Distributed Optimization With Its Applications To Power Systems

Mathematical optimization techniques are among the most successful tools for controlling technical systems optimally with feasibility guarantees. Yet, they are often centralized—all data has to be collected in one central and computationally powerful entity. Methods from distributed optimization overcome this limitation. Classical approaches, however, are often not applicable due to non-convexities. This work develops one of the first frameworks for distributed non-convex optimization.

This book provides a detailed overview of possible applications of distributed optimization in power systems. Centralized algorithms are widely used for optimization and control in power system applications. These algorithms require all the measurements and data to be accumulated at a central location and hence suffer from single-point-of-failure. Additionally, these algorithms lack scalability in the number of sensors and actuators, especially with the increasing integration of distributed energy resources (DERs). As the power system becomes a confluence of a diverse set of decision-making entities with a multitude of objectives, the preservation of privacy and operation of the system with limited information has been a growing concern. Distributed optimization techniques solve these challenges while also ensuring resilient computational solutions for the power system operation in the presence of both natural and man-made adversaries. There are numerous commonly-used distributed optimization approaches, and a comprehensive classification of these is discussed and detailed in this work. All of these algorithms have displayed efficient identification of global optimum solutions for convex continuous distributed optimization problems. The algorithms discussed in the literature thus far are predominantly used to manage continuous state variables, however, the inclusion of integer variables in the decision support is needed for specific power system problems.The mixed integer programming (MIP) problem arises in a power system operation and control due to tap changing transformers, capacitors and switches. There are numerous global optimization techniques for MIPs. Whilst most are able to solve NP-hard convexified MIP problems centrally, they are time consuming and do not scale well for large scale distributed problems. Decomposition and a solution approach of distributed coordination can help to resolve the scalability issue. Despite the fact that a large body of work on the centralized solution methods for convexified MIP problems already exists, the literature on distributed MIPs is relatively limited. The distributed optimization algorithms applied in power networks to solve MIPs are included in this book. Machine Learning (ML) based solutions can help to get faster convergence for distributed optimization or can replace optimization techniques depending on the problem. Finally, a summary and path forward are provided, and the advancement needed in distributed optimization for the power grid is also presented.

Distributed Optimization and Learning: A Control-Theoretic Perspective illustrates the underlying principles of distributed optimization and learning. The book presents a systematic and self-contained description of distributed optimization and learning algorithms from a control-theoretic perspective. It focuses on exploring control-theoretic approaches and how those approaches can be utilized to solve distributed optimization and learning problems over network-connected, multi-agent systems. As there are strong links between optimization and learning, this book provides a unified platform for understanding distributed optimization and learning algorithms for different purposes. Provides a series of the latest results, including but not limited to, distributed cooperative and competitive optimization, machine learning, and optimal resource allocation Presents the most recent advances in theory and applications of distributed optimization and machine learning, including insightful connections to traditional control techniques Offers numerical and simulation results in each chapter in order to reflect engineering practice and demonstrate the main focus of developed analysis and synthesis approaches

This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike. Focusing on the natures and functions of agents, communication networks and algorithms in the context of distributed optimization for networked control systems, this book introduces readers to the background of distributed optimization; recent developments in distributed algorithms for various types of underlying communication networks; the implementation of computation-efficient and communication-efficient strategies in the execution of distributed algorithms; and the frameworks of convergence analysis and performance evaluation. On this basis, the book then thoroughly studies 1) distributed constrained optimization and the random sleep scheme, from an agent perspective; 2) asynchronous broadcast-based algorithms, event-triggered communication, quantized communication, unbalanced directed networks, and time-varying networks, from a communication network perspective; and 3) accelerated algorithms and stochastic gradient algorithms, from an algorithm perspective. Finally, the applications of distributed optimization in large-scale statistical learning, wireless sensor networks, and for optimal energy management in smart grids are discussed.

