Mathematical Programming for Power Systems Operation with Python Applications

Description

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 Contents Acknowledgment Introduction 1 Power systems operation 1.1 Mathematical programming for power systems operation 1.2 Continuous models 1.2.1 Economic and environmental dispatch 1.2.2 Hydrothermal dispatch 1.2.3 Effect of the grid constraints 1.2.4 Optimal power flow 1.2.5 Hosting capacity 1.2.6 Demand-side management 1.2.7 Energy storage management 1.2.8 State estimation and grid identification 1.3 Binary problems in power systems operation 1.3.1 Unit commitment 1.3.2 Optimal placement of distributed generation and capacitors 1.3.3 Primary feeder reconfiguration and topology identification 1.3.4 Phase balancing 1.4 Real-time implementation 1.5 Using Python Part I Mathematical programming 2 A brief introduction to mathematical optimization 2.1 About sets and functions 2.2 Norms 2.3 Global and local optimum 2.4 Maximum and minimum values of continuous functions 2.5 The gradient method 2.6 Lagrange multipliers 2.7 The Newton’s method 2.8 Further readings 2.9 Exercises 3 Convex optimization 3.1 Convex sets 3.2 Convex functions 3.3 Convex optimization problems 3.4 Global optimum and uniqueness of the solution 3.5 Duality 3.6 Further readings 3.7 Exercises 4 Convex Programming in Python 4.1 Python for convex optimization 4.2 Linear programming 4.3 Quadratic forms 4.4 Semidefinite matrices 4.5 Solving quadratic programming problems 4.6 Complex variables 4.7 What is inside the box? 4.8 Mixed-integer programming problems 4.9 Transforming MINLP into MILP 4.10 Further readings 4.11 Exercises 5 Conic optimization 5.1 Convex cones 5.2 Second-order cone optimization 5.2.1 Duality in SOC problems 5.3 Semidefinite programming 5.3.1 Trace, determinant, and the Shur complement 5.3.2 Cone of semidefinite matrices 5.3.3 Duality in SDP 5.4 Semidefinite approximations 5.5 Polynomial optimization 5.6 Further readings 5.7 Exercises 6 Robust optimization 6.1 Stochastic vs robust optimization 6.1.1 Stochastic approach 6.1.2 Robust approach 6.2 Polyhedral uncertainty 6.3 Linear problems with norm uncertainty 6.4 Defining the uncertainty set 6.5 Further readings 6.6 Exercises Part II Power systems operation 7 Economic dispatch of thermal units 7.1 Economic dispatch 7.2 Environmental dispatch 7.3 Effect of the grid 7.4 Loss equation 7.5 Further readings 7.6 Exercises 8 Unit commitment 8.1 Problem definition 8.2 Basic unit commitment model 8.3 Additional constraints 8.4 Effect of the grid 8.5 Further readings 8.6 Exercises 9 Hydrothermal scheduling 9.1 Short-term hydrothermal coordination 9.2 Basic hydrothermal coordination 9.3 Non-linear models 9.4 Hydraulic chains 9.5 Pumped hydroelectric storage 9.6 Further readings 9.7 Exercises 10 Optimal power flow 10.1 OPF in power distribution grids 10.1.1 A brief review of power flow analysis 10.2 Complex linearization 10.2.1 Sequential linearization 10.2.2 Exponential models of the load 10.3 Second-order cone approximation 10.4 Semidefinite approximation 10.5 Further readings 10.6 Exercises 11 Active distribution networks 11.1 Modern distribution networks 11.2 Primary feeder reconfiguration 11.3 Optimal placement of capacitors 11.4 Optimal placement of distributed generation 11.5 Hosting capacity of solar energy 11.6 Harmonics and reactive power compensation 11.7 Further readings 11.8 Exercises 12 State estimation and grid identification 12.1 Measurement units 12.2 State estimation 12.3 Topology identification 12.4 Ybus estimation 12.5 Load model estimation 12.6 Further readings 12.7 Exercises 13 Demand-side management 13.1 Shifting loads 13.2 Phase balancing 13.3 Energy storage management 13.4 Further readings 13.5 Exercises A The nodal admittance matrix B Complex linearization C Some Python examples C.1 Basic Python C.2 NumPy C.3 MatplotLib C.4 Pandas Bibliography Index EULA