Decomposition of n-winding transformers for unbalanced optimal power flow

Abstract

This study proposes a model for multi-phase, multi-winding, lossy transformers. A methodology is developed to decompose such transformers into a sub-network of multi-conductor Π-sections, shunts and idealised (lossless) two-winding transformers. The approach, therefore, can be used to include three-phase transformer models in any unbalanced power flow or optimal power flow tool that is able to represent these three basic components. The study derives the mathematical formulation and an implementation is provided in Julia/JuMP/PowerModelsDistribution.jl. The obtained voltage profile for several distribution test cases deviates from OpenDSS by at most 4 × 10−7. A case study applies this model to optimise the tap settings in the context of conservative voltage reduction. This illustrates that the optimised tap settings can vary by as much as 30% depending on the vector group of the transformer.