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 Ybus.

4.1.1 Primary Admittance

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

𝐘𝐩𝐩=𝐘𝐋+𝐘𝐌a2\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

𝐘𝐩𝐩=t2(gL+gM)+jt2(bL+bM)\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

𝐘𝐩𝐩=t2gL+jt2bL\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

𝐘𝐬𝐬=𝐘𝐋\mathbf{Y_{ss}=Y_{L}} (29)

which is expressed in rectangular coordinates as

𝐘𝐬𝐬=gL+jbL\mathbf{Y_{ss}}=g_{L}+jb_{L} (30)