Digital model for transient studies of a three-phase five-legged transformer

Abstract
A flux linkage model for a three-phase five-legged transformer is derived for the first time. The effects of mutual and leakage inductances, saturation, eddy current loss, hysteresis and residual fluxes of the nonlinear iron core are included. A straightforward and novel method for determining both the apparent and incremental inductance matrices for a loaded two-winding five-legged transformer is derived. Simulations presented in this study are based on apparent inductance (λ/i) rather than incremental inductance (dλ/di) because this approach was found to be preferable for predicting the behaviour of the laboratory transformer used. Eddy current and hysteresis losses are combined into one core loss term which is accounted for by a voltage-dependent resistance load on the secondary. The flux in each segment of the iron core and in the air gaps and tank are computed at each step. The model thus yields a completely detailed description of the transformer's behaviour. A predictor-corrector algorithm written in FORTRAN is used to solve the set of nonlinear differential equations that describe the transformer. A 386-based computer has been used to generate voltage and current waveforms faithful to laboratory data. Transformer inrush current and ferroresonance are selected as test cases because of the extreme computational demands that these transients place on the computer model. The model can be implemented using only nameplate and conventional test data along with the B-H curve of the core material. The method is thus well suited to the practical needs of engineers in industry.

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