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Convex Optimization of Power Systems

Book Description

Optimization is ubiquitous in power system engineering. Drawing on powerful, modern tools from convex optimization, this rigorous exposition introduces essential techniques for formulating linear, second-order cone, and semidefinite programming approximations to the canonical optimal power flow problem, which lies at the heart of many different power system optimizations. Convex models in each optimization class are then developed in parallel for a variety of practical applications like unit commitment, generation and transmission planning, and nodal pricing. Presenting classical approximations and modern convex relaxations side-by-side, and a selection of problems and worked examples, this is an invaluable resource for students and researchers from industry and academia in power systems, optimization, and control.

Table of Contents

  1. Cover
  2. Half-title page
  3. Title page
  4. Copyright page
  5. Dedication
  6. Contents
  7. Preface
  8. Acknowledgments
  9. Notation
  10. 1. Introduction
    1. 1.1 Recent history
    2. 1.2 Structure and outline
    3. 1.3 On approximations
    4. References
  11. 2. Background
    1. 2.1 Convexity and computational complexity
    2. 2.2 Optimization classes
      1. 2.2.1 Linear and quadratic programming
      2. 2.2.2 Cone programming
      3. 2.2.3 Quadratically constrained programming
      4. 2.2.4 Mixed-integer programming
      5. 2.2.5 Algorithmic maturity
    3. 2.3 Relaxations
      1. 2.3.1 Lift-and-project
      2. 2.3.2 Detour: graph theory
      3. 2.3.3 Preview: How to use a relaxation
    4. 2.4 Classical optimization versus metaheuristics
    5. 2.5 Power system modeling
      1. 2.5.1 Voltage, current, and power in steady-state
      2. 2.5.2 Balanced three-phase operation
      3. 2.5.3 Generator and load modeling
      4. 2.5.4 The per unit system
    6. 2.6 Summary
    7. References
  12. 3. Optimal power flow
    1. 3.1 Basic formulation
      1. 3.1.1 Nonlinear programming approaches
    2. 3.2 Linear approximations in voltage-polar coordinates
      1. 3.2.1 Linearized power flow
      2. 3.2.2 Decoupled power flow
      3. 3.2.3 Network flow
    3. 3.3 Relaxations
      1. 3.3.1 Exactness in radial networks
      2. 3.3.2 Real coordinate systems
      3. 3.3.3 Branch flow models
      4. 3.3.4 Further discussion
    4. 3.4 Load flow
      1. 3.4.1 Exact load flow
      2. 3.4.2 Linearized load flow
    5. 3.5 Extensions
      1. 3.5.1 Direct current networks
      2. 3.5.2 Reactive power capability curves
      3. 3.5.3 Nonconvex generator cost curves
      4. 3.5.4 Polyhedral relaxation of the second-order cone
    6. 3.6 Summary
    7. References
  13. 4. System operation
    1. 4.1 Multi-period optimal power flow
      1. 4.1.1 Ramp constraints
      2. 4.1.2 Energy storage and inventory control
      3. 4.1.3 Implementation via model predictive control
    2. 4.2 Stability and control
      1. 4.2.1 The swing equation
      2. 4.2.2 Linear quadratic regulation
    3. 4.3 Unit commitment
      1. 4.3.1 Objective
      2. 4.3.2 Constraints
    4. 4.4 Reconfiguration
      1. 4.4.1 Radiality constraints
      2. 4.4.2 Power flow and objectives
      3. 4.4.3 Transmission switching
    5. 4.5 Summary
    6. References
  14. 5. Infrastructure planning
    1. 5.1 Nodal placement and sizing
      1. 5.1.1 Problem types and greedy algorithms
      2. 5.1.2 Power sources
      3. 5.1.3 Multiple scenarios
      4. 5.1.4 Energy storage
    2. 5.2 Transmission expansion
      1. 5.2.1 Basic approach
      2. 5.2.2 Linearized models
      3. 5.2.3 Branch flow approximation
      4. 5.2.4 Relaxations
      5. 5.2.5 Feasibility issues
    3. 5.3 Summary
    4. References
  15. 6. Economics
    1. 6.1 Background
      1. 6.1.1 Lagrangian duality
      2. 6.1.2 Pricing and the welfare theorems
      3. 6.1.3 Game theory
    2. 6.2 Electricity markets
      1. 6.2.1 Nodal pricing
      2. 6.2.2 Multi-period and dynamic pricing
      3. 6.2.3 Transmission cost allocation
      4. 6.2.4 Pricing under nonconvexity
    3. 6.3 Market power
      1. 6.3.1 Supply function equilibrium
      2. 6.3.2 Complementarity models
      3. 6.3.3 Capacitated price competition
    4. 6.4 Summary
    5. References
  16. 7. Future directions
    1. 7.1 Uncertainty modeling
      1. 7.1.1 Stochastic programming
      2. 7.1.2 Robust optimization
    2. 7.2 Decentralization and distributed optimization
    3. 7.3 More game theory
      1. 7.3.1 Dynamic games
      2. 7.3.2 Mechanism design
    4. References
  17. Index