Operational Flexibility Boundary Assessment of Electricity–Heating–Gas Virtual Power Plants Based on a Dynamic Unified Energy Circuit Model

Multi-energy virtual power plants (VPPs) aggregate electricity, heating, and natural gas resources to provide flexible regulation services to the external power grid. Their operational flexibility, however, cannot be accurately characterized using equipment capacities or single-period energy balances alone, because district heating and natural gas networks introduce heat transport delays, pipeline thermal storage, pressure dynamics, and linepack effects. This paper proposes an operational flexibility boundary assessment method for electricity–heating–gas VPPs based on a dynamic energy circuit model (ECM). The frequency-domain ECM converts heating-network temperature dynamics and gas-network pressure dynamics into algebraic constraints, which are integrated with electric-network and multi-energy coupling-device constraints. The net exchange power at the point of common coupling (PCC) is used as the external flexibility interface, and the period-wise upper and lower boundaries are determined subject to network and device constraints, terminal-state recovery requirements, and an economic feasibility limit. Case studies on an electricity–heating–gas VPP demonstrate that the dynamic ECM captures the intertemporal regulation capability provided by pipeline thermal storage and gas-network linepack. Compared with the static model, the dynamic ECM exhibits consistently greater downward flexibility and comparable or lower upward flexibility in several periods, thereby correcting the underestimation of electrical absorption capability and the optimistic estimation of power-export capability caused by the static approximation. The economic feasibility constraint further excludes high-cost boundary schedules, yielding a technically feasible and economically acceptable flexibility range.