参数不确定性和饱和非线性对电力系统稳定影响的研究
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摘要
以超高压、长距离输电、大容量机组、大范围互联和大容量的区域间交换为显著特征的现代电力系统，其稳定性一旦遭受破坏，必将造成巨大的经济损失和灾难性的后果，致使电力系统安全稳定问题一直是研究的热点，其中功角稳定分析作为电力系统安全稳定分析中最基本的问题尤为引人注目。虽然国内外对此作了大量的研究，有些方法在实际中已经得到了应用，但仍然有一些重要的问题没有得到很好的解决，如考虑不确定参数时的暂态稳定问题、考虑控制器饱和非线性时的小干扰稳定问题等。本文针对这几个问题，从稳定域的角度对电力系统的功角稳定进行深入地研究，扩展和补充了一些非线性系统的理论和分析方法。
在电力系统暂态稳定方面，论文研究了自治系统稳定域的估计方法、参数可行域的拓扑性质、参数不确定性对暂态稳定的影响、基于暂态稳定约束的优化最优解的存在性问题以及暂态稳定约束的等价变换问题。在此方面，论文具体的研究成果为，
1．基于泰勒展开式和拉萨尔不变性原理，针对普通的自治系统提出了一组稳定域的估计方法，并将此方法应用于电力系统暂态稳定分析。不同于传统的基于能量函数法的估计方法，此方法具有假设条件少，避免计算不稳定平衡点、稳定域可以用简明的数学公式表示，无需复杂的计算等优点。
2．提出了基于微分代数方程的参数可行域的概念，得到了参数可行域的一些拓扑性质和结论。在此基础上，讨论了一类含暂态稳定约束的优化问题并得到一些理论上的结论，如最优解的存在性，利用经验判据代替暂态稳定约束的充分条件等，为深入分析和快速计算含暂态稳定约束的优化问题提供了一些理论基础。
3．提出了一种分析参数不确定性对暂态稳定影响的解析方法。该方法基于“一致最终有界”思想，通过比较某一运行方式下的计算指标与极限指标，为断言该系统的参数偏差不会引起暂态稳定性变化提供了充分条件。方法本质是解析的，虽然结果保守，但方法严格可靠，而且计算量小。
在电力系统小干扰稳定方面，论文研究了饱和线性系统稳定域的估计方法，以及奇异的饱和线性系统稳定域估计的降阶方法，并将这些方法应用于电力系统。以饱和PSS控制系统为例，论文分析了控制器的饱和非线性环节对电力系统小干扰稳定的影响。在此方面，论文具体的研究成果为，
1．在忽略外界干扰的情况下，讨论了饱和线性系统稳定域的估计方法，并利用单目标LMI凸优化减少稳定域估计的保守性。论文证明了此优化问题的最优解位于可行域的边界、最优解与饱和约束的上界成线性关系等结论，这些结论为求解此LMI优化问题和奇异系统的降阶方法提供了理论基础。论文将此方法应用于电力系统，以饱和PSS控制系统为例，提出一种定量分析电力系统饱和控制器控制性能的解析方法。
2．当外界扰动和饱和非线性并存时，论文通过构建一个多目标的LMI优化问题估计系统的实用稳定域和最大可承受扰动量，并利用交叉迭代算法求解此优化问题的Pareto最优解，从理论上证明了此迭代算法的收敛性。在此基础上，论文也以饱和PSS系统为例，基于Pareto最优解，定量地分析了饱和控制器的控制性能，并利用电力系统算例验证了分析方法的有效性。
3．由于在含饱和PSS控制器的电力系统中，变量的振荡模式差别很大，出现奇异性的问题。论文基于奇异摄动理论，提出一种奇异饱和系统稳定域估计的降阶方法。该方法利用低维系统来估计高维饱和系统的稳定域，不仅可以克服原来系统的奇异性，还减少了稳定域估计的计算量。此外，论文从理论上证明了此降阶方法的严格性，数值仿真也验证法了方法的有效性。
The insecurity and instability problems will certainly cause enormous losses and catastrophic results for modern power systems featured with extra high voltage and long-distance transmission lines, large capacity generators, cross-regional inter-connections and huge inter-area power exchanges. Therefore, studies on the power system security and stability have been paid much attention for a long time. Since the angle stability of power systems is the basic problem in the analysis of the power system security and stability, studies on angle stability have become more and more essential and important. Although much research work on angle stability has been done, there are still many important issues to be solved, such as the impact of parameter uncertainties on the transient stability, and the impact of the saturation nonlinearities on the small-signal stability. This dissertation focuses these problems concerning the angle stability, and some theoretical contributions to nonlinear systems are provided.
In the first part of this dissertation, some research work is done, including the stability region estimation of a large class of general autonomous systems, the topological properties of the parameter feasible regions, the impact of parameter uncertainties on the transient stability, the existence of an optimal solution and the equivalent condition about the transient stability constraint. Details are as follows,
1. Based on the Taylor Series Expansion and the LaSalle Invariance Principle, a class of methods for estimating the stability region of nonlinear autonomous systems is suggested, and they are used to analyze the transient stability of a power system. Compared to other methods based on the energy function, the methods provided in this dissertation need fewer assumptions and can avoid calculating the unstable equilibrium points. The estimated stability region can be expressed analytically, and the complex calculation is avoided as well.
2. The concept of the parameter feasible regions is provided based on the differential-Algeria equations, and some topological properties about the region are obtained as well. Further more, a class of optimization problems consisting of the constraint of transient stability are analyzed with emphasis on the feasible region. Some theoretical conclusions are derived, i.e., the optimal solution may not exist; under certain conditions, the constraints of transient stability can be replaced by an engineering criterion. These results are useful for analyzing and solving the optimized problem.
3. An analytical method is suggested to deal with the impact of parameter uncertainties on the transient stability. This method is based on the idea of"Uniformly Ultimately Bound", and a sufficient condition that judges whether the stability characteristics will be changed or not is derived by comparing the limit index and the calculated index in some operating point. The methods suggested are analytically sound, thus the advantage lies in the few calculation and reliability, although they are conservative to some extent.
In the second part of this dissertation, some research work is done, including a method for estimating the stability region of a linear system with saturation nonlinearities, a reduced-order method for estimating the stability region of singular linear system with saturation nonlinearities. Further more, these methods are applied to analyze the impact of saturation nonlinearities on power system small-signal stability with the saturated PSS controller. Details are as follows,
1. When the disturbance rejection is not considered, a method is suggested to estimate the stability region of linear system with saturation nonlinearities. To reduce the conservativeness in the estimation, a simple convex optimization with linear matrix inequality(LMI) constraints is presented, and it is proved that the optimal solution lies on the boundary of the feasible region, and the optimal solution is in proportion to the upper-bound of the saturation function. Furthermore, an analytical method is suggested to evaluate the performance of saturated PSS controller.
2. When both the disturbance rejection and saturation nonlinearities are considered, a multi-objective optimization model is presented to estimate the practical stability region and maximum tolerable disturbance rejection. This optimization problem is solved by an iterative method, which converges to the Pareto Optimal Solution(POS) of the optimization problem in theory. Moreover, as an application of this approach to power systems, an analytical method, based on the POS, to analyze the performance of a controller with saturation nonlinearities and disturbance rejection is introduced to deal with the saturated PSS. Numerical results of a test power system are described, indicating the reliability and simplicity of the approach.
3. In the PSS control system mentioned above, there is large difference in the decay speeds of the transient, so the dynamical system is fundamentally singular. To overcome the singularity, a reduced-order method is suggested to estimate the stability region of the singular system with saturation nonlinearities based on the singular perturbation theory. In the reduced-order method, a low system model is constructed to estimate the stability region of the primary high order system, so that the singularity is eliminated, and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proved in theory, and it is validated by some numerical examples.
