To optimize the dispatch of batteries, a model is required that can predict the state of energy (SOE) trajectory for a chosen open-loop power schedule to ensure admissibility (i.e., that schedule can be realized). However, battery dispatch optimization is inherently challenging when batteries cannot simultaneously charge and discharge, which begets a non-convex complementarity constraint. In this paper, we develop a novel composition of energy storage elements that can charge or discharge independently and provide a sufficient linear energy storage model of the composite battery. This permits convex optimization of the composite battery dispatch while ensuring the admissibility of the resulting (aggregated) power schedule and its disaggregation to the individual elements.