Optimal Long-Term Operation of Electric Power Systems

1. Introduction.- 1.1. A Historical Survey.- 1.2. Hydro Plant Modeling for Long-Term Operation.- 1.2.1. Pumped Storage Plants.- 1.2.2. Run-of-River Plants.- 1.2.3. Storage Plants.- 1.2.4. Reservoir Models.- 1.2.5. Operational Constraints.- 1.3. Outline of the Book.- References.- 2. Mathematical Optimization Techniques.- 2.1. Introduction.- 2.2. A Review of Matrices.- 2.2.1. Vectors.- 2.2.2. Matrices.- 2.2.3. Quadratic Forms and Definiteness.- 2.3. Discrete Variational Calculus.- 2.3.1. Unconstrained Discrete Optimization.- 2.3.2. Constrained Discrete Optimization.- 2.4. Discrete Maximum Principle.- 2.4.1. Stochastic Discrete Maximum Principle.- 2.5. Dynamic Programming.- 2.6. Functional Analysis Optimization Technique.- 2.6.1. Norms and Inner Products.- 2.6.2. Hilbert Space.- 2.6.3. Hilbert Space of Random Variables.- 2.6.4. A Minimum Norm Theorem.- References.- 3. Long-Term Operation of Reservoirs in Series.- 3.1. Introduction.- 3.2. Problem Formulation.- 3.2.1. The System under Study.- 3.2.2. The Objective Function.- 3.3. The Problem Solution.- 3.3.1. Turgeon Approaches.- 3.3.2. A Minimum Norm Approach.- 3.3.3. A Nonlinear Model: Minimum Norm Approach.- References.- 4. Long-Term Operation of Multichain Power Systems.- 4.1. Introduction.- 4.2. Problem Formulation.- 4.2.1. The System under Study.- 4.2.2. The Objective Function.- 4.3. The Aggregation Approach (Turgeon Approach).- 4.3.1. The Objective.- 4.3.2. The Solution by Dynamic Programming.- 4.3.3. The One-at-a-Time Method.- 4.3.4. The Aggregation-Decomposition Method.- 4.3.5. Comments.- 4.4. Discrete Maximum Principle.- 4.4.1. General Problem Formulation.- 4.4.2. Solution Algorithm.- 4.4.3. Practical Example.- 4.4.4. Comments.- 4.5. A Minimum Norm Approach, Linear Model.- 4.5.1. The Objective Function.- 4.5.2. A Minimum Norm Formulation.- 4.5.3. The Optimal Solution.- 4.5.4. Algorithm of Solution.- 4.5.5. Practical Example.- 4.6. A Minimum Norm Approach, Nonlinear Model.- 4.6.1. Modeling of the System.- 4.6.2. The Optimal Solution.- 4.6.3. Algorithm of Solution.- 4.6.4. Practical Example.- 4.6.5. Comments.- References.- 5. Modeling and Optimization of a Multireservoir Power System for Critical Water Conditions.- 5.1. Introduction.- 5.2. Problem Formulation.- 5.2.1. The System under Study.- 5.2.2. The Objective Function.- 5.2.3. A Minimum Norm Approach.- 5.2.4. The Optimal Solution.- 5.2.5. Computer Logic.- 5.2.6. Practical Example.- 5.2.7. Concluding Remarks.- 5.3. Nonlinear Storage Model.- 5.3.1. Objective Function.- 5.3.2. A Minimum Norm Formulation.- 5.3.3. The Optimal Solution.- 5.4. A Discrete Maximum Principle Approach (Linear Model).- 5.4.1. Problem Formulation.- 5.4.2. Optimal Equations.- 5.5. Optimization of Power System Operation with a Specified Monthly Generation.- 5.5.1. Problem Formulation.- 5.5.2. The Optimal Solution.- 5.5.3. Algorithm of Solution.- 5.5.4. Practical Example.- 5.5.5. Concluding Remarks.- References.