在电力系统暂态稳定方面，论文研究了自治系统稳定域的估计方法、参数可行域的拓扑性质、参数不确定性对暂态稳定的影响、基于暂态稳定约束的优化最优解的存在性问题以及暂态稳定约束的等价变换问题。在此方面，论文具体的研究成果为，
1．基于泰勒展开式和拉萨尔不变性原理，针对普通的自治系统提出了一组稳定域的估计方法，并将此方法应用于电力系统暂态稳定分析。不同于传统的基于能量函数法的估计方法，此方法具有假设条件少，避免计算不稳定平衡点、稳定域可以用简明的数学公式表示，无需复杂的计算等优点。
2．提出了基于微分代数方程的参数可行域的概念，得到了参数可行域的一些拓扑性质和结论。在此基础上，讨论了一类含暂态稳定约束的优化问题并得到一些理论上的结论，如最优解的存在性，利用经验判据代替暂态稳定约束的充分条件等，为深入分析和快速计算含暂态稳定约束的优化问题提供了一些理论基础。
3．提出了一种分析参数不确定性对暂态稳定影响的解析方法。该方法基于“一致最终有界”思想，通过比较某一运行方式下的计算指标与极限指标，为断言该系统的参数偏差不会引起暂态稳定性变化提供了充分条件。方法本质是解析的，虽然结果保守，但方法严格可靠，而且计算量小。
在电力系统小干扰稳定方面，论文研究了饱和线性系统稳定域的估计方法，以及奇异的饱和线性系统稳定域估计的降阶方法，并将这些方法应用于电力系统。以饱和PSS控制系统为例，论文分析了控制器的饱和非线性环节对电力系统小干扰稳定的影响。在此方面，论文具体的研究成果为，
1．在忽略外界干扰的情况下，讨论了饱和线性系统稳定域的估计方法，并利用单目标LMI凸优化减少稳定域估计的保守性。论文证明了此优化问题的最优解位于可行域的边界、最优解与饱和约束的上界成线性关系等结论，这些结论为求解此LMI优化问题和奇异系统的降阶方法提供了理论基础。论文将此方法应用于电力系统，以饱和PSS控制系统为例，提出一种定量分析电力系统饱和控制器控制性能的解析方法。
2．当外界扰动和饱和非线性并存时，论文通过构建一个多目标的LMI优化问题估计系统的实用稳定域和最大可承受扰动量，并利用交叉迭代算法求解此优化问题的Pareto最优解，从理论上证明了此迭代算法的收敛性。在此基础上，论文也以饱和PSS系统为例，基于Pareto最优解，定量地分析了饱和控制器的控制性能，并利用电力系统算例验证了分析方法的有效性。
3．由于在含饱和PSS控制器的电力系统中，变量的振荡模式差别很大，出现奇异性的问题。论文基于奇异摄动理论，提出一种奇异饱和系统稳定域估计的降阶方法。该方法利用低维系统来估计高维饱和系统的稳定域，不仅可以克服原来系统的奇异性，还减少了稳定域估计的计算量。此外，论文从理论上证明了此降阶方法的严格性，数值仿真也验证法了方法的有效性。
The insecurity and instability problems will certainly cause enormous losses and catastrophic results for modern power systems featured with extra high voltage and long-distance transmission lines, large capacity generators, cross-regional inter-connections and huge inter-area power exchanges. Therefore, studies on the power system security and stability have been paid much attention for a long time. Since the angle stability of power systems is the basic problem in the analysis of the power system security and stability, studies on angle stability have become more and more essential and important. Although much research work on angle stability has been done, there are still many important issues to be solved, such as the impact of parameter uncertainties on the transient stability, and the impact of the saturation nonlinearities on the small-signal stability. This dissertation focuses these problems concerning the angle stability, and some theoretical contributions to nonlinear systems are provided.
In the first part of this dissertation, some research work is done, including the stability region estimation of a large class of general autonomous systems, the topological properties of the parameter feasible regions, the impact of parameter uncertainties on the transient stability, the existence of an optimal solution and the equivalent condition about the transient stability constraint. Details are as follows,
1. Based on the Taylor Series Expansion and the LaSalle Invariance Principle, a class of methods for estimating the stability region of nonlinear autonomous systems is suggested, and they are used to analyze the transient stability of a power system. Compared to other methods based on the energy function, the methods provided in this dissertation need fewer assumptions and can avoid calculating the unstable equilibrium points. The estimated stability region can be expressed analytically, and the complex calculation is avoided as well.
2. The concept of the parameter feasible regions is provided based on the differential-Algeria equations, and some topological properties about the region are obtained as well. Further more, a class of optimization problems consisting of the constraint of transient stability are analyzed with emphasis on the feasible region. Some theoretical conclusions are derived, i.e., the optimal solution may not exist; under certain conditions, the constraints of transient stability can be replaced by an engineering criterion. These results are useful for analyzing and solving the optimized problem.
3. An analytical method is suggested to deal with the impact of parameter uncertainties on the transient stability. This method is based on the idea of"Uniformly Ultimately Bound", and a sufficient condition that judges whether the stability characteristics will be changed or not is derived by comparing the limit index and the calculated index in some operating point. The methods suggested are analytically sound, thus the advantage lies in the few calculation and reliability, although they are conservative to some extent.
In the second part of this dissertation, some research work is done, including a method for estimating the stability region of a linear system with saturation nonlinearities, a reduced-order method for estimating the stability region of singular linear system with saturation nonlinearities. Further more, these methods are applied to analyze the impact of saturation nonlinearities on power system small-signal stability with the saturated PSS controller. Details are as follows,
1. When the disturbance rejection is not considered, a method is suggested to estimate the stability region of linear system with saturation nonlinearities. To reduce the conservativeness in the estimation, a simple convex optimization with linear matrix inequality(LMI) constraints is presented, and it is proved that the optimal solution lies on the boundary of the feasible region, and the optimal solution is in proportion to the upper-bound of the saturation function. Furthermore, an analytical method is suggested to evaluate the performance of saturated PSS controller.
2. When both the disturbance rejection and saturation nonlinearities are considered, a multi-objective optimization model is presented to estimate the practical stability region and maximum tolerable disturbance rejection. This optimization problem is solved by an iterative method, which converges to the Pareto Optimal Solution(POS) of the optimization problem in theory. Moreover, as an application of this approach to power systems, an analytical method, based on the POS, to analyze the performance of a controller with saturation nonlinearities and disturbance rejection is introduced to deal with the saturated PSS. Numerical results of a test power system are described, indicating the reliability and simplicity of the approach.
3. In the PSS control system mentioned above, there is large difference in the decay speeds of the transient, so the dynamical system is fundamentally singular. To overcome the singularity, a reduced-order method is suggested to estimate the stability region of the singular system with saturation nonlinearities based on the singular perturbation theory. In the reduced-order method, a low system model is constructed to estimate the stability region of the primary high order system, so that the singularity is eliminated, and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proved in theory, and it is validated by some numerical examples.
引文
[1] Kundur P. Power System Stability and Control. New York: McGraw-Hill, 1994
[2] 倪以信，陈寿孙，张宝霖．动态电力系统的理论和分析．北京：清华 大学出版社，2002
[3] 倪以信，陈寿孙，卢卫星．现代电网的稳定性和安全性．电力系统自 动化，1994，11(4)：12-16
[4] 薛禹胜．电力系统暂态稳定快速分析和控制的现状和发展．电力系统自动化，1995，19(1)：6-13
[5] 周孝信，郑健超，沈国荣等．从美加东北部电网大面积停电事故中吸取教训．电网技术，2003，27(9)：T1
[6] 甘德强，胡江溢，韩祯祥．2003年国际若干停电事故思考．电力系统自动化，2004，28(3)：1-4，9
[7] Kundur P, Paserba J, Ajjarapu V, et al. Definition and classification of power system stability. IEEE Transactions on Power Systems, 2004, 19(3): 1387-1401
[8] 孙华东，汤涌，马世英．电力系统稳定的定义与分类评述．电网技术，2006，30(7)：31-35
[9] 王锡凡，方万良，杜正春．现代电力系统分析．北京：科学出版社，2003
[10] 贾宏杰．电力系统小扰动稳定域的研究．天津市：天津大学博士论文，2001
[11] 甘德强，辛焕海，王建全等．暂态稳定预防控制和优化新进展．电力系统自动化，2004，28(10)：1-7
[12] Rodrigues H M, Alberto L F C, Bretas N G. Uniform Invariance Principle: Robustness with Respect to Parameter Variation. Journal of Differential Equations, 2001, 169(1): 228-254
[13] Bretas N G, Alberto L F C. Transient Stability Analysis of Power Systems: Robustness with Respect to Parameter Uncertainties. IEEE Power Engineering Society Winter Meeting, 2002, New York
[14] Gan D, Thomas R J, Zimmerman R D. Stability-constrained Optimal Power Flow. IEEE Yransacitons on Power Systems, 2000, 5(2): 535-540
