On the Solvability of Steady-State Load Flow Problems for Multi-Carrier Energy Systems

Abstract

The coupling of single-carrier network into multicarrier energy systems (MES) has recently become more important. Conventional single-carrier steady-state load flow models are not able to capture the full extent of the coupling. Different models for multi-carrier networks have been proposed, either based on the energy hub concept or using a case specific approach. However, the effect of the coupling on solvability and well-posedness of the integrated system of non-linear equations has not been discussed. Using a general load flow model on a small example MES, this paper discusses the problems arising due the coupling of single-carrier networks, and provides guidelines to obtain a solvable steady-state load flow model for MES.

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

“…All SC links representing a physical component have a link equation that relates link and nodal variables. We use the same load flow equations as used in [6], with the following changes. All equations and variables are in SI units.…”

“…The SCNs are connected through a coupling node to form a MCN [6]. The coupling variables are associated with the (terminal) links connected to the coupling node.…”

“…A node type is assigned to every node based on the known variables. Moreover, the coupling models generally introduce more variables than equations, such that additional BCs are needed for the MCN [6]. The load flow equations and the BCs can be combined in various ways to form the system of equations for the SCNs and MCNs.…”

“…Load flow models for singlecarrier networks (SCNs) have been widely studied, but only recently load flow models for MESs have been proposed. For instance, in [1] and [2] the energy hub concept (EH) is used, in [3]- [5] a more ad hoc approach, and in [6] a graph-based framework. All these approaches lead to one integrated system of nonlinear equations.…”

“…We use a graph-based formulation for general MESs [6], to solve the steady-state LFP for several example MESs. We consider a base network and a larger extended network, both consisting of gas, electricity, and heat.…”