When are Lossy Energy Storage Optimization Models Convex?

We consider a class of optimization problems involving the optimal operation of a single lossy energy storage system that incurs energy loss when charging or discharging. Such inefficiencies in the energy storage dynamics are known to result in a nonconvex set of feasible charging and discharging power profiles. In this letter, we provide an equivalent reformulation for this class of optimization problems, along with sufficient conditions for the convexity of the proposed reformulation. The conditions provided generalize existing conditions for convexity in the literature.