  In this paper we provide non-simultaneous charging and discharging guarantees
for a linear energy storage system (ESS) model for a model predictive control
(MPC) based home energy management system (HEMS) algorithm. The HEMS optimally
controls the residential load and residentially-owned power sources, such as
photovoltaic (PV) power generation and energy storage, given residential
customer preferences such as energy cost sensitivity and ESS lifetime. Under
certain problem formulations with a linear ESS model, simultaneous charging and
discharging can be observed as the optimal solution when there is high
penetration of PV power. We present analysis for a proposed HEMS optimization
formulation that ensures non-simultaneous ESS charging and discharging
operation for a linear ESS model that captures both charging and discharging
efficiency of the ESS. The energy storage system model behavior guarantees are
shown for various electricity pricing schemes such as time of use (TOU) pricing
and net metering. Simulation results demonstrating desirable ESS behavior are
provided for each electricity pricing scheme.
