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Two buses, $\text{i and j}$, are connected with a transmission line admittance $\text{y}$, at the

two ends of which there are ideal transformers with turns ratios as shown. Bus

admittance matrix for the system is:

- $\begin{bmatrix} -t_{i}t_{j}Y\:\:\:t_{j}^{2} Y& \\ t_{i}^{2}Y\:\:\:-t_{i}t_{j}Y & \end{bmatrix}$
- $\begin{bmatrix} t_{i}t_{j}Y\:\:\:-t_{j}^{2} Y& \\ -t_{i}^{2}Y\:\:\:t_{i}t_{j}Y & \end{bmatrix}$
- $\begin{bmatrix} t_{i}^{2}Y\:\:\:-t_{i}t_{j}Y& \\ -t_{i}t_{j}Y\:\:\:t_{j}^{2}Y & \end{bmatrix}$
- $\begin{bmatrix} t_{i}t_{j}Y\:\:\:-\left ( t_{i}-t_{j} \right )^{2}Y& \\ -\left ( t_{i}-t_{j}\right )^{2}Y\:\:\:\:t_{i}t_{j}Y & \end{bmatrix}$

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