Improved lumped parameter model for transformer fast transient simulations

To accurately simulate fast transient phenomena in transformer windings, a turn-to-turn-based multiple transmission line (MTL) model is regarded as the best approach because it is valid in a wide frequency range and capable to describe discontinuity of capacitive coupling among the turns of a non-uniform winding. However this MTL modelling approach also means that a series of large dimensional equations characterised by fully coupled admittance matrices need to be numerically dealt with, when simulating a winding typically having thousands of turns. In this study an improved lumped Resistor-Inductor-Capacitor (RLC) model is presented, which has lower computational complexity than but almost equal accuracy to the MTL model. Firstly, both the MTL and conventional lumped RLC model were compared and it was concluded that the conventional lumped RLC model is only valid in the frequency range below 2 MHz. Secondly, an improved lumped RLC model was derived in which a negative-value capacitive branch is added in parallel with the inductive branch to compensate the decrease of susceptance with the increase of frequency. Both numerical analysis and laboratory measurements were conducted on large power transformer windings, and it is confirmed that the valid frequency range of the improved lumped RLC model can be extended to about 4 MHz with no significant increase of computational cost.