Design of High-Voltage Cable Joints H. D. S H O R T

M E M B E R A I E E

WH I L E there exists a large volume of printed matter on all the aspects of high-voltage cables, the design

of the related joints on a theoretically rigorous basis has not hitherto been published in a comprehensive manner. Joints can be classified as the homogeneous case and the heterogeneous case. In the former case the joint and cable insulants are assumed of identical material, whereas in the latter the conditions pertain where the cable insulant is of the usual graded construction and the joint insulant of some different material or dielectric constant.

The cable joint as such may be considered to be com­posed of three elemental parts—the ferrule or connector, Figure 1, which joins together electrically and mechanically the two cable ends; the tapering down of the cable insulant adjacent to the ferrule, called the "stepping" or the stepping profile, Figure 1, which forms the transitional bounding curve between the cable insulant diameter and the con­ductor diameter; and the stress control cone profile, Figure 2, which forms the bounding curve between the joint insulant diameter and the cable insulant diameter.

The long-time voltage breakdown strength of impregnated paper in cable form normal to the paper, and at atmospheric pressure, has been found to be 15 times greater than that in the longitudinal plane of the paper. Hence the longi­tudinal component of the electric field gradient (called the longitudinal stress) along the stress control cone profile and the stepping profile must be controlled with due regard to this 15:1 relationship. Under atmospheric transient surge voltages (impulse voltage breakdown strength) the same failing is exhibited so that from this point of view the longitudinal stress, particularly along the stepping treads, must be accommodated appropriately. The limiting value of the longitudinal stresses, which come into play when the electric field is disturbed, is that at which incipient deterioration of the insulating tapes along and within the stress control cone profile and along the stepping profile is amply prevented.

CABLE INSULANT

4FERRULE

TREA

CONDUCTOR

F i g u r e 1 (Left) Ferru le (or connector ) j o i n i n g electrical ly a n d m e c h a n i c a l l y t h e conductors of the t w o cable e n d s ; (r ight) t h e " s t e p p i n g " of t h e cable insu lant of o n e of t h e cable e n d s , i n t h e

jo in t adjacent to t h e ferrule

STRESS CONTROL CONE F i g u r e 2 . T h e stress control c o n e profile

- x 4 -

F i g u r e 3 . A family of stress control c o n e profiles for var ious v a l u e s of l ong i tud i ­na l stress a long t h e stress control c o n e

profile, g p

g P I > g P 2 > g p 3 > g p 4 > g p 5

F i g u r e 4 . A family of s t epp ing profi les for var ious v a l u e s of l ong i tud ina l stress a long t h e s t e p p i n g

profile, gt

The longitudinal stress then becomes the criterion, and the corollary transpires that these transitional boundaries will be functions of the longitudinal stress along them. Formulas for the longitudinal stress along the stress control cone may be derived by resolving the 3-dimensional electric field. The equation for this stress is an exponential func­tion of the potential drop, the conductor diameter, and the cable insulant diameter from which the χ andy co-ordinates of the stress control cone may be computed. Hence a curve may be drawn to reveal the proper profile for the transitional boundary and some particular value of the related longitudinal stress. By this method a stress control cone may be determined having a constant longitudinal stress along its profile. For varying values of this stress a series of curves may be developed, as shown in Figure 3, which have a common origin to reveal the significance of the longitudinal stress along the stress control cone in determining the over-all length of the joint.

By similar reasoning formulas for the longitudinal stress along the stepping profile may be derived, and once again a family of exponential curves may be developed for varying values of this stress (Figure 4). By choosing suitable minimum and maximum values for the stress along the stepping profile the actual risers and treads of the stepping may be found such that a constant longi­tudinal stress obtains from the conductors up the stepping.

All the formulas are readily applicable to the practical design of cable joints and permit of a less cumbersome method of calculating the desired profiles than has been available up to now.

Digest of paper 49-267, "A Theoretical and Practical Approach to the Design of High-Voltage Cable Joints," recommended by the AIEE Committee on Insulated Conductors and approved by the AIEE Technical Program Committee for presentation at the AIEE Fall General Meeting, Cincinnati, Ohio, October 17-21, 1949. Scheduled for publication in AIEE Transactions, volume 6 8 , 1949.

H. D . Short is with the Canada Wire and Cable Company, Toronto, Ontario, Canada.

328 Short—Design of High-Voltage Cable Joints ELECTRICAL ENGINEERING