1.

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:

A. \(\left[ {\begin{array}{*{20}{c}} { - {t_i}{t_j}Y}&{t_j^2Y}\\ {t_i^2}Y&{ - {t_i}{t_j}Y} \end{array}} \right]\)
B. \(\left[ {\begin{array}{*{20}{c}} {{t_i}{t_j}Y}&{ - t_j^2Y}\\ { - t_i^2Y}&{{t_i}{t_j}Y} \end{array}} \right]\)
C. \(\left[ {\begin{array}{*{20}{c}} {t_i^2Y}&{ - {t_i}{t_j}Y}\\ { - {t_i}{t_j}Y}&{t_j^2Y} \end{array}} \right]\)
D. \(\left[ {\begin{array}{*{20}{c}} {{t_i}{t_j}Y}&{ - {{\left( {{t_i} - {t_j}} \right)}^2}Y}\\ { - {{\left( {{t_i} - {t_j}} \right)}^2}Y}&{{t_i}{t_j}Y} \end{array}} \right]\)
Answer» D. \(\left[ {\begin{array}{*{20}{c}} {{t_i}{t_j}Y}&{ - {{\left( {{t_i} - {t_j}} \right)}^2}Y}\\ { - {{\left( {{t_i} - {t_j}} \right)}^2}Y}&{{t_i}{t_j}Y} \end{array}} \right]\)


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