Comparing the T and $\pi$ Equivalent Circuits for the Calculation of Transformer Inrush Currents

The most commonly used equivalent circuit for transformers is the traditional (Steinmetz) T-equivalent proposed toward the end of the 19th century. This model has two leakage impedance branches and one magnetizing branch. The T model properly represents the terminal behavior of the transformer for most low-frequency operating conditions. Another model derived from the principle of duality between magnetic and electric circuits exists, the π equivalent circuit, which has two magnetizing branches and one leakage branch. This paper shows that while the two equivalent circuits provide the same accuracy in steady state, better accuracy for the calculation of inrush currents is obtained with the π -equivalent circuit. Laboratory tests performed on three transformers with different characteristics demonstrate that inrush current simulations with the T equivalent circuit can have errors up to 73%, while the π equivalent estimates the measurements in every case within a few percent.