Research on Master–Slave Game Strategy of Integrated Energy System Considering Integrated Demand Response: Improved Snake Optimizer-Quadratic Programming

With the advancement of energy market reform, integrated energy systems (IESs) have achieved rapid development. Considering insufficient research on an electricity–heat coupled master–slave game and the local optimum defect of traditional algorithms, this paper proposes a Stackelberg game optimization strategy for IES considering integrated demand response (IDR), with microgrid operator (MGO) as the leader and load aggregator (LA) as the follower. Firstly, an IDR model containing rigid, shiftable electric loads and reducible thermal loads is established, and a bi-level game model is built: the upper MGO optimizes electricity and heat pricing to maximize profit, while the lower LA adjusts flexible loads for maximum consumer surplus. Secondly, an improved snake optimizer (ISO) is constructed via Hammersley sequence initialization, Lévy flight and random perturbation and combined with quadratic programming (QP) to form the ISO-QP hybrid solving method. Benchmark function and CEC2017 tests verify the superior convergence and stability of ISO against multiple classical intelligent algorithms. Case simulation obtains the Stackelberg equilibrium result, and repeated experiments and parameter sensitivity analysis verify model robustness. Results show that the proposed method smooths load fluctuations via price guidance and synchronously improves MGO revenue and LA consumer surplus on the premise of guaranteed user satisfaction.