Nonlinear transformer model in the frequency domain and with symmetrical components

Abstract

Purpose

The aim is to develop a nonlinear transformer model to achieve an accurate model to obtain the frequency components of the magnetizing current based on the harmonic voltages at the primary and secondary side. So, it can easily be implemented in a harmonic load‐flow program.

Design/methodology/approach

The transformer model is based on the harmonic balance method. The electric and magnetic equations of the transformer are derived from the electric and magnetic equivalent circuits.

Findings

The transformer model can be easily implemented in a harmonic load‐flow program. The accuracy of the model has been shown by comparing it with a finite element simulation. The transformer model can be used with asymmetrical supply voltages, because different saturation levels of the phases can occur. There is a coupling between the phases which can be concluded out of the asymmetrical currents in the transformer under symmetrical supply voltages.

Research limitations/implications

The transformer model does not consider the iron losses and the interharmonics. In future work the transformer model will be used to study the harmonic losses in distribution networks, so the transformer losses due to these harmonics have to be considered. This can be achieved with a postcalculation process where the magnetic flux density is used to calculate the eddy current losses and the magnetic field intensity will be applied in a static Preisach model to quantify the hysteresis losses.

Practical implications

The model can be used in a harmonic load‐flow program in order to obtain more accurate simulations for the power system analysis and design.

Originality/value

The model presented in this paper is more detailed than similar papers found in literature (saturation of the yokes, coupling between the phases, interaction between different harmonics) and still it takes a brief simulation time.

Citation

Degroote, L., Vandevelde, L., Renders, B. and Gyselinck, J. (2008), "Nonlinear transformer model in the frequency domain and with symmetrical components", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 6, pp. 1418-1437. https://doi.org/10.1108/03321640810905873