Recently, the European Union has recognized that more ambitious plans in reducing emissions are needed in order to comply with the target 1.5–2° warming limit for this century. Along this line, the main objective of this paper is to study the evolution of the power sector in Spain, taking into account the Paris Agreement and the further European Union Directives. In particular, we have studied the substitution by renewable energies of all coal power plants before 2030. For this study, we have applied linear programming techniques to optimize the deployment of the additional wind and solar resources. If, in addition to the substitution of coal power plants, we also consider the expected increase in demand for the period 2019–2030, we find that the present park of renewables should be increased by a factor of about 115%. We have also statistically analyzed the amount of surpluses and shortages in energy, assuming that the demand curve would have a daily shape similar to the present one. As a result, we have found that additional storage capabilities of around 55 GWh for 11 h would be needed in order not to waste more than 25% surplus energy by curtailment. As for backup, we propose in a first step to use the overwhelming amount of gas combined cycle units which are available.