Steady-state power flow models are essential for daily operation of the electricity grid. The changing electrical environment requires a shift from separated power flow models to integrated transmission-distribution power flow models. Integrated models incorporate the coupling of the networks and the interaction that they have on each other, representing the power flow within this changing environment accurately. In this paper we conduct a comparison study on the numerical performance of methods that solve the integrated power flow problem. The methods of study can be divided into unified or splitting methods. In addition, the integrated networks can be modeled as homogeneous or as hybrid networks. Our study shows that the methods have several advantages and disadvantages, but that unified methods in combination with hybrid network models have the best numerical performance. Splitting methods running on hybrid network models have an advantage when full network data sharing between system operators is not allowed.

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This paper compares and assesses several numerical methods that solve the steady-state power flow problem on integrated transmission-distribution networks. The integrated network model consists of a balanced transmission and an unbalanced distribution network. It is important to analyze these integrated electrical power systems due to the changes related to the energy transition. We classified the existing integration methods as unified and splitting methods. These methods can be applied to homogeneous (complete three-phase) and hybrid (single-phase/three-phase) network models, which results in four approaches in total. These approaches were compared on their accuracy and numerical performance—CPU time and number of iterations—to demonstrate their applicability on large-scale electricity networks. Furthermore, their sensitivity towards the amount of distributed generation and the addition of multiple distribution feeders was investigated. The methods were assessed by running power flow simulations using the Newton–Raphson method on several integrated power systems up to 25,000 unknowns. The assessment showed that unified methods applied to hybrid networks performed the best on these test cases. The splitting methods are advantageous when complete network data sharing between system operators is not allowed. The use of high-performance techniques for larger test cases containing multiple distribution networks will make the difference in speed less significant.

Power system simulations should be adapted to be applicable to the trends that are currently evoked by the energy transition. This transition is pushing our power system from a traditional hierarchical system to a modern interactive system. In order to keep the supply and transport of energy safe and reliant, we need to change the way we perform power system simulations. This requires a comprehensive framework in which both transmission and distribution systems are simultaneously analyzed. This chapter describes how transmission and distribution networks are modeled together as an integrated network and used to do steady-state operation analysis in order to assess the interaction of these two networks. Furthermore, we investigate the influence of the increasing amount of imbalance at distribution level on the transmission network that is evoked by the increase of highly variable resources and loads at distribution level. This influence is not taken into account in traditional power system simulations as power networks are analyzed on its own. We show that the hybrid network representation is a powerful tool to analyze modern power systems and that the effects of increased PV penetration under normal operating conditions are limited.