Mathematical Programming for Power Systems Operation with Python Applications

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. Mathematical Programming for Power Systems Operation 2 Contents 6 Acknowledgment 10 Introduction 12 1 Power systems operation 16 1.1 Mathematical programming for power systems operation 16 1.2 Continuous models 18 1.2.1 Economic and environmental dispatch 18 1.2.2 Hydrothermal dispatch 18 1.2.3 Effect of the grid constraints 20 1.2.4 Optimal power flow 20 1.2.5 Hosting capacity 22 1.2.6 Demand-side management 22 1.2.7 Energy storage management 24 1.2.8 State estimation and grid identification 24 1.3 Binary problems in power systems operation 26 1.3.1 Unit commitment 27 1.3.2 Optimal placement of distributed generation and capacitors 27 1.3.3 Primary feeder reconfiguration and topology identification 28 1.3.4 Phase balancing 28 1.4 Real-time implementation 29 1.5 Using Python 30 Part I Mathematical programming 32 2 A brief introduction to mathematical optimization 34 2.1 About sets and functions 34 2.2 Norms 37 2.3 Global and local optimum 39 2.4 Maximum and minimum values of continuous functions 40 2.5 The gradient method 41 2.6 Lagrange multipliers 47 2.7 The Newton’s method 48 2.8 Further readings 50 2.9 Exercises 50 3 Convex optimization 54 3.1 Convex sets 54 3.2 Convex functions 60 3.3 Convex optimization problems 62 3.4 Global optimum and uniqueness of the solution 65 3.5 Duality 67 3.6 Further readings 71 3.7 Exercises 73 4 Convex Programming in Python 76 4.1 Python for convex optimization 76 4.2 Linear programming 77 4.3 Quadratic forms 82 4.4 Semidefinite matrices 84 4.5 Solving quadratic programming problems 86 4.6 Complex variables 89 4.7 What is inside the box? 90 4.8 Mixed-integer programming problems 91 4.9 Transforming MINLP into MILP 94 4.10 Further readings 95 4.11 Exercises 96 5 Conic optimization 100 5.1 Convex cones 100 5.2 Second-order cone optimization 100 5.2.1 Duality in SOC problems 105 5.3 Semidefinite programming 107 5.3.1 Trace, determinant, and the Shur complement 107 5.3.2 Cone of semidefinite matrices 110 5.3.3 Duality in SDP 112 5.4 Semidefinite approximations 113 5.5 Polynomial optimization 117 5.6 Further readings 120 5.7 Exercises 121 6 Robust optimization 124 6.1 Stochastic vs robust optimization 124 6.1.1 Stochastic approach 125 6.1.2 Robust approach 125 6.2 Polyhedral uncertainty 126 6.3 Linear problems with norm uncertainty 128 6.4 Defining the uncertainty set 130 6.5 Further readings 136 6.6 Exercises 136 Part II Power systems operation 140 7 Economic dispatch of thermal units 142 7.1 Economic dispatch 142 7.2 Environmental dispatch 148 7.3 Effect of the grid 151 7.4 Loss equation 155 7.5 Further readings 158 7.6 Exercises 158 8 Unit commitment 160 8.1 Problem definition 160 8.2 Basic unit commitment model 161 8.3 Additional constraints 165 8.4 Effect of the grid 166 8.5 Further readings 168 8.6 Exercises 168 9 Hydrothermal scheduling 170 9.1 Short-term hydrothermal coordination 170 9.2 Basic hydrothermal coordination 171 9.3 Non-linear models 174 9.4 Hydraulic chains 177 9.5 Pumped hydroelectric storage 180 9.6 Further readings 183 9.7 Exercises 184 10 Optimal power flow 186 10.1 OPF in power distribution grids 186 10.1.1 A brief review of power flow analysis 188 10.2 Complex linearization 192 10.2.1 Sequential linearization 196 10.2.2 Exponential models of the load 197 10.3 Second-order cone approximation 199 10.4 Semidefinite approximation 203 10.5 Further readings 205 10.6 Exercises 205 11 Active distribution networks 210 11.1 Modern distribution networks 210 11.2 Primary feeder reconfiguration 211 11.3 Optimal placement of capacitors 215 11.4 Optimal placement of distributed generation 218 11.5 Hosting capacity of solar energy 220 11.6 Harmonics and reactive power compensation 223 11.7 Further readings 227 11.8 Exercises 227 12 State estimation and grid identification 230 12.1 Measurement units 230 12.2 State estimation 231 12.3 Topology identification 236 12.4 Ybus estimation 239 12.5 Load model estimation 243 12.6 Further readings 246 12.7 Exercises 247 13 Demand-side management 250 13.1 Shifting loads 250 13.2 Phase balancing 255 13.3 Energy storage management 261 13.4 Further readings 264 13.5 Exercises 264 A The nodal admittance matrix 268 B Complex linearization 272 C Some Python examples 278 C.1 Basic Python 278 C.2 NumPy 281 C.3 MatplotLib 283 C.4 Pandas 283 Bibliography 286 Index 296 EULA 298 Descripción del editor: "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 capacityComprehensive explorations of the mathematical background of power system operation, including quadratic forms and norms and the basic theory of optimizationPractical discussions of convex functions and convex sets, including affine and linear spaces, politopes, balls, and ellipsoidsIn-depth examinations of convex optimization, including global optimums, and first and second order conditionsPerfect 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." (Amazon) **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