt G. T. On-Line Transient Stability Evaluation by System Decomposition-Aggregation and High Order Derivatives [J]. IEEE Trans. PAS. 1983,104(2)2038-2054
[37]杜正春,甘德强,刘玉田等.电力系统在线动态安全评价的一种快速数值积分方法[J].中国电机工程学报.1996,16(1)29-32
[38]郭志忠,周文东,柳焯等.电力系统暂态稳定的快速时域仿真判定法[J].电工技术学报,1994,8(2)：47-49
[39]林曦,薛峰等.广西电网在线动态安全性分析系统[C].中国科协2004年学术年会电力分会场暨中国电机工程学会2004年学术年会论文集,中国海南.
[40]林曦,高文建等.广西电网在线动态安全性分析系统[C].广西电机工程学会第八届青年学术年会论文集,2004
[41]房大中,周保荣等.修正的暂态能量裕度评估策略[J].中国电机工程学报,2002,22(3)：94-98.
[42]房大中,池云莉.归一化能量函数在河南电网暂态稳定性评估中的应用[J].电网技术,2003,27(3)：18-22
[43]房大中,张尧等.修正的暂态能量函数及其在电力系统稳定性分析中的应用[J].中国电机工程学报,1998,18(3)200-203
[44]常辉,刘文颖,行舟等.电力系统暂态稳定计算的在线应用[J].电网技术,2007
[45]孙闻,房大中,薛振宇.电力系统在线暂态稳定分析方法[J].电网技术,2009
[46]阮前途,刘笙.上海电网暂态稳定的能量函数分析[J].电力系统自动化,1995,19(8)20-23
[47]蔡斌,吴素农,王诗明等.电网在线安全稳定分析和预警系统[J].电网技术,2007,31(2)：36-41
[48]高维新.李雅普诺夫函数的造法[J].北京大学学报,1962/3212-225
[49]Bartels. R. H, G. W. Stewart. Solution of the Matrix Equation AX+XB= C[C]. Comm. of the ACM,1972,15(9),820-826
[50]贾继灏,马丽丽,刘宪林.基于等值单机无穷大系统的多机系统PSS设计[J].电力系统保护与控制,2009,37(23)：70-74
[51]赵书强,常鲜戎,贺仁睦等.PSS控制过程中的借阻尼现象与负阻尼效应[J].中国电机工程学报,2004,24(5)：7-11
[52]王宗义,余志文,郭志忠.混合法暂态稳定实用计算的几点改进[J].继电器,2008,36(11)：37-41
[53]刘宪林.基于同步机和水系统详细模型的电力系统小扰动稳定研究[D].哈尔滨工业大学,2002
[54]安德逊M,佛阿德A A.电力系统的控制与稳定翻译组译,电力系统的控制与稳定(第一卷)[M].北京：水利电力出版社,1979
[55]傅书逷,倪以信,薛禹胜.直接法稳定分析[M].北京：中国电力出版社.1999
[56]阙志宏.线性系统理论[M].西安：西北工业大学出版社.1995
[57]赵国良,曲军.李雅普诺夫方程的一个计算机解法—分解矩阵合并同类项法[J].自动化技术与应用,1985/0247-51
[58]黄琳,郑应平,张迪.李雅普诺夫第二方法与最优控制器分析设计问题[J].自动化学报,1964,2(4)202-218
[59]韩英铎,王仲鸿,陈淮金.电力系统最优分散协调控制[M].北京：清华大学出版社,1997
[60]薛禹胜.不可积项和临界能量--关于暂态能量函数的几点注释[J].电力系统自动化,1991.01：16-21
[61]薛禹胜.再论暂态能量函数和临界能量[J].电力系统自动化1991.06：9-18
[62]薛禹胜.暂态能量校正和临界群识别—三论暂态能量函数直接法[J].电力系统自动化,1993,17(1)：22-31
[63]薛禹胜.失稳模式变化的机理—五论暂态能量函数直接法[J].电力系统自动化,1994,18(10)：11-24
[2]曾德文.全国电力系统联网的基本格局及其分析[J].中国电力,1999,932(10):29-33
[3]周孝信.研究开发面向21世纪的电力系统技术[J].电网技术,1997,21(11)：11-15
[4]周小谦,丁功扬,郭日彩.三峡电力系统的形成和发展[J].电网技术,1998,22(3)：1-3,10
[5]丁功扬.三峡电站的特点、特性及其在系统中的地位和作用[J].电网技术,2000,24(8)：1-4
[6]胡学浩.美加联合电网大面积停电事故的反思和启示[J].电网技术,2003,27(9)：T2-T6
[7]周孝信,郑建超,沈国荣等.从美加东北部电网大面积停电事故中吸取教训[J].电网技术,2003,27(9)：T1
[8]王康,金宇清,甘德强等.电力系统小信号稳定分析与控制综述[J].电力自动化设备,2009,29(5)：10-19
[9]王锡凡,方万良,杜正春.现代电力系统分析[M].北京：科学出版社,2003
[10]徐光虎,苏寅生,孙衢等.基于特征值分析法的PSS最佳安装地点的确定[J].继电器,2004,32(8)：1-4
[11]罗国俊,徐显华,龙绍清等.广东-香港联网系统的低频振荡[J].中国电机工程学报,1986,6(1)：29-35
[12]王海风,陈珩,李乃湖等.多机电力系统中灵活交流输电稳定器安装地点和反馈信号选择的降阶模态分析法[J].中国电机工程学报,1998,18(6)：399-404
[13]律方成,王亚玲,杨以涵等TCSC阻尼系统低频振荡的控制策略分析[J].电力系统自动化,1998,22(7)：23-27
[14]Watkins D S. Forward stability and transmission of shifts in the QR algorithm[J]. SIAM,1995,16(2):469-487
[15]L.Rouco, I.J.Perez-Arriaga. Multi-area Analysis of Small Signal Stability in Large Electric Power System by SMA[J].IEEE Trans on PWRS,1993,8(3):1257-1265
