Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications
Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications
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DOI：
10.1002/9780470872130
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发表时间：
2010-12
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影响因子：
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通讯作者：
H. Chiang
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作者：
H. Chiang
前言。鸣谢。1。简介与概述。1.1简介。1.2运行环境趋势。1.3在线TSA。1.4对新工具的需求。1.5直接方法：限制和挑战。1.6本书的目的。系统建模与稳定性问题。2.1导论。2.2电力系统稳定性问题。2.3模型结构与参数。2.4基于测量的建模。2.5电力系统稳定性问题。2.6稳定性分析方法。2.7结束语。非线性动力系统的Lyapunov稳定性与稳定区域。3.1简介。3.2平衡点与Lyapunov稳定性。3.3 Lyapunov函数理论。3.4稳定流形与不稳定流形。3.5稳定区域。3.6稳定边界的局部表征。3.7稳定边界的全局表征。3.8确定稳定边界的算法。3.9结论。5.准稳定区域：分析与表征。4.1简介。4.2准稳定区域。4.3准稳定区域的表征。4.4结论。能量函数理论与直接方法。5.1简介。5.2能量函数。5.3能量函数理论。5.4用能量函数估计稳定区域。5.5估计稳定区域的最优方案。5.6准稳定区域与能量函数。5.7结论。构造暂态稳定模型的解析能量函数。6.1简介。6.2无损网络约简模型的能量函数。6.3无损结构保持模型的能量函数。6.4有损模型的能量函数的不存在性。6.5局部能量函数的存在性。6.6结束语。有耗瞬态稳定模型的数值能量函数的构造。7.1导论。7.2两步过程。7.3基于第一积分的过程。7.4病态数值问题。7.5近似格式的数值评估。7.6多步梯形格式。7.7关于修正的数值能量函数。7.8结束语。稳定性分析的直接方法：简介。8.1简介。8.2简单系统。8.3最接近UEP方法。8.4控制UEP方法。8.5 PEBS方法。8.6结束语。最接近UEP方法的基础。9.1简介。9.2结构保持模型。9.3最接近UEP。9.4最近UEP的表征。9.5最接近UEP方法。9.6改进的最接近UEP方法。9.7最接近UEP的鲁棒性9.8数值研究9.9结论势能边界面法的基础。10.1导论。10.2 PEBS方法的步骤。10.3原始模型与人工模型。10.4广义梯度系统。10.5一类二阶动力系统。10.6原始模型与人工模型的关系。10.7 PEBS方法的分析。10.8结束语。控制UEP方法：理论。11.1简介。11.2控制UEP。11.3存在性与唯一性。11.4控制UEP方法。11.5控制UEP方法的分析。11.6数值算例。11.7动态和几何表征。11.8结束语。控制UEP方法：计算。12.1简介。12.2计算挑战。12.3平衡点的约束非线性方程。12.4计算平衡点的数值技术。12.5平衡点的收敛区域。12.6计算控制UEP的概念方法。12.7数值研究。12.8结束语13.保持网络暂态稳定模型的控制UEP方法的基础。13.1引言。13.2系统模型。13.3稳定区域。13.4奇异摄动方法。13.5保持网络模型的能量函数。13.6 DAE系统的控制UEP。13.7 DAE系统的控制UEP方法。13.8数值研究。13.9结论。网络约简BCU方法及其理论基础。14.1导论。14.2约简状态系统。14.3分析结果。14.4静态与动态关系。14.5动态性质（D3）。14.6一个概念性网络约简BCU方法。14.7结语。16.数值网络约简BCU方法。15.1导论。15.2计算退出点。15.3稳定边界跟随过程。15.4保障方案。15.5举例说明。15.6数值说明。15.7 IEEE测试系统。15.8结束句。保持网络的BCU方法及其理论基础。16.1导论。16.2状态简化模型。16.3静态和动态特性。16.4分析结果。16.5总体静态和动态关系。16.6动态特性（D3）。16.7概念网络保持BCU方法。16.8结束语。数值保网BCU方法。17.1简介。17.2计算注意事项。17.3检测出口点的数值方案。17.4计算MGP。18. 17.5平衡点的计算。17.6数值例子。17.7大型试验系统。17.8结束语。稳定性边界视角下BCU方法的数值研究。18.1导论。18.2网络约简模型的稳定性边界。18.3网络保持模型。18.4控制UEP的一个动态性质。18.5结束语。20. BCU方法的横向条件研究。19.1导论。19.2参数化研究。19.3边界性质的解析研究。19.4双机无限总线（TMIB）系统。19.5数值研究。19.6结束语。21. bcu -出口点法。20.1简介。20.2边界性质。20.3 bcu -出口点的计算。20.4 bcu -出口点和临界能量。20.5 bcu -出口点法。20.6结束语。电力系统中偶然性的群性质。21.1引言。21.2相干偶然性群。21.3相干偶然性群的识别。21.4静态群性质。21.5动态群性质。21.6结束语。基于组的BCU-Exit方法。22.1简介。22.2基于组的验证方案。22.3线性与非线性关系。22.4基于组的BCU-Exit点法。22.5数值研究。22.6结束语。23。基于组的BCU-CUEP方法。23.1简介。23.2控制UEP的精确计算方法。23.3基于群的BCU-CUEP方法。23.4数值研究。23.5结束语。基于组的BCU方法。24.1简介。24.2精确临界能量的基于组的BCU方法。24.3 cuep的基于组的BCU方法。24.4数值研究。24.5结语。展望与未来方向。25.1当前发展。25.2在线动态应急筛选。25.3进一步改进。25.4相量测量单元（PMU）辅助在线ATC确定。25.5新兴应用。25.6结语。合同附件。A1.1数学基础。A1.2第九章定理的证明。第10章的定理证明。参考书目。索引。
Preface. Acknowledgments. 1. Introduction and Overview. 1.1 Introduction. 1.2 Trends of Operating Environment. 1.3 Online TSA. 1.4 Need for New Tools. 1.5 Direct Methods: Limitations and Challenges. 1.6 Purposes of This Book. 2. System Modeling and Stability Problems. 2.1 Introduction. 2.2 Power System Stability Problem. 2.3 Model Structures and Parameters. 2.4 Measurement-Based Modeling. 2.5 Power System Stability Problems. 2.6 Approaches for Stability Analysis. 2.7 Concluding Remarks. 