Computational Techniques for Voltage Stability Assessment and Control

Cover -- Contents -- Preface -- CH 1 Introduction -- 1.1 What is voltage stability? -- 1.2 Voltage Collapse Incidents -- 1.3 Two Bus Example -- 1.3.1 Derivation for critical voltage and critical power -- 1.3.2 Q-V curves -- 1.3.3 Discussion on PV and QV Curves -- 1.3.4 Maximum power and power flow Jacobian -- References -- CH 2 Numerical Bifurcation Techniques -- 2.1 Various Types of Bifurcation -- 2.2 Bifurcation of Dynamical Systems -- 2.2.1 Center manifold -- 2.3 Detection of Bifurcation Points -- 2.3.1 Static bifurcations -- 2.3.2 Homotopy Method -- 2.3.3 Continuation methods -- 2.3.4 Curve Tracing -- 2.3.5 Direct method in computing the Saddle node bifurcation point: a one step continuation -- 2.4 Hopf Bifurcation -- 2.4.1 Existence of Hopf bifurcation point -- 2.5 Complex Bifurcation -- References -- CH 3 Continuation Power Flow -- 3.1 Introduction -- 3.2 Locally Parameterized Continuation -- 3.3 Formulation of Power Flow Equations -- 3.4 The Predictor-corrector Process -- 3.4.1 Selecting the continuation parameter -- 3.4.2 Identifying the critical point -- 3.5 Examples -- 3.6 Simultaneous Equilibria Tracing in Power Systems -- 3.6.1 Total solution at an equilibrium -- 3.6.2 Traditional approach -- 3.7 Power Flow Methodology and Assumptions -- 3.7.1 Nonlinearity in power flow -- 3.7.2 Slack bus assumption -- 3.7.3 PV bus assumption -- 3.8 Total Power System Equilibria Solutions -- 3.8.1 Formulation of power system DAE model -- 3.8.2 Bifurcation modeling of power system dynamics -- 3.8.3 Manifold models in power systems -- 3.8.4 Equilibrium manifold Tracing of power systems -- 3.8.5 Initialization for power system equilibrium tracing -- 3.8.6 Continuation method with local parametrization -- 3.8.7 Linerization of power system DAE -- 3.8.8 Detection of Saddle Node Bifurcation with System Total Jacobian -- 3.8.9 Limits implementation -- 3.9 Numerical examples for EQTP -- References -- CH 4 Sensitivity Analysis for Voltage Stability -- 4.1 Introduction -- 4.2 Given State Based Indices -- 4.3 Large Deviation Based Indices -- 4.4 Stability Studies via Sensitivity Analysis -- 4.4.1 Identification of critical elements -- 4.4.2 Eigenvalue sensitivity -- 4.4.3 Modal analysis -- 4.4.4 Sensitivity analysis via CPF -- 4.4.5 Tangent vector, right eigenvector, and right singular vector of J -- 4.4.6 Voltage stability index from the tangent vector -- 4.4.7 Sensitivity analysis from the tangent vector -- 4.4.8 Bus sensitivities -- 4.4.9 Branch sensitivities -- 4.4.10 Generator sensitivities -- 4.4.11 Qualitative vs. quantitative sensitivities -- 4.5 Margin Sensitivity -- 4.5.1 Transfer margin estimation -- 4.5.2 Multi-parameter margin sensitivity -- 4.5.3 Sensitivity formulas -- 4.6 Test System Studies -- 4.6.1 Two bus example: -- 4.6.2 The New England system -- References -- CH 5 Voltage Stability Margin Boundary Tracing -- 5.1 Introduction -- 5.2 Natural Parameterization for Margin Bo.