[15] Gan D, Chattopadhyay D, Luo X. Enhancements to Stability Constrained OPF to Overcome Sub-optimality. Electric Power Components and Systems, 2005, 33(5): 481-491
[16] Bettiol AL, Wehenkel L, Pavella M. Transient Stability-constrained Maximum Allowable Transfer. IEEE Transactions on Power Systems, 1999, 14(2): 654-659
[17] Crow M L, Ayyagari J. The Effect of Excitation Limits on Voltage Stability. IEEE Transactions on Circuits and Systems Ⅰ: Fundamental Theory and Applications, 1995, 42(12): 1022-1026
[18] 贾宏杰，余贻鑫，王成山．考虑励磁顶值与PSS的混沌和分岔现象．电力系统自动化，2001，25(11-14，58)
[19] Xin H, Gan D, Chung T S, et al. A Method for Evaluating the Performance of PSS with Saturated Input. Electric Power Systems Research, 2006, : in press
[20] Chiang H D, Wang C S, Li H. Development of BCU Classifiers for On-line Dynamic Contingency Screening of Electric Power Systems. IEEE Transactions on Power Systems, 1999, 14(2): 660-666
[21] Khalil H K. Nonlinear Systems. 2nd ed. New Jersey: Prentice Hall, 1996
[22] Qu Z. Robust Control of Nonlinear Uncertain Systems. New York: Wiley, 1998
[23] Chiang H D, Wu F F, Varaiya P P. Foundations of the Potential Energy Boundary Surface Method for Power System Transient Stability Analysis. IEEE Transactions on Circuit and Systems, 1988, 25(6): 712-728
[24] Venkatasubramanian V, Schattler H, Zaborszky J. Local Bifurcations and Feasiblity Regions in Differentia-Algebraic Systems. IEEE Transactions on Automatic Control, 1995, 40(12): 1992-2013
[25] Chiang H D. Study of the Existence of Energy Functions for Power Systems with Loses. IEEE Transaction on Circuits and Systems, 1989, 36(11): 1423-1429
[26] Chiang H D, Hirsch M W, Wu F F. Stability Regions of Nonlinear Autonomous Dynamical Systems. IEEE Transactions on Automatic Control, 1988, 33(1): 16-27
[27] Chiang H D, Chu C C, Cauley G. Direct Stability Analysis of Electric Power Systems Using Energy Functions: Theory, Applications and Perspective. Proceedings of the IEEE, 1995, 83(11): 1497-1529
[28] Dandeno P L. Current Usage & Suggested Practices in Power System Stability Simulations for Synchronous Machines. IEEE Transactions on Energy Conversion, 1986, EC-1(1): 77-93
[29] Stubbe M, Bihain A, Deuse J. STAG-a New Unified Software Program for the Study of the Dynamic Behaviour of Electrical Power Systems. IEEE Transactions on Power Systems, 1989, 4( 1): 129-138
[30] LaVoie M, Que-Do V, Houle J L. Real-Time Simulation of Power System Stability Using Parallel Digital Signal Processors. Mathematics and Computers in Simulation, 1995, 38(4-6): 283-292
[31 ] Elder L. An Efficient Method for Real-time Simulation of Large Power System Disturbance. IEEE Transactions on Power Apparatus and Systems, 1982, 101(2): 334-339
[32] Johnson RB. Improved Simulation Techniques for Power System Dynamics. IEEE Transactions on Power Systems, 1988, 3(4): 1691-1698
[33] Wu Z Q. Single Machine Equal Area Criterion for Multimachine System Stability Assessment Based on Time Domain Simulation. IEEE Power Engineering Review, 2001, 21(11): 51-52
[34] Lee S T Y, SchweppeFC. Distance measures and coherency recognition transient stability equivalents. IEEE Transactions on Power Apparatus and Systems., 1973, 92(10): 1555-1557
[35] Wu F F, Narasimhamurthi N. Coherency identification for power system dynamic equivalents. IEEE Transactions on Circuit and Systems, 1983, 30(3): 140-147
[36] Tamura J, Takeda I. New Model of Saturated Synchronous Machines for Power System Transient Stability Simulations. IEEE Transactions on Energy Conversion, 1995, EC-10(2): 218-224
[37] Kumar R S, Ramanujam R, Jenkis L, et al. Transient Stability Simulation of Unbalanced Large Scale Power Systems. Electric Machines and Power Systems, 1995, 23(1): 93-102
[38] Arabi S, Kundur P, Sawada J H. Appropriate HVDC Transmission Simulation Models for Various Power System Stability Studies. IEEE Transactions on Power Systems, 1998, 13(4): 1292-1297
[39] 刘笙，汪静．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，1996
[40] 薛禹胜．运动稳定性量化理论．南京：江苏科学技术出版社，1999
[41] Miyagi H, Taniguchi T. Construction of Lyapunov Function for Power System. Proceedings of the IEE, 1977, 124(12): 1197-1202
[42] 刘峰，辛焕海，甘德强等．一个基于上界函数的暂态稳定域估计方法．中国电机工程学报，2005，25(5)：15-20
[43] Fouad A A, Vittal V, oh T K. Critical Energy for Direct Transient Stability Assessment of a Multi-machine Power System. IEEE Transactions on Power Apparatus and Systems, 1984, 103(8): 2199-2206
[44] Chiang H D, Thorp J S. The closest unstable equilibrium point method for power system dynamic security assessment. IEEE Transactions on Circuit and Systems, 1989, 39(9): 1187-1200
[45] Rahimi F A, Lauby M G. Evaluation of the Transient Energy Function Method for On-line Dynamic Security Analysis. IEEE Transactions on Apparatus and Systems, 1993, 8(2): 497-507
[46] Chiang H-D, Chu C-C. Theoretical Foundation of the BCU Method for Direct Stability Analysis of Network-Reduction Power System Models with Small Transfer Conductances. IEEE Transactions On Circuits and Systems -Ⅰ: Fundamental Theory and Applications, 1995, 42(5): 252-265
[47] Tong J, Chiang H D, Conneen Y P. A Sensitivity- based BCU Method for Fast Derivation of Stability Limits in Electric Power Systems. IEEE Transactions on Power Systems, 1993, 8(4): 1418-1428
[48] Xue Y, Rousseaux P, Gao Z, et al. Dynamic Extended Equal Area Criterion. Proceedings of Joint International Power Conference on Athens Power Tech, 1993, Athens
[49] Xue Y, Van Ribbens Pavella M. A Simple Direct Method of Transient Stability Assessment of Large Power Systems. IEEE Transactions on Power Systems, 1988, 3(1): 400-412
[50] 薛禹胜．不可积项和临界能量．电力系统自动化，1994，16(1)：16-22
[51] 杜正春，甘德强，刘玉用等．电力系统在线动态安全评价的一种快速数值积分方法．中国电机工程学报，1996，16(1)：29-32
[52] Fang D Z, Chung T S, Zhang Y, et al. Transient Stability Limit Conditions Analysis Using a Corrected Transient Energy Function Approach IEEE Transactions on Power System, 2000, 15(2): 804-810
[53] Fang D, Chung T S, David A K. Evaluation of Transient Stability Limit Using a Transient Time-margin Sensitivity . Electric Power Systems Research, 1999, 52(1): 19-27
[54] Bose A. Application of Direct Methods to Transient Stability Analysis of Power Systems. IEEE Transactions on Apparatus and Systems, 1984, 103(7): 1629-1636
[55] Rahimi F, Lauby A, Wrubel M G, et al. Evaluation of the Transient Energy Function Method for on-line Dynamic Security Analysis. IEEE Transactions on Power Systems, 1993, 8(2): 497-507
[56] Maria G A, Tang C, Kim J. Hybrid Transient Stability Analysis. IEEE Transactions on Power Systems, 1990, 5(2): 384-393
[57] Vaahedi E, Mansour Y, Chang A Y. Enhanced Second Kick Methods for on-line Dynamic Security Assessment. IEEE Transactions on Power Systems, 1996, 11(4): 1976-1982
[58] Pai M A. Energy Function Analysis for Power System Stability. Boston: Kluwer Academic Publishers, 1989
[59] Fouad A A. Power System Transient Stability Analysis Using the Transient Energy Function Method. New Jersey: Prentice Hall, 1992
[60] 褚晓东，刘玉田，邱夕兆．基于径向基函数网络的暂态稳定极限估计与预防控制．电力系统自动化，2004，28(10)：45-48
[61] Hiskens I A, Pai M A, Nguyen T B. Bounding Uncertainty in Power System Dynamic Simulations. IEEE Power Engineering Society Winter Meeting, 2000, Singapore
[62] Hiskens I A, Pai M A. Trajectory Sensitivity Analysis of Hybrid Systems. IEEE Transaction on Circuit and Systems, 2000, 47(2): 204-220
[63] Kosterev D N, Taylor C W, Mittelstadt WA. Model validation for the August 10, 1996 WSCC system outage. IEEE Transactions on Power Systems, 1999, 14(3): 967-974
[64] 冯飞，余贻鑫．电力系统动态安全域的微分拓扑特性．电力系统及其自动化学报，1991，(4)：1-6
[65] Kaye R J, Wu F F. Dynamic Security Regions of Power Systems. I EEE Transactions on Circuits and Systems, 1982, 29(9): 612-623
[66] Wu F F, Tsai Y K. Probabalistic Dynamic Security Assessment of Power Systems: Part Ⅰ-Basic Model. IEEE Transactions on Circuit and Systems, 1983, 30(3): 148-159
[67] 杨志辉，唐云．关于拟动态安全域的理论分析．工程数学学报，2004，21(5)：761-768
[68] 余贻鑫．基于实用动态安全域的最优暂态稳定紧急控制．中国科学，E辑，2004，34(5)：556-563
