In this paper is presented a rule-based strategy to the predictive management of the energy resources in a residential building one can equip with power generators (i.e. photovoltaic solar panels and a vertical-axis wind turbine) and batteries for electricity storage. The strategy takes the status of the electricity grid into consideration (via grid thresholds) and aims at both favouring self-consumption of the electricity produced from renewables and minimizing the negative impact of local power generation on the grid operation. It is based on anticipating the total-occupant load of the building, the grid load as well as the variable power that comes from renewables, using a rolling forecast horizon. Note that we have previously proposed a non-predictive strategy and pointed out possible improvements, in particular regarding the management of the batteries (Chabaud et al., 2015). So, a grid-connected residential building located in Perpignan (southern France) has been modelled using the TRNSYS software. Performance has been evaluated thanks to energy and economic criteria. Taking a look at the results we have obtained in simulation, one can highlight configurations that offer a good compromise between self-consumption of electricity and the renewable energy coverage rate. The combination of photovoltaic solar panels and a vertical-axis wind turbine has been highlighted as a viable energy mix option for residential buildings in southern France. Clearly, optimally designing and managing the power generators and batteries added to the building using the predictive strategy improve the way that building and the electricity grid interact. In particular, the batteries are better handled, allowing electricity to be injected to the grid and extracted from the grid at more favourable times.