Electrical Engineering - Power System
Exam Duration: 45 Mins Total Questions : 30
Load factor of a power station is generally
- (a)
equal to unity
- (b)
less than unity
- (c)
more than unity
- (d)
more than 10
A river has discharge of 6000 m/s3/s with a head of 25 m. The overall efficiency \(\eta \) being 75%, the power generated is
- (a)
10 MW
- (b)
1103625kW
- (c)
10265 kW
- (d)
Data is insufficient
An industrial consumer has a daily load pattern of 2000 kW, 0.8 lag for 12 h and 1000 kW at UPF for 12 h. The load factor is
- (a)
0.65
- (b)
0.5
- (c)
0.6
- (d)
2.0
A medium line with parameters A, B, C, and D is extended by connecting a short line of impedance Z in series. The overall ABCD parameters of the series. The overall ABCD parameters of the series combination will be
- (a)
A, AZ; C + DZ, D
- (b)
A + BZ, B; C + DZ, D
- (c)
A, AZ + B; CZ + D
- (d)
AZ, B; C/Z, D
Shut capacitors are used to raise the power factor of the load of 100 kW from 0.8 lag to unity, the supply being 3-phase at 10 kV. In star bank, the capacitance will be
- (a)
0.8 \(\mu\)F
- (b)
2.4 \(\mu\)F
- (c)
1.6 \(\mu\)F
- (d)
3.2 \(\mu\)F
If a 3-phase transmission line has a horizontal configuration with a spacing of 5 m between adjacent conductor and 10 m between outer conductors. The radius of each conductor is 1.75 cm. Then, the inductance per phase per km of the line will be
- (a)
1.2272 mH/km
- (b)
1.6 mH/km
- (c)
Data is insufficient
- (d)
None of these
The diagonal elements of a nodal admittance matrix are strengthened by adding
- (a)
shunt inductances
- (b)
shunt capacitors
- (c)
loads
- (d)
generators
A power system network consists of three elements 0-1, 1-2 and 2-0 of per unit impedances 0.2, 0.4 and 0.4 respectively. It's bus impedance matrix is given by
- (a)
\( \ \ \ \quad \begin{matrix} 1\quad \ \ & 2 \end{matrix}\\ \begin{matrix} 1 \\ 2 \end{matrix}\left[ \begin{matrix} 7.5 \\ -2.5 \end{matrix}\begin{matrix} -2.5 \\ 5.0 \end{matrix} \right] \)
- (b)
\( \ \ \ \quad \begin{matrix} \ 1\ \ \ & \ \ \ 2 \end{matrix}\\ \begin{matrix} 1 \\ 2 \end{matrix}\left[ \begin{matrix} 0.16 \\ 0.08 \end{matrix}\begin{matrix} \ \ \ 0.08 \\ \ \ \ 0.24 \end{matrix} \right] \)
- (c)
\( \ \ \ \quad \begin{matrix} \ 1\ \ \ & \ \ \ \ \ \ \ 2 \end{matrix}\\ \begin{matrix} 1 \\ 2 \end{matrix}\left[ \begin{matrix} \ \ \ 0.16 \\ - 0.08 \end{matrix}\begin{matrix} \ \ \ -0.08 \\ \ \ \ 0.24 \end{matrix} \right] \)
- (d)
\( \ \ \ \quad \begin{matrix} 1\quad \ \ & 2 \end{matrix}\\ \begin{matrix} 1 \\ 2 \end{matrix}\left[ \begin{matrix} 0.6 \\0.4 \end{matrix}\begin{matrix} \ \ \ \ 0.4 \\ \ \ \ \ 0.8 \end{matrix} \right] \)
A round rotor generator with internal voltage E1 = 2.0 pu and X = 1.1 pu is connected to a round rotor synchronous motor with internal voltage E = 1.3 pu and X=1.2 pu. The reactance of the line connecting the generator to the motor is 0.5 pu. When the generator supplies 0.5 pu power, the rotor angle difference between the machines will be
- (a)
\({ 57.42 }^{ \circ }\)
- (b)
\({ 1 }^{ \circ }\)
- (c)
\({ 32.58 }^{ \circ }\)
- (d)
\({122.58 }^{ \circ }\)
A three-phase breaker is rated at 2000 MVA, 33 kV, its making current will be
- (a)
35 kA
- (b)
49 kA
- (c)
70 kA
- (d)
89 kA
Consider the following statements with reference to protective relays:
1. The minimum relay coil current at which the relay operates is called pick-up value.
2. The pick-up value of a relay is 7.5 A and fault current is 30 A. Therefore, its plug setting multiplier is 5.
3. An earth fault current is generally lesser than the short circuit current.
4. Induction relays are used with both AC and DC quantities.
Which of these statements are correct?
