4 Computing Admittances 4 Computing Admittances 4.2 Transfer Admittances

4.1 Self Admittances

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.

4.1.1 Primary Admittance

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)

4.1.2 Secondary Admittance

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)