A physics-based integer-linear battery modeling paradigm

Optimal steady-state dispatch of a stand-alone hybrid power system determines a fuel-minimizing distribution strategy while meeting a forecasted demand over six months to a year. Corresponding optimization models that integrate hybrid technologies such as batteries, diesel generators, and photovoltaics with system interoperability requirements are often large, nonconvex, nonlinear, mixed-integer programming problems that are difficult to solve even using the most state-of-the-art algorithms. The rate-capacity effect of a battery causes capacity to vary nonlinearly with discharge current; omitting this effect simplifies the model, but leads to over-estimation of discharge capabilities. We present a physics-based set of integer-linear constraints to model batteries in a hybrid system for a steady-state dispatch optimization problem that minimizes fuel use. Starting with a nonlinear set of constraints, we empirically derive linearizations and then compare them to a commonly used set of constraints that assumes a constant voltage and neglects rate-capacity. Numerical results demonstrate that assuming a fixed voltage and capacity may lead to over-estimating discharge quantities by up to 16% compared to our overestimations of less than 1%.