[16]Byerly R T, Bennon R J, Sherman D E. Eigenvalue Analysis of Synchronizing Power Flow Oscillations in Large Electric Power System[J]. IEEE Trans on PAS,1982,101(9):3117-3134
[17]Naoyuki Uchida, Taiji Nagao. A New Eigen-Analysis Method of Steady-State Stability Studies for Large Power Systems:S Matrix Method[J].IEEE Trans. on PWRS, 1988,3(2):706-714
[18]谷寒雨,陈陈.一种新的大型电力系统低频机电模式计算方法[J].中国电机工程学报,2000,20(9)：50-54
[19]徐贤,万秋兰.低频振荡模式选择法的再改进[J].电力系统自动化,2003,27(17):23-25
[20]刘豹.现代控制理论(第2版)[M].北京：机械工业出版社,2000
[21]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
[22]余贻鑫,陈礼义.电力系统的安全性与稳定性[M].北京：科学出版社,1988
[23]Magnusson P.C. The Transient-energy Method of Calculating Stability[J]. T-AIEE,1947, 66(1):747-755
[24]Magnusson P.C. Transients in Coupled Inductance-Capacitance Circuits Analyzed in Terms of a Rolling-Ball Analogue[J]. T-AIEE.1950,69(2):1525-1530
[25]Ayllett P D. The Energy Integral Criterion of Transient Stability Limits of Power Systems[J]. Proceedings of Iee,1958,105(8):527-536
[26]Gless G E. Direct Method of Liapunov Applied to Transient Power System Stability[J]. IEEE Trans. PAS,1966,PAS-85(2):159-168
[27]El-Abiad A, Nagappan H K. Transient Stability Regions of Multimachine Power System[J]. IEEE Trans. PAS,1966, PAS-85(2):169-178
[28]Athay T, Podmore R, Virmani S. A Practical Method for the Direct Analysis of Transient Stability[J]. IEEE Trans. PAS,1979, PAS-98(2):573-584
[29]Kakimoto N, Ohsawa Y, Hayashi M. Transient Stability Analysis of Multimachine Power System with Field Flux Decays via Lyapunov's Direct Method[J], IEEE Trans.PAS, 1980,PAS-99(5):1819-1827
[30]Michel A N, Fouad A A, Vittal V Power System Transient Stability Using Individual Machine Energy Functions[J]. IEEE Trans.1983,30(5)266-276
[31]Chiang H D, Wu F F, Varaiya P P. Foundations of Direct Methods for Power System Transient Stability Analysis[J]. IEEE Trans.1987,34(2):160-173
[32]Chiang H D, Wu F F,Varaiya P P. Foundations of The Potential Energy Boundary Surface Method for Power System Transient Stability Analysis[J]. IEEE Trans.1988,35(6):712-718
[33]Chiang H D, Wu F F, Varaiya P P. A BCU method for direct analysis of power system transient stability [J]. IEEE Trans.1994,9(3):1194-1208
[34]Xue Y, Cutsem T V,Ribbens-Pavella V. A simple direct method for fast transient stability assessment of large power systems [J]. IEEE Trans.1988,3(2):400-412
[35]石恒初,严正.基于时域仿真的暂态稳定裕度研究现状分析[J].华东电力,2008.36(1)：76-80
[36]Xia Daozhi, heydt G. T. On-Line Transient Stability Evaluation by System Decomposition-Aggregation and High Order Derivatives [J]. IEEE Trans. PAS. 1983,104(2)2038-2054
[37]杜正春,甘德强,刘玉田等.电力系统在线动态安全评价的一种快速数值积分方法[J].中国电机工程学报.1996,16(1)29-32
[38]郭志忠,周文东,柳焯等.电力系统暂态稳定的快速时域仿真判定法[J].电工技术学报,1994,8(2)：47-49
[39]林曦,薛峰等.广西电网在线动态安全性分析系统[C].中国科协2004年学术年会电力分会场暨中国电机工程学会2004年学术年会论文集,中国海南.
