A comparison on power flow models for optimal power flow studies in integrated medium-low voltage unbalanced distribution systems

Abstract

The uptake of distributed energy resources has led to new challenges in distribution system operation. These challenges include voltage and congestion issues along with a higher degree of unbalance due to the installation of mostly single-phase resources. This calls for more accurate distribution system modelling to perform three-phase power flow and optimal power flow analysis to ensure a safe operation. This paper provides a comparison of four unbalanced three-phase power flow formulations to be utilised in optimal power flow-based studies. To adapt these formulations to realistic-sized integrated medium and low voltage unbalanced distribution networks, we propose a linear model for low voltage transformers that is suitable to apply in convex power flow models. The accuracy of these models is compared to the non-linear model considering voltage and current magnitude errors, as well as voltage unbalance factor as performance indices. Our results show that out of the convex formulations, the linear approximated model, which takes the couplings between phases into account, combined with our transformer linearisation, is the most accurate at capturing voltage and current magnitudes. The voltage error of this model in our 5336-node and 3148-node medium-low voltage test networks remains less than 0.38% under a variety of loading and generation scenarios.