Computer Modelling of Non-linear Transformer Iron Core in Calculations of Transients


A. Tokic. Uglesic and V. Madzarevic

1 University of Tuzla Faculty of Electrical Engineering, Department of Power Systems ' Franjevacka 2, 75000 Tuzla, Bosnia and Herzegovina phone: +387 35 259 600 - fax: +387 35 259 600 - e-mail: atokic2001.@yahoo.com
2 University of Zagreb Faculty of Electrical Engineering and Computing, Department of Power Systems Unska 3, 10000 Zagreb, Croatia e-mail: ivo.uglesic@fer.hr

Abstract - In this paper is described a transformer model for low frequency electromagnetic studies, for frequencies from 0.1 Hz to 1 kHz. A non-linear magnetizing curve is presented with a finite number of linear regions. "Stiff" differential equations, which described behavior of transients, are solved by trapezoidal rule. The developed algorithm is successfully applied in low frequency transients, where the main subject of analysis is a nonlinear transformer iron core: inrush current and ferroresonance. Results of the "program" were compared to results in MATLAB/PSB.

1. Introduction

A model of single-phase transformer is shown in figure 1.



The main non-linear element îf transformer is an iron core inductance, which is defined by magnetizing curve Ô-im • In this paper, the curve wiJl be approximated by a finite number of linear regions, figure 2.



Slopes of some linear regions define inductance series Lm1 Lm2 ,... LmN . These inductances are being switched on/off depending on absolute value of the main linkage magnetic flux. We can assume that we are positioned on the current linear region k , 1 < k < N , whose slope is Lmk. An increase of the magnetic flux, during transients, above the value of Ôsk+1 means that the inductance Lmk is switched off and the inductance Lmk+1 is switched on. On the contrary, decrease of the flux bellow the value of Ôsk means that the inductance Lmk is switched off and the inductance Lmk_, is switched on. The magnetizing current of the k-linear region, k =1,2,..., N , can be calculated from the following relation.



- An algorithm can be made that will, depending on actual value of the linkage magnetic flux, resolve the equation system which describe circuit behavior. For a real data model, defines a system of "stiff differential equations, those equations can be resolved by trapezoidal rule:



2. Test Cases

In this part of the paper we will consider low frequency transients of transformer such as: inrush current or ferroresonance. The results of simulations made by the "program", we will compare with the MA TLAB/Simulink/Power System Blockset.

3. Conclusions

A low frequency model transformer is presented in this paper. The transformer non-linear characteristic magnetic fiux - magnetization current is presented through a finite number of linear regions. The proposed algorithm for the simulation of the transient phenomenon was made for inrush current and ferroresonance cases. The stiff differential equation system is solved by trapezoidal rule. The computing time of the developed program is similar to commercial software such as MATLAB/Power System Blockset. Simulation results were compared to PSB results, on actual examples obtained from known references.