[69] 冯飞，余贻鑫．电力系统功率注入空间的动态安全域．中国电机工程学报，1993，13(3)：14-21
[70] Newton G B, Luis F C A. Transient stability analysis of power systems: robustness with respect to parameter uncertainties. IEEE Power Engineering Society Winter Meeting, 2002,
[71] Hiskens I A, Lesieutre B C. Modeling Post-Disturbance Consequences: Uncertainty in Power System Dynamic Simulation. Power System Engineering Research Center (PSERC) Background Paper, 2003,
[72] Hiskens I A, Pai M A, Sauer P W. An Iterative Approach to Calculating Dynamic ATC. Proceedings of International Symposium on Bulk Power System Dynamics and Control-Ⅳ, 1998, Greece
[73] 潘组梁．非线性问题的数学方法及其应用．杭州：浙江大学出版社，2001
[74] Hiskens I A, Pai M A. Power System Applications of Trajectory Sensitivities. Proceeding of IEEE Power Engineering Society Winter Meeting, 2002, New York (USA)
[75] Hiskens I A, Alseddiqui J. Sensitivity, Approximation, and Uncertainty in Power System Dynamic Simulation. IEEE Transactions on Power Systems, 2006, 21(4): 1808-1820
[76] Hockenberry J, Lesieutre B. Evaluation of Uncertainty in Dynamic Simulation of Power System Models: The Probabilistic Collocation Method. IEEE Transactions on Power Systems, 2004, 19(3): 1483-1491
[77] Jones D. Estimation of Power System Parameters. IEEE Transactions on Power Systems, 2004, 19(4): 1980-1989
[78] Ju P, Handschin E, Karlsson D. Nonlinear Dynamic Load Modeling, Model and Parameter Estimation. IEEE Transactions on Power Systems, 1996, 11(4): 1689-1697
[79] 辛焕海，甘德强，邱家驹等．一种包含不确定参数的暂态稳定分析方法．中国电机工程学报，2006，26(20)：15-21
[80] 马大强．电力系统机电暂态过程．北京：水利电力出版社，1985
[81] Wang L, Semlyen A. Application of Sparse Eigenvalue Techniques to the Small Signal Stability Analysis of Large Power Systems. IEEE Transactions on Power Systems, 1990, 5(2): 635-642
[82] Perez-Arriaga I J, Verghese G C, Pagola F L, et al. Developments in Selective Modal Analysis of Small-Signal Stability in Electric Power Systems. Automatica, 1990, 26(2): 215-231
[83] Martins N, Ferraz J C R, Quintao P E M, et al. Linear Techniques Applied to Small-signal Electromechanical Stability, Model Order Reduction and Harmonic Studies. Intelligent Automation and Soft Computing, 2006, 12(1): 103-115
[84] Gao B, Morison G K, Kundur P. Voltage Stability Ealuation Using Modal Analysis. IEEE Transactions on Power Systems, 1992, 7(4): 1529-1542
[85] Angelidis G, Semlyen A. Efficient Calculation of Critical Eigenvalue Clusters in the Small Signal Stability Analysis of Large Power Systems. IEEE Transactions on Power Systems, 1995, 10(1): 427-432
[86] Wu H X, Tsakalis K S, Heydt G T. Evaluation of Time Delay Effects to Wide-area Power System Stabilizer Design. IEEE Transactions on Power Systems, 2004, 19(4): 1935-1941
[87] Wu K T, Liu C C, Taylor C W, et al. Voltage Instability: Mechanisms and Control Strategies. Proceeding of the IEEE, 1995, 83(11): 1442-1455
[88] Zhang P, Coonick A H. Coordinated Synthesis of PSS Parameters in Multi-machine Power Systems Using the Method of Inequalities Applied to Genetic Algorithms. IEEE Transactions on Power Systems, 2000, 15(2): 811-816
[89] Rao P S, Boje E S. A Quantitative Design Approach to PSS Tuning. Electric Power Systems Research, 2005, 73(3): 249-256
[90] Tse C T, Wang K W, Chung C Y, et al. Robust PSS Design by Probabilistic Eigenvalue Sensitivity Analysis. Electric Power Systems Research, 2001, 59(1): 47-54
[91] Liu S, Messina A R, Vittal V. A normal form analysis approach to siting power system stabilizers (PSSs) and assessing power system nonlinear behavior. IEEE Transactions on Power Systems, 2006, 21(4): 1755-1762
[92] Nijmeijer H, Schaft A V D. Nonlinear Dynamical Control Systems. 3 edition. New York: Springer-Verlag New York Inc., 1990
[93] Lu J, Chiang H D, Thorp J S. Identification of Optimum Sites for Power System Stabilizer Applications. IEEE Transactions on Power Systems, 1990, 5(4): 1302-1308
[94] Ji W, Venkatasubramanianian V. Hard-limit Induced Chaos in a Fundamental Power System Model. Electrical Power and Energy Systems, 1996, 18(5): 279-295
[95] Tan C W, VargheseM, VaraiyaP, et al. Bifurcation, Chaos, and Voltage Collapse in Power Systems. Proceedings of the IEEE, 1995, 33(11): 1484-1495
[96] Chiang H D, Liu C C, Varaiya P P. Chaos in a Simple Power System. IEEE Transactions on Power Systems, 1993, 8(4): 1407-1417
[97] Venkatasubramanian V, Schattler H, Zaborszky J. On the Dynamics of Differential-algebraic Systems such as the Balanced Large Electric Power System. Berlin: Springer-Verlag, 1994
[98] Venkatasubramanian V, Schattler H, Zaborszky J. Dynamics of Large Constrained Nonlinear Systems-A Taxonomy Theory. Proceeding of the IEEE, 1995, 83(11): 1530-1561
[99] Lu Q, Sun Y Z, Mei S W. Nonlinear controlsystems and power system dynamics. Boston: Kluwer Academic Publishers, 2001
[100] Rajkumar V, Mohler R R. Nonlinear Control Methods for Power Systems: A Comparison. IEEE Transactions on Control Systems Technology, 1995, 3(2): 231-237
[101] Gan D, Qu Z, Cai H. Multi-machine System Excitation Control via Theories of Feedback Linearization Control and Nonlinear Robust Control. International Journal of Systems Science, 2000, 31(4): 519-527
[102] Hu T, Lin Z. Control Systems with Actuator Saturation: Analysis and Design. Boston: Birkhauser, 2001
[103] Xi Z, Feng G, Cheng D, et al. Nonlinear Decentralized Saturated Controller Design for Power Systems. IEEE Transactions on Control Systems Technology，2003，11(4)：539-547
[104] 甘德强，王锡凡，杜正春等．暂态稳定性分析的自动事故选择方法．电力系统自动化，1994，18(1)：25-30
[105] 朱方，汤涌，张东霞等．我国交流互联电网动态稳定性的研究及解决策略．电网技术，2004，28(15)：1-5
[106] PAGANINI F, LESIEUTRE B C. Generic properties, one-parameter deformations, and the BCU method. IEEE transactions On Circuits and Systems-Ⅰ: Fundamental Theory and Applications, 1999, 46(6): 760-763
[107] Zaborszky J, Huang G, Zheng B. A Counterexample of a Theorem by Tsolas et al. and an Independentresult by Zaborszky et al. IEEE Transactions on Automatic Control, 1988, 33(316-317)
[108] 李明节，王世缨．电力系统在线动态安全分析新方法．清华大学学报：自然科学版，1993，33(1)：99-108
[109] Liamas A, De La Ree Lopez J, Mili L. Clarifications of the BCU Method for Transient Stability Analysis. IEEE Transactions on Power Systems, 1995, 10(1): 210-219
[110] 关天祺，梅生伟，徐政．分散励磁与超导储能装置的干扰抑制控制．电力系统自动化，2002，26(1)：1-6
[111] 陈菊明，梅生伟，刘锋．多机系统TCSC多目标H∞控制器设计．电力系统自动化，2000，24(21)：11-13，18
[112] Davison E J, Kurak E M. A Computational Method for Determining Quadratic Lyapunov Functions for Non-linear Systems. Automatica, 1971, 7(1): 627-636
[113] Qu Z, Dorsey J F. Application of Robust Control to Sustained Oscillations in Power systems. IEEE Transactions on Circuits and Systems, 1992, 39(6): 470-476
[114] 石景海，贺仁睦．动态负荷建模中的负荷时变性研究．中国电机工程学报，2004，24(4)：85-90
[115] Gan D, Chattopadhyay D, Luo X. An Improved Method for Optimal Operation under Stability Constraints. Proceedings of IEEE PES Transmission and Distribution Conference, 2003, Dallas (Texas)
[116] 李颖晖，张保会，李勐．电力系统稳定边界的研究．中国电机工程学报，2002，22(3)：72-77
[117] Kato Y, Iwamoto S. Transient Stability Preventive Control for Stable. Operating Condition With Desired CCT. IEEE Transactions on Power Systems, 2002, 17(4): 1154-1161
[118] Fouad A A, Tong J. Stability Constrained Optimal Rescheduling of Generation. IEEE Transactions On Power Systems, 1993, 8(1): 105-112
[119] Gan D, Qu Z, Wu X. Loadability of Power Systems with Steady-state and Dynamic Security Constraints. International Journal of Electrical Power & Energy Systems, 2003, 25(2): 91-96
[120] Reibig G. Differential-Algebraic Equations and Impasse Points. IEEE Transactions on Circuit and Systems-Ⅰ: Fundamental Theory and Applications, 1996, 43(2): 122-133
[121] Venkatasubramanian V, Schattler H, Zaborszky J. Fast Time-Varying Phasor Analysis in the Balanced Three-Phase Large Electric Power System. IEEE Transactions on Automatic Control, 1995, 40(11): 1975-1982
[122] 陈维桓．微分流形初步．北京：高等教育出版社，2002
[123] Hirsch M W. Differential Topology. New York: Springer-Verlag, 1976
[124] Bartle R G. The Elements of Real Analysis. 2nd ed. New York: John Wiley & Sons, Inc., 1976.
