Cooperative optimal scheduling of IESP-VPP in electricity-gas market based on Stackelberg game

With the continuous refinement of energy market mechanisms and the growing demand for multi-energy complementarity, the virtual power plant (VPP), as a key form of distributed resource aggregation, has become an important participant in regional energy management and market response. However, in an electricity–gas coupled multi-energy market environment, VPPs still face significant challenges in coordinating diverse energy carriers and responding to price signals, particularly due to the lack of efficient collaboration mechanisms with integrated energy service provider (IESP). This study proposes a bi-level IESP–VPP Stackelberg game model tailored for multi-energy markets. In the upper level, the IESP, endowed with gas price-setting authority, optimizes electricity purchase and sale prices through game-theoretic strategies to guide market operations. In the lower level, the VPP, acting as a price taker, optimizes the coordinated scheduling of multi-energy units in response to price signals to minimize its operating costs. To address the nonlinear coupled game problem, a solution method based on the Kriging surrogate model and an improved particle swarm optimization (IPSO) algorithm is proposed, aiming to reduce solver calls while maintaining optimization accuracy and computational efficiency. Case study results demonstrate that the proposed method and model effectively reduces the total operating cost of the VPP system by approximately 4.2%, enhances the overall economic performance, and promotes efficient coordination and utilization of multi-energy resources. Moreover, compared with conventional algorithms, the proposed approach increases the average profit of the IESP by approximately 4.3% and reduces the average solution time by about 77.5%, verifying its efficiency and feasibility in multi-energy market coordination and optimization.