Effects of Corona on Traveling Waves C. F. W A G N E R B. L. L L O Y D

F E L L O W A I E E A S S O C I A T E M E M B E R A I E E

TH E effect of corona on traveling waves is to retard any given point on a voltage wave above the corona thresh­

old value by an amount proportional to the distance traveled. Thus the effect is equivalent to a reduction in velocity. If a linear circuit can be characterized by assign­ing to it a certain inductance L and capacitance C, per unit length, then a wave impressed upon such a circuit will propagate along the circuit with a velocity z>, such that

v = l/VLC ( 1 )

This relation indicates the possibility of explaining corona effects by an increase in capacitance.

The results of laboratory tests show that the corona characteristics under impulse conditions can be approxi­mated by a variable capacitance. Oscillograms of charge vs voltage show that with increasing voltage the trace is es­sentially independent of the front of the wave and the time to reach crest.

In Fig. \A the fundamental q-e curve of the conductor is shown. The slope of this curve is given by the C-\-AC curve. The C+AC curve in turn permits the determina­tion of the velocity by replacing C by C+AC in equation 1.

+ ΞAC/C) (2 )

where vL is the velocity of light, which is correct for the front of the wave.

Fig. 1C shows an arbitrary volt-time curve which is ap­plied at χ = 0. Assuming that the traveling wave has moved a distance d, the undistorted portion of the wave below the corona threshold voltage, eo, requires a time ti = d/vL to

Digest of paper 55-453, "Effects of Corona on Traveling Waves," recommended by the AIEE Committee on Transmission and Distribution and approved by the AIEE Com­mittee on Technical Operations for presentation at the AIEE Summer General Meeting, Swampscott, Mass., June 27-July 1, 1955. Published in AIEE Ptwer Apparatus and Systems, October 1955, pp. 858-72.

C. F. Wagner and B. L. Lloyd are with Westinghouse Electric Corporation, East Pitts­burgh, Pa.

ο <3

travel this distance. A point on the voltage wave above eo will require the time / ι + Δ Γ . This total time is related to the instantaneous velocity corresponding to the particular point on the voltage wave by the relation

h+AT=-, or AT d _ _d __d_ ν ν vL

= d[ VUC+AC) - Vlc] = dVLC\

AT

~d l|~ / AC

(3)

(4 )

The curve for AT/d is plotted in Fig. \A, and for conveni­ence is replotted in Fig. \B. To determine the retarda­tion AT, multiply the value in Fig. \B by the distance traveled. This provides the curve shown in Fig. 1C for χ = d. Thus, a method is available for determining the dis­tortion of a wave traveling on a line whose q-e characteristic is known.

Using the laboratory determined values of AC for a par­ticular conductor, the quantity AT/d was computed. These results checked the independently derived retarda­tion curves, Δ Τ/d, for the same conductor, obtained during field tests on the 500-kv lines at the Tidd power station.

With this characterization of corona, it is possible to de­vise analogues which can be used for computer studies or analytical work. An incremental element of a line can be represented by a combination of an inductance, capacitors, a battery, and a rectifier.

Under corona the voltage and current no longer have the same wave forms. I t is possible to calculate the current wave in terms of the voltage and characteristics of the con­ductor. It should also be noted that the voltage-time and the voltage-distance wave forms are no longer related un­der corona conditions, as they are below corona, by the simple distance-time relations corresponding to the velocity of light.

x = d

0 0.2 0.4 μ SEC / 1000 FT. TIME IN MICROSECONDS

CONDUCTOR VOLTAGE e

Fig. 1. M e t h o d of d e t e r m i n i n g distortion of trave l ing w a v e s from q-e c u r v e s

DECEMBER 1955 Wagner, Lloyd—Effects of Corona 1071