The series impedance matrix of a short three-phase transmission line in phase coordinates is $$\left[ {\matrix{ {{Z_s}} & {{Z_m}} & {{Z_m}} \cr {{Z_m}} & {{Z_s}} & {{Z_m}} \cr {{Z_m}} & {{Z_m}} & {{Z_s}} \cr } } \right]$$.

If the positive sequence impedance is (1 + 𝑗 10) $$\Omega $$, and the zero sequence is (4 + 𝑗 31) $$\Omega $$, then the imaginary part of Z_m (in $$\Omega $$) is ______(up to 2 decimal places).

A three phase star-connected load is drawing power at a voltage of 0.9 pu and 0.8 power factor lagging. The three phase base power and base current are 100 MVA and 437.38 A respectively. The line-to-line load voltage in kV is __________.

For a fully transposed transmission line

A 2-bus system and corresponding zero sequence network are shown in the figure.

The transformers T₁ and T₂ are connected as