Power systems miscellaneous
- A 1 km of a three phase metal sheathed belted cable gave a measured capacitance of 0.7 µF bet ween one conduct or and the other two conductors bunched together with the earth sheath and 1.5 µF measured between the three bunched conductors and the sheath. What is the charging current, when the cable is connected at 11 kV, 50 Hz supply?
-
View Hint View Answer Discuss in Forum
2Cc + Cs = 0.7
⇒ 3Cs = 1.5
⇒ Cs = 0.5
Now, 2 Cc + 0.5 = 0.7⇒ Cc = 0.2 = 0.1 F 2 CL = 1 C0 2 = 1 (3Cc + Cs) 2 = 1 (3 × 0.1 + 0.5) = 0.4 F 2
Charging current =Vp ω C0Diversity factor = VL × 2π × ƒ × 2CL √3 = 11000 × 2π × 50 × 2 × 0.4 × 10-6 √3
= 1.59 Ampere/phaseCorrect Option: C
2Cc + Cs = 0.7
⇒ 3Cs = 1.5
⇒ Cs = 0.5
Now, 2 Cc + 0.5 = 0.7⇒ Cc = 0.2 = 0.1 F 2 CL = 1 C0 2 = 1 (3Cc + Cs) 2 = 1 (3 × 0.1 + 0.5) = 0.4 F 2
Charging current =Vp ω C0Diversity factor = VL × 2π × ƒ × 2CL √3 = 11000 × 2π × 50 × 2 × 0.4 × 10-6 √3
= 1.59 Ampere/phase
- A 1 – φ load of 200 kVA is delivered at 2500 V over a transmission line having R = 1.4 Ω, X = 0.8 Ω. What is the power at the sending end when the power factor of the load is 0.8 leading?
-
View Hint View Answer Discuss in Forum
I = 200 × 1000 = 80A 2500
Z = R + jX = 1.4 + j0.8 = 1.6 |29.74°
cos φ = 0.8 (lagging)
φr = 36.86° (lagging)
Ir = Ir |+φr = 80 |+36.86°
Vs = Vr + ZIr
= 2500 + 1.6 × |29.74° × (80 × |36.86°)
= 2500 + 128 |66.61°
= 2500 + 128 (cos 66.61° + jsin 66.61°)
= 2500 + 50.8 + j117.84
= (2550.8 + j117.84)= 2553.5 tan-1 
117.84 
2550.8
= 2553.5 |2.63°
φs = 2.63° + 36.86° = 34.23°
cos φs = cos 34.23° = 0.82 (leading)Correct Option: B
I = 200 × 1000 = 80A 2500
Z = R + jX = 1.4 + j0.8 = 1.6 |29.74°
cos φ = 0.8 (lagging)
φr = 36.86° (lagging)
Ir = Ir |+φr = 80 |+36.86°
Vs = Vr + ZIr
= 2500 + 1.6 × |29.74° × (80 × |36.86°)
= 2500 + 128 |66.61°
= 2500 + 128 (cos 66.61° + jsin 66.61°)
= 2500 + 50.8 + j117.84
= (2550.8 + j117.84)= 2553.5 tan-1 117.84 2550.8
= 2553.5 |2.63°
φs = 2.63° + 36.86° = 34.23°
cos φs = cos 34.23° = 0.82 (leading)
- What is the capacitance of neutral/km of a 1 – φ phase line composed of number 2 single strand conductor radius is 0.328 cm, spaced 3 m apart and 7.5 m above the ground ? Neglecting earth effect.
-
View Hint View Answer Discuss in Forum
Neglecting the presence of earth, we have
Cn = 0.0242 F/km log D r = 0.0242 = 0.00817 F/km log 300 0.328 Correct Option: B
Neglecting the presence of earth, we have
Cn = 0.0242 F/km log D r = 0.0242 = 0.00817 F/km log 300 0.328
- What is the time of operation of a relay of rating 5 amp 2.2 sec, IDMT and having a relay setting of 125% Tms = 0.6 ? It is connected to a supply circuit through a CT, 400 ratio. The fault current is 4000 amp.
-
View Hint View Answer Discuss in Forum
The pick up value of the relay is 5 amp but since the relay setting is 125%,
Operating current of the relay
= 5 × 1.25 = 6.25 Amp.PSM = Secondary current Relay current setting = Primary current (fault current) Relay current setting × CT ratio = 4000 = 8 6.25 × 80
From the standard 2.2 sec curve, the operating time for PSM = 8 is 3.2 sec.
Since the TMS is 0.6, the actual operating time of the relay is 1.92 sec.Correct Option: B
The pick up value of the relay is 5 amp but since the relay setting is 125%,
Operating current of the relay
= 5 × 1.25 = 6.25 Amp.PSM = Secondary current Relay current setting = Primary current (fault current) Relay current setting × CT ratio = 4000 = 8 6.25 × 80
From the standard 2.2 sec curve, the operating time for PSM = 8 is 3.2 sec.
Since the TMS is 0.6, the actual operating time of the relay is 1.92 sec.
- A two conductor 1 – φ line operates at 50 Hz. The diameter of each conductor is 2 cm and are spaced 3m apart. What is the line to line capacitance?
-
View Hint View Answer Discuss in Forum
Here, D = 3m, r = 2/2 = 1 cm = 10–2 m
∴ Cn = 2πε0 = 1 In(D/r) 18 × 109In 3 2
= 9.74 × 10-12 F/m = 9.74 × 109 F/km
Line to line capacitance,CL = Cn = 1 × 9.74 × 10-9 2 2
= 4.87 × 10-9 F/kmCorrect Option: B
Here, D = 3m, r = 2/2 = 1 cm = 10–2 m
∴ Cn = 2πε0 = 1 In(D/r) 18 × 109In 3 2
= 9.74 × 10-12 F/m = 9.74 × 109 F/km
Line to line capacitance,CL = Cn = 1 × 9.74 × 10-9 2 2
= 4.87 × 10-9 F/km
