We address the demand-side management (DSM) problem for smart grids where the users have energy generation and storage capabilities, and where the energy price depends on the renewable energy sources and on the aggregate electricity demand. Each user aims at reducing its economic cost by selecting the best energy schedule subject to its local preferences and global restrictions on the aggregate net demand. From a game-theoretic perspective, we model the problem as a generalized Nash equilibrium problem. We propose a shrinking-horizon semi-decentralized DSM algorithm that exploits the most recent forecast on the renewable energy sources to perform real-time adjustments on the energy usage of the users. We investigate the potential of the proposed approach via numerical simulations on realistic scenarios, where we observe improved social welfare compared to day-ahead DSM algorithms.