Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design

Microgrids are frequently employed in remote regions, in part because access to a larger electric grid is impossible, difficult, or compromises reliability and independence. Although small microgrids often employ spot generation, in which a diesel generator is attached directly to a load, microgrids that combine these individual loads and augment generators with photovoltaic cells and batteries as a distributed energy system are emerging as a safer, less costly alternative. We present a model that seeks the minimum-cost microgrid design and ideal dispatched power to support a small remote site for one year with hourly fidelity under a detailed battery model; this mixed-integer nonlinear program (MINLP) is intractable with commercial solvers but loosely coupled with respect to time. A mixed-integer linear program (MIP) approximates the model, and a partitioning scheme linearizes the bilinear terms. We introduce a novel policy for loosely coupled MIPs in which the system reverts to equivalent conditions at regular time intervals; this separates the problem into subproblems that we solve in parallel. We obtain solutions within 5% of optimality in at most six minutes across 14 MIP instances from the literature and solutions within 5% of optimality to the MINLP instances within 20 minutes.