In the context of modeling and analysis of electrical networks, the self admittances
of a transformer can be thought of as the device’s impact on the diagonal elements of
of the nodal admittance matrix Y_{bus}.

Considering the self admittance of the transformer’s primary, Equation 17 states

$\mathbf{Y_{pp}}=\frac{\mathbf{Y_{L}+Y_{M}}}{a^{2}}$ | (26) |

Expressing the complex equation in rectangular form and making the substitution defined in Equation 25

$\mathbf{Y_{pp}}=t^{2}(g_{L}+g_{M})+jt^{2}(b_{L}+b_{M})$ | (27) |

When the magnetizing admittance is ignored, Equation 27 reduces to

$\mathbf{Y_{pp}}=t^{2}{g_{L}}+jt^{2}{b_{L}}$ | (28) |

Equation 18 defines the self admittance of the transformer’s secondary as

$\mathbf{Y_{ss}=Y_{L}}$ | (29) |

which is expressed in rectangular coordinates as

$\mathbf{Y_{ss}}=g_{L}+jb_{L}$ | (30) |