Upon injection, the discharge current pulse splits itself into two identical current pulses of half
amplitude propagating in opposite directions away from the discharge site. At a point of observation
located at a distancexalong the line from the discharge site, the noise current is distorted according to
iðÞv,x dx¼i 0 ðÞv expðÞgx dx¼i 0 ðÞv expðÞax dx (15:4)
wheregrepresents the propagation constant, which can be approximated by its real componenta.
The total noise current circulating in the line conductor is the sum of all contributions from the
corona discharges along the conductor and is given by
IðÞ¼v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(^1) ð
1
½iðÞv,x^2 dx
vu
u
ut ¼i^0 ðÞvffiffiffi
a
p (15:5)
For a multiphase line, because of the high-frequency nature of the noise current, the calculation of the
interference field must take account of the mutual coupling among the conductors, which further
complicates the process (Gary, 1972; Moreau and Gary, 1972a,b). Modal analysis provides a convenient
means of evaluating the noise currents on the line conductors. In this approach, the noise currents are
first transposed into their modal components, which propagate without distortion along the line
conductors at their own velocity according to the relation
½¼i 0 ðÞv dx ½M ½j 0 ðÞv dx (15:6)
Consequently,
½¼j 0 ðÞv dx ½M^1 ½i 0 ðÞv dx (15:7)
where [M] is the modal transposition matrix andj0(v) are the modal components of the injected noise
current. The modal current at the measuring point located at a distancexfrom the injection point is
jðÞv,x dx¼j 0 ðÞv expðÞax dx (15:8)
and the modal current component at the measuring point is
JðÞ¼v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð^1
1
½jðÞv,x^2 dx
vu
uu
t ¼
j 0 ðÞv
ffiffiffi
a
p (15:9)
or, in a general way
½¼JðÞv
1
ffiffiffi
a
p
½
½¼j 0 ðÞv
1
ffiffiffi
a
p
½
½M^1 ½i 0 ðÞv (15:10)
Finally, the line current can be obtained from
½¼IðÞv ½M ½JðÞv (15:11)
The magnetic and electric fields produced by the noise currents in the line conductors can then be
evaluated for assessment of the electromagnetic interferences. Moreau and Gary (1972a,b) obtained
good agreement between calculated and experimental results with the symmetrical modes of Clarke for
the modal transposition: