Adaptive Stochastic-Robust Model Predictive Control with Dual Shadow Pricing and Battery Degradation Mitigation for Solar Photovoltaic Microgrids

This paper proposes an Adaptive Stochastic-Robust Model Predictive Control (SR-MPC) framework for grid-connected PV-BESS microgrids in arid desert environments. The method couples scenario-based sample average approximation with robust uncertainty bounds while penalizing battery degradation and rapid micro-cycling. Lagrangian duality theory is employed to derive real-time energy shadow prices, establishing optimal switching thresholds between battery dispatch and grid exchange under Time-of-Use tariffs. Validated against meteorological and demand telemetry from Karakalpakstan, the proposed SR-MPC reduces energy imbalances by 56.7%, decreases operational costs by 23.4%, and suppresses battery degradation stress by 38.2%.