27/03/2021

Capacitance of Three Core Cable

In this theory, formula for capacitance of three core to core cable and core to sheath is given.

Capacitance of Three Core Belted Cable

Let us consider the three-core belted cable.
As there is potential difference exists between core to core of cable and core to sheath of cable, electrostatic field set up between them.
There is core to core capacitance C_c and core to sheath capacitance C_e exists in the three-core cable.
The core-to-core capacitance is delta connected whereas core to sheath capacitance is star connected.

Core to core capacitance = C_cand Core to sheath capacitance = C_e

The three cores to core delta connected capacitance is converted into equivalent star connection.

C_eq = 3C_c

Where C_eq = Equivalent star connection of delta connected core to core capacitance
Therefore, the total capacitance is equal to parallel combination of core to sheath capacitance and equivalent star connection of core-to-core capacitance of cable. The capacitance between core to neutral
C_N = C_e + C_eq = C_e + 3C_c

_{Measurement of capacitance of cable

Three
Cores Bunched Together

The three cores of cable are bunched
together and capacitance is measured between cores and sheath of cable.
As the
three cores are bunched together, there is no capacitance between cores.
There
exists capacitance between core and sheath C_e which are in parallel.
Let us consider that this capacitor is C₁ therefore

C₁ = 3C_e

C_e = C₁ / 3……..
( 1 )}

Capacitance Between Two Cores Is Measured with Third Core Connected to The Sheath

The capacitance between two cores is measured with the third core connected to the sheath.
This eliminated one core to sheath capacitance. Let us consider that this capacitance is C₂.

C₂ = C_c + C_c / 2 + C_s / 2

= ( C_c + C_c / 2 ) + C_s / 2

= ( 3C_c / 2 ) + C_s / 2

= ½ ( 3C_c + C_s )

= ½ C_N