A two machine power system in shown below. Transmission line $$XY$$ has positive sequence impedance of $${Z_1}\Omega $$ and zero sequence impedance of $${Z_0}\Omega $$
An $$'a'$$ phase to ground fault with zero fault impedance occurs at the centre of the transmission line. Bus voltage at $$X$$ and line current from $$X$$ to $$F$$ for the phase $$'a',$$ are given by $${V_a}$$ Volts and $${{\rm I}_a}$$ Amperes, respectively. Then, the impedance measured by the ground distance relay located at the terminal $$X$$ of line $$XY$$ will be given by

A 3-phase transmission line is shown in figure:

Voltage drop across the transmission line is given by the following equation: $$$\left[ {\matrix{ {\Delta {V_a}} \cr {\Delta {V_b}} \cr {\Delta {V_c}} \cr } } \right] = \left[ {\matrix{ {{Z_s}} & {{Z_m}} & {{Z_m}} \cr {{Z_m}} & {{Z_s}} & {{Z_m}} \cr {{Z_m}} & {{Z_m}} & {{Z_s}} \cr } } \right]\left[ {\matrix{ {{i_a}} \cr {{i_b}} \cr {{i_c}} \cr } } \right]$$$
Shunt capacitance of the line can be neglect. If the line has positive sequence impedance of $$15\,\,\Omega $$ and zero sequence in impedance of $$48\,\,\Omega ,$$ then the values of $${{Z_s}}$$ and $${{Z_m}}$$ will be

An extra high voltage transmission line of length $$300$$ km can be approximate by a lossless line having propagation constant $$\beta = 0.00127$$ radians per km. then the percentage ratio of line length to wavelength will be given by

A lossless single machine infinite bus power system is shown below:

The synchronous generator transfers $$1.0$$ per unit of power to the infinite bus. The critical clearing time of circuit breaker is $$0.28$$ s. If another identical synchronous generator is connected in parallel to the existing generator and each generator is scheduled to supply $$0.5$$ per unit of power, then the critical clearing time of the circuit breaker will