Convergence of Newton's Method for Steady-State Load Flow Problems in Multi-Carrier Energy Systems

Coupling single-carrier networks into multi-carrier energy systems (MESs) has recently become more important. Various formulations of the single-carrier load flow problem (LFP) are used. Moreover, different coupling models lead to different integrated systems of equations for the LFP of MESs. Both could affect the convergence of the Newton-Raphson method (NR) used to solve the nonlinear system of equations. This paper considers the steady-state LFP for example MESs of varying size, with various coupling models and topologies, and various formulations in the single-carrier parts. Based on numerical experiments, this paper compares the convergence behavior of NR for the various single- and multi-carrier systems. For these examples, NR of the steady-state LFP of the MESs is independent of the size of the network and of the coupling, and NR requires at most as many iterations as the slowest single-carrier network.