[40]林曦,高文建等.广西电网在线动态安全性分析系统[C].广西电机工程学会第八届青年学术年会论文集,2004
[41]房大中,周保荣等.修正的暂态能量裕度评估策略[J].中国电机工程学报,2002,22(3)：94-98.
[42]房大中,池云莉.归一化能量函数在河南电网暂态稳定性评估中的应用[J].电网技术,2003,27(3)：18-22
[43]房大中,张尧等.修正的暂态能量函数及其在电力系统稳定性分析中的应用[J].中国电机工程学报,1998,18(3)200-203
[44]常辉,刘文颖,行舟等.电力系统暂态稳定计算的在线应用[J].电网技术,2007
[45]孙闻,房大中,薛振宇.电力系统在线暂态稳定分析方法[J].电网技术,2009
[46]阮前途,刘笙.上海电网暂态稳定的能量函数分析[J].电力系统自动化,1995,19(8)20-23
[47]蔡斌,吴素农,王诗明等.电网在线安全稳定分析和预警系统[J].电网技术,2007,31(2)：36-41
[48]高维新.李雅普诺夫函数的造法[J].北京大学学报,1962/3212-225
[49]Bartels. R. H, G. W. Stewart. Solution of the Matrix Equation AX+XB= C[C]. Comm. of the ACM,1972,15(9),820-826
[50]贾继灏,马丽丽,刘宪林.基于等值单机无穷大系统的多机系统PSS设计[J].电力系统保护与控制,2009,37(23)：70-74
[51]赵书强,常鲜戎,贺仁睦等.PSS控制过程中的借阻尼现象与负阻尼效应[J].中国电机工程学报,2004,24(5)：7-11
[52]王宗义,余志文,郭志忠.混合法暂态稳定实用计算的几点改进[J].继电器,2008,36(11)：37-41
[53]刘宪林.基于同步机和水系统详细模型的电力系统小扰动稳定研究[D].哈尔滨工业大学,2002
[54]安德逊M,佛阿德A A.电力系统的控制与稳定翻译组译,电力系统的控制与稳定(第一卷)[M].北京：水利电力出版社,1979
[55]傅书逷,倪以信,薛禹胜.直接法稳定分析[M].北京：中国电力出版社.1999
[56]阙志宏.线性系统理论[M].西安：西北工业大学出版社.1995
[57]赵国良,曲军.李雅普诺夫方程的一个计算机解法—分解矩阵合并同类项法[J].自动化技术与应用,1985/0247-51
[58]黄琳,郑应平,张迪.李雅普诺夫第二方法与最优控制器分析设计问题[J].自动化学报,1964,2(4)202-218
[59]韩英铎,王仲鸿,陈淮金.电力系统最优分散协调控制[M].北京：清华大学出版社,1997
[60]薛禹胜.不可积项和临界能量--关于暂态能量函数的几点注释[J].电力系统自动化,1991.01：16-21
[61]薛禹胜.再论暂态能量函数和临界能量[J].电力系统自动化1991.06：9-18
[62]薛禹胜.暂态能量校正和临界群识别—三论暂态能量函数直接法[J].电力系统自动化,1993,17(1)：22-31
[63]薛禹胜.失稳模式变化的机理—五论暂态能量函数直接法[J].电力系统自动化,1994,18(10)：11-24