Modeling arbitrage of an energy storage unit without binary variables

Energy storage device cannot be operated in charging and discharging modes simultaneously. Existing model utilizes binary variables to enforce such a request of complementarity. This paper discusses the implementation of a non-complementary strategy and reveals that strict complementarity can be replaced with a weaker yet linear constraint without jeopardizing practical viability. Hence, the arbitrage of an energy storage unit can be modeled via a linear program. The proposed model provides additional dimension of flexibility which can improve the profit of electricity arbitrage. The linearity benefits theoretical analysis on more sophisticated optimization problems that entails using duality and convex analysis.