## 26/03/2021

### 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 is given by

Ex = [Q / 2πε0εr ] ( 1 / x )  volt / meter

Where

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

εr = Relative Permittivity

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

g =  [Q / 2πε0εr ] ( 1 / x )  volt / meter… ( 1 )

As capacitance C = 2πε0εr / Loge ( D / d ) and C = Q / V… ( 2 )
Q = CV

= [ 2πε0εr / Loge ( D / d )] V…. ( 3 )

From equation ( 1 ) and ( 3 )

g = [ V / Loge ( D / d )]  ( 1 / x )

g = V / [ x Loge ( 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 potential gradient at x = d / 2

gmax = 2V / [ d Loge ( D / d )]   ( ⸫ x = d / 2 )….. ( 5 )

Minimum potential gradient at x = D / 2

gmin = 2V / [ D Loge ( D / d )]   ( ⸫ x = D / 2 )…. ( 6 )

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

( gmax / gmin ) = {2V / [ d Loge ( D / d )] } / { 2V / [ D Loge ( D / d )] }

( gmax / gmin ) =  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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