[125] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear Programming-Theory and Algorithms. Second. : John Wiley & Sons, 1993
[126] Guillemin V, Pollack A. Differential Topology. New Jersey: Prentice-Hall, Inc., Englewood Cliffs,
[127] Kundur P, Klein M, Rogers G. Application of Power System Stabilizers for Enhancement of Overall System Stability. IEEE Transactions on Power Systems, 1989, 4(2): 614-626
[128] Arapostathis A, Shankar Sastry S, Varaiya P. Global Analysis of Swing Dynamics. IEEE Transactions on Circuit and Systems, 1982, 29(10): 673-679
[129] Ian A H, Pai M A. Trajectory Sensitivity Analysis of Hybrid Systems. IEEE Transactions on Circuit and Systems, 2000, 47(2): 204-220
[130] 孙景强，房大中，钟德成．暂态稳定约束下的最优潮流．中国电机工程学报，2005，25(12)：12-17
[131] Laufenberg M J, Pai M A. Sensitivity Theory in Power Systems: Applicationin Dynamic Security Analysis. Proceedings of the IEEE International Conference on Control Applications, 1996, Dearborn, MI, USA
[132] 辛焕海，甘德强，邱家驹．一组估计自治系统稳定域严格子集的通用方法．电力系统自动化，2005，29(13)：24-28,75
[133] 王铁强，贺仁睦，王卫国等．电力系统低频振荡机理的研究．中国电机工程学报，2002，22(2)：21-25
[134] 牛振勇，杜正春，方万良等．基于进化策略的多机系统PSS参数优化．中国电机工程学报，2004，24(2)：22-27
[135] Fang W, Ngan H W. Enhancing Small Signal Power System Stability by Coordinating Unified Power Flow Controller with Power System Stabilizer. Electric Power Systems Research, 2003, 65(2): 91-99
[136] Venkatasubramanian V. Stability Boundary Analysis of Nonlinear Dynamics Subject to State Limits. Proceedings of the 34th Hawaii International Conference on System Science, 2001, USA
[137] Sussmann H J, Sontag E D, Yang Y. A General Result on the Stabilization of Linear Systems Using Bounded Controls. IEEE Transactions on Automatic Control, 1994, 39(12): 2411-2425
[138] Hindi H, Boyd S. Analysis of Linear Systems with Saturation using Convex Optimization. Proceedings of the 37th IEEE Conference on Decision & Control, 1998, Tampa, Florida, USA
[139] Suarez R, Alvarez J, Alvarez J. Linear Systems with Single Saturated Input: Stability Analysis. Proceedings of the 30th Conference on Decision and Control, 1991, Brighton, UK
[140] Gutman P O, Hangander P. ANew Design of Constrained Controllers for Linear Systems. IEEE Transactions on Automatic Control, 1985, 30(1): 22-33
[141] Hu T, Lin Z. Composite Quadratic Lyapunov Functions for Constrained Control Systems. IEEE Transactions on Automatic Control, 2003, 48(3): 440-450
[142] Hu T, Lin Z, Chen B M. An Analysis and Design Method for Linear Systems Subject to Actuator Saturation and Disturbance. Automatica, 2002, 38(2): 351-359
[143] 俞立．鲁棒控制-线形矩阵不等式处理方法．北京：清华大学出版社，2002
[144] 李颖晖，张保会．运用非线性系统理论确定电力系统暂态稳定域的应用．中国电机工程学报，2000，20(2)：24-27
[145] Hurwicz L. Programming in Linear Spaces, Studies in Linear and Nonlinear Programming. 2nd. London: Oxford University, 1964
[146] Noble B, James W D. Applied Linear Algebra. Second. New Jersey: Prentice-Hall. Inc., 1977
[147] 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．中国电机工程学报，2004，24(5)：7-11
[148] Jiang H, DorseT J F, Qu Z, et al. Global Robust Adaptive Control of Power Systems. IEE Proceedings, Part C, Generation, Transmission and Distribution, 1994, 141(5): 429-436
[149] Yee H, Muir M J. Transient Stability of Multi-machine Systems with Saturable Exciters. Proceedings of IEE-Generation, Transmission and Distribution, 1980, 127(1)
[150] Escarela-Perez R, Niewierowicz T, Campero-Littlewood E. A Study of the Variation of Synchronous Machine Parameters Due to Saturation: A Numerical Approach. Electric Power Systems Research, 2004, 72(1): 1-11
[151] Hill D J, Mareels I M. Stability Theory for Differential/Algebraic Systems with Application to Power Systems. IEEE Transactions on Circuit and Systems, 1990, 37(11): 1416-1422
[152] Da Silva J M G, Tarbouriech S. Antiwindup Dsign with Guaranteed Regions of Stability: An LMI-based Approach. IEEE Transactions on Automatic Control, 2005, 50(1): 106-111
[153] Mantri R, Saberi A, Venkatasubramanian V. Stability Analysis of Continuous Time Planar Systems with State Saturation Nonlinearity. IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, 1998, 45(9): 989-993
[154] Cao Y, Lin Z, Ward D G. An Anti-windup Approach to Enlarging Domain of Attraction for Linear Systems Subject to Actuator Saturation. IEEE Transactions on Automatic Control, 2002, 47(1): 140-145
[155] Deb K. Multi-Objective Optimization Using Evolutionary Algorithms. England: John Wiley & Sons Ltd, 2001
[156] 李大虎，曹一家，江全元等．基于多目标进化算法的相量测量单元优化配置．电网技术，2005，29(22)：45-49,75
[157] 邹振宇，江全元，张鹏翔等．基于多目标进化算法的TCSC与SVC控制器协调设计．电力系统自动化，2005，29(6)：60-65
[158] Tarbouriech S, Queinnec I, Garcia G. Stability Region Enlargement through Anti-windup Strategy for Linear Systems with Dynamics Restricted Actuator. International Journal of Systems Science, 2006, 37(2): 79-90
[159] 袁亚湘，孙文瑜．最优化理论与方法．北京：科学出版社，1995
[160] Kokotovic P V, Khalil H K, O'Reilly J. Singular Perturbation Methods in Control: Analysis and Design. London: Academic Press, 1986
[161] Singh H, Brown R H, Naidu D S, et al. Robust Stability of Singularly Perturbed State Feedback Systems Using Unified Approach. IEE Proceedings- Control Theory and Applications, 2001, 148(5): 391-396
[162] 刘永强，杨志辉，唐云等．多时间尺度电力系统的模型降阶及稳定性 分析(一)基本理论．电力系统自动化，2003，27(1)：5-10
[163] Saksena V R, O'Reilly J, Kokotovic P V. Singular Perturbations in Control Theory-A Survey. Automatica, 1984, 20(2): 1976-1983
[164] 刘永强，严正，倪以信．双时间尺度电力系统动态模型降阶研究(一)—电力系统奇异摄动模型．电力系统自动化，2002，26(18)：1-5
[165] Kokotovic P V, Sauer P W. Integral Manifold as a Tool for Reduced-order Modeling of Nonlinear System: A Synchronous Machine Case Study. IEEE Transactions on Circuit and Systems, 1989, 36(3): 403-410
[166] Sauer P W, Pai M A. Modeling and Simulation of Multi-machine Power System Dynamics. : Academic Press, 1991
[167] Sauer P W, Ahmed-Zaid S, Kokotovic P V. an Integral Manifold Approach to Reduced Order Dynamic Modeling of Synchronous Machine. IEEE Transactions on Power Systems, 1988, 2(1):17-23
[168] 刘永强，雷文，吴捷等．多时问尺度电力系统的模型降阶及稳定性分析(二)电力系统的降阶与中长期失稳．电力系统自动化，2003，27(2)：1-7
[2] 倪以信，陈寿孙，张宝霖．动态电力系统的理论和分析．北京：清华 大学出版社，2002
[3] 倪以信，陈寿孙，卢卫星．现代电网的稳定性和安全性．电力系统自 动化，1994，11(4)：12-16
[4] 薛禹胜．电力系统暂态稳定快速分析和控制的现状和发展．电力系统自动化，1995，19(1)：6-13
[5] 周孝信，郑健超，沈国荣等．从美加东北部电网大面积停电事故中吸取教训．电网技术，2003，27(9)：T1
[6] 甘德强，胡江溢，韩祯祥．2003年国际若干停电事故思考．电力系统自动化，2004，28(3)：1-4，9
[7] Kundur P, Paserba J, Ajjarapu V, et al. Definition and classification of power system stability. IEEE Transactions on Power Systems, 2004, 19(3): 1387-1401
[8] 孙华东，汤涌，马世英．电力系统稳定的定义与分类评述．电网技术，2006，30(7)：31-35
[9] 王锡凡，方万良，杜正春．现代电力系统分析．北京：科学出版社，2003
[10] 贾宏杰．电力系统小扰动稳定域的研究．天津市：天津大学博士论文，2001
[11] 甘德强，辛焕海，王建全等．暂态稳定预防控制和优化新进展．电力系统自动化，2004，28(10)：1-7
[12] Rodrigues H M, Alberto L F C, Bretas N G. Uniform Invariance Principle: Robustness with Respect to Parameter Variation. Journal of Differential Equations, 2001, 169(1): 228-254
[13] Bretas N G, Alberto L F C. Transient Stability Analysis of Power Systems: Robustness with Respect to Parameter Uncertainties. IEEE Power Engineering Society Winter Meeting, 2002, New York
[14] Gan D, Thomas R J, Zimmerman R D. Stability-constrained Optimal Power Flow. IEEE Yransacitons on Power Systems, 2000, 5(2): 535-540
[15] Gan D, Chattopadhyay D, Luo X. Enhancements to Stability Constrained OPF to Overcome Sub-optimality. Electric Power Components and Systems, 2005, 33(5): 481-491
[16] Bettiol AL, Wehenkel L, Pavella M. Transient Stability-constrained Maximum Allowable Transfer. IEEE Transactions on Power Systems, 1999, 14(2): 654-659
[17] Crow M L, Ayyagari J. The Effect of Excitation Limits on Voltage Stability. IEEE Transactions on Circuits and Systems Ⅰ: Fundamental Theory and Applications, 1995, 42(12): 1022-1026
[18] 贾宏杰，余贻鑫，王成山．考虑励磁顶值与PSS的混沌和分岔现象．电力系统自动化，2001，25(11-14，58)
