Graded Insulation

Some high-voltage cables use two or more different kinds of insulation (dielectric) in order to achieve a smaller difference in voltage gradient or electric field intensity throughout the insulation. Equation 2-38 shows that in coaxial cable, the electric field intensity varies inversely as the distance from the center of the inner conductor and also inversely as the relative dielectric constant. Therefore, in some types of high-voltage cable, next to the inner conductor a material is used that has a higher relative dielectric constant k_r than the material further out. It is then necessary to take the difference in the dielectrics into account in determining the capacitance of the cable. This is done as follows: in Fig. 2-16 the voltage across the dielectric, which has the relative dielectric constant k_r12, is expressed by

[2-40]

Figure 2-16. Coaxial cable with graded insulation

and the voltage across the outer shell of the dielectric having a dielectric constant k_r23 is expressed by

[2-41]

The total voltage from conductor to sheath is expressed by

[2-42]

and the capacitance is expressed by

[2-43]

The electric field intensity at the surface of the inner conductor is

[2-44]

and that inside the sheath is

The ratio of these electric field intensities is

[2-45]

whereas in the case of a homogeneous dielectric this ratio is

[2-46]

It can be seen, therefore, that if the dielectric k_r12 is greater than k_r23 the voltage gradient in the dielectric is more nearly uniform than it is in a homogeneous medium. Generally in high-voltage cables, in the absence of mechanical imperfections, the dielectric deteriorates more rapidly near the inner conductor because the electric field intensity and the temperature in the dielectric are the greatest at that location.