A 3-phase, 3-core, metal sheathed cable gave the following results on test for capacitance: (i) Capacitance between two conductors bunched with the sheath and the third conductor 0.4 μF per km. (ii) Capacitance between bunched conductors and sheath 0.625 μF/km. Determine the capacitance (a) between

Question

A 3-phase, 3-core, metal sheathed cable gave the following results on test for capacitance:

(i) Capacitance between two conductors bunched with the sheath and the third conductor 0.4 μF per km.

(ii) Capacitance between bunched conductors and sheath 0.625 μF/km.

Determine the capacitance (a) between any two conductors, and (b) between any two bunched conductors and the third conductor if the sheath is insulated. (c) Also calculate the charging current per phase per km. when it is connected to 10 kV, 50 Hz supply.

Accepted Answer

From Figs. 9.13 (a) and 9.13 (b),

[latex]C_{x}=3 C_{1}=0.625[/latex]

and [latex]\quad C_{y}=C_{1}+2 C_{2}=0.4[/latex]

and from equation (9.19),

[latex]\begin{aligned} C_{0} &=C_{1}+3 C_{2} \ &=\frac{C_{x}}{3}+\frac{3}{2}\left(C_{y}-\frac{C_{x}}{3} ight) \ &=\frac{C_{x}}{3}+\frac{3}{2} C_{y}-\frac{C_{x}}{2} \ &=\frac{3}{2} C_{y}-\frac{C_{x}}{6} (9.19) \end{aligned}[/latex]

[latex]C_{0}=\frac{3}{2} C_{y}-\frac{C_{x}}{6}=\frac{3}{2} 0.4-\frac{0.625}{6}=0.496 \mu \mathrm{F} / \mathrm{km}[/latex]

[latex] herefore[/latex] capacitance between any two conductors =0.248 μF/km.

(ii) From the measurement

[latex]\begin{aligned}&C_{1}=0.208 \mu \mathrm{F} / \mathrm{km} \ ext {and} \quad &C_{2}=0.096 \mu \mathrm{F} / \mathrm{km}\end{aligned}[/latex]

The equivalent circuit for measuring capacitance between two bunched conductors and the third conductor will be as in Fig. E.9.6.

The equivalent capacitance C will be

[latex]C=2 C_{2}+\frac{2}{3} C_{1}[/latex]

Substituting the values for [latex]C_{1}[/latex] and [latex]C_{2}[/latex], the capacitor

C = 0.33 μF/km.

(iii) The charging current per phase per km will be

[latex]\begin{aligned}\frac{V}{\sqrt{3}} \omega C_{0} imes 10^{3} \mathrm{amps} &=\frac{10}{\sqrt{3}} imes 314 imes 0.496 imes 10^{-6} imes 10^{3} \&=0.899 A .\end{aligned}[/latex]

Question 9.6: A 3-phase, 3-core, metal sheathed cable gave the following r...

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