Previous Year Questions- Performance of Transmission Lines, Line Parameters and Corona - 1 | Power Systems - Electrical Engineering (EE) PDF Download

Q1: A 50 Hz, 275kV line of length 400 km has the following parameters:
Resistance, R = 0.035Ω/km;
Inductance, L = 1mH/km;
Capacitance, C = 0.01μF/km;
The line is represented by the nominal −π model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by V_S and V_R, respectively) maintained at 275 kV, the phase angle difference (θ) between V_S and V_R required for maximum possible active power to be delivered to the receiving end, in degree is ____ (Round off to 2 decimal places).     (2023)
(a) 42.36
(b) 64.88
(c) 83.64
(d) 98.25
Ans: (c)
Sol: We have,
At max. power,
δ = β
where,  β = angle of T-parameter of  B.
π-Model :

Q2: The bus admittance (Y_bus) matrix of a 3-bus power system is given below.  
Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?       (2023)
(a) Line charging capacitor of finite value is present in all three lines
(b) Line charging capacitor of finite value is present in line 2-3 only
(c) Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 1 only
(d) Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 3 only
Ans: (a, c)
Sol: From Y_Bus matrix
Power system network :
Hence, option (A) and (C) will not be correct.

Q3: The geometric mean radius of a conductor, having four equal strands with each strand of radius  ′r′, as shown in the figure below, is      (2022)
(a) 4r
(b) 1.414 r
(c) 2r
(d) 1.723 r
Ans: (d)
Sol: Redraw the configuration:

Q4: Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:     (2020)
(a) (b) (c) (d) Ans: (c)
Sol: 
Q5: A lossless transmission line with 0.2 pu reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to 80% of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:    (2020)
(a) 1
(b) 3.61
(c) 5
(d) 6.25
Ans: (d)
Sol: = 5 pu for 100% of line
Relay is operated for 80%
Z_f = 0.8 Z_t ⇒ 0.8 × 0.2 = 0.16p.u.
For 80% of line,

Q6: A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 μF/km per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be ___________.      (2019)
(a) 418.85
(b) 256.25
(c) 458.45
(d) 369.28
Ans: (a)
Sol: 
Q7: A three-phase load is connected to a three-phase balanced supply as shown in the figure. If  V_an = 100∠ 0°V, V_bn = 100∠ −120°V and V_cn = 100∠ −240°V (angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________Ω (up to 2 decimal places).     (2018)
(a) 5.77
(b) 2.45
(c) 4.75
(d) 6.25
Ans: (a)
Sol: From the given voltages,

Q8: For the balanced Y-Y connected 3-Phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.
The approximate value of the impedance Z is       (SET-2(2017))
(a) 33∠ −53.1°Ω
(b) 60∠53.1°Ω
(c) 60∠ −53.1°Ω
(d) $180\angle -53.1\circ \Omega$180∠ −53.1°Ω
Ans: (c)
Sol: For star connection,

Q9: Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length D_ab = D_bc = D_ca = 1m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω/ km (rounded off to three decimal places) is ________        (SET-2 (2017))
(a) 0.572
(b) 5.721
(c) 0.289
(d) 2.892
Ans: (c)
Sol: 
Q10: The nominal- π circuit of a transmission line is shown in the figure.
Impedance Z = 100∠80°Ω and reactance X = 3300 Ω. The magnitude of the characteristic impedance of the transmission line, in Ω, is _______________. (Give the answer up to one decimal place.)     (SET-2 (2017))
(a) 406.2
(b) 201.5
(c) 635.8
(d) 52.4
Ans: (a)
Sol: 
Q11: A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are V_an = 220sin(100πt)V and i_a = 10sin(100πt)A, respectively. Similarly for phase-b the instantaneous voltage and current are  V_bn = 220cos(100πt)V and i_b = 10cos (100πtA, respectively The total instantaneous power flowing form the source to the load is      (SET-1(2017))
(a) 2200W
(b) 2200sin² (100πt)W
(c) 440W
(d) $2200sin\left(100\pi t\right)cos\left(100\pi t\right)W$2200sin(100πt)cos(100πt)W
Ans: (a)
Sol: 
Q12: At no load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is ____________.       (SET-2 (2016))
(a) 148.68
(b) 224.45
(c) 294.52
(d) 326.86
Ans: (c)
Sol: At no load,
then,

Q13: A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three-phase system is to be 5% more than that of the inductance per conductor of the single-phase system. The distance D, in meters, is _______.      (SET-1 (2016))
(a) 0.64
(b) 1.25
(c) 1.43
(d) 2.36
Ans: (c)
Sol: In first case,

Q14: A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR . The value of k is ______       (SET-2(2015))
(a) 0.75
(b) 1.44
(c) 1.91
(d) 2.48
Ans: (c)
Sol: 
Q15: For a 400 km long transmission line, the series impedance is (0.0 + j0.5)Ω/km and the shunt admittance is (0.0 + j5.0)μmho/km. The magnitude of the series impedance (in Ω ) of the equivalent π circuit of the transmission line is ____.      (SET-3 (2014))
(a) 88
(b) 142
(c) 187
(d) 268
Ans: (c)
Sol: Equivalent π-network:

Q16: In a long transmission line with r, l, g and c are the resistance, inductance, shunt conductance and capacitance per unit length, respectively, the condition for distortionless transmission is       (SET-3 (2014))
(a) rc = lg
(b) r = √l/c
(c) rg = lc
(d) g = √c/l
Ans: (a)
Sol: The condition for a transmission line to be distortionless is r/g = l/c

Q17: The horizontally placed conductors of a single phase line operating at 50 Hz are having outside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854 × 10⁻¹² F/m. The capacitance to ground per kilometer of each line is       (SET-2 (2014))
(a) $4.2\times 10-9F$4.2 × 10⁻⁹F
(b) 8.4 × 10⁻⁹F
(c) 4.2 × 10⁻¹²F
(d) 8.4 × 10⁻¹²F
Ans: (b)
Sol: 
Q18: A 50 Hz synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator ?      (2010)
(a) The magnitude of terminal voltage decreases, and the field current does not change.
(b) The magnitude of terminal voltage increases, and the field current does not change.
(c) The magnitude of terminal voltage increases, and the field current increases
(d) The magnitude of terminal voltage does not change and the field current decreases.
Ans: (a)
Sol: As field voltage is held constant, so field current does not change.
When the generator is connected with open-circuit transmission line, line draws charging current.
Therefore, Vt is higher than E_g i.e. V_t > E_g
But when the generator is disconnected from the line, no charging current is delivered by the generator i.e.  I_C = 0. In this V_t = E_g
So, terminal voltage decreases.