LIGHTNING PROTECTION OF BURIED TOLL CABLE 285 



A lightning stroke at the distance y will cause cable failure when the crest 

 current i exceeds a certain value which depends on the distance: 



i = f(y) ■ (84) 



The fraction of all lightning strokes which has a crest current larger 

 than i will be designated Po(i)- The fraction of the lightning strokes dN 

 which will cause cable failures is then: 



dn = dNP,{i) = 2NsPo(i) dy ' (85) 



The number of cable failures along the length 5 due to all lightning strokes 

 to ground up to the maximum distance V that need to be considered is: 



n = 2Ns [ PS) dy (86) 



For the purpose of computation it is convenient to change the variable 

 in the latter integral from y to i. With y = f~ (i) = y{i), di = dy-f\y), 

 {q = /(O) and / = f{y), the following integral is obtained: 



n = 2Ns FPo(0 - / y{i)Po(i) di (87) 



In (87), / is the maximum stroke current that needs to be considered and 

 may actually be replaced by infinity, as will be evident later on. The 

 current /o , which is the minimum current that will cause insulation puncture 

 in the case of a direct stroke, may readily be determined from the breakdown 

 voltage of the insulation and the calculated voltage between core and sheath 

 per kiloampere, in the manner illustrated in Section 2.4. 



In order to evaluate the integral of (87), it is divided as follows: 



n = 2Ns 



YPoiD - f ' Vi(OA'(/) di - f y-2{i)P',{i) di\ (88) 



When i < ii , failures of the cables will be due to arcing of the stroke 

 to the cable and when i > /i , failures will occur before arcing takes place, 

 due to the leakage current entering the sheath. Within each of the above 

 two ranges the relationship of y to i is different and is designated yi{i) and 

 Viii), respectively. 



As already shown, failures due to arcing will take place when: 



vi(/) < qipiV (89) 



where q is defined as before and p is the earth resistivity in meter-ohms. 

 In Section 1.7 it was shown that failures due to leakage current will 

 occur when 



i > io/\{y) 



