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E-raamat: Mathematical Programming for Power Systems Operation: From Theory to Applications in Python

(Universidad Tecnol¿gica de Pereira, Colombia)
  • Formaat: EPUB+DRM
  • Sari: IEEE Press
  • Ilmumisaeg: 01-Dec-2021
  • Kirjastus: Wiley-IEEE Press
  • Keel: eng
  • ISBN-13: 9781119747284
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Mathematical Programming for Power Systems Operation: From Theory to Applications in PythonSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: IEEE Press
  • Ilmumisaeg: 01-Dec-2021
  • Kirjastus: Wiley-IEEE Press
  • Keel: eng
  • ISBN-13: 9781119747284
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Explore the theoretical foundations and real-world power system applications of convex programming

In Mathematical Programming for Power System Operation with Applications in Python, Professor Alejandro Garces delivers a comprehensive overview of power system operations models with a focus on convex optimization models and their implementation in Python. Divided into two parts, the book begins with a theoretical analysis of convex optimization models before moving on to related applications in power systems operations.

The author eschews concepts of topology and functional analysis found in more mathematically oriented books in favor of a more natural approach. Using this perspective, he presents recent applications of convex optimization in power system operations problems.

Mathematical Programming for Power System Operation with Applications in Python uses Python and CVXPY as tools to solve power system optimization problems and includes models that can be solved with the presented framework. The book also includes:

  • A thorough introduction to power system operation, including economic and environmental dispatch, optimal power flow, and hosting capacity
  • Comprehensive explorations of the mathematical background of power system operation, including quadratic forms and norms and the basic theory of optimization
  • Practical discussions of convex functions and convex sets, including affine and linear spaces, politopes, balls, and ellipsoids
  • In-depth examinations of convex optimization, including global optimums, and first and second order conditions

Perfect for undergraduate students with some knowledge in power systems analysis, generation, or distribution, Mathematical Programming for Power System Operation with Applications in Python is also an ideal resource for graduate students and engineers practicing in the area of power system optimization.

