A Stackelberg Game Framework for Energy Internet System by Operator Approach

This paper proposes a Stackelberg game framework for managing an Energy Internet System that integratesrenewable energy generation, energy conversion, and energy trading. The system comprises hubs controlled by competing energy companies, incorporating both external energy trading and peer-to-peer energy exchanges. It involves multiple stakeholders whose decisions are interdependent, creating challenges in decision-making. To tackle these challenges, we propose a networked Stackelberg game framework with two main objectives. First, from the energy companies' perspective, the companies make decisions by considering strategic interactions with other companies while accounting for the best responses of passive consumers within peer-to-peer constraints. Second, from the consumer side, consumers adjust their decisions based on their observations of the companies' strategies. The framework adopts a hierarchical decision-making structure in which energy companies act as leaders, formulating strategies that anticipate consumer demand responses, while competing within a Nash game. Meanwhile, consumer clusters, managed by demand management centers, modify their energy usage based on an incentive price mechanism. To search for the equilibrium, we develop an operator-theoretic approach that combines implicit gradient methods with proximal operator splitting techniques, and prove its convergence. Numerical studies and simulations on a combined IEEE 37-bus and gas source model with multiple energy hubs validate the model's effectiveness and the efficiency of the proposed algorithms. The results demonstrate the operational efficiency and strategic stability of the system, emphasizing the advantages of active market participation for both energy companies and consumers.