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Two buses, $i$ and $j$, are connected with a transmission line of admittance $Y$, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:

  1. $\begin{bmatrix} -t_{i}t_{j}Y & t_{j}^{2}Y\\ t_{i}^{2}Y& -t_{i}t_{j}Y \end{bmatrix}$
  2. $\begin{bmatrix} t_{i}t_{j}Y &- t_{j}^{2}Y\\ - t_{i}^{2}Y& t_{i}t_{j}Y \end{bmatrix}$
  3. $\begin{bmatrix} t_{i}^{2}Y & -t_{i}t_{j}Y\\ -t_{i}t_{j}Y& t _{j}^{2}Y \end{bmatrix}$
  4. $\begin{bmatrix} t_{i}t_{j}Y& -(t_{i}-t_{j})^{2}Y\\ -(t_{i}-t_{j})^{2}Y&t_{i}t_{j}Y \end{bmatrix}$
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