Accurate forecasting of solar irradiance and photovoltaic (PV) power generation is critical for optimizing renewable energy integration and enhancing energy management systems. This study addresses the dual prediction of solar irradiance and PV power generation by developing a hybrid deep learning model that combines gated recurrent unit (GRU) and temporal convolutional network (TCN) along with scaled exponential linear unit (SELU) activation functions. The proposed GRU-TCN-SELU model leverages the strengths of GRUs in capturing temporal dependencies and TCNs in handling long-range patterns, while SELU activation ensures self-normalizing properties that enhance model convergence and performance. The model was trained and evaluated using datasets from Jeju Island, South Korea, and Alice Springs, Australia, encompassing various meteorological variables and historical solar data. Experimental results demonstrate that the GRU-TCN-SELU model outperforms traditional single-model approaches in terms of mean absolute error (MAE) and root mean square error (RMSE), achieving higher accuracy in both solar irradiance and PV power forecasts. These findings highlight the effectiveness of integrating GRU and TCN architectures with SELU activation for reliable renewable energy prediction, facilitating improved energy generation planning and smart energy management systems.