The complex nodal admittance matrix is referred to as Y_{bus}. In the current formulation, the admittances of Y_{bus} are stored in rectangular form. The real part of Y_{bus} (the conductance matrix) is called G_{bus}. The imaginary part of Y_{bus} (the susceptance matrix) is called B_{bus}. Y_{bus} is formed according to two simple rules.
The diagonal terms of Y_{bus} (i.e. y_{ii}) are the driving point admittances of the network. They are the algebraic sum of all admittances incident upon vertex i. These values include both the self admittances of incident edges (with respect to vertex i) and shunts to ground at the vertex itself.
The off-diagonal terms of Y_{bus} (i.e. y_{ij} where i $\neq$ j) are the transfer admittances of the edge connecting vertices i and j.
Assuming that each transformer is modeled as two vertices (representing its primary and secondary terminals) and a connecting edge in the network graph, the procedure for incorporating a transformer into the nodal admittance matrix is as follows.
Compute the admittance matrix of the transformer (i.e. Y_{pp}, Y_{ss}, Y_{ps}, and Y_{sp}) at the nominal tap setting. See Section 4 for details.
Include the transformer’s primary admittance Y_{pp} as its contribution to the self admittance of the primary vertex p. That is, add Y_{pp} to the corresponding diagonal element of the nodal admittance matrix y_{pp}.
Include the transformer’s secondary admittance Y_{ss} as its contribution to the self admittance of the secondary vertex s. That is, add Y_{ss} to the corresponding diagonal element of the nodal admittance matrix y_{ss}.
Use Y_{ps} as the transfer admittance of the edge from the primary vertex p to the secondary vertex s (i.e. set the corresponding off-diagonal element of the nodal admittance matrix y_{ps} to Y_{ps}).
Use Y_{sp} as the transfer admittance of the edge from the secondary vertex s to the primary vertex p (i.e. set the corresponding off-diagonal element of the nodal admittance matrix y_{sp} to Y_{sp}).
Note: Examining Equation 19 and Equation 20, you can see that asymmetries introduced into Y_{bus} by a transformer are due to the fact that a${}^{\star}$ is used to compute Y_{ps} and a is used to compute Y_{sp}. When a = a${}^{\star}$, Y_{bus} is symmetric with respect to transformers. This condition is only true when a is real. In this situation, $\delta$ is zero and there is no phase shift across the transformer.