This study addresses Generation Expansion Planning (GEP) with the primary objectives of cost reduction, emissions minimization, and enhanced grid reliability through a lower Loss of Load Probability (LOLP). We proposed a hybrid system integrating nuclear and renewable sources to pave the way for a carbon-free grid, effectively mitigating the limitations inherent in each technology when operated independently. A key innovation of this research lies in the strategic integration of a Battery Energy Storage System (BESS) to directly address the intermittency of renewable sources and substantially improve grid reliability. To accurately model the real-world uncertainties affecting this hybrid system, including energy demand, fuel prices, wind speed, solar irradiation, and plant depreciation rates, we employ Probability Density Functions (PDFs) and Beta distributions. The stochastic behavior of these variables is then simulated using a Markov Chain Monte Carlo (MCMC) method for robust forecasting. The model is subsequently optimized using a Stochastic Dynamic Optimization algorithm. The efficacy of our introduced BESS is demonstrated through a significant improvement in a critical reliability metric. Our simulation results show that the cumulative LOLP index over a 13-year planning horizon was reduced from 2.85 to 2.38. This marked improvement was achieved with an initial BESS capacity of only 20 MW in the first year, expanded at a modest annual growth rate of 10%, highlighting the practical efficiency and scalability of our presented solution.