Capacitance of conductors

Info Letter No. 20

Conductors as capacitors

In the conductors of electrical power supplies, a distinction is made between the operating capacitance Cb, the three phase-phase capacitances CL and the three phase-earth capacitances Ce. The operating capacitance is determined by the capacitive reactive power demand of a conductor and the phase-earth capacitance of the single-phase fault current in the insulated or compensated networks. Single conductor cables are designed to have no phase-phase capacitance.

The capacitance of a parallel plate capacitor depends on the size of the plates, the electrical properties of the dielectric and the distance between the plates.

C= \frac{A * ε}{a}

A = Plate size
ε = Dielectric constand
a = Distant between plates

An electrical conductor is a cylindrical capacitance where the surface is a circle. And thus the equation changes.

C= \frac{2*\pi *l * ε}{ln\frac{a}{r}}

l     =    Length of the cylinder
ln   =    Natural logarithm
a    =    Radius of the insulation
r     =    Conductor radius

Single core radial field cable

C_{b}=C{e}
C= \frac{2*\pi *l * ε_{0}*ε_{r}}{ln\frac{a}{r}}

Cb =    Operating capacitance
Ce =    Phase-earth capacitance
e0 =    Electrical field constant 8.85 pF/m
er =    Relative dielectric constant
a  =    Radius of the insulation
r  =    Radius of the conductor

Three-core belted cables

C_{b}=C_{e}+3*C_{L}
C= \frac{2*\pi *l * ε_{0}*ε_{r}}{ln\frac{a^{6}-c^{6}}{3*c^{2}*r*a^{3}}}

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