This book provides a detailed overview of possible applications of distributed optimization in power systems. Centralized algorithms are widely used for optimization and control in power system applications. These algorithms require all the measurements and data to be accumulated at a central location and hence suffer from single-point-of-failure. Additionally, these algorithms lack scalability in the number of sensors and actuators, especially with the increasing integration of distributed energy resources (DERs). As the power system becomes a confluence of a diverse set of decision-making entities with a multitude of objectives, the preservation of privacy and operation of the system with limited information has been a growing concern. Distributed optimization techniques solve these challenges while also ensuring resilient computational solutions for the power system operation in the presence of both natural and man-made adversaries. There are numerous commonly-used distributed optimization approaches, and a comprehensive classification of these is discussed and detailed in this work. All of these algorithms have displayed efficient identification of global optimum solutions for convex continuous distributed optimization problems. The algorithms discussed in the literature thus far are predominantly used to manage continuous state variables, however, the inclusion of integer variables in the decision support is needed for specific power system problems.The mixed integer programming (MIP) problem arises in a power system operation and control due to tap changing transformers, capacitors and switches. There are numerous global optimization techniques for MIPs. Whilst most are able to solve NP-hard convexified MIP problems centrally, they are time consuming and do not scale well for large scale distributed problems. Decomposition and a solution approach of distributed coordination can help to resolve the scalability issue. Despite the fact that a large body of work on the centralized solution methods for convexified MIP problems already exists, the literature on distributed MIPs is relatively limited. The distributed optimization algorithms applied in power networks to solve MIPs are included in this book. Machine Learning (ML) based solutions can help to get faster convergence for distributed optimization or can replace optimization techniques depending on the problem. Finally, a summary and path forward are provided, and the advancement needed in distributed optimization for the power grid is also presented.

This book presents an interesting sample of the latest advances in optimization techniques applied to electrical power engineering. It covers a variety of topics from various fields, ranging from classical optimization such as Linear and Nonlinear Programming and Integer and Mixed-Integer Programming to the most modern methods based on bio-inspired metaheuristics. The featured papers invite readers to delve further into emerging optimization techniques and their real application to case studies such as conventional and renewable energy generation, distributed generation, transport and distribution of electrical energy, electrical machines and power electronics, network optimization, intelligent systems, advances in electric mobility, etc.

Go in-depth with this comprehensive discussion of distributed energy management Distributed Energy Management of Electrical Power Systems provides the most complete analysis of fully distributed control approaches and their applications for electric power systems available today. Authored by four respected leaders in the field, the book covers the technical aspects of control, operation management, and optimization of electric power systems. In each chapter, the book covers the foundations and fundamentals of the topic under discussion. It then moves on to more advanced applications. Topics reviewed in the book include: System-level coordinated control Optimization of active and reactive power in power grids The coordinated control of distributed generation, elastic load and energy storage systems Distributed Energy Management incorporates discussions of emerging and future technologies and their potential effects on electrical power systems. The increased impact of renewable energy sources is also covered. Perfect for industry practitioners and graduate students in the field of power systems, Distributed Energy Management remains the leading reference for anyone with an interest in its fascinating subject matter.

Classical and Recent Aspects of Power System Optimization presents conventional and meta-heuristic optimization methods and algorithms for power system studies. The classic aspects of optimization in power systems, such as optimal power flow, economic dispatch, unit commitment and power quality optimization are covered, as are issues relating to distributed generation sizing, allocation problems, scheduling of renewable resources, energy storage, power reserve based problems, efficient use of smart grid capabilities, and protection studies in modern power systems. The book brings together innovative research outcomes, programs, algorithms and approaches that consolidate the present state and future challenges for power. Analyzes and compares several aspects of optimization for power systems which has never been addressed in one reference Details real-life industry application examples for each chapter (e.g. energy storage and power reserve problems) Provides practical training on theoretical developments and application of advanced methods for optimum electrical energy for realistic engineering problems

The book aims to equalize the theoretical involvement with industrial practicality and build a bridge between academia and industry by reducing the mathematical difficulties. It provides an overview of distributed control and distributed optimization theory, followed by specific details on industrial applications to smart grid systems, with a special focus on micro grid systems. Each of the chapters is written and organized with an introductory section tailored to provide the essential background of the theories required. The text includes industrial applications to realistic renewable energy systems problems and illustrates the application of proposed toolsets to control and optimization of smart grid systems.