Transformer Model 3 Transformer Admittance Model 4.1 Self Admittances

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 Y_L is derived from the leakage impedance Z_L 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)

Transformer Admittances in Rectangular Form

4.1 Self Admittances
4.2 Transfer Admittances