[19] Xin H, Gan D, Chung T S, et al. A Method for Evaluating the Performance of PSS with Saturated Input. Electric Power Systems Research, 2006, : in press
[20] Chiang H D, Wang C S, Li H. Development of BCU Classifiers for On-line Dynamic Contingency Screening of Electric Power Systems. IEEE Transactions on Power Systems, 1999, 14(2): 660-666
[21] Khalil H K. Nonlinear Systems. 2nd ed. New Jersey: Prentice Hall, 1996
[22] Qu Z. Robust Control of Nonlinear Uncertain Systems. New York: Wiley, 1998
[23] Chiang H D, Wu F F, Varaiya P P. Foundations of the Potential Energy Boundary Surface Method for Power System Transient Stability Analysis. IEEE Transactions on Circuit and Systems, 1988, 25(6): 712-728
[24] Venkatasubramanian V, Schattler H, Zaborszky J. Local Bifurcations and Feasiblity Regions in Differentia-Algebraic Systems. IEEE Transactions on Automatic Control, 1995, 40(12): 1992-2013
[25] Chiang H D. Study of the Existence of Energy Functions for Power Systems with Loses. IEEE Transaction on Circuits and Systems, 1989, 36(11): 1423-1429
[26] Chiang H D, Hirsch M W, Wu F F. Stability Regions of Nonlinear Autonomous Dynamical Systems. IEEE Transactions on Automatic Control, 1988, 33(1): 16-27
[27] Chiang H D, Chu C C, Cauley G. Direct Stability Analysis of Electric Power Systems Using Energy Functions: Theory, Applications and Perspective. Proceedings of the IEEE, 1995, 83(11): 1497-1529
[28] Dandeno P L. Current Usage & Suggested Practices in Power System Stability Simulations for Synchronous Machines. IEEE Transactions on Energy Conversion, 1986, EC-1(1): 77-93
[29] Stubbe M, Bihain A, Deuse J. STAG-a New Unified Software Program for the Study of the Dynamic Behaviour of Electrical Power Systems. IEEE Transactions on Power Systems, 1989, 4( 1): 129-138
[30] LaVoie M, Que-Do V, Houle J L. Real-Time Simulation of Power System Stability Using Parallel Digital Signal Processors. Mathematics and Computers in Simulation, 1995, 38(4-6): 283-292
[31 ] Elder L. An Efficient Method for Real-time Simulation of Large Power System Disturbance. IEEE Transactions on Power Apparatus and Systems, 1982, 101(2): 334-339
[32] Johnson RB. Improved Simulation Techniques for Power System Dynamics. IEEE Transactions on Power Systems, 1988, 3(4): 1691-1698
[33] Wu Z Q. Single Machine Equal Area Criterion for Multimachine System Stability Assessment Based on Time Domain Simulation. IEEE Power Engineering Review, 2001, 21(11): 51-52
[34] Lee S T Y, SchweppeFC. Distance measures and coherency recognition transient stability equivalents. IEEE Transactions on Power Apparatus and Systems., 1973, 92(10): 1555-1557
[35] Wu F F, Narasimhamurthi N. Coherency identification for power system dynamic equivalents. IEEE Transactions on Circuit and Systems, 1983, 30(3): 140-147
[36] Tamura J, Takeda I. New Model of Saturated Synchronous Machines for Power System Transient Stability Simulations. IEEE Transactions on Energy Conversion, 1995, EC-10(2): 218-224
[37] Kumar R S, Ramanujam R, Jenkis L, et al. Transient Stability Simulation of Unbalanced Large Scale Power Systems. Electric Machines and Power Systems, 1995, 23(1): 93-102
[38] Arabi S, Kundur P, Sawada J H. Appropriate HVDC Transmission Simulation Models for Various Power System Stability Studies. IEEE Transactions on Power Systems, 1998, 13(4): 1292-1297
[39] 刘笙，汪静．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，1996
[40] 薛禹胜．运动稳定性量化理论．南京：江苏科学技术出版社，1999
[41] Miyagi H, Taniguchi T. Construction of Lyapunov Function for Power System. Proceedings of the IEE, 1977, 124(12): 1197-1202
[42] 刘峰，辛焕海，甘德强等．一个基于上界函数的暂态稳定域估计方法．中国电机工程学报，2005，25(5)：15-20
[43] Fouad A A, Vittal V, oh T K. Critical Energy for Direct Transient Stability Assessment of a Multi-machine Power System. IEEE Transactions on Power Apparatus and Systems, 1984, 103(8): 2199-2206
[44] Chiang H D, Thorp J S. The closest unstable equilibrium point method for power system dynamic security assessment. IEEE Transactions on Circuit and Systems, 1989, 39(9): 1187-1200
[45] Rahimi F A, Lauby M G. Evaluation of the Transient Energy Function Method for On-line Dynamic Security Analysis. IEEE Transactions on Apparatus and Systems, 1993, 8(2): 497-507
[46] Chiang H-D, Chu C-C. Theoretical Foundation of the BCU Method for Direct Stability Analysis of Network-Reduction Power System Models with Small Transfer Conductances. IEEE Transactions On Circuits and Systems -Ⅰ: Fundamental Theory and Applications, 1995, 42(5): 252-265
[47] Tong J, Chiang H D, Conneen Y P. A Sensitivity- based BCU Method for Fast Derivation of Stability Limits in Electric Power Systems. IEEE Transactions on Power Systems, 1993, 8(4): 1418-1428
[48] Xue Y, Rousseaux P, Gao Z, et al. Dynamic Extended Equal Area Criterion. Proceedings of Joint International Power Conference on Athens Power Tech, 1993, Athens
[49] Xue Y, Van Ribbens Pavella M. A Simple Direct Method of Transient Stability Assessment of Large Power Systems. IEEE Transactions on Power Systems, 1988, 3(1): 400-412
[50] 薛禹胜．不可积项和临界能量．电力系统自动化，1994，16(1)：16-22
[51] 杜正春，甘德强，刘玉用等．电力系统在线动态安全评价的一种快速数值积分方法．中国电机工程学报，1996，16(1)：29-32
[52] Fang D Z, Chung T S, Zhang Y, et al. Transient Stability Limit Conditions Analysis Using a Corrected Transient Energy Function Approach IEEE Transactions on Power System, 2000, 15(2): 804-810
[53] Fang D, Chung T S, David A K. Evaluation of Transient Stability Limit Using a Transient Time-margin Sensitivity . Electric Power Systems Research, 1999, 52(1): 19-27
[54] Bose A. Application of Direct Methods to Transient Stability Analysis of Power Systems. IEEE Transactions on Apparatus and Systems, 1984, 103(7): 1629-1636
[55] Rahimi F, Lauby A, Wrubel M G, et al. Evaluation of the Transient Energy Function Method for on-line Dynamic Security Analysis. IEEE Transactions on Power Systems, 1993, 8(2): 497-507
[56] Maria G A, Tang C, Kim J. Hybrid Transient Stability Analysis. IEEE Transactions on Power Systems, 1990, 5(2): 384-393
[57] Vaahedi E, Mansour Y, Chang A Y. Enhanced Second Kick Methods for on-line Dynamic Security Assessment. IEEE Transactions on Power Systems, 1996, 11(4): 1976-1982
[58] Pai M A. Energy Function Analysis for Power System Stability. Boston: Kluwer Academic Publishers, 1989
[59] Fouad A A. Power System Transient Stability Analysis Using the Transient Energy Function Method. New Jersey: Prentice Hall, 1992
[60] 褚晓东，刘玉田，邱夕兆．基于径向基函数网络的暂态稳定极限估计与预防控制．电力系统自动化，2004，28(10)：45-48
[61] Hiskens I A, Pai M A, Nguyen T B. Bounding Uncertainty in Power System Dynamic Simulations. IEEE Power Engineering Society Winter Meeting, 2000, Singapore
[62] Hiskens I A, Pai M A. Trajectory Sensitivity Analysis of Hybrid Systems. IEEE Transaction on Circuit and Systems, 2000, 47(2): 204-220
[63] Kosterev D N, Taylor C W, Mittelstadt WA. Model validation for the August 10, 1996 WSCC system outage. IEEE Transactions on Power Systems, 1999, 14(3): 967-974
[64] 冯飞，余贻鑫．电力系统动态安全域的微分拓扑特性．电力系统及其自动化学报，1991，(4)：1-6
[65] Kaye R J, Wu F F. Dynamic Security Regions of Power Systems. I EEE Transactions on Circuits and Systems, 1982, 29(9): 612-623
[66] Wu F F, Tsai Y K. Probabalistic Dynamic Security Assessment of Power Systems: Part Ⅰ-Basic Model. IEEE Transactions on Circuit and Systems, 1983, 30(3): 148-159
[67] 杨志辉，唐云．关于拟动态安全域的理论分析．工程数学学报，2004，21(5)：761-768
[68] 余贻鑫．基于实用动态安全域的最优暂态稳定紧急控制．中国科学，E辑，2004，34(5)：556-563
[69] 冯飞，余贻鑫．电力系统功率注入空间的动态安全域．中国电机工程学报，1993，13(3)：14-21
[70] Newton G B, Luis F C A. Transient stability analysis of power systems: robustness with respect to parameter uncertainties. IEEE Power Engineering Society Winter Meeting, 2002,
