In this theory, dielectric stress on cable, electric intensity, maximum potential gradient, minimum potential gradient, ratio of maximum to minimum potential gradient and dielectric stress on stranded cable is given.

Dielectric Stress

It is electrostatic stress on cable insulation under operating conditions.
The dielectric stress at any point is equal to potential gradient at that point therefore in order to find dielectric stress at any point in cable, we have to find out potential gradient at that point.

Electric intensity

The electric intensity at any distance x from the center of cable O is given by

E_x = [Q / 2πε₀ε_r] ( 1 / x ) volt / meter

Where

ε₀=Absolute Permittivity = 8.854 × 10 ^{– 12} Farad / meter

ε_r= Relative Permittivity

Potential Gradient

The potential gradient ( E ) at any point is equal to electric intensity ( g ) at that point therefore

g = [Q / 2πε₀ε_r] ( 1 / x ) volt / meter… ( 1 )

As capacitance C = 2πε₀ε_r/ Log_e ( D / d ) and C = Q / V… ( 2 )
Q = CV

= [ 2πε₀ε_r/ Log_e ( D / d )] V…. ( 3 )

From equation ( 1 ) and ( 3 )

g = [ V/ Log_e ( D / d )] ( 1 / x )

g = V / [ x Log_e ( D / d )] …. ( 4 )

We can say that the potential gradient at any point on cable is inversely proportional to x. The potential gradient is minimum when x is maximum and potential gradient is maximum when x is minimum.

X is maximum at distance = D ( Internal diameter of sheath ) / 2
X is minimum at distance = d ( Diameter of conductor ) / 2

Maximum & Minimum Potential Gradient

Maximum potential gradient at x = d / 2

g_max = 2V / [ d Log_e ( D / d )] ( ⸫ x = d / 2 )….. ( 5 )

Minimum potential gradient at x = D / 2

g_min = 2V / [ D Log_e ( D / d )] ( ⸫ x = D / 2 )…. ( 6 )

Ratio of Maximum to Minimum Potential Gradient

Therefore, the ratio of maximum potential gradient to the minimum potential gradient

( g_max/ g_min ) = {2V / [ d Log_e ( D / d )] } / { 2V / [ D Log_e ( D / d )] }

( g_max/ g_min ) = D / d

The formula for maximum and minimum potential gradient is applicable only for smooth cylindrical cable.
The dielectric stress for the stranded conductor increases by 20% due to conductor surface of the individual wires (strands).

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