# GATE Questions & Answers of Symmetrical and Unsymmetrical Fault Analysis

## What is the Weightage of Symmetrical and Unsymmetrical Fault Analysis in GATE Exam?

Total 25 Questions have been asked from Symmetrical and Unsymmetrical Fault Analysis topic of Power Systems subject in previous GATE papers. Average marks 1.68.

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).

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The positive, negative and zero sequence impedances of a three phase generator are $Z_1Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$ the fault current $I_{f1}=kI_f$ , where $I_f$ is the fault current with zero fault impedance. The relation between $Z_{f\;}and\;k$ is

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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 faults 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).(Give the answer up to one decimal place.)

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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 ________.

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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 (Xn) 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 Xn (in p.u.) that will limit the positive sequence generator current to 4270 A is _________.

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

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A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a synchronousreactance 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 ________.

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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 _________.

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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 ___________.

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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?

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Three-phase to ground fault takes place at locations F1 and F2 in the system shown in the figure

If the fault takes place at location F1, then the voltage and the current at bus A are VF1 and IF1 respectively. If the fault takes place at location F2, then the voltage and the current at bus A are VF2 and IF2 respectively. The correct statement about voltages and currents during faults at F1 and F2 is

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

The transformers T1 and T2 are connected as

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In an unbalanced three phase system, phase current Ia =1(-90o) pu, negative sequence current Ib2= 4(150o) pu, zero sequence current Ic0 390o pu. The magnitude of phase current Ib in pu is

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A three phase, 100 MVA, 25 kV generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are 0.2 pu, 0.2 pu, and 0.05 pu, respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is _______

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The figure shows the single line diagram of a single machine infinite bus system.

The inertia constant of the synchronous generator H=5 MW-s/MVA. Frequency is 50 Hz. Mechanical power is 1 pu. The system is operating at the stable equilibrium point with rotor angle δ equal to 30o. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in pu is Pmax sinδ. If the values of δ and $d\delta }{dt}$ at the instant of fault clearing are 45o and 3.762 radian/s respectively, then Pmax (in pu) is _______.

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The sequence components of the fault current are as follows: Ipositive = j1.5 pu, Inegative = –j0.5 pu, Izero = –j1 pu. The type of fault in the system is

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Two generator units G1 and G2 are connected by 15 kV line with a bus at the midpoint as shown below

G1 = 250MVA, 15 kV, positive sequence reactance X=25%  on its own base

G2 = 100MVA, 15 kV, positive sequence reactance X=10%  on its own base L1 and L2 = 10 km, positive sequence reactance X = 0.225 Ω/km

For the above system,positive sequence diagram with p.u values on the 100 MVA common base is

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Two generator units G1 and G2 are connected by 15 kV line with a bus at the midpoint as shown below

G1 = 250MVA, 15 kV, positive sequence reactance X=25%  on its own base

G2 = 100MVA, 15 kV, positive sequence reactance X=10%  on its own base L1 and L2 = 10 km, positive sequence reactance X = 0.225 Ω/km

In the above system, the three-phase fault MVA at the bus 3 is

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The zero-sequence circuit of the three phase transformer shown in the figure is

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A 3-phase transmission line is shown in figure :

Voltage drop across the transmission line is given by the following equation :

$\left[\begin{array}{c}\Delta {V}_{a}\\ \Delta {V}_{b}\\ \Delta {V}_{c}\end{array}\right]=\left[\begin{array}{ccc}{Z}_{s}& {Z}_{m}& {Z}_{m}\\ {Z}_{m}& {Z}_{s}& {Z}_{m}\\ {Z}_{m}& {Z}_{m}& {Z}_{s}\end{array}\right]\left[\begin{array}{c}{I}_{a}\\ {I}_{b}\\ {I}_{c}\end{array}\right]$

Shunt capacitance of the line can be neglected. If the has positive sequence impedance of 15 Ω  and zero sequence impedance of 48 Ω, then the  values of Zs and Zm  will be

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Consider a power system shown below:

Given that:

;

The positive sequence impedences are and .

3-phase Base MVA=100

Voltage base=400kV (Line to Line)

Nominal system frequency = 50Hz

The reference coltage for phase 'a' is defined as $v\left(\mathrm{t}\right)\mathit{=}{V}_{\mathit{m}}\mathrm{cos}\left(\mathit{\omega }\mathit{t}\right)$.