3. Lyapunov Stability and Stability Regions of Nonlinear Dynamical Systems. 3.1 Introduction. 3.2 Equilibrium Points and Lyapunov Stability. 3.3 Lyapunov Function Theory. 3.4 Stable and Unstable Manifolds. 3.5 Stability Regions. 3.6 Local Characterizations of Stability Boundary. 3.7 Global Characterization of Stability Boundary. 3.8 Algorithm to Determine the Stability Boundary. 3.9 Conclusion. 4. Quasi-Stability Regions: Analysis and Characterization. 4.1 Introduction. 4.2 Quasi-Stability Region. 4.3 Characterization of Quasi-Stability Regions. 4.4 Conclusions. 5. Energy Function Theory and Direct Methods. 5.1 Introduction. 5.2 Energy Functions. 5.3 Energy Function Theory. 5.4 Estimating Stability Region Using Energy Functions. 5.5 Optimal Schemes for Estimating Stability Regions. 5.6 Quasi-Stability Region and Energy Function. 5.7 Conclusion. 6. Constructing Analytical Energy Functions for Transient Stability Models. 6.1 Introduction. 6.2 Energy Functions for Lossless Network-Reduction Models. 6.3 Energy Functions for Lossless Structure-Preserving Models. 6.4 Nonexistence of Energy Functions for Lossy Models. 6.5 Existence of Local Energy Functions. 6.6 Concluding Remarks. 7. Construction of Numerical Energy Functions for Lossy Transient Stability Models. 7.1 Introduction. 7.2 A Two-Step Procedure. 7.3 First Integral-Based Procedure. 7.4 Ill-Conditioned Numerical Problems. 7.5 Numerical Evaluations of Approximation Schemes. 7.6 Multistep Trapezoidal Scheme. 7.7 On the Corrected Numerical Energy Functions. 7.8 Concluding Remarks. 8. Direct Methods for Stability Analysis: An Introduction. 8.1 Introduction. 8.2 A Simple System. 8.3 Closest UEP Method. 8.4 Controlling UEP Method. 8.5 PEBS Method. 8.6 Concluding Remarks. 9. Foundation of the Closest UEP Method. 9.1 Introduction. 9.2 A Structure-Preserving Model. 9.3 Closest UEP. 9.4 Characterization of the Closest UEP. 9.5 Closest UEP Method. 9.6 Improved Closest UEP Method. 9.7 Robustness of the Closest UEP. 9.8 Numerical Studies. 9.9 Conclusions. 10. Foundations of the Potential Energy Boundary Surface Method. 10.1 Introduction. 10.2 Procedure of the PEBS Method. 10.3 Original Model and Artifi cial Model. 10.4 Generalized Gradient Systems. 10.5 A Class of Second-Order Dynamical Systems. 10.6 Relation between the Original Model and the Artifi cial Model. 10.7 Analysis of the PEBS Method. 10.8 Concluding Remarks. 11. Controlling UEP Method: Theory. 11.1 Introduction. 11.2 The Controlling UEP. 11.3 Existence and Uniqueness. 11.4 The Controlling UEP Method. 11.5 Analysis of the Controlling UEP Method. 11.6 Numerical Examples. 11.7 Dynamic and Geometric Characterizations. 11.8 Concluding Remarks. 12. Controlling UEP Method: Computations. 12.1 Introduction. 12.2 Computational Challenges. 12.3 Constrained Nonlinear Equations for Equilibrium Points. 12.4 Numerical Techniques for Computing Equilibrium Points. 12.5 Convergence Regions of Equilibrium Points. 12.6 Conceptual Methods for Computing the Controlling UEP. 12.7 Numerical Studies. 12.8 Concluding Remarks. 13. Foundations of Controlling UEP Methods for Network-Preserving Transient Stability Models. 13.1 Introduction. 13.2 System Models. 13.3 Stability Regions. 13.4 Singular Perturbation Approach. 13.5 Energy Functions for Network-Preserving Models. 