Three-Mode Gaussian Mixture Model for Renewable Energy Output in Provincial Power Grids: Empirical Study and Energy Storage Optimization

Provincial power grids with over 32% renewable penetration face critical intraday imbalances from multi-modal power fluctuations. This paper proposes a tri-mode Gaussian Mixture Model (GMM) framework resolving the limitations of conventional static methods (25% power redundancy, <95% coverage) through physics-informed spatiotemporal decoupling. Three key innovations are presented: firstly, a five-dimensional feature space identifies three physical modes (PV-dominated τ=3.83h, wind-baseload τ=9.0h, hybrid τ=6.75h) with 92.7% explained variance, verified through a provincial historical dataset; second, a standard deviation weighted correction method is proposed to quantify modal interactions; last, a probability-weighted superposition strategy enables adaptive storage sizing, reducing costs by 37.7% versus Q95 baselines while maintaining 81.9% coverage. Empirical validation on a provincial grid demonstrates 15.4-37.7% cost savings through mode-specific duration matching and volatility-aligned thresholds. The framework reduces power redundancy from 25% to 12% and enhances energy utilization efficiency by 21.8%.