Spatially Distributed Multi-Period Optimal Power Flow with Battery Energy Storage Systems

The growing presence of battery-based distributed energy resources (DERs) in power distribution systems necessitates the development of multi-period optimal power flow (MPOPF) algorithms. Generally, an MPOPF problem is formulated as a mixed integer non-convex programming (MINCP) problem and solved in centralized manner. The centralized solutions for MPOPF problem, termed as MPCOPF, suffer from scalability challenges. A typical solution time for a medium-sized (~100 bus system) is in the order of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10^{3}$</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10^{4}$</tex> seconds; such solution time-scales are too slow for operational decision-making. This paper introduces a spatially distributed algorithm to solve MPOPF problems, termed MPDOPF, designed to address these shortcomings. Our method breaks down the centralized MPOPF problem into smaller sub-problems, which are solved in parallel. We achieve network-level optimality using the Equivalent Network Approximation (ENApp) algorithm, where neighboring agents iteratively exchange boundary voltage and power flow variables until convergence. We analyze the performance of the proposed MPDOPF algorithm using the IEEE 123 bus test system, providing insights into the advantages of distributed MPOPF frameworks in terms of solution time compared to centralized approaches.