A symmetrical three phase fault occurs at centre of the line., i.e. point 'F' at time t0. The positive sequence impedance from source S1 to point 'F' equals . The waveform corresponding to phase 'a' fault current from bus X reveals that decayinf dc offset current is negative and in magnitude at its maximum initial value. Assume that the negative sequence impedances are equal to positive sequence impedances, and the zero sequence impedances are three times positive sequence impedances.

The instant (t0) of the fault will be

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Consider a power system shown below:

Given that:

;

The positive sequence impedences are and .

3-phase Base MVA=100

Voltage base=400kV (Line to Line)

Nominal system frequency = 50Hz

The reference coltage for phase 'a' is defined as $v\left(\mathrm{t}\right)\mathit{=}{V}_{\mathit{m}}\mathrm{cos}\left(\mathit{\omega }\mathit{t}\right)$.

A symmetrical three phase fault occurs at centre of the line., i.e. point 'F' at time t0. The positive sequence impedance from source S1 to point 'F' equals . The waveform corresponding to phase 'a' fault current from bus X reveals that decayinf dc offset current is negative and in magnitude at its maximum initial value. Assume that the negative sequence impedances are equal to positive sequence impedances, and the zero sequence impedances are three times positive sequence impedances.

The rms value of the component of fault current (If ) will be

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Consider a power system shown below:

Given that:

;

The positive sequence impedences are and .

3-phase Base MVA=100

Voltage base=400kV (Line to Line)

Nominal system frequency = 50Hz

The reference coltage for phase 'a' is defined as $v\left(\mathrm{t}\right)\mathit{=}{V}_{\mathit{m}}\mathrm{cos}\left(\mathit{\omega }\mathit{t}\right)$.

A symmetrical three phase fault occurs at centre of the line., i.e. point 'F' at time t0. The positive sequence impedance from source S1 to point 'F' equals . The waveform corresponding to phase 'a' fault current from bus X reveals that decayinf dc offset current is negative and in magnitude at its maximum initial value. Assume that the negative sequence impedances are equal to positive sequence impedances, and the zero sequence impedances are three times positive sequence impedances.

Instead of the three phase fault, if a single line to ground fault occurs on phase ‘a’ at point ‘F’ with zero fault impedance, then the rms of the ac component of fault current (Ix) for phase ‘a’ will be

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A three phase balanced star connected voltage source with frequency $\omega$ rad/s is connected to a star connected balanced load which is purely inductive. The instantaneous line currents and phase to neutral voltages are denoted by (ia, ib, ic) and (van, vbn, vcn) respectively, and their rms values are denoted by V and I.

If $\mathrm{R}=\left[\begin{array}{ccc}{v}_{an}& {v}_{bn}& {v}_{cn}\end{array}\right]\left[\begin{array}{ccc}0& \frac{1}{\sqrt{3}}& -\frac{1}{\sqrt{3}}\\ -\frac{1}{\sqrt{3}}& 0& \frac{1}{\sqrt{3}}\\ \frac{1}{\sqrt{3}}& -\frac{1}{\sqrt{3}}& 0\end{array}\right]\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ {i}_{c}\end{array}\right]$, then the magnitude of R is

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Suppose we define a sequence transformation between ‘‘a-b-c’’ and ‘‘p-n-o’’ variables as follows:

$\left[\begin{array}{c}{f}_{a}\\ {f}_{b}\\ {f}_{c}\end{array}\right]=k\left[\begin{array}{ccc}1& 1& 1\\ {\alpha }^{2}& \alpha & 1\\ \alpha & {\alpha }^{2}& 1\end{array}\right]\left[\begin{array}{c}{f}_{p}\\ {f}_{n}\\ {f}_{o}\end{array}\right]$ where $\alpha ={e}^{j\frac{2\pi }{3}}$ and k is constant.

Now, if it is given that: $\left[\begin{array}{c}{V}_{p}\\ {V}_{n}\\ {V}_{o}\end{array}\right]=\left[\begin{array}{ccc}0.5& 0& 0\\ 0& 0.5& 0\\ 0& 0& 2.0\end{array}\right]\left[\begin{array}{c}{i}_{p}\\ {i}_{n}\\ {i}_{o}\end{array}\right]$ and $\left[\begin{array}{c}{V}_{a}\\ {V}_{b}\\ {V}_{c}\end{array}\right]=Z\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ {i}_{c}\end{array}\right]$ then,