A mixed-integer program for the design and dispatch of a hybrid power generation system

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from the grid. If sized correctly, hybrid systems reduce fuel consumption compared to generator-only alternatives. We present an optimization model to solve the hybrid power system design and dispatch problem for remote locations, modeling the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, nonlinear, mixed-integer program contains a detailed set of battery-only constraints that (i) considers rate-capacity effects in assigning discharge current; (ii) calculates both voltage and lifetime as a function of state-of-charge and current; and (iii) adjusts rate-capacity and resistance parameters to temperature. We demonstrate that neglecting these characteristics, which is common to facilitate tractability of the problem, could lead to over-estimation of battery performance by as much as 30%. Due to the complexities of this model, we present symmetry reduction and linearizations, the latter of which includes exact and convex under-estimation techniques. Specifically, we demonstrate how to employ the convex envelope of a bilinear term as a relaxation to bound and solve the problem, and also how to tighten this relaxation by partitioning on one or both of these variables in the bilinear term. Although partitioning is computationally expensive, we demonstrate that by providing the solver with an initial feasible solution as a “warm-start,” we are able to solve model instances in a reasonable amount of time. We determine, in a matter of hours, solutions within 5% of global optimality that closely resemble those from the nonlinear model. Our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.