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
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
Nominal system frequency $$= 50$$ $$Hz.$$ The reference voltage for phase $$'a'$$ is defined as $$\,\,V\left( t \right) = {V_m}\,\cos \left( {\omega t} \right).\,\,\,$$ A symmetrical $$3\phi $$ fault occurs at centre of the line, i.e., at point $$'F'$$ at time 'to' the $$+ve$$ sequence impedance from source $${S_1}$$ to point $$'F'$$ equals $$(0.004 + j \,\,0.04)$$ $$p.u.$$ The wave form corresponding to phase $$'a'$$ fault current from bus $$X$$ reveals that decaying $$d.c.$$ offset current is $$-ve$$ and in magnitude at its maximum initial value. Assume that the negative sequence are equal to $$+ve$$ sequence impedances and the zero sequence $$(Z)$$ are $$3$$ times $$+ve$$ sequence $$(Z).$$
The $$rms$$ value of the ac component of fault current $$\,\left( {{{\rm I}_x}} \right)$$ will be