An Affine Arithmetic-Based Energy Management System for Isolated Microgrids

This paper presents a mathematical formulation of an energy management system (EMS) for isolated microgrids, which addresses uncertainty using the affine arithmetic (AA) method. The proposed EMS algorithm is based on an AA unit commitment (AAUC) problem for day-ahead dispatch, using uncertainty intervals of both load and renewable energy (RE) to provide robust commitment and dispatch solutions in AA form, which are feasible for all the possible realizations within the predetermined uncertainty bounds. A real-time dispatch solution is then found by the proposed algorithm, which computes the noise symbols values of the affine forms obtained by the AAUC, based on the current and actual load and RE power levels and available reserves. If the actual forecast error is outside the uncertainly bounds considered in the AAUC solution process, leading to possible load and/or RE curtailment, the AAUC is recalculated with updated forecast information. The proposed AA-based EMS is tested on a modified CIGRE microgrid benchmark and is compared against day-ahead deterministic, model predictive control (MPC), stochastic optimization, and stochastic-MPC approaches. The simulation results show that the proposed EMS provides robust and adequate cost-effective solutions, without the need of frequent re-calculations as with MPC-based approaches, or assumptions regarding statistical characteristics of the uncertainties as in the case of stochastic optimization.