[71] Hiskens I A, Lesieutre B C. Modeling Post-Disturbance Consequences: Uncertainty in Power System Dynamic Simulation. Power System Engineering Research Center (PSERC) Background Paper, 2003,
[72] Hiskens I A, Pai M A, Sauer P W. An Iterative Approach to Calculating Dynamic ATC. Proceedings of International Symposium on Bulk Power System Dynamics and Control-Ⅳ, 1998, Greece
[73] 潘组梁．非线性问题的数学方法及其应用．杭州：浙江大学出版社，2001
[74] Hiskens I A, Pai M A. Power System Applications of Trajectory Sensitivities. Proceeding of IEEE Power Engineering Society Winter Meeting, 2002, New York (USA)
[75] Hiskens I A, Alseddiqui J. Sensitivity, Approximation, and Uncertainty in Power System Dynamic Simulation. IEEE Transactions on Power Systems, 2006, 21(4): 1808-1820
[76] Hockenberry J, Lesieutre B. Evaluation of Uncertainty in Dynamic Simulation of Power System Models: The Probabilistic Collocation Method. IEEE Transactions on Power Systems, 2004, 19(3): 1483-1491
[77] Jones D. Estimation of Power System Parameters. IEEE Transactions on Power Systems, 2004, 19(4): 1980-1989
[78] Ju P, Handschin E, Karlsson D. Nonlinear Dynamic Load Modeling, Model and Parameter Estimation. IEEE Transactions on Power Systems, 1996, 11(4): 1689-1697
[79] 辛焕海，甘德强，邱家驹等．一种包含不确定参数的暂态稳定分析方法．中国电机工程学报，2006，26(20)：15-21
[80] 马大强．电力系统机电暂态过程．北京：水利电力出版社，1985
[81] Wang L, Semlyen A. Application of Sparse Eigenvalue Techniques to the Small Signal Stability Analysis of Large Power Systems. IEEE Transactions on Power Systems, 1990, 5(2): 635-642
[82] Perez-Arriaga I J, Verghese G C, Pagola F L, et al. Developments in Selective Modal Analysis of Small-Signal Stability in Electric Power Systems. Automatica, 1990, 26(2): 215-231
[83] Martins N, Ferraz J C R, Quintao P E M, et al. Linear Techniques Applied to Small-signal Electromechanical Stability, Model Order Reduction and Harmonic Studies. Intelligent Automation and Soft Computing, 2006, 12(1): 103-115
[84] Gao B, Morison G K, Kundur P. Voltage Stability Ealuation Using Modal Analysis. IEEE Transactions on Power Systems, 1992, 7(4): 1529-1542
[85] Angelidis G, Semlyen A. Efficient Calculation of Critical Eigenvalue Clusters in the Small Signal Stability Analysis of Large Power Systems. IEEE Transactions on Power Systems, 1995, 10(1): 427-432
[86] Wu H X, Tsakalis K S, Heydt G T. Evaluation of Time Delay Effects to Wide-area Power System Stabilizer Design. IEEE Transactions on Power Systems, 2004, 19(4): 1935-1941
[87] Wu K T, Liu C C, Taylor C W, et al. Voltage Instability: Mechanisms and Control Strategies. Proceeding of the IEEE, 1995, 83(11): 1442-1455
[88] Zhang P, Coonick A H. Coordinated Synthesis of PSS Parameters in Multi-machine Power Systems Using the Method of Inequalities Applied to Genetic Algorithms. IEEE Transactions on Power Systems, 2000, 15(2): 811-816
[89] Rao P S, Boje E S. A Quantitative Design Approach to PSS Tuning. Electric Power Systems Research, 2005, 73(3): 249-256
[90] Tse C T, Wang K W, Chung C Y, et al. Robust PSS Design by Probabilistic Eigenvalue Sensitivity Analysis. Electric Power Systems Research, 2001, 59(1): 47-54
[91] Liu S, Messina A R, Vittal V. A normal form analysis approach to siting power system stabilizers (PSSs) and assessing power system nonlinear behavior. IEEE Transactions on Power Systems, 2006, 21(4): 1755-1762
[92] Nijmeijer H, Schaft A V D. Nonlinear Dynamical Control Systems. 3 edition. New York: Springer-Verlag New York Inc., 1990
[93] Lu J, Chiang H D, Thorp J S. Identification of Optimum Sites for Power System Stabilizer Applications. IEEE Transactions on Power Systems, 1990, 5(4): 1302-1308
[94] Ji W, Venkatasubramanianian V. Hard-limit Induced Chaos in a Fundamental Power System Model. Electrical Power and Energy Systems, 1996, 18(5): 279-295
[95] Tan C W, VargheseM, VaraiyaP, et al. Bifurcation, Chaos, and Voltage Collapse in Power Systems. Proceedings of the IEEE, 1995, 33(11): 1484-1495
[96] Chiang H D, Liu C C, Varaiya P P. Chaos in a Simple Power System. IEEE Transactions on Power Systems, 1993, 8(4): 1407-1417
[97] Venkatasubramanian V, Schattler H, Zaborszky J. On the Dynamics of Differential-algebraic Systems such as the Balanced Large Electric Power System. Berlin: Springer-Verlag, 1994
[98] Venkatasubramanian V, Schattler H, Zaborszky J. Dynamics of Large Constrained Nonlinear Systems-A Taxonomy Theory. Proceeding of the IEEE, 1995, 83(11): 1530-1561
[99] Lu Q, Sun Y Z, Mei S W. Nonlinear controlsystems and power system dynamics. Boston: Kluwer Academic Publishers, 2001
[100] Rajkumar V, Mohler R R. Nonlinear Control Methods for Power Systems: A Comparison. IEEE Transactions on Control Systems Technology, 1995, 3(2): 231-237
[101] Gan D, Qu Z, Cai H. Multi-machine System Excitation Control via Theories of Feedback Linearization Control and Nonlinear Robust Control. International Journal of Systems Science, 2000, 31(4): 519-527
[102] Hu T, Lin Z. Control Systems with Actuator Saturation: Analysis and Design. Boston: Birkhauser, 2001
[103] Xi Z, Feng G, Cheng D, et al. Nonlinear Decentralized Saturated Controller Design for Power Systems. IEEE Transactions on Control Systems Technology，2003，11(4)：539-547
[104] 甘德强，王锡凡，杜正春等．暂态稳定性分析的自动事故选择方法．电力系统自动化，1994，18(1)：25-30
[105] 朱方，汤涌，张东霞等．我国交流互联电网动态稳定性的研究及解决策略．电网技术，2004，28(15)：1-5
[106] PAGANINI F, LESIEUTRE B C. Generic properties, one-parameter deformations, and the BCU method. IEEE transactions On Circuits and Systems-Ⅰ: Fundamental Theory and Applications, 1999, 46(6): 760-763
[107] Zaborszky J, Huang G, Zheng B. A Counterexample of a Theorem by Tsolas et al. and an Independentresult by Zaborszky et al. IEEE Transactions on Automatic Control, 1988, 33(316-317)
[108] 李明节，王世缨．电力系统在线动态安全分析新方法．清华大学学报：自然科学版，1993，33(1)：99-108
[109] Liamas A, De La Ree Lopez J, Mili L. Clarifications of the BCU Method for Transient Stability Analysis. IEEE Transactions on Power Systems, 1995, 10(1): 210-219
[110] 关天祺，梅生伟，徐政．分散励磁与超导储能装置的干扰抑制控制．电力系统自动化，2002，26(1)：1-6
[111] 陈菊明，梅生伟，刘锋．多机系统TCSC多目标H∞控制器设计．电力系统自动化，2000，24(21)：11-13，18
[112] Davison E J, Kurak E M. A Computational Method for Determining Quadratic Lyapunov Functions for Non-linear Systems. Automatica, 1971, 7(1): 627-636
[113] Qu Z, Dorsey J F. Application of Robust Control to Sustained Oscillations in Power systems. IEEE Transactions on Circuits and Systems, 1992, 39(6): 470-476
[114] 石景海，贺仁睦．动态负荷建模中的负荷时变性研究．中国电机工程学报，2004，24(4)：85-90
[115] Gan D, Chattopadhyay D, Luo X. An Improved Method for Optimal Operation under Stability Constraints. Proceedings of IEEE PES Transmission and Distribution Conference, 2003, Dallas (Texas)
[116] 李颖晖，张保会，李勐．电力系统稳定边界的研究．中国电机工程学报，2002，22(3)：72-77
[117] Kato Y, Iwamoto S. Transient Stability Preventive Control for Stable. Operating Condition With Desired CCT. IEEE Transactions on Power Systems, 2002, 17(4): 1154-1161
[118] Fouad A A, Tong J. Stability Constrained Optimal Rescheduling of Generation. IEEE Transactions On Power Systems, 1993, 8(1): 105-112
[119] Gan D, Qu Z, Wu X. Loadability of Power Systems with Steady-state and Dynamic Security Constraints. International Journal of Electrical Power & Energy Systems, 2003, 25(2): 91-96
[120] Reibig G. Differential-Algebraic Equations and Impasse Points. IEEE Transactions on Circuit and Systems-Ⅰ: Fundamental Theory and Applications, 1996, 43(2): 122-133
[121] Venkatasubramanian V, Schattler H, Zaborszky J. Fast Time-Varying Phasor Analysis in the Balanced Three-Phase Large Electric Power System. IEEE Transactions on Automatic Control, 1995, 40(11): 1975-1982
[122] 陈维桓．微分流形初步．北京：高等教育出版社，2002
[123] Hirsch M W. Differential Topology. New York: Springer-Verlag, 1976
[124] Bartle R G. The Elements of Real Analysis. 2nd ed. New York: John Wiley & Sons, Inc., 1976.
