Stackelberg Game-Based Optimal Operation of a Flexible Integrated Energy System with Dual Energy Storage for Source-Load Interaction

Abstract

Renewable-energy fluctuations and the conflicting economic objectives of independent stakeholders pose simultaneous physical and market challenges to the operation of flexible integrated energy systems (FIESs). To address these issues, this paper develops a market–physical coupled Stackelberg game-based coordinated operation framework incorporating the intertemporal flexibility of electrical and thermal energy storage. The integrated energy operator (IEO) acts as the leader and determines the internal electricity and heat purchase and sale prices, while the multi-energy cogeneration system (MECS) operator and the load aggregator act as followers and independently optimize generation-storage schedules and demand-response decisions, respectively. The load-aggregator response is formulated as a quadratic programming problem, whereas the MECS-side problem is formulated as a mixed-integer quadratic programming problem because of the binary storage-state variables. A nested Differential Evolution–CPLEX solution framework is employed to obtain a numerical Stackelberg equilibrium solution. A 24-h typical winter-day case study demonstrates the effectiveness of the proposed strategy. The peak electrical load decreases from 1845 kW to 1515 kW, corresponding to a reduction of 17.89%, while the peak-to-valley difference is reduced by 45.26%. The total user energy-purchasing cost decreases by 8.56%. Although the total electricity purchased from the external grid increases by 15.61%, the corresponding purchasing cost decreases by 30.98%, indicating that the coordinated strategy restructures grid transactions toward lower-price periods rather than simply minimizing grid imports. Comparative simulations with the no-storage and no-demand-response benchmark cases further confirm the complementary contributions of dual-storage flexibility and demand response to multi-agent economic performance. Moreover, the renewable curtailment rate is reduced from 6.51% to 0%, indicating that the proposed strategy enhances the local accommodation of wind-PV generation. These results show that the framework contributes to sustainable community energy operation by improving renewable-energy utilization, reducing peak-load pressure, lowering user energy expenditure, and supporting incentive-compatible coordination among independent stakeholders. Compared with conventional Stackelberg formulations that mainly focus on operator–user pricing or treat storage primarily as a balancing resource, the proposed framework explicitly embeds the intertemporal flexibility of electrical and thermal storage into the strategic response of the supply-side follower under endogenous multi-energy price signals.