- (a)
1 and 2
- (b)
2 and 4
- (c)
1 and 3
- (d)
1, 2 and 4
Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are
IC1 = 20 + 0.3 P1
IC2 = 30 + 0.4 P2
IC3 = 30
where, P1 is the power in MW generated by unit i, for i =1,2 and 3. Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are 50 MW and 3'00 MW respectively. If the plant is operating on economic load dispatch to supply the total power demand of 700 MW, the power generated by each unit is
- (a)
P1 = 242.86 MW; Pz = 157.14 MW and P3 = 300MW
- (b)
P1 = 157.14 MW; P2 = 242.86 MW and P3 =300 MW
- (c)
P1 = 300.0 MW; P2 = 300.0 MW and P3 = 100MW
- (d)
P1 = 233.3 MW; P2 = 233.3 MW and P3 =23304 MW
Out of the following plant categories:
(I) Nuclear
(II) Run of river
(Ill) Pump storage
(IV) Diesel
The base load power plants are
- (a)
(I) and (II)
- (b)
(II) and (III)
- (c)
(I), (II) and (IV)
- (d)
(I) (III) and (IV)
A single-phase overhead line consists of two conductors of radius 1 cm each. Also, spacing between conductor is 1.25 m and frequency is 50 Hz. Then, reactance per km will be
- (a)
\(0.64 \ \Omega /km\)
- (b)
\(0.64 \ k\Omega /m\)
- (c)
\(0.7 \ \Omega /m\)
- (d)
Data is insufficient
High voltage DC (HVDC) transmission is mainly used for
- (a)
bulk power transmission over very long distances
- (b)
interconnecting two systems with the same nominal frequency
- (c)
eliminating reactive power requirement in the operation
- (d)
minimizing harmonics at the converter stations
Consider a bundled conductor of an overhead line, consisting of three identical sub-conductors placed at the corners of an equilateral triangle as shown in the figure. If we neglect the charges on the other phase conductors and ground and assume that spacing between sub-conductors is much larger than their radius, the maximum electric field intensity is experienced at
- (a)
point X
- (b)
point Y
- (c)
point Z
- (d)
point W
A 50 MVA, 11 kV, 3-\(\phi \) synchronous generators is generated to 3-phase short circuit fault and the fault current is 2000 A. Then, the per unit value of positive sequence reactance is
- (a)
1.5 pu
- (b)
1.312 pu
- (c)
1.274 pu
- (d)
1.516 pu
A round rotor generator with internal voltage E1 = 2.0pu and X = 1.1pu is connected to a round rotor synchronous motor with internal voltage E2 = 1.3pu and X = 1.2pu The reactance of the line connecting generator to the motor is 0.5 pu when the generator supplies 0.5 pu power, the rotor angle difference between the machines will be
- (a)
\({ 57.42 }^{ \circ }\)
- (b)
\({ 1 }^{ \circ }\)
- (c)
\({ 32.58 }^{ \circ }\)
- (d)
\({ 122.58 }^{ \circ }\)
A shunt reactor at 100 MVAR is operated at 98% of its rated voltage and at 96% of its rated frequency. The reactive power absorbed by the reactor is
- (a)
98 MVAR
- (b)
104.02 MVAR
- (c)
100.04 MVAR
- (d)
96.04 MVAR
A 400 V, 3-phase installation takes current of 36 A at 0.8 power factor lagging. A synchronous motor improves the overall power factor of 0.92 power factor (lagging). Simultaneously, the synchronous motor drives a 15 HP (metric) load at an efficiency (11)85%. Determine the power factor of synchronous motor.
