The process of achieving uniformity in dielectric stress is known as grading of cables. There are two methods of grading viz.: 1. Capacitance Grading 2. Intersheath Grading.
Method # 1. Capacitance Grading:
In this method of cable grading, the uniformity in dielectric stress is achieved by using various layers of different dielectrics in such a manner that the permittivity, ∈r of any layer is inversely proportional to its radius of distance from the centre, i.e.
Thus we see that if such a condition is attained, the value of dielectric stress at any point is constant and is independent of distance from the centre, and the grading will be ideal one. But it is not possible to use infinite number of dielectrics for a single cable and in practice two or three dielectrics are used in such a manner that the permittivity of the dielectric near the core has got highest value and then it decreases and finally it has got minimum value in the outer most layers.
Now consider a cable in which 3-layers of dielectrics of outer diameters d1, d2 and D and of relative permittivity ∈r1, ∈r2 and ∈r3 have been used. If the permittivities are such that ∈r1 > ∈r2 > ∈r3 and if the maximum stress to which each dielectric is subjected is constant then,
∈r1 d = ∈r2 d1 = ∈r3 d2
For the pd across the inner layer we have,
and the pd between core and earthed sheath,
V = V1 + V2 + V3
The advantage of grading is that if the overall diameter is same for a non-graded and graded cable, then the permissible safe potential of the cable is increased i.e., for the same permissible safe potential, the size of the graded cable will be smaller than that of the non-graded cable.
Method # 2. Intersheath Grading:
In this method of cable grading a homogeneous dielectric is used, which is divided into various layers, by suitably placing the metallic intersheaths. These metallic intersheaths are held at certain potentials which are in between the core potential and the earth potential. There is thus a definite potential difference between the inner and outer layers of each sheath, so that each sheath can be treated like a homogeneous single core cable and we have,
But for a homogeneous dielectric we have,
Again, since all these potential differences are in phase, since the cable is, in effect, a series of capacitors in series, we also have,
V = V1 + V2 + V3 … (11.14)
Grading in Practice:
Grading is only useful for very high voltage cables for which the ratio D/d is large. If D/d is 2, grading will increase the permissible safe working voltage by only 30% but if D/d = 5, grading will increase the safe working voltage by 100%. With capacitance grading the chief handicap is due to the fact that there are such few high grade insulating materials of reasonable cost, whose permittivities can be made to vary over the required range.
The use of rubber (∈r = 4-6) and impregnated paper (∈r = 3-4) have been suggested. However, rubber is very expensive and the cost of dielectric becomes prohibitive. A second difficulty is the possibility of change of permittivity with time that may completely alter the distribution of dielectric stress and lead to the breakdown of insulation even at the normal operating voltage.
With intersheath grading, the main objection is the possibility of damage to the intersheath during transportation and installation. Due to charging currents there are losses in the intersheaths. The modern trend is to avoid grading as far as possible and employ oil-filled or gas-pressure cables.