Accurate forecasting of renewable energy generation is essential for efficient grid management and sustainable power planning. However, traditional supervised models often require access to labeled data from the target site, which may be unavailable due to privacy, cost, or logistical constraints. In this work, we propose FreeGNN, a Continual Source-Free Graph Domain Adaptation framework that enables adaptive forecasting on unseen renewable energy sites without requiring source data or target labels. Our approach integrates a spatio-temporal Graph Neural Network (GNN) backbone with a teacher--student strategy, a memory replay mechanism to mitigate catastrophic forgetting, graph-based regularization to preserve spatial correlations, and a drift-aware weighting scheme to dynamically adjust adaptation strength during streaming updates. This combination allows the model to continuously adapt to non-stationary environmental conditions while maintaining robustness and stability. We conduct extensive experiments on three real-world datasets: GEFCom2012, Solar PV, and Wind SCADA, encompassing multiple sites, temporal resolutions, and meteorological features. The ablation study confirms that each component memory, graph regularization, drift-aware adaptation, and teacher--student strategy contributes significantly to overall performance. The experiments show that FreeGNN achieves an MAE of 5.237 and an RMSE of 7.123 on the GEFCom dataset, an MAE of 1.107 and an RMSE of 1.512 on the Solar PV dataset, and an MAE of 0.382 and an RMSE of 0.523 on the Wind SCADA dataset. These results demonstrate its ability to achieve accurate and robust forecasts in a source-free, continual learning setting, highlighting its potential for real-world deployment in adaptive renewable energy systems. For reproducibility, implementation details are available at: https://github.com/AraoufBh/FreeGNN.