In this paper, a detailed home energy management system structure is developed to determine the optimal day-ahead appliance scheduling of a smart household under hourly pricing and peak power-limiting (hard and soft power limitation)based demand response strategies. All types of controllable assets have been explicitly modeled, including thermostatically controllable (air conditioners and water heaters) and nonthermostatically controllable (washing machines and dishwashers) appliances, together with electric vehicles (EVs). Furthermore, an energy storage system (ESS) and distributed generation at the end-user premises are taken into account. Bidirectional energy flow is also considered through advanced options for EV and ESS operation. Finally, a realistic test-case is presented with a sufficiently reduced time granularity being thoroughly discussed to investigate the effectiveness of the model. Stringent simulation results are provided using data gathered from real appliances and real measurements.