As the growing integration of rooftop solar and batteries in the residential area, home energy usage becomes more flexible and solar-battery systems can offer promising benefits to households. This paper narrates a research work of how home energy management systems maximize profits from buying electricity at a fixed price from utility and selling surplus energy to an aggregator. Appropriate optimization problems are formulated with technical constraints of household devices and from connection requirements including a volt-watt function installed in the inverter of the rooftop solar-battery system. On the day of operation, the energy plan, which has been optimally committed to be sold to an aggregator since the day before, is considered for determining optimal HEMS responses under the actual real-time condition. Simulation results of a Japanese low-voltage system show that a consideration of volt-watt functions when performing optimization helps reduce wasted energy due to possible active power curtailments and improve home profits.