Calculation of the flux distribution of three phase five limb power transformers considering nonlinear material properties

Abstract

Purpose

Depending on the load the flux‐density distribution inside power transformers core shows significant local variations due to stray fluxes which enter the transformer core. As saturation of the core has to be avoided the flux‐density distribution has to be determined early in the design stage of the transformer. This paper seeks to address these issues.

Design/methodology/approach

To determine the load dependent flux‐density distribution the operating point of the transformer is calculated considering linear and non‐linear material properties. The operating point is determined using a linearised lumped parameter model of the transformer under various load conditions. Considering non‐linear material properties the inductance matrix depends on the operating point and will be extracted by means of the FEM whenever the magnetic energy within the transformer changes notably.

Findings

This paper presents a numerical stable approach to calculate the operating point of a transformer by using the magnetic flux linkage as state variable for the coupled field problem.

Research limitations/implications

The proposed approach uses a fixed time‐step to update the lumped parameters by means of the FEM. This results in long simulation times. In further research it is planned to implement an adaptive time‐step method based on the change of the magnetic energy.

Originality/value

A numerical stable approach to calculate the operating point of a transformer by using the magnetic flux linkage as state variable for the coupled field problem is proposed. The methodology is applied to a 2D model of a three‐phase transformer. However, it also can be applied to 3D FE models. Based on the calculated operating point, the flux‐density distribution can be determined and several post‐processing methods can be executed (e.g. determination of core losses, …).

Citation

Riemer, B., Lange, E. and Hameyer, K. (2013), "Calculation of the flux distribution of three phase five limb power transformers considering nonlinear material properties", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 4, pp. 1230-1243. https://doi.org/10.1108/03321641311317059