Optimizing integrated energy systems with a virtual energy station framework: Exergy-based scheduling and multi-energy integration

The increasing complexity of Integrated Energy Systems (IES) poses significant challenges for achieving efficient, reliable, and sustainable multi-energy management. Conventional Virtual Power Plant (VPP) approaches remain limited by their electricity-centric design and insufficient handling of uncertainty. To address these gaps, this study develops a Virtual Energy Station (VES) framework that integrates electricity, heat, natural gas, and hydrogen within a unified bi-level exergy-based optimization model. The methodology combines an equal-exergy representation of multi-energy flows with a stochastic scheduling formulation to account for uncertainties in renewable generation, demand fluctuations, and day-ahead market prices. A key innovation of this study is the integration of the Energy Quality Coefficient (EQC) for evaluating multi-energy interactions, which ensures optimal energy conversion and utilization. Also, an Improved Walrus Optimization Algorithm (IWOA) is employed as the solution engine, incorporating adaptive search dynamics and chaotic parameter tuning to enhance convergence accuracy and stability. Simulation results on a coupled IEEE 33-bus electrical distribution system and a 6-node gas network demonstrate that the proposed framework reduces operational costs while improving exergy utilization and load flexibility. Quantitative performance evaluation confirms the robustness of the approach: realized profits deviate from expectations by less than 4% (MAPE ≈ 3.6%), convergence is achieved in 27% fewer iterations compared with the standard WOA, and solution variance across independent runs is reduced by half. These outcomes show that the VES framework not only ensures reliable multi-energy scheduling under uncertainty but also delivers measurable computational efficiency and stability gains.