Eigenvalue problems in power systems. (2020)

• Record Type: Book
• Further Information: Note: Federico Milano, Ioannis Dassios, Muyang Liu, Georgios Tzounas.
• Authors: Milano, Federico; Dassios, Ioannis; Liu, Muyang; Tzounas, Georgios
• Contents: Introduction 1 Power System Outlines 1.1 Differential Equations 1.2 Discrete Maps 1.3 Power System Models 1.3.1 Nodes 1.3.2 Transmission System 1.3.3 Loads 1.3.4 Synchronous Machine 1.3.5 Primary Frequency Control 1.3.6 Automatic Voltage Regulator 1.3.7 Power System Stabilizer 1.4 Equilibria 1.5 Linearization 1.6 Lyapunov Stability Criterion 1.7 Definition of Small-Signal Stability 2 Mathematical Outlines 2.1 Matrix Pencils 2.2 Taxonomy of Eigenvalue Problems 2.3 Canonical Forms of Matrix Pencils II Linear Eigenvalue Problems 3 Differential Equations with Regular Pencil 3.1 Formulation 3.2 Solutions and Eigenvalue Analysis 3.3 Applications to Electrical Circuits and Systems 4 Explicit Differential-Algebraic Equations 4.1 Formulation 4.2 Power Systems Modeled as Explicit DAEs 5 Implicit Differential-Algebraic Equations 5.1 Formulation 5.2 Power Systems Modeled as Implicit DAEs 5.3 Floquet Multipliers 5.4 Lyapunov Exponents 6 Differential Equations with Singular Pencil 6.1 Formulation 6.2 Singular Power System Models 7 Möbius transform 7.1 Formulation 7.2 Special cases 7.3 Applications of the Möbius Transform 8 Participation Factors 8.1 Classical Participation Factors 8.1.1 Residues 8.1.2 Power Flow Modal Analysis 8.2 Generalized Participation Factors 8.3 Participation Factors of Algebraic Variables III Non-linear Eigenvalue Problems 9 Polynomial Eigenvalue Problem 9.1 Formulation 9.2 Quadratic Eigenvalue Problem 9.3 Fractional Calculus 10 Delay Differential Equations 10.1 Formulation 10.1.1 Retarded Delay Differential Equations 10.1.2 Neutral Delay Differential Equations 10.2 Pade Approximation 10.3 Quasi-Polynomial Mapping-based Root-finder 10.4 Spectrum Discretization 10.4.1 Infinite-dimensional Eigenvalue Problem 10.4.2 Approximated Eigenvalue Computation 10.4.3 Methods for Sparse Delay 10.5 Newton Correction 11 Systems with Constant Delays 11.1 Delay Differential-Algebraic Equations 11.2 Retarded Index-1 Hessenberg Form DDAEs 11.3 Retarded Non-Index-1 Hessenberg Form DDAEs 11.4 Modeling Transmission Lines as a Continuum 11.5 Descriptor Transform for NDDEs 11.6 Neutral DDAEs 11.7 Delay Compensation in Power Systems 12 Systems with Time-Varying Delays 12.1 Analysis of Time-Varying Delay Systems 12.2 RDDEs with Distributed Delays 12.3 RDDEs with Time-Varying Delays 12.4 Effect of Time-Varying Delays on Power Systems 12.4.1 Simplified Power System Model 12.4.2 Stability Margin of Delay Models 12.4.3 Power System Model with a Gamma-distributed Delay 12.5 Realistic Delay Models for Power System Analysis 12.5.1 Physical Structure of a WAMS 12.5.2 WAMS Delay Model IV Numerical methods 13 Numerical Methods for Eigenvalue Problems 13.1 Introduction 13.2 Algorithms 13.2.1 Vector Iteration 13.2.2 Rayleigh-Ritz Procedure 13.2.3 Schur Decomposition Methods 13.2.4 Krylov Subspace 13.2.5 Contour Integration Methods 14 Open Source Libraries 14.1 Overview 14.1.1 LAPACK 14.1.2 ARPACK 14.1.3 SLEPc 14.1.4 FEAST 14.1.5 z-PARES 14.1.6 Summary of Library Features 14.2 Left Eigenvectors 14.3 Spectral Transforms 15 Large Eigenvalue Problems V Appendices Three-bus System A.1 Network data A.2 Static data A.3 Dynamic data A.4 Reduction to OMIB B LEP Matrices C GEP Matrices Bibliography Index
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2020
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 621.31; Electric power systems -- Mathematical models; Eigenvalues
• Languages: English
• ISBNs: 9781000335224; 9781000335200; 9781000335217; 9780429325311
• Related ISBNs: 9780367343675
• Notes: Note: Description based on CIP data; resource not viewed.
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