  In this study, we investigate the operation of an optimal home energy
management system (HEMS) with integrated renewable energy system (RES) and
energy storage system (ESS) supporting electricity selling functions. A
multi-objective mixed integer nonlinear programming model, including RES, ESS,
home appliances and the main grid, is proposed to optimize different and
conflicting objectives which are energy cost, user comfort and PAR. The effect
of different selling prices on the objectives is also considered in detail. We
further develop a formula for the lower bound of energy cost to help residents
or engineers quickly choose best parameters of RES and ESS for their homes
during the installation process. The performance of our system is verified
through extensive simulations under three different scenarios of normal,
economic, and smart with different selling prices using real data, and
simulation results are compared in terms of daily energy cost, PAR, user's
convenience and consecutive waiting time to use appliances. Numerical results
clearly show that the economic scenario achieves 51.6% reduction of daily
energy cost compared to the normal scenario while sacrificing the user's
convenience, PAR, and consecutive waiting time by 49%, 132%, and 1 hour,
respectively. On the other hand, the smart scenario shows only slight
degradation of user's convenience and PAR by 2% and 18%, respectively while
achieving 46.4% reduction of daily energy cost and the same level of
consecutive waiting time. Furthermore, our simulation results show that a
decrease of selling prices has tiny impacts on PAR and user comfort even though
the daily energy cost increases.
