Multi-entity pricing-enabled supply recovery for electricity-gas energy system with coordinated flexibilities: a hierarchical game approach

Multiple stakeholders coexist in electricity-gas energy system (EGES), challenging multi-resource coordinated recovery in case of emergencies under market circumstances. This paper proposes a multi-entity pricing-enabled resource synergy strategy for supply recovery and benefit equilibrium via hierarchical game approach. Firstly, a Stackelberg game-based pricing framework, with power distribution network (PDN) as leader and integrated energy station cluster (IESC) as follower, is established for price-incentive restoration. By optimal emergency response transactive price incentive, exploitable flexibilities from islanding partition of PDN and bidirectional gas flow of natural gas system (NGS), as well as peer-to peer (P2P) interaction within IESC, are synergistically leveraged with recovery level facilitated. Through leader's convexification and follower's Karush-Kuhn-Tucker (KKT) condition generation constrained by NGS's cone model, bi-level price-guidance recovery is tackled into single-level problem, which is a tractable mixed-integer second-order cone programming (MISOCP) formulation. Secondly, considering recovery contribution related to energy and importance factors, a bargaining ability-aware P2P trading cooperative model is elaborated to obtain fair benefit allocation for individuals in IESC. The asymmetric Nash pricing embedding alternating direction method of multiplier (ADMM) is applied to achieve benefit equilibrium. Finally, numerical simulations are conducted to validate the effectiveness and priority of the employed model in coordinating multi-entity flexibility for fault recovery and balancing conflicts of interest.