A hybrid Stackelberg–Markov framework for adaptive load scheduling and dynamic pricing in smart grids

Abstract This paper proposes a Hybrid Stackelberg-Markov framework for adaptive load scheduling and dynamic pricing in smart grids. The framework integrates a Stackelberg game to model the interaction between the utility and consumers with a Markov process that captures consumer behavioral dynamics. By combining economic incentives with behavioral adaptation, the model achieves a balance between reducing the peak-to-average ratio (PAR), lowering consumer costs, and increasing utility profit. Simulation results demonstrate that the proposed approach reduces PAR by 43% compared with the baseline, decreases average consumer costs by 28%, and improves utility profit by 10%. The behavioral state analysis further shows that most consumers transition into the Content state, indicating long-term acceptance of dynamic pricing strategies. Moreover, the computational analysis confirms faster convergence and reduced run time compared with conventional demand response schemes. These results establish the proposed framework as a scalable and practical demand response solution for modern smart grids.