[125] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear Programming-Theory and Algorithms. Second. : John Wiley & Sons, 1993
[126] Guillemin V, Pollack A. Differential Topology. New Jersey: Prentice-Hall, Inc., Englewood Cliffs,
[127] Kundur P, Klein M, Rogers G. Application of Power System Stabilizers for Enhancement of Overall System Stability. IEEE Transactions on Power Systems, 1989, 4(2): 614-626
[128] Arapostathis A, Shankar Sastry S, Varaiya P. Global Analysis of Swing Dynamics. IEEE Transactions on Circuit and Systems, 1982, 29(10): 673-679
[129] Ian A H, Pai M A. Trajectory Sensitivity Analysis of Hybrid Systems. IEEE Transactions on Circuit and Systems, 2000, 47(2): 204-220
[130] 孙景强，房大中，钟德成．暂态稳定约束下的最优潮流．中国电机工程学报，2005，25(12)：12-17
[131] Laufenberg M J, Pai M A. Sensitivity Theory in Power Systems: Applicationin Dynamic Security Analysis. Proceedings of the IEEE International Conference on Control Applications, 1996, Dearborn, MI, USA
[132] 辛焕海，甘德强，邱家驹．一组估计自治系统稳定域严格子集的通用方法．电力系统自动化，2005，29(13)：24-28,75
[133] 王铁强，贺仁睦，王卫国等．电力系统低频振荡机理的研究．中国电机工程学报，2002，22(2)：21-25
[134] 牛振勇，杜正春，方万良等．基于进化策略的多机系统PSS参数优化．中国电机工程学报，2004，24(2)：22-27
[135] Fang W, Ngan H W. Enhancing Small Signal Power System Stability by Coordinating Unified Power Flow Controller with Power System Stabilizer. Electric Power Systems Research, 2003, 65(2): 91-99
[136] Venkatasubramanian V. Stability Boundary Analysis of Nonlinear Dynamics Subject to State Limits. Proceedings of the 34th Hawaii International Conference on System Science, 2001, USA
[137] Sussmann H J, Sontag E D, Yang Y. A General Result on the Stabilization of Linear Systems Using Bounded Controls. IEEE Transactions on Automatic Control, 1994, 39(12): 2411-2425
[138] Hindi H, Boyd S. Analysis of Linear Systems with Saturation using Convex Optimization. Proceedings of the 37th IEEE Conference on Decision & Control, 1998, Tampa, Florida, USA
[139] Suarez R, Alvarez J, Alvarez J. Linear Systems with Single Saturated Input: Stability Analysis. Proceedings of the 30th Conference on Decision and Control, 1991, Brighton, UK
[140] Gutman P O, Hangander P. ANew Design of Constrained Controllers for Linear Systems. IEEE Transactions on Automatic Control, 1985, 30(1): 22-33
[141] Hu T, Lin Z. Composite Quadratic Lyapunov Functions for Constrained Control Systems. IEEE Transactions on Automatic Control, 2003, 48(3): 440-450
[142] Hu T, Lin Z, Chen B M. An Analysis and Design Method for Linear Systems Subject to Actuator Saturation and Disturbance. Automatica, 2002, 38(2): 351-359
[143] 俞立．鲁棒控制-线形矩阵不等式处理方法．北京：清华大学出版社，2002
[144] 李颖晖，张保会．运用非线性系统理论确定电力系统暂态稳定域的应用．中国电机工程学报，2000，20(2)：24-27
[145] Hurwicz L. Programming in Linear Spaces, Studies in Linear and Nonlinear Programming. 2nd. London: Oxford University, 1964
[146] Noble B, James W D. Applied Linear Algebra. Second. New Jersey: Prentice-Hall. Inc., 1977
[147] 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．中国电机工程学报，2004，24(5)：7-11
[148] Jiang H, DorseT J F, Qu Z, et al. Global Robust Adaptive Control of Power Systems. IEE Proceedings, Part C, Generation, Transmission and Distribution, 1994, 141(5): 429-436
[149] Yee H, Muir M J. Transient Stability of Multi-machine Systems with Saturable Exciters. Proceedings of IEE-Generation, Transmission and Distribution, 1980, 127(1)
[150] Escarela-Perez R, Niewierowicz T, Campero-Littlewood E. A Study of the Variation of Synchronous Machine Parameters Due to Saturation: A Numerical Approach. Electric Power Systems Research, 2004, 72(1): 1-11
[151] Hill D J, Mareels I M. Stability Theory for Differential/Algebraic Systems with Application to Power Systems. IEEE Transactions on Circuit and Systems, 1990, 37(11): 1416-1422
[152] Da Silva J M G, Tarbouriech S. Antiwindup Dsign with Guaranteed Regions of Stability: An LMI-based Approach. IEEE Transactions on Automatic Control, 2005, 50(1): 106-111
[153] Mantri R, Saberi A, Venkatasubramanian V. Stability Analysis of Continuous Time Planar Systems with State Saturation Nonlinearity. IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, 1998, 45(9): 989-993
[154] Cao Y, Lin Z, Ward D G. An Anti-windup Approach to Enlarging Domain of Attraction for Linear Systems Subject to Actuator Saturation. IEEE Transactions on Automatic Control, 2002, 47(1): 140-145
[155] Deb K. Multi-Objective Optimization Using Evolutionary Algorithms. England: John Wiley & Sons Ltd, 2001
[156] 李大虎，曹一家，江全元等．基于多目标进化算法的相量测量单元优化配置．电网技术，2005，29(22)：45-49,75
[157] 邹振宇，江全元，张鹏翔等．基于多目标进化算法的TCSC与SVC控制器协调设计．电力系统自动化，2005，29(6)：60-65
[158] Tarbouriech S, Queinnec I, Garcia G. Stability Region Enlargement through Anti-windup Strategy for Linear Systems with Dynamics Restricted Actuator. International Journal of Systems Science, 2006, 37(2): 79-90
[159] 袁亚湘，孙文瑜．最优化理论与方法．北京：科学出版社，1995
[160] Kokotovic P V, Khalil H K, O'Reilly J. Singular Perturbation Methods in Control: Analysis and Design. London: Academic Press, 1986
[161] Singh H, Brown R H, Naidu D S, et al. Robust Stability of Singularly Perturbed State Feedback Systems Using Unified Approach. IEE Proceedings- Control Theory and Applications, 2001, 148(5): 391-396
[162] 刘永强，杨志辉，唐云等．多时间尺度电力系统的模型降阶及稳定性 分析(一)基本理论．电力系统自动化，2003，27(1)：5-10
[163] Saksena V R, O'Reilly J, Kokotovic P V. Singular Perturbations in Control Theory-A Survey. Automatica, 1984, 20(2): 1976-1983
[164] 刘永强，严正，倪以信．双时间尺度电力系统动态模型降阶研究(一)—电力系统奇异摄动模型．电力系统自动化，2002，26(18)：1-5
[165] Kokotovic P V, Sauer P W. Integral Manifold as a Tool for Reduced-order Modeling of Nonlinear System: A Synchronous Machine Case Study. IEEE Transactions on Circuit and Systems, 1989, 36(3): 403-410
[166] Sauer P W, Pai M A. Modeling and Simulation of Multi-machine Power System Dynamics. : Academic Press, 1991
[167] Sauer P W, Ahmed-Zaid S, Kokotovic P V. an Integral Manifold Approach to Reduced Order Dynamic Modeling of Synchronous Machine. IEEE Transactions on Power Systems, 1988, 2(1):17-23
[168] 刘永强，雷文，吴捷等．多时问尺度电力系统的模型降阶及稳定性分析(二)电力系统的降阶与中长期失稳．电力系统自动化，2003，27(2)：1-7