Suppose we define a sequence transformation between ''a-b-c'' and ''p-n-0''' variables as follows:
$$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\matrix{ 1 & 1 & 1 \cr {{\alpha ^2}} & \alpha & 1 \cr \alpha & {{\alpha ^2}} & 1 \cr } } \right]\left[ {\matrix{ {{f_p}} \cr {{f_n}} \cr {{f_o}} \cr } } \right]$$ where $$\,\alpha = {e^{j{{2\pi } \over 3}}}\,\,$$ and $$k$$ is a constant
Now, if it is given that:
$$\left[ {\matrix{ {{V_p}} \cr {{V_n}} \cr {{V_o}} \cr } } \right] = k\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.5} & 0 \cr 0 & 0 & {2.0} \cr } } \right]\left[ {\matrix{ {{i_p}} \cr {{I_n}} \cr {{i_o}} \cr } } \right]\,\,$$ and $$\left[ {\matrix{ {{V_a}} \cr {{V_b}} \cr {{V_c}} \cr } } \right] = z\left[ {\matrix{ {{i_a}} \cr {{I_b}} \cr {{i_c}} \cr } } \right]\,\,$$ then,

Three identical star connected resistors of $$1.0$$ $$p.u$$ are connected to an unbalanced $$3$$ phase supply. The load neutral is isolated. The symmetrical components of the line voltages in $$p.u.$$ calculations are with the respective base values, the phase to neutral sequence voltages are

The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and Mutual reactance $$\,{X_m} = 0.1\,\,\Omega /km.\,\,$$ The positive sequence reactance $${X_1}$$ and zero sequence reactance $${X_0}$$ respectively in $$\Omega /km$$ are

At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the resistance and the shunt susceptances of the system.

The positive sequence driving point reactance at the bus is