One of the most accepted expressions to determine the number of direct strikes to an overhead line in an open ground with no nearby trees or buildings, is that described by Eriksson (1987):
N = Ng (58h^06 + n)/10 eq 10.3
h is the pole or tower height (m) — negligible for distribution lines
b is the structure width (m)
Ng is the Ground Flash Density (flashes/km2/year)
N is the number of flashes striking the line/100 km/year. For unshielded distribution lines, this is comparable to the fault index due to direct lightning hits. For transmission lines, this is an indicator of the exposure of the line to direct strikes. (The response of the line being a function of overhead ground wire shielding angle on one hand and on conductor-tower surge impedance and footing resistance on the other hand).
Note the dependence of the incidence of strikes to the line with height of the structure. This is important since transmission lines are several times taller than distribution lines, depending on their operating voltage level.
Also important is that in the real world, power lines are to different extents shielded by nearby trees or other objects along their corridors. This will decrease the number of direct strikes estimated by Eq. (10.3) to a degree determined by the distance and height of the objects.
In IEEE Std. 1410-1997, a shielding factor is proposed to estimate the shielding effect of nearby objects to the line. An important aspect of this reference work is that objects within 40 m from the line, particularly if equal or higher that 20 m, can attract most of the lightning strikes that would otherwise hit the line.
Likewise, the same objects would produce insignificant shielding effects if located beyond 100 m from the line. On the other hand, sectors of lines extending over hills or mountain ridges may increase the number of strikes to the line.
The above-mentioned effects may, in some cases, cancel each other so that the estimation obtained form Eq. (10.3) can still be valid. However, it is recommended that any assessment of the incidence of lightning strikes to a power line be performed by taking into account natural shielding and orographic
conditions along the line route.
This also applies when identifying troubled sectors of the line for installation of metal oxide surge arresters to improve its lightning performance.
Finally, although meaningful only for distribution lines, the inducing effects of lightning, also described in De la Rosa et al. (1998) and Anderson et al. (1984), have to be considered to properly understand their lightning performance or when dimensioning the outage rate improvement after application of any