An efficient multi-energy vector power flow modeling and solution approach with unified loop-free formulation for heat and gas hydraulic equations

Integrated energy networks will be key to develop low-carbon multi-energy systems. Steady-state multi-energy vector power flow (MEVPF) analysis is the cornerstone of integrated network studies. However, despite a wide range of recently developed models, there are still significant challenges that have not been fully addressed, including applicability of different MEVPF formulations to different network topologies and node types, flexibility in adapting new connections and components, and appropriate convergence behavior for different loading levels and initial conditions. This paper analyzes different formulations and their relevant applicability and convergence properties for the steady-state MEVPF problem and proposes a new unified, loop-free formulation for heat and gas hydraulic equations. Both theoretical and numerical analyses conducted on a canonical system show the superiority of the proposed approach over the other available formulations analysed in terms of flexibility of applications and convergence performance.