Fault Analysis Practice Questions

The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being $P_{\max } \sin \delta$ . where $\delta$ is the load angle and the mechanical power input is $0.5 P_{\max }$ . A fault occurs on line 2 such that the power output of the generator is less than 0.5. $P_{\max }$ during the fault. After the fault is cleared by opening line 2. The power output of the generator is $\left\{P_{\max } / \sqrt{2}\right\} \sin \delta$ . If the critical fault clearing angle is $\pi / 2$ radians, the accelerating area on the power angle carve is ______ times $P_{\max }$ (rounded off to 2 decimal places)

The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a $Y-\Delta$ transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance $=$ zero) between phases ' $b$ ' and ' $c$ ' at bus 1, neglecting all pre-fault currents, the magnitude of the fault current (from phase ' $b$ ' to ' $c$ ') in p.u. is _____ (Round off to 2 decimal places).

The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are

In the circuit shown below, the switch is closed at t=0. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of switching is

Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is_________

A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactancesof 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a reactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ______

The series impedance matrix of a short three-phase transmission line in phase coordinates is

. If the positive sequence impedance is $(1 + j10)\Omega$ , and the zero sequence is $(4 + j31)\Omega$ , then the imaginary part of $Z_{m}$ (in $\Omega$ ) is ______(up to 2 decimal places).

The positive, negative and zero sequence impedances of a three phase generator are $Z_{1},Z_{2}$ and $Z_{0}$ respectively. For a line-to-line fault with fault impedance $Z_{f}$ ,the fault current is $I_{f1}=kI_{f}$ , where $I_{f}$ is the fault current with zero fault impedance. The relation between $Z_{f}$ and k is

The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are j0.1 pu, j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero).

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then

The magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is 1.0 pu. The voltage magnitude at bus B during a three-phase fault at bus A is 0.8 pu. The voltage magnitude at bus A during a three-phase fault at bus B, in pu, is ________.

A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a synchronous reactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to the generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is ________.

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of j0.4 p.u., j0.3 p.u. and j0.15 p.u., respectively. If the pre-fault voltage is 1 p.u., for a line-to-ground (L-G) fault at the terminals of the generators, the fault current, in p.u., is ___________.

A 30 MVA, 3-phase, 50 Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactances, 15%, 15% and 5% respectively. A reactance ( $X_n$ ) is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phases 'b' and 'c', with a fault impedance of j0.1 p.u. The value of $X_n$ (in p.u.) that will limit the positive sequence generator current to 4270 A is _________.

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and 1.0 p.u. The p.u. reactances of different components in the system are also shown in the figure. The infinite bus voltage magnitude is 1.0 p.u. A three phase fault occurs at the middle of line 2. The ratio of the maximum real power that can be transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is _________.

A sustained three-phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?

For a fully transposed transmission line

In an unbalanced three phase system, phase current $I_a = 1\angle -90^{\circ}$ pu, negative sequence current $I_{b2}=4 \angle( -150^{\circ})$ , zero sequence current $I_{c0}=3 \angle -90^{\circ}$ pu. The magnitude of phase current $I_{b}$ in pu is