Non-cooperative game theoretic-based two-stage nested optimization model for energy hub pricing and management considering extreme conditions

Extreme conditions pose severe challenges to the reliable operation of energy systems. In this context, the energy hub (EH) effectively integrates heterogeneous energy, facilitating strategic decision-making of energy producers and consumers, while also bringing opportunities to improve the sustainable power supply capacity of the energy system in extreme conditions. This paper characterizes the resilience of EH via minimum load loss as a key metric conditions, and establishes an innovative two-stage nested optimization model to achieve the synergistic optimization of the economic objectives and sustainable power supply capabilities of EH operators (EHO). In modeling, the diversity of Nash equilibrium (NE) is emphasized, and the resilience of EH is maximized through the collaborative supply of heterogeneous energy sources while ensuring NE. Specifically, a bilevel Stackelberg game (BSG) is formulated in the first stage to derive numerical characteristics of NE, which are subsequently embedded into the second-stage model along with the NE constraints and BSG framework. In solving, the BSG is transformed into a tractable form through the application of Karush-Kuhn-Tucker (KKT) optimality conditions, duality theory, and linearization techniques. Finally, a multi-objective optimization problem is formulated to explore the mapping between economic goals and sustainable power supply capacity, and an interval division-based fixed-step search algorithm (IDFSA) is proposed for its solution. The results show that the proposed strategy improves the economic benefits of EHO by 4.1%, 2.5%, 2.7%, and 4.9% in different scenarios, and can reduce the load loss by up to 22.5% in the most extreme scenario. Furthermore, sensitivity analysis indicates that the economic benefits of the EH are significantly influenced by the comfort sensitivity of electricity consumers (EC), while the number of electric vehicles (EV) has a relatively minor impact on the electricity costs of EC.