Acknowledgment ix
Introduction xi
1 Power systems operation
1(16)
1.1 Mathematical programming for power systems operation
1(2)
1.2 Continuous models
3(8)
1.2.1 Economic and environmental dispatch
3(1)
1.2.2 Hydrothermal dispatch
3(2)
1.2.3 Effect of the grid constraints
5(1)
1.2.4 Optimal power flow
5(2)
1.2.5 Hosting capacity
7(1)
1.2.6 Demand-side management
7(2)
1.2.7 Energy storage management
9(1)
1.2.8 State estimation and grid identification
9(2)
1.3 Binary problems in power systems operation
11(3)
1.3.1 Unit commitment
12(1)
1.3.2 Optimal placement of distributed generation and capacitors
12(1)
1.3.3 Primary feeder reconfiguration and topology identification
13(1)
1.3.4 Phase balancing
13(1)
1.4 Real-time implementation
14(1)
1.5 Using Python
15(2)
Part I Mathematical programming
17(108)
2 A brief introduction to mathematical optimization
19(20)
2.1 About sets and functions
19(3)
2.2 Norms
22(2)
2.3 Global and local optimum
24(1)
2.4 Maximum and minimum values of continuous functions
25(1)
2.5 The gradient method
26(6)
2.6 Lagrange multipliers
32(1)
2.7 The Newton's method
33(2)
2.8 Further readings
35(1)
2.9 Exercises
35(4)
3 Convex optimization
39(22)
3.1 Convex sets
39(6)
3.2 Convex functions
45(2)
3.3 Convex optimization problems
47(3)
3.4 Global optimum and uniqueness of the solution
50(2)
3.5 Duality
52(4)
3.6 Further readings
56(2)
3.7 Exercises
58(3)
4 Convex Programming in Python
61(24)
4.1 Python for convex optimization
61(1)
4.2 Linear programming
62(5)
4.3 Quadratic forms
67(2)
4.4 Semidefinite matrices
69(2)
4.5 Solving quadratic programming problems
71(3)
4.6 Complex variables
74(1)
4.7 What is inside the box?
75(1)
4.8 Mixed-integer programming problems
76(3)
4.9 Transforming MINLP into MILP
79(1)
4.10 Further readings
80(1)
4.11 Exercises
81(4)
5 Conic optimization
85(24)
5.1 Convex cones
85(1)
5.2 Second-order cone optimization
85(7)
5.2.1 Duality in SOC problems
90(2)
5.3 Semidefinite programming
92(6)
5.3.1 Trace, determinant, and the Shur complement
92(3)
5.3.2 Cone of semidefinite matrices
95(2)
5.3.3 Duality in SDP
97(1)
5.4 Semidefinite approximations
98(4)
5.5 Polynomial optimization
102(3)
5.6 Further readings
105(1)
5.7 Exercises
106(3)
6 Robust optimization
109(16)
6.1 Stochastic vs robust optimization
109(2)
6.1.1 Stochastic approach
110(1)
6.1.2 Robust approach
110(1)
6.2 Polyhedral uncertainty
111(2)
6.3 Linear problems with norm uncertainty
113(2)
6.4 Defining the uncertainty set
115(6)
6.5 Further readings
121(1)
6.6 Exercises
122(3)
Part II Power systems operation
125(128)
7 Economic dispatch of thermal units
127(18)
7.1 Economic dispatch
127(4)
7.2 Environmental dispatch
133(3)
7.3 Effect of the grid
136(4)
7.4 Loss equation
140(3)
7.5 Further readings
143(1)
7.6 Exercises
143(2)
8 Unit commitment
145(110)
8.1 Problem definition
145(1)
8.2 Basic unit commitment model
146(4)
8.3 Additional constraints
150(2)
8.4 Effect of the grid
152(1)
8.5 Further readings
153(1)
8.6 Exercises
153(2)
9 Hydrothermal scheduling
155(1)
9.1 Short-term hydrothermal coordination
155(1)
9.2 Basic hydrothermal coordination
156(3)
9.3 Non-linear models
159(3)
9.4 Hydraulic chains
162(3)
9.5 Pumped hydroelectric storage
165(1)
9.6 Further readings
165(4)
9.7 Exercises
169(3)
10 Optimal power flow
172(1)
10.1 OPF in power distribution grids
172(1)
10.1.1 A brief review of power flow analysis
173(4)
10.2 Complex linearization
177(4)
10.2.1 Sequential linearization
181(1)
10.2.2 Exponential models of the load
182(2)
10.3 Second-order cone approximation
184(4)
10.4 Semidefinite approximation
188(2)
10.5 Further readings
190(1)
10.6 Exercises
190(5)
11 Active distribution networks
195(20)
11.1 Modern distribution networks
195(1)
11.2 Primary feeder reconfiguration
196(4)
11.3 Optimal placement of capacitors
200(3)
11.4 Optimal placement of distributed generation
203(2)
11.5 Hosting capacity of solar energy
205(3)
11.6 Harmonics and reactive power compensation
208(4)
11.7 Further readings
212(1)
11.8 Exercises
212(3)
12 State estimation and grid identification
215(20)
12.1 Measurement units
215(1)
12.2 State estimation
216(5)
12.3 Topology identification
221(3)
12.4 Fbus estimation
224(4)
12.5 Load model estimation
228(3)
12.6 Further readings
231(1)
12.7 Exercises
232(3)
13 Demand-side management
235(18)
13.1 Shifting loads
235(5)
13.2 Phase balancing
240(6)
13.3 Energy storage management
246(3)
13.4 Further readings
249(1)
13.5 Exercises
249(4)
A The nodal admittance matrix
253(4)
B Complex linearization
257(6)
C Some Python examples
263(8)
C.1 Basic Python
263(3)
C.2 NumPy
266(2)
C.3 MatplotLib
268(1)
C.4 Pandas
268(3)
Bibliography 271(11)
Index 282
Alejandro Garcés, PhD, is a Professor at Universidad Tecnológica de Pereira in Colombia. Previously, he was a research fellow at the Norwegian University of Science and Technology in Trondheim-Norway, and an External Consultant for the Latin-American Organization of Energy and the Inter-American Development Bank. He is also Senior member of the IEEE, and Associate Editor of different IEEE and IET journals. In 2021 he was awarded with the Georg Forster Research fellow at the Alexander von Humboldt Foundation in Germany to continue his research in collaboration with TU-Dortmund.
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