This paper reviews distributed/decentralized algorithms to solve the optimal power flow (OPF) problem in electric power systems. Six decomposition coordination algorithms are studied, including analytical target cascading, optimality condition decomposition, alternating direction method of multipliers, auxiliary problem principle, consensus+innovations, and proximal message passing. The basic concept, the general formulation, the application for dc-OPF, and the solution methodology for each algorithm are presented. We apply these six decomposition coordination algorithms on a test system, and discuss their key features and simulation results.

The need for the coordination of distributed energy resources in the future electric power system provides motivation to move from the current highly centralized control of resources toward a more distributed control structure. This paper presents an agent-based fully distributed dc security constrained optimal power flow (DC-SCOPF) approach. The algorithm is based on a multi-agent system, in which geographically distributed network entities are designated as agents with local sensing, communication, and computation abilities as envisioned for a smart grid. This distributed approach is based on solving the first order optimality conditions associated with DC-SCOPF formulation through an iterative process. At each iteration, each agent updates a few local variables through simple computations, and exchanges information with its neighboring agents. In particular, the updates for each agent incorporate local information such as the Lagrange multipliers, as well as enforcing the supply/demand balance through a local innovation term. Also, the performance is evaluated using the IEEE test systems with 14 and 57 buses and a 944-bus system consisting of eight IEEE 118-bus systems. Finally, analytical arguments concerning the convergence of the proposed method to the optimal solution of the DC-SCOPF are provided.

Battery storage is essential for the future smart grid. The inevitable cell degradation renders the battery lifetime volatile and highly dependent on battery dispatch, and thus incurs opportunity cost. This paper rigorously derives the marginal degradation cost of battery for power system dispatch. The derived optimal marginal degradation cost is time-variant to reflect the time value of money and the functionality fade of battery and takes the form of a constant value divided by a discount factor plus a term related to battery state of health. In case studies, we demonstrate the evolution of the optimal marginal costs of degradation that corresponds to the optimal long-term dispatch outcome. We also show that the optimal marginal cost of degradation depends on the marginal cost of generation in the grid.

Constrained optimization problems have appeared in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems relied on iterative algorithms that explored the feasible domain in the search for the best solution. These iterative methods often became the computational bottleneck in decision-making and adversely impacted time-sensitive applications. Recently, neural approximators have shown promise as a replacement for the iterative solvers that can output the optimal solution in a single feed-forward providing rapid solutions to optimization problems. However, enforcing constraints through neural networks remains an open challenge. In this paper, we have developed a neural approximator that maps the inputs to an optimization problem with hard linear constraints to a feasible solution that is nearly optimal. Our proposed approach consists of five main steps: 1) reducing the original problem to optimization on a set of independent variables, 2) finding a gauge function that maps the ℓ _∞ -norm unit ball to the feasible set of the reduced problem, 3) learning a neural approximator that maps the optimization’s inputs to a virtual optimal point in the ℓ _∞ -norm unit ball, and 4) gauge mapping to project the virtual optimal point in the ℓ _∞ -norm unit ball onto the feasible space, then 5) finding the values of the dependent variables from the independent variable to recover the solution to the original problem. We can guarantee hard feasibility through this sequence of steps. Unlike the current learning-assisted solutions, our method is free of parameter-tuning (compared to penalty-based methods) and removes iterations altogether. We have demonstrated the performance of our proposed method in quadratic programming in the context of optimal power dispatch (critical to the resiliency of our electric grid) and constrained non-convex optimization in the context of image registration problems. Our results have supported our theoretical findings and demonstrate superior performance in terms of computational time, optimality, and the feasibility of the solution compared to existing approaches.

The flexibility of plug-in electric vehicles (PEVs) in shifting their charging schedules can be utilized to reduce charging costs. Given the ever-increasing adoption of PEVs and their geographical spread, coordinated charging schedules could be enabled by distributed algorithms. Here, we propose a fully distributed solution for PEVs cooperative charging (PEV-CC) problem. The PEV-CC minimizes the charging costs for a PEV fleet whilst considering limitations of PEVs and charging infrastructure. The PEV-CC is a convex multi-time step problem and a receding horizon is employed to integrate feedback into the decision-making process. Driving uncertainties are accounted for by considering multiple driving scenarios for individual PEVs. Our distributed iterative procedure achieves a distributed solution of the underlying convex optimization problem through local computations and limited communication. The algorithm is designed to reach an agreement on a price signal among PEVs over the course of iterations, while local PEV constraints are enforced at each iteration. Therefore, each iteration yields a feasible solution for the PEV-CC problem. The performance of our proposed algorithm is evaluated on a fleet of PEVs as a test case.

The electrification of personal transportation holds great potential for lowering greenhouse gas emissions and reducing climate change. The promise of electric vehicles (EVs) to serve these goals has resulted in a broad range of supporting policies aimed at encouraging widespread EV adoption at both the state and federal levels in the United States and around the world. While the EV revolution and prospects of a world with ubiquitous EVs are impacting various industries and many aspects of daily life, strategic interactions between the power grid and EVs are crucial for a successful energy transition. However, managing the interplay between EVs and the power grid remains a challenge. Motivated by that tension, this paper surveys a variety of solutions, policies, and incentives that are focused on effectively managing EV charging behaviors. The paper’s objective is to explore these tools to ensure that EV owners have ultimate control over their personal vehicles while simultaneously allowing the power grid to mitigate adverse network impacts. Furthermore, this paper examines the role of charging infrastructure technology and its strategic placement in facilitating the seamless integration of EVs into the grid. Additionally, the paper highlights financial mechanisms associated with EV integration and discusses the consequences of these mechanisms.