Two-Stage Coordinated Scheduling for Enhanced Economic Capability in User-Side Integrated Energy Systems

This study presents a distributionally robust coordinated scheduling framework for user-side integrated energy systems (IES), which incorporates power, thermal, and cooling energy interactions. The core innovation lies in a multi-timescale optimization model that synergistically links monthly-scale strategic planning with day-ahead operational dispatch under uncertainty. A vectorized energy balance formulation captures bidirectional multi-energy flows, while a multi-service energy storage system (ESS) is designed to support arbitrage, peak shaving, and spinning reserve provisioning. To address renewables and demand variability, a distributionally robust chance-constrained programming (DRCCP) model is introduced, accounting for forecast uncertainty via ambiguity sets, which are characterized by moment statistics. The optimization trackable convex is available through a Mahalanobis-norm-based risk bounds. Furthermore, the framework incorporates a degradation-aware ESS cost model based on SOC-dependent wear, which is approximated via a piecewise linear surrogate for integration into MILP solvers. The day-ahead layer dynamically adjusts generator and ESS decisions in response to real-time deviations, constrained by dual-reserve and DR flexibility requirements. To solve this high-dimensional, non-convex problem space efficiently, an enhanced Particle Swarm Optimization (PSO) algorithm is proposed. This includes adaptive inertia weighting, chaotic learning dynamics, and elite-guided perturbation, significantly improving convergence and diversity in multimodal landscapes.