- 6. Optimization of the Firm Hydro Energy Capability for Hydroelectric Systems.- 6.1. Introduction.- 6.2. Nonlinear Programming Model (Hicks et al. Approach).- 6.2.1. System Modeling and Relationships.- 6.2.2. Optimization Objective and Constraints.- 6.2.3. Method of Solution.- 6.2.4. Practical Example.- 6.2.5. Conclusion.- 6.3. A Minimum Norm Approach.- 6.3.1. Optimization Objective and Constraints.- 6.3.2. A Minimum Norm Formulation.- 6.3.3. The Optimal Solution.- 6.3.4. Algorithm of Solution.- 6.4. A Nonlinear Model (Minimum Norm Approach).- 6.4.1. Optimization Objective and Constraints.- 6.4.2. Modeling of the System.- 6.4.3. A Minimum Norm Formulation.- 6.4.4. The Optimal Solution.- References.- 7. Long-Term Optimal Operation of Hydrothermal Power Systems.- 7.1. Introduction.- 7.2. All-Thermal Power Systems.- 7.2.1. Linear Fuel-Cost Function.- 7.2.2. Quadratic Fuel-Cost Function.- 7.2.3. General Solution Method for Nonlinear Functions.- 7.2.4. Dynamic Programming Approach for Nonmonotonic Heat Rate Curves.- 7.2.5. Conclusion.- 7.3. Optimal Scheduling of Hydrothermal Power Systems.- 7.3.1. A Direct Method Approach.- 7.4. Discrete Maximum Principle.- 7.4.1. Concluding Remarks.- 7.5. Stochastic Nonlinear Programming.- 7.5.1. Optimal Stochastic Control Policy.- 7.5.2. Computer Algorithm.- 7.5.3. Practical Example.- 7.5.4. Concluding Remarks.- 7.6. Aggregation with Stochastic Dynamic Programming Approach.- 7.6.1. Aggregation of Reservoirs and Hydro Storage Characteristics.- 7.6.2. Optimization Problem Formulation.- 7.6.3. Optimization Algorithm.- 7.6.4. Practical Example.- 7.6.5. Concluding Remarks.- 7.7. Aggregation-Decomposition Approach.- 7.7.1. Spatial Decomposition.- 7.7.2. Algorithm of Solution.- 7.7.3. Stage Optimization, Optimization Procedure.- 7.7.4. Practical Example.- 7.7.5. Concluding Remarks.- 7.8. A Minimum Norm Approach, Linear Storage-Elevation Model.- 7.8.1. Problem Formulation and the Objective Function.- 7.8.2. A Minimum Norm Formulation.- 7.8.3. Optimal Solution.- 7.8.4. Algorithm of Solution.- 7.8.5. Concluding Remarks.- 7.9. A Minimum Norm Approach, Nonlinear Storage-Elevation Curve.- 7.9.1. Problem Formulation and Objective Functional.- 7.9.2. A Minimum Norm Formulation.- 7.9.3. Optimal Solution.- 7.9.4. Algorithm of Solution.- 7.9.5. Concluding Remarks.- 7.10. Nuclear, Hydrothermal Power Systems.- 7.10.1. Problem Formulation.- 7.10.2. A Minimum Norm Formulation.- 7.10.3. The Optimal Solution.- 7.10.4. Algorithm of Solution, Computer Logic.- 7.10.5. Conclusion.- 7.11. General Comments.- Appendix A: One Dimension Minimization.- Appendix B: Projection Matrix P.- Appendix C: Some Probability Characteristics of Electric Power Systems.- C.l. Approximate Evaluation of Expected Value and Variance of g(x).- C.2. Variances of Thermal Power Generation.- C.3. Probability Properties of Hydroelectric Generation.- C.4. Expected Transmission Losses.- C.5. Expected Cost of Thermal Generation.- References.- 8. Conclusion.- 8.1. Summary.- 8.2. Future Work.