Applied Mathematics for Restructured Electric Power Systems

Cover -- Contents -- List of Figures -- List of Tables -- Preface -- Contributing Authors -- 1 Applied Mathematics for Restructured Electric Power Systems -- 1 Introduction -- 2 Workshop Presentations -- 3 Synopses of the Articles in this Compilation -- 4 Conclusions -- 2 Reactive Power and Voltage Control Issues in Electric Power Systems -- 1 Introduction -- 2 Reactive Power -- 3 Reactive Power in Operations -- 4 A Fundamental Illustration -- 5 Challenges in Voltage Control and Related Security -- 6 Conclusions -- 3 Identification of Weak Locations using Voltage Stability Margin Index -- 1 Introduction -- 2 Basic Mathematical Model -- 3 Application of the New Method to Large Scale Power Systems -- 4 Simulation Results -- 5 Conclusions -- 6 Future Work -- 4 Bifurcation and Manifold Based Aproach for Voltage and Oscillatory Stability Assessment and Control -- 1 Introduction -- 2 Identification of Saddle Node, Hopf Bifurcation, and Damping Margins -- 2.1 Identification of critical eigenvalue -- 2.2 Damping margin identification -- 2.3 Example -- 3 Tracing Margin Boundaries -- 3.1 Boundary predictor -- 3.2 Boundary corrector -- 3.3 Computation result -- 4 Further Extensions -- 4.1 Optimal margin boundary: cost based security -- 4.2 Fast and slow time scales -- 4.3 Impact on power system security -- 5 Research Needs -- 5 On-Line ATC Evaluation for Large-Scale Power Systems: Framework and Tool -- 1 Introduction -- 2 Transfer Capability -- 3 Transaction-Dependent ATC -- 4 System Modeling -- 5 Identify Critical Contingencies for Static Security -- 6 Estimating Load Margins to Nose Points -- 7 Estimating Load Margins to Static Security Violations -- 8 Identify Critical Contingencies for Dynamic Security -- 9 Solution Algorithm -- 10 Numerical Studies -- 11 Conclusions -- 6 Automating Operation of Large Electric Power Systems Over Broad Ranges of Supply/Demand and Equipment Status -- 1 Introduction -- 2 Electric Power Grids as Complex Network Systems -- 2.1 Assumptions underlying today's operation of hierarchical systems -- 2.2 Implications of violating monotone response -- 2.3 The major challenge: monitoring and control outside monotone response system conditions -- 3 Current Operating Practice: Problems and Open Questions -- 3.1 Historic problems of operating under stress -- 3.2 Some possible solutions and their shortcomings -- 4 Multi-Layered Modeling, Estimation and Control Approach to Managing Electric Power Networks Over Broad Ranges of Operating Conditions -- 4.1 Full non-linear dynamics of electric power systems -- 4.2 Disturbance- and control-driven multi-layered models -- 4.3 A large-scale quasi-stationary model -- 4.4 Multi-layered system constraints -- 5 Multi-Layered Estimation and Control -- 5.1 Quasi-stationary state estimators -- 5.2 Multi-layered control approach -- 5.3 Automated short-term dispatch and unit commitment over broad ranges of conditions and equipment status -- 5.4 Particular case: Today's hiera.