13.6 Controlling UEP for DAE Systems. 13.7 Controlling UEP Method for DAE Systems. 13.8 Numerical Studies. 13.9 Concluding Remarks. 14. Network-Reduction BCU Method and Its Theoretical Foundation. 14.1 Introduction. 14.2 Reduced-State System. 14.3 Analytical Results. 14.4 Static and Dynamic Relationships. 14.5 Dynamic Property (D3). 14.6 A Conceptual Network-Reduction BCU Method. 14.7 Concluding Remarks. 15. Numerical Network-Reduction BCU Method. 15.1 Introduction. 15.2 Computing Exit Points. 15.3 Stability-Boundary-Following Procedure. 15.4 A Safeguard Scheme. 15.5 Illustrative Examples. 15.6 Numerical Illustrations. 15.7 IEEE Test System. 15.8 Concluding Remarks. 16. Network-Preserving BCU Method and Its Theoretical Foundation. 16.1 Introduction. 16.2 Reduced-State Model. 16.3 Static and Dynamic Properties. 16.4 Analytical Results. 16.5 Overall Static and Dynamic Relationships. 16.6 Dynamic Property (D3). 16.7 Conceptual Network-Preserving BCU Method. 16.8 Concluding Remarks. 17. Numerical Network-Preserving BCU Method. 17.1 Introduction. 17.2 Computational Considerations. 17.3 Numerical Scheme to Detect Exit Points. 17.4 Computing the MGP. 17.5 Computation of Equilibrium Points. 17.6 Numerical Examples. 17.7 Large Test Systems. 17.8 Concluding Remarks. 18. Numerical Studies of BCU Methods from Stability Boundary Perspectives. 18.1 Introduction. 18.2 Stability Boundary of Network-Reduction Models. 18.3 Network-Preserving Model. 18.4 One Dynamic Property of the Controlling UEP. 18.5 Concluding Remarks. 19. Study of the Transversality Conditions of the BCU Method. 19.1 Introduction. 19.2 A Parametric Study. 19.3 Analytical Investigation of the Boundary Property. 19.4 The Two-Machine Infi nite Bus (TMIB) System. 19.5 Numerical Studies. 19.6 Concluding Remarks. 20. The BCU-Exit Point Method. 20.1 Introduction. 20.2 Boundary Property. 20.3 Computation of the BCU-Exit Point. 20.4 BCU-Exit Point and Critical Energy. 20.5 BCU-Exit Point Method. 20.6 Concluding Remarks. 21. Group Properties of Contingencies in Power Systems. 21.1 Introduction. 21.2 Groups of Coherent Contingencies. 21.3 Identifi cation of a Group of Coherent Contingencies. 21.4 Static Group Properties. 21.5 Dynamic Group Properties. 21.6 Concluding Remarks. 22. Group-Based BCU-Exit Method. 22.1 Introduction. 22.2 Group-Based Verifi cation Scheme. 22.3 Linear and Nonlinear Relationships. 22.4 Group-Based BCU-Exit Point Method. 22.5 Numerical Studies. 22.6 Concluding Remarks. 23. Group-Based BCU-CUEP Methods. 23.1 Introduction. 23.2 Exact Method for Computing the Controlling UEP. 23.3 Group-Based BCU-CUEP Method. 23.4 Numerical Studies. 23.5 Concluding Remarks. 24. Group-Based BCU Method. 24.1 Introduction. 24.2 Group-Based BCU Method for Accurate Critical Energy. 24.3 Group-Based BCU Method for CUEPs. 24.4 Numerical Studies. 24.5 Concluding Remarks. 25. Perspectives and Future Directions. 25.1 Current Developments. 25.2 Online Dynamic Contingency Screening. 25.3 Further Improvements. 25.4 Phasor Measurement Unit (PMU)-Assisted Online ATC Determination. 25.5 Emerging Applications. 25.6 Concluding Remarks. Appendix. A1.1 Mathematical Preliminaries. A1.2 Proofs of Theorems in Chapter 9. A1.3 Proofs of Theorems in Chapter 10. Bibliography. Index.