On the Equivalence Between Mixed-Integer Linear and Linear Programming Problems in MPC for Photovoltaic Plants with Energy Storage

This paper investigates the equivalence between a class of mixed-integer linear and linear programming prob-lems. By utilizing the addition of slack variables theorem, we demonstrate that certain optimization problems arising in Model Predictive Control strategies, which involve logical constraints, can be solved as linear programming problems. Consequently, the equivalent linear programming problem can be solved using the standard and numerically efficient method named the Sim-plex method, as opposed to mixed-integer linear programming problems for which the best solution method is not clear. As a case study, we address the control problem of photovoltaic plants with energy storage systems. We design a model-based predictive control scheme based on our proposed equivalent linear programming problem to maximize economic benefits derived from energy delivered by both photovoltaic panels and energy storage systems to the grid in a deregulated electricity market, achieved by managing the charge and discharge of the energy storage. Additionally, the proposed scheme allows for the consideration of rate-based variable efficiency in the energy stor-age system model, offering a more comprehensive implementation compared to the previous approach in the literature, where only an ideal battery was considered. Furthermore, simulations reveal that the proposed control methodology reduces the execution time of model-predictive control iterations compared to another approach based on mixed-integer linear programming schemes with similar considerations, thereby enhancing the scalability of the solution.