Coordinated Source–Grid–Load–Storage System Operation under Uncertainty: A Chance-Constrained SOCP-based ACOPF with Industrial Load Flexibility

The integrated source-grid-load-storage (SGLS) system combines generation, transmission, loads, and storage to improve energy efficiency, integrate renewable energy sources, and enhance power system resilience. However, dynamic coordination among these multiple elements is currently underdeveloped, necessitating a refined dispatch framework for coordinated interactions. To address this challenge, a chanceconstrained second-order cone programming (SOCP)-based AC optimal power flow (ACOPF) model with a detailed industrial load demand response (DR) component is proposed to achieve coordinated optimal operation of the SGLS system. The approach begins with a deterministic SOCP-based ACOPF formulation, to which the DR component, reflecting equipment limits and production characteristics, is added. Next, renewable generation uncertainty is accounted for using a chance-constrained SOCPbased ACOPF. The resulting chance-constrained model is simplified via characteristics of the integrated SGLS system. This simplification improves solution efficiency while preserving the accuracy of the convex relaxation. Simulation results demonstrate that the proposed model effectively coordinates multi-element operational strategies in the SGLS system, balancing system security constraints with economic operation under high renewable penetration.