Duality-based lumped transformer equivalent circuit at low frequencies under single-phase excitation

The lumped transformer equivalent circuit has been recently adapted based on duality principle and verified for the purposes of transient analysis with reasonable accuracy and frequency response analysis. However such circuit is developed and validated for balanced and unbalanced three-phase excitation. On the other hand, several diagnostic tests such as Frequency Response Analysis (FRA), ratio, short-circuit impedance measurements etc. are performed only under single-phase excitation in open- and short-circuit conditions. Therefore, there is a requirement to develop an equivalent circuit for power transformers under single-phase excitation to analyse relevant tests, which has not been completely investigated until now. The required equivalent circuit should in general include all windings of three phases as suggested by several recent publications since the influence from other non-tested windings to the tested phase winding was confirmed. The paper´s main contribution is to introduce a duality-principle-based lumped equivalent circuit for a three-phase two-winding transformer under single-phase excitation at low frequencies for the purpose of impedance and frequency response analyses. More importantly, a method for determining internal, i.e. per-phase, parameters of the circuit based on impedance tests is also proposed. Results show that, thanks to frequency-dependent functions of the parameters and their connection in the circuit, inter-phase effect and quantitative interpretation of several first parallel- and series resonances in frequency response of winding impedances in transformer bulk are now possible. Furthermore, these physical parameters can be useful as input for machine-learning algorithms to diagnose transformer failures.