## How Calculate Capacitance of Underground Power Cable?

Capacitor is nothing but a two parallel metal plate separated by a dielectric that store electrical energy; formally we can define capacitor is a passive two terminal electrical component that used to store energy electrostatically in electric field, it also known as condenser. Practically a capacitor usually used a thin films of metal, aluminum foil or disks, etc.

The property of capacitor is known as capacitance, means the capacitance is the ability of a body to store an electric charge. The unit of capacitance is farad, symbol of farad is F, mostly common is micro farad µF.

The formula to calculate the capacitance between two cables is as
C = (Permittivity*Area)/D,

Where, A is the area is that of one cable, D is the distance between the center of the cable and the permitivity is that of the material between the cables.

Capacitance may measure as
C= Q/V= Charge/Potential difference.

### How Calculate Single Core Cable

Let,r = radius of the inner conductor and d = 2rR = radius of the sheath and D = 2Rε0 = permittivity of free space = 8.854 x 10-12εr = relative permittivity of the mediumConsider a cylinder of radius x meters and axial length 1 meter. x be such that, r < x < R.Now, electric intensity Ex at any point P on the considered cylinder is given as shown in the following equations.Then, the potential difference between the conductor and sheath is V, as calculated in equations below.After that, capacitance of the cable can be calculated as C= Q/V

### Capacitance Between Two Parallel Cables

Practically in electrical transmission lines both in overhead and underground cable system. Simply we can find two wire system both in dc or ac type. If the transmission system so long and voltage is high, charging current drawn by the metallic line conductor due to their capacitance property between two conductors.

If two conductor A & B are placed apart distance between d, consider r is radius of  each conductor, Q is the charge in conductor/meter (if +Q at A & –Q at B); then electric intensity

= Q/ (2π€0rx) V/m

### How Calculate Capacitance Of Three Core Cable

Consider a three cored symmetric underground cable as shown in the following figure (i). Let Cs be the capacitance between any core and the sheath and Cc be the core to core capacitance (i.e. capacitance between any two conductors).

In the above figure (ii), the three Cc (core to core capacitance) are delta connected and the core to sheath capacitance Cs are star connected due to the sheath forming a single point N. The circuit in figure (ii) can be simplified as shown in figure (iii). Outer points A, B and C represent cable cores and the point N represents the sheath (shown at the middle for simplification of the circuit).

Therefore, the whole three core cable is equivalent to three star connected capacitors each of capacitance Cs + 3Cc as shown in fig. (iii).The charging current can be given as,Ic = 2πf(Cs+3Cc)Vph      A

### Measurement Of Cs And Cc

In order to calculate Cs and Cc we perform various experiments like:
1. First, the three cores are connected together and capacitance between the shorted cores and the sheath is measured. Shorting the three cores eliminates all the three Cc capacitors, leaving the three Cs capacitors in parallel. Therefore, if C1 is the now measured capacitance, Cs can be calculated as, Cs = C1/3.
2. In the second measurement, any two cores and the sheath are connected together and the capacitance between them and the remaining core is measured. If C2 is the measured capacitance, then C2 = 2Cc+Cs (imagine the above figure (iii) in which points A, B and N are short circuited). Now, as the value of Cs is known from the first measurement, Cc can be calculated.