Power systems miscellaneous
- If the sheath resistance is 2.14 Ω/km and that of the conduct or is 0.1625 Ω/k m, and mutual inductance of the shealth is 3.13 × 10–7 H/m. When the cable is 2 km long and supply is 50 Hz, the ratio of sheath loss to core loss of the cable will be_______
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Sheath loss = Rs..M²ω² Core loss R(R²s + M²ω²)
Here, Rs = 2 × 214
ω = 2πƒ = 2 × 3.14 × 50 = 314
M = 2 × 3.13 × 10–7 × 10³
R = 2 × 0.1625 = 0.3250ΩSheath loss = (2 × 2.14) × (2 × 3.13 × 10-4)² × 314² Core loss 2 × 0.1625[(2 × 2.14)² + 314² × 6.26 × 10-8]
= 0.0277.Correct Option: C
Sheath loss = Rs..M²ω² Core loss R(R²s + M²ω²)
Here, Rs = 2 × 214
ω = 2πƒ = 2 × 3.14 × 50 = 314
M = 2 × 3.13 × 10–7 × 10³
R = 2 × 0.1625 = 0.3250ΩSheath loss = (2 × 2.14) × (2 × 3.13 × 10-4)² × 314² Core loss 2 × 0.1625[(2 × 2.14)² + 314² × 6.26 × 10-8]
= 0.0277.
- The capacitance of a 3 core lead sheathed cable measured between any two of the conductors with sheath earthed is 0.19 µF per km. The kvA required to keep 16 kms of the cable charged when connected to 20 k V, 50 Hz supply will be ______kVA
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The capacitance measured is 3.04 µF between the conductors.
Capacitance per phase = 2 × 3.04 = 6.08 µF.
3 phase MVA required = V²ωC
= (20)² × (2π × 50) × 6.08 × 10–6 = 0.763 MVA
= 763 kVA.Correct Option: A
The capacitance measured is 3.04 µF between the conductors.
Capacitance per phase = 2 × 3.04 = 6.08 µF.
3 phase MVA required = V²ωC
= (20)² × (2π × 50) × 6.08 × 10–6 = 0.763 MVA
= 763 kVA.
- A 60 kV (rms) single core metal sheathed cable is to be graded by means of a metallic intersheath. The safe electric stress of the insutating material is 6 kV/mm (rms). The overal diameter of the intersheath is ________ mm
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V = 60 kV (rms),
gmax = 6 kV/mm (rms)V1 = V = 60 = 22.1 kV e 2.718 r = V = 60 = 3.67 mm egmax 2.718
Radius of intersheath,r1 = V = 60 = 10 mm gmax 6
Diameter of intersheath = 2r1 = 20 mmCorrect Option: B
V = 60 kV (rms),
gmax = 6 kV/mm (rms)V1 = V = 60 = 22.1 kV e 2.718 r = V = 60 = 3.67 mm egmax 2.718
Radius of intersheath,r1 = V = 60 = 10 mm gmax 6
Diameter of intersheath = 2r1 = 20 mm
- What is the overall diameter of a single core cable when its working on a three phase 264 kV system? The maximum permissible stress in the dieletric is not to exceed 20 kV/mm is ________ mm
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Effective value (rms) of the phase voltage = 264 = 152.4 kV. √3 Peak value of phase voltage = 264 × √2 = 215.5 kV. √3
For economical size of the cable, optimum ratio of sheath and core radii is given by R/r = egmax = V = V = V rIn(R/r) r × 1 r or 20 = 215.5 r r = 215.5 = 10.7 mm 20
Economical core diameter
= 10.7 × 2 = 21.4 mmCorrect Option: A
Effective value (rms) of the phase voltage = 264 = 152.4 kV. √3 Peak value of phase voltage = 264 × √2 = 215.5 kV. √3
For economical size of the cable, optimum ratio of sheath and core radii is given by R/r = egmax = V = V = V rIn(R/r) r × 1 r or 20 = 215.5 r r = 215.5 = 10.7 mm 20
Economical core diameter
= 10.7 × 2 = 21.4 mm
- In the above question find the sending end voltage of the tran86.314smission line ________ kV/ph
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Ir = (174.96 – j131.22) Amp.
IC1 = j14.356 Amp.
IL = IC1 + Ir = 210.39 |33.73°
Vs = 76200 + (174.96 – j116.86) (24 + j48.38)
= 76200 + 4199 + j (8596) – j (2804) + 5723 = 86122 + j5765
= 86.314 |3.82° volts.Correct Option: C
Ir = (174.96 – j131.22) Amp.
IC1 = j14.356 Amp.
IL = IC1 + Ir = 210.39 |33.73°
Vs = 76200 + (174.96 – j116.86) (24 + j48.38)
= 76200 + 4199 + j (8596) – j (2804) + 5723 = 86122 + j5765
= 86.314 |3.82° volts.
