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E-book: Convex Optimization of Power Systems

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(University of Toronto)
  • Format: PDF+DRM
  • Pub. Date: 12-Feb-2015
  • Publisher: Cambridge University Press
  • Language: eng
  • ISBN-13: 9781316236918
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Convex Optimization of Power SystemsLarger Image
  • Format: PDF+DRM
  • Pub. Date: 12-Feb-2015
  • Publisher: Cambridge University Press
  • Language: eng
  • ISBN-13: 9781316236918
Other books in subject:

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"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"--

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A mathematically rigorous guide to convex optimization for power systems engineering.
Preface xi
Acknowledgments xii
Notation xiii
1 Introduction
1(4)
1.1 Recent history
1(1)
1.2 Structure and outline
2(1)
1.3 On approximations
3(2)
References
4(1)
2 Background
5(38)
2.1 Convexity and computational complexity
5(3)
2.2 Optimization classes
8(10)
2.2.1 Linear and quadratic programming
8(1)
2.2.2 Cone programming
9(4)
2.2.3 Quadratically constrained programming
13(2)
2.2.4 Mixed-integer programming
15(2)
2.2.5 Algorithmic maturity
17(1)
2.3 Relaxations
18(8)
2.3.1 Lift-and-project
20(4)
2.3.2 Detour: graph theory
24(1)
2.3.3 Preview: How to use a relaxation
25(1)
2.4 Classical optimization versus metaheuristics
26(1)
2.5 Power system modeling
27(10)
2.5.1 Voltage, current, and power in steady-state
28(3)
2.5.2 Balanced three-phase operation
31(3)
2.5.3 Generator and load modeling
34(2)
2.5.4 The per unit system
36(1)
2.6 Summary
37(6)
References
39(4)
3 Optimal power flow
43(38)
3.1 Basic formulation
44(4)
3.1.1 Nonlinear programming approaches
47(1)
3.2 Linear approximations in voltage-polar coordinates
48(3)
3.2.1 Linearized power flow
48(1)
3.2.2 Decoupled power flow
49(1)
3.2.3 Network flow
50(1)
3.3 Relaxations
51(16)
3.3.1 Exactness in radial networks
55(3)
3.3.2 Real coordinate systems
58(4)
3.3.3 Branch flow models
62(3)
3.3.4 Further discussion
65(2)
3.4 Load flow
67(3)
3.4.1 Exact load flow
67(2)
3.4.2 Linearized load flow
69(1)
3.5 Extensions
70(5)
3.5.1 Direct current networks
70(1)
3.5.2 Reactive power capability curves
71(1)
3.5.3 Nonconvex generator cost curves
72(2)
3.5.4 Polyhedral relaxation of the second-order cone
74(1)
3.6 Summary
75(6)
References
77(4)
4 System operation
81(31)
4.1 Multi-period optimal power flow
81(9)
4.1.1 Ramp constraints
83(1)
4.1.2 Energy storage and inventory control
84(5)
4.1.3 Implementation via model predictive control
89(1)
4.2 Stability and control
90(6)
4.2.1 The swing equation
91(3)
4.2.2 Linear quadratic regulation
94(2)
4.3 Unit commitment
96(5)
4.3.1 Objective
97(1)
4.3.2 Constraints
98(3)
4.4 Reconfiguration
101(6)
4.4.1 Radiality constraints
102(1)
4.4.2 Power flow and objectives
103(3)
4.4.3 Transmission switching
106(1)
4.5 Summary
107(5)
References
108(4)
5 Infrastructure planning
112(20)
5.1 Nodal placement and sizing
113(7)
5.1.1 Problem types and greedy algorithms
114(2)
5.1.2 Power sources
116(2)
5.1.3 Multiple scenarios
118(2)
5.1.4 Energy storage
120(1)
5.2 Transmission expansion
120(9)
5.2.1 Basic approach
121(2)
5.2.2 Linearized models
123(2)
5.2.3 Branch flow approximation
125(1)
5.2.4 Relaxations
126(2)
5.2.5 Feasibility issues
128(1)
5.3 Summary
129(3)
References
130(2)
6 Economics
132(52)
6.1 Background
133(11)
6.1.1 Lagrangian duality
133(6)
6.1.2 Pricing and the welfare theorems
139(2)
6.1.3 Game theory
141(3)
6.2 Electricity markets
144(23)
6.2.1 Nodal pricing
148(9)
6.2.2 Multi-period and dynamic pricing
157(3)
6.2.3 Transmission cost allocation
160(6)
6.2.4 Pricing under nonconvexity
166(1)
6.3 Market power
167(9)
6.3.1 Supply function equilibrium
170(2)
6.3.2 Complementarity models
172(1)
6.3.3 Capacitated price competition
173(3)
6.4 Summary
176(8)
References
178(6)
7 Future directions
184
7.1 Uncertainty modeling
184(2)
7.1.1 Stochastic programming
184(1)
7.1.2 Robust optimization
185(1)
7.2 Decentralization and distributed optimization
186(2)
7.3 More game theory
188
7.3.1 Dynamic games
188(1)
7.3.2 Mechanism design
189(1)
References
190(3)
Index
193
Joshua Adam Taylor is an Assistant Professor of Electrical and Computer Engineering at the University of Toronto.
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