Learning Regionally Decentralized AC Optimal Power Flows with ADMM

One potential future for the next generation of smart grids is the use of decentralized optimization algorithms and secured communications for coordinating renewable generation (e.g., wind/solar), dispatchable devices (e.g., coal/gas/nuclear generations), demand response, battery & storage facilities, and topology optimization. The Alternating Direction Method of Multipliers (ADMM) has been widely used in the community to address such decentralized optimization problems and, in particular, the AC Optimal Power Flow (AC-OPF). This paper studies how machine learning may help in speeding up the convergence of ADMM for solving AC-OPF. It proposes a novel decentralized machine-learning approach, namely ML-ADMM, where each agent uses deep learning to learn the consensus parameters on the coupling branches. The paper also explores the idea of learning only from ADMM runs that exhibit high-quality convergence properties, and proposes filtering mechanisms to select these runs. Experimental results on test cases based on the French system demonstrate the potential of the approach in speeding up the convergence of ADMM significantly.Comment: 11 page

Coordination of smart home energy management systems in neighborhood areas: A systematic review

High penetration of selfish Home Energy Management Systems (HEMSs) causes adverse effects such as rebound peaks, instabilities, and contingencies in different regions of distribution grid. To avoid these effects and relieve power grid stress, the concept of HEMSs coordination has been suggested. Particularly, this concept can be employed to fulfill important grid objectives in neighborhood areas such as flattening aggregated load profile, decreasing electricity bills, facilitating energy trading, diminishing reverse power flow, managing distributed energy resources, and modifying consumers' consumption/generation patterns. This paper reviews the latest investigations into coordinated HEMSs. The required steps to implement these systems, accounting for coordination topologies and techniques, are thoroughly explored. This exploration is mainly reported through classifying coordination approaches according to their utilization of decomposition algorithms. Furthermore, major features, advantages, and disadvantages of the methods are examined. Specifically, coordination process characteristics, its mathematical issues and essential prerequisites, as well as players concerns are analyzed. Subsequently, specific applications of coordination designs are discussed and categorized. Through a comprehensive investigation, this work elaborates significant remarks on critical gaps in existing studies toward a useful coordination structure for practical HEMSs implementations. Unlike other reviews, the present survey focuses on effective frameworks to determine future opportunities that make the concept of coordinated HEMSs feasible. Indeed, providing effective studies on HEMSs coordination concept is beneficial to both consumers and service providers since as reported, these systems can lead to 5% to 30% reduction in electricity bills

Decentralised Optimisation and Control in Electrical Power Systems

Emerging smart-grid-enabling technologies will allow an unprecedented degree of observability and control at all levels in a power system. Combined with flexible demand devices (e.g. electric vehicles or various household appliances), increased distributed generation, and the potential development of small scale distributed storage, they could allow procuring energy at minimum cost and environmental impact. That however presupposes real-time coordination of demand of individual households and industries down at the distribution level, with generation and renewables at the transmission level. In turn this implies the need to solve energy management problems of a much larger scale compared to the one we currently solve today. This of course raises significant computational and communications challenges. The need for an answer to these problems is reflected in today’s power systems literature where a significant number of papers cover subjects such as generation and/or demand management at both transmission and/or distribution, electric vehicle charging, voltage control devices setting, etc. The methods used are centralized or decentralized, handling continuous and/or discrete controls, approximate or exact, and incorporate a wide range of problem formulations. All these papers tackle aspects of the same problem, i.e. the close to real-time determination of operating set-points for all controllable devices available in a power system. Yet, a consensus regarding the associated formulation and time-scale of application has not been reached. Of course, given the large scale of the problem, decentralization is unavoidably part of the solution. In this work we explore the existing and developing trends in energy management and place them into perspective through a complete framework that allows optimizing energy usage at all levels in a power system

Optimally Managing the Impacts of Convergence Tolerance for Distributed Optimal Power Flow

The future power grid may rely on distributed optimization to determine the set-points for huge numbers of distributed energy resources. There has been significant work on applying distributed algorithms to optimal power flow (OPF) problems, which require separate computing agents to agree on shared boundary variable values. Looser tolerances for the mismatches in these shared variables generally yield faster convergence at the expense of exacerbating constraint violations, but there is little quantitative understanding of how the convergence tolerance affects solution quality. To address this gap, we first quantify how convergence tolerance impacts constraint violations when the distributed OPF generator dispatch is applied to the power system. Using insights from this analysis, we then develop a bound tightening algorithm which guarantees that operating points from distributed OPF algorithms will not result in violations despite the possibility of shared variable mismatches within the convergence tolerance. We also explore how bounding the cumulative shared variable mismatches can prevent unnecessary conservativeness in the bound tightening. The proposed approach enables control of the trade-off between computational speed, which improves as the convergence tolerance increases, and distributed OPF solution cost, which increases with convergence tolerance due to tightened constraints, while ensuring feasibility

Distributed Optimization with Application to Power Systems and Control

In many engineering domains, systems are composed of partially independent subsystems—power systems are composed of distribution and transmission systems, teams of robots are composed of individual robots, and chemical process systems are composed of vessels, heat exchangers and reactors. Often, these subsystems should reach a common goal such as satisfying a power demand with minimum cost, flying in a formation, or reaching an optimal set-point. At the same time, limited information exchange is desirable—for confidentiality reasons but also due to communication constraints. Moreover, a fast and reliable decision process is key as applications might be safety-critical. Mathematical optimization techniques are among the most successful tools for controlling 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 control the subsystems in a distributed or decentralized fashion, reducing or avoiding central coordination. These methods have a long and successful history. Classical distributed optimization algorithms, however, are typically designed for convex problems. Hence, they are only partially applicable in the above domains since many of them lead to optimization problems with non-convex constraints. This thesis develops one of the first frameworks for distributed and decentralized optimization with non-convex constraints. Based on the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm, a bi-level distributed ALADIN framework is presented, solving the coordination step of ALADIN in a decentralized fashion. This framework can handle various decentralized inner algorithms, two of which we develop here: a decentralized variant of the Alternating Direction Method of Multipliers (ADMM) and a novel decentralized Conjugate Gradient algorithm. Decentralized conjugate gradient is to the best of our knowledge the first decentralized algorithm with a guarantee of convergence to the exact solution in a finite number of iterates. Sufficient conditions for fast local convergence of bi-level ALADIN are derived. Bi-level ALADIN strongly reduces the communication and coordination effort of ALADIN and preserves its fast convergence guarantees. We illustrate these properties on challenging problems from power systems and control, and compare performance to the widely used ADMM. The developed methods are implemented in the open-source MATLAB toolbox ALADIN-—one of the first toolboxes for decentralized non-convex optimization. ALADIN- comes with a rich set of application examples from different domains showing its broad applicability. As an additional contribution, this thesis provides new insights why state-of-the-art distributed algorithms might encounter issues for constrained problems

Distributed Optimization with Application to Power Systems and Control

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