Power ow simulations form an essential tool for electricity network analysis but conventional models are designed to work on a separated transmission or distribution network only. The continuing growth of electricity consumption, demand side participation, and renewable resources makes the electricity net- works co-dependent. Integrated models incorporate the coupling of the net- works and interaction that they have on each other, representing the power ow within this changing environment accurately. Several numerical methods are available to solve the power ow problem on integrated networks. They can be categorized as a untied or as a splitting method and networks can be modelled as a homogeneous or hybrid network. In this paper, we review and assess these methods on the network models by running simulations on small test networks and comparing the outcome on their numerical performance, ie on convergence rate and CPU-time. The re- view shows that the convergence rate is comparable for most of the methods, but that hybrid networks have a slight advantage in computational time. Realistic network models, running on millions of buses and with large distribution networks, should give a better insight into the speed of the computations.

Coupling single-carrier networks (SCNs) into multi-carrier energy systems (MESs) has recently become more important. Steady-state load flow analysis of energy systems leads to a system of nonlinear equations, which is usually solved using the Newton-Raphson method (NR). Due to various physical scales within a SCN, and between different SCNs in a MES, scaling might be needed to solve the nonlinear system. In single-carrier electrical networks, per unit scaling is commonly used. However, in the gas and heat networks, various ways of scaling or no scaling are used. This paper presents a per unit system and matrix scaling for load flow models for a MES consisting of gas, electricity, and heat. The effect of scaling on NR is analyzed. A small example MES is used to demonstrate the two scaling methods. This paper shows that the per unit system and matrix scaling are equivalent, assuming infinite precision. In finite precision, the example shows that the NR iterations are slightly different for the two scaling methods. For this example, both scaling methods show the same convergence behavior of NR in finite precision.

Coupling single-carrier networks into multi-carrier energy systems (MESs) has recently become more important. Conventional load flow models for the separate single-carrier networks are not able to capture the full extend of the coupling. Recently, different models for multi-carrier energy networks have been proposed, either using the energy hub (EH) concept, or using a case specific approach. Although the EH concept can be applied to a general MES, it is unclear how the EH should be represented in the graph of the MES. On the other hand, the case specific approaches are not easily applicable to general MESs. This paper presents a graph-based framework for steady-state load flow analysis of general MESs. Furthermore, the effect of coupling on the resulting integrated system of equations is investigated. The proposed framework is validated using a small MES. This example shows that our framework is applicable to a general MES, and that it generalizes both the EH concept and the case specific approach.