- (a)
0.85 leading
- (b)
0.8948 leading
- (c)
0.94 leading
- (d)
0.9974 leading
In a 3-step distance protection, the reach of the three zones of the relay at the beginning of the first line typically extends up to
- (a)
100% of the first line, 50% of the second line and 20% of the third line
- (b)
80% of the first line, 50% of the second line and 20% of the third line
- (c)
80% of the first line, 20% of the second line and 10% of the third line
- (d)
50% of the first line, 50% of second line and 20% of the third line
The voltage phasor of a circuit is 10 \(\angle { 15 }^{ \circ }\)V and the current phasor Is 2\(\angle { -45 }^{ \circ }\)A. The active and the reactive powers in the circuit are
- (a)
10 W an 17.32 VAR
- (b)
5 Wand 8.66 VAR
- (c)
20 Wand 60 VAR
- (d)
20\(\sqrt { 2 } \) and 10\(\sqrt { 2 } \) VAR
The incremental cost characteristics of two generators delivering 200 MW are as follows:
\(\frac { { dF }_{ 1 } }{ { d }P_{ 1 } } =2.0+0.01{ P }_{ 1 },\ \frac { { dF }_{ 2 } }{ { d }P_{ 2 } } =1.6+0.02\ P_{ 2 }\)
For economic operation, the generators P1 and P2 should be
- (a)
P1 = P2 = 100 MW
- (b)
P1 = 80 MW, P2 = 120 MW
- (c)
P1 = 200 MW, P2 = 0
- (d)
P1 = 120 MW, P2 = 80 MW
A single-phase transmission line and a telephone line are both symmetrically strung one below the other, in horizontal configurations, on a common tower. The shortest and longest distances between the phases and telephone conductors are 2.5 m and 3 m, respectively. The voltage (in V/km) induced in the telephone circuit, due to 50 Hz current of 100 A in the power circuit is
- (a)
4.81
- (b)
3.56
- (c)
2.29
- (d)
1.27
A generator is connected to a transformer which feeds another transformer through a short feeder (see figure). The zero sequence impedance values are expressed in pu on a common base and are indicated in figure. The Thevenin equivalent zero sequence impedance at point B is
- (a)
0.8 + j 0.6
- (b)
0.75 + j 0.22
- (c)
0.75 + j 0.25
- (d)
1.5 + j 0.25
The bus impedance matrix of a 4-bus power system is given by
\({ Z }_{ bus }=\begin{bmatrix} j0.3435 & \ j0.2860 & \ j0.2723 & \ j0.2277 \\ j0.2860 & \ j0.3408 & \ j0.2586 & \ j0.2414 \\ j0.2723 & \ j0.2586 & \ j0.2791 & \ j0.2209 \\ j0.2277 & \ j0.2414 & \ j0.2209 & \ j0.2791 \end{bmatrix}\)
A branch having an impedance of j0.2\(\Omega \) is connected between bus 2 and the reference. Then, the values of Z22(new) and Z23(new) of the bus impedance matrix of the modified network are respectively
- (a)
j 0.5408 \(\Omega \). and j 0.4586 \(\Omega \)
- (b)
j 0.1260 \(\Omega \) and jO.0956 \(\Omega \)
- (c)
j 0.5408 \(\Omega \) and jO.0956 \(\Omega \)
- (d)
j 0.1260 \(\Omega \) and jO.1630 \(\Omega \)
For a power system, the admittance and impedance matrices for the fault studies are as follows :
\({ Y }_{ bus }=\left[ \begin{matrix} -8.75 & j1.25 & j2.50 \\ j1.25 & -j6.25 & j2.50 \\ j2.50 & j2.50 & -j5.00 \end{matrix} \right] \)
\(Z_{ bus }=\left[ \begin{matrix} J0.16 & j0.08 & j0.12 \\ j0.08 & j0.24 & j0.16 \\ j0.12 & j0.16 & j0.34 \end{matrix} \right] \)
The pre-fault voltages are 1.0 pu at all the buses.The system was unloaded prior to the fault.A solid three phase fault takes place at bus 2.The post fault voltages at buses 1 and 3 in per unit respectively, are
- (a)
0.24 and 0.63
- (b)
0.31 and 0.76
- (c)
0.33 and 0.67
- (d)
0.67 and 0.33
Match List I (Type of transmission line) withList II (Type of distance relay preferred and select the correct answer using the codes given below the lists.
List I | List II |
P. Short Line | 1. ohm relay |
Q. Medium line | 2. Reactance relay |
R. Long line | 3. Mho relay |
- (a)
P Q R 2 1 3 - (b)
P Q R 3 2 1 - (c)
P Q R 1 2 3 - (d)
P Q R 1 3 2
Consider a power system shown below:
Given that Vs1 = Vs2 = 1.0+j 0.0 pu
The positive sequence impedances are Zs1 = Zs2 = 0.001 + j 0.01 pu and ZL = 0.006+j 0.06 pu. Three-phase base MVA = 100
Voltage base = 400 kV (line to line)
Nominal system frequency = 50 Hz
The rms value of the AC component of fault current (Ix) will be
- (a)
3.59 kA
- (b)
5.07 kA
- (c)
7.18 kA
- (d)
10.15 kA
The network shown in figure has impedances in per unit as indicated. The diagonal element Y22 of the bus admittance matrix Ybus of the network is
- (a)
-j 19.8
- (b)
+j 20.0
- (c)
+j0.2
- (d)
-j 19.95