## 1 Introduction  
To prevent global warming and the exhaustion of fossil fuels, the introduction of renewable energies such as the photovoltaic generation (PV) and wind energy generation (WG), has been gaining attention in power systems. Moreover, an energy storage system (ESS) such as a battery is expected to play a significant role in stabilization of power flow fluctuation caused by the varying power output of the renewable generators due to unstable weather conditions [1, 2]. Recently, in the residential side, the introduction of PV and battery (either electric vehicle or small fixed type) system is gaining attention, since the PV and batteries can contribute to reduction of peak load. In order to reduce peak load and electricity cost in demand side, an optimal scheduling of household appliances is required and have been investigated [3; 4; 5; 6]. Where, it is very important to consider uncertainties of PV output in the day-ahead scheduling, because the actual PV output often deviates from forecasted value. In order to cope with the uncertainties imposed by the forecasting error of PV output, a stochastic optimization programming such as a scenario-based approach has been studied and used to solve the scheduling optimization. The scenario-based approach can deal with the forecast error deriving various scenarios based on a certain probability density function and can minimize the expected cost under certain conditions [7; 8; 9; 10]. The literature [9] provides a stochastic model for an optimal scheduling of REs and thermal units in micro grids to maximize the expected value of profit in electrical market. In the paper, the uncertainties of PV output are considered using scenario-based approach in which the scenarios of PV is generated on the basis of the probability distribution function of forecasted error. In Reference [10], a stochastic programming model for an optimal scheduling of distributed energy resources such as ESS with PV system is presented. The paper is taking into account the uncertainties for PV output and presents the setting of the probability of solar irradiance in detail. The literature [7; 8; 9] addresses the scenario-based method's problem which the calculation time increases as the number of scenarios increase. This problem has been improved by a countermeasure such as reduction of scenario [7; 8; 9]. Another approach that focuses on a forecasting method for uncertain REs output, is proposed in References [11; 12; 13]. Reference [12] describes the significance of the accuracy of the forecasted value using the re-forecasting model in order to maximize the benefit in electricity market. Reference [13] presents dispatch scheduling of generators and ESS where the probabilistic forecast method is used in order to deal with the uncertain REs output. Additionally, the data used to forecast is updated every hour and the forecast accuracy can be improved. From above background, the uncertainties caused by the forecasted error of PV output should be considered in the scheduling of controllable appliances such as batteries in residential side. Moreover, the consideration of re-forecast is necessary to improve forecast accuracy as well. In our previous work [14], we proposed an optimal scheduling method by applying the scenario-based approach in a smart home, however re-forecast and re-plan has not been considered in the optimization process in the paper. It is expected that operational cost can be even reduced using the latest data which are atmosphere, humidity, and so forth, and needed to forecast PV output. These factors are generally updated every several hours [11]. The objectives of this paper are to minimize the expected operational cost for the resident using controllable loads such as batteries and electric vehicle (EV) installed in a smart home while also considering uncertain PV output. In this paper, it is assumed that the power company provides a suitable command value for power flow in the smart home.