# 4 Computing Admittances

This section examines Equation 17 through Equation 20 with an eye for streamlining their computation. The resulting computational sequence explicitly decomposes the complex equations into real operations.

A transformer’s leakage admittance YL is derived from the leakage impedance ZL in the usual manner. Expressing the leakage impedance in rectangular form

 $\mathbf{Z_{L}}=r_{L}+jx_{L}$ (21)

then

 $\mathbf{Y_{L}}=\frac{1}{\mathbf{Z_{L}}}=\frac{1}{r_{L}+jx_{L}}=g_{L}+jb_{L}$ (22)

where

 $g_{L}=\frac{r_{L}}{r_{L}^{2}+x_{L}^{2}}$ (23)
 $b_{L}=-\frac{x_{L}}{r_{L}^{2}+x_{L}^{2}}$ (24)

For the sake of convenience, define the tap ratio as

 $\mathbf{t}=\frac{1}{\mathbf{a}}=te^{j-\delta}$ (25)