Q6Power System - I

In a single-core cable, the electric field (voltage stress) within the dielectric is not uniform; it is inversely proportional to the radial distance from the core, so the stress g at radius x is g(x) = V/(x·ln(R/r)), where V is applied voltage, r is conductor radius and R is the sheath (outer) radius. This means the stress is maximum right at the conductor surface and falls off toward the outer sheath. Since the insulation must be designed to withstand the maximum stress (at the conductor surface) throughout its entire thickness, the dielectric material farther from the core is significantly under-utilized, requiring a thicker (and hence costlier, heavier, more expensive) cable than would be needed if the stress were uniform. Grading is the technique of modifying the dielectric so that this stress distribution is made more uniform, allowing higher operating voltages for a given cable size, or a smaller/cheaper cable for a given voltage.

1. Capacitance Grading

In this method, the single homogeneous dielectric is replaced by two or more concentric layers of different dielectric materials, each having a different permittivity, arranged such that the layer with the highest permittivity is placed nearest to the conductor and permittivity progressively decreases outward. Since in a series arrangement of capacitive layers, voltage stress is inversely proportional to permittivity, deliberately grading the permittivity to be highest near the core (where geometric stress concentration is greatest) helps to counteract that concentration and flattens the overall stress distribution across the full insulation thickness, achieving more uniform utilization of the dielectric.

2. Intersheath Grading

In this method, the dielectric remains a single homogeneous material, but one or more thin conducting (metallic) intersheaths are inserted at suitable intermediate radii within the insulation, dividing the single dielectric into two or more coaxial capacitive layers of different thickness (but same material) connected effectively in series. Each intersheath is maintained at a potential intermediate between the core and outer sheath potentials (typically by connecting it through a suitably tapped transformer or potential divider arrangement), so that the voltage is distributed across the layers in a controlled way, achieved by proportioning the layer thicknesses appropriately — thinner layers nearer the core, where the natural voltage gradient is steepest — again equalizing the overall stress distribution. Intersheath grading requires more complex construction (physically embedding metallic sheath layers within the cable and providing electrical connections to intermediate potentials) but avoids the need for exotic, precisely graded permittivity dielectric materials, unlike capacitance grading.

Both grading methods aim to bring the voltage stress at the conductor surface (the point of maximum natural stress) closer to the average stress across the whole dielectric, allowing a substantial reduction in insulation thickness (and hence cable cost and weight) for a given working voltage, or conversely permitting a higher working voltage for a given cable diameter.