  In this letter, we model the day-ahead price-based demand response of a
residential household with battery energy storage and other controllable loads,
as a convex optimization problem. Further using duality theory and
Karush-Kuhn-Tucker optimality conditions, we derive a sufficient criterion
which guarantees non-simultaneous charging and discharging of the battery
energy storage, without explicitly modelling it as a constraint

Systems and Control;Systems and Control