The transition to intelligent, low-carbon power systems necessitates advanced optimization strategies for managing renewable energy integration, energy storage, and carbon emissions. Generative Large Models (GLMs) provide a data-driven approach to enhancing forecasting, scheduling, and market operations by processing multi-source data and capturing complex system dynamics. This paper explores the role of GLMs in optimizing load-side management, energy storage utilization, and electricity carbon, with a focus on Smart Wide-area Hybrid Energy Systems with Storage and Carbon (SGLSC). By leveraging spatiotemporal modeling and reinforcement learning, GLMs enable dynamic energy scheduling, improve grid stability, enhance carbon trading strategies, and strengthen resilience against extreme weather events. The proposed framework highlights the transformative potential of GLMs in achieving efficient, adaptive, and low-carbon power system operations.