This paper proposes a hybrid robust-stochastic optimization model for smart home energy management in day-ahead (DA) and real-time (RT) energy markets which the uncertainties of energy prices and PV generation are investigated in the proposed model. A flexible robust optimization approach (ROA) is employed to create a tractable equivalent of the problem and manages the uncertainty of DA market prices when the PV generation is assumed in the worst-case. The ROA conservatism level can be adjusted by a control parameter and solutions with different levels of conservatism are obtained. Also, the proposed optimization framework considers the RT energy market and takes into account the associated uncertainties using stochastic programming (SP). At this stage, probable scenarios are used to model the uncertain characteristics of PV generation and energy prices. Loads are also considered to be controllable, while the comfort of inhabitants is considered. Results analysis show the advantage of the proposed hybrid method which makes sure decision-maker about the profitability of energy management. In the most conservatism case, the summation of profits of DA and RT markets is about 2.5 $/day.
