Question

A 1 km long single core cable has a core diameter of 0.4 cm and diameter of under sheath is 1.6 cm. The relative permittivity of the insulating material is 4. The power factor on open circuit is 0.08 and the supply voltage is 11 kV, 50 Hz. Then the dielectric loss is

• A. 2014.7 W
• B. 161.4 W
• C. 80.7 W
• D. 488.28 W

Answer 1

The correct option is D 488.28 W

Capacitance of the cable, $C=\frac{2\pi {\in }_r{\in }_0}{ln\left(\frac{R}{r}\right)}F/m=\frac{2\pi \times 4\times 8.854\times {10}^{-12}}{ln\left(\frac{0.8}{0.2}\right)}=0.16\mu F/km$

Power factor on open circuit

$cos\varphi =0.08$
$\varphi =co{s}^{-1}\left(0.08\right)={85.41}^o$
$\therefore$ Dielectric loss angle, $\delta ={90}^o-{85.41}^o={4.59}^o$

$\therefore$ Dielectric loss $=\omega C{V}^{2}tan\delta$

$=2\pi \times 50\times 0.16\times {10}^{-6}\times (11\times {10}^3{)}^2\times tan{4.59}^o=488.28W$