386 ALTERNATING CURRENTS 



161. Transmission Line Capacitance; Three-phase. Figure 

 349 shows the three conductors A, B, C, of a three-phase line, 

 these conductors being symmetrically spaced. There is ca- 

 pacitance between each pair of conductors, which can be rep- 

 resented by three equal capacitances c', c', c', Fig. 349 (a), 

 connected in delta. In determining the capacitive relations in 

 this type of system, it simplifies the problem to substitute an 

 equivalent Y-system for the delta-system. It is obvious that 

 any delta-load may be replaced by an equivalent Y-load. This 

 is the same as considering that each conductor has capacitance c 

 to a fictitious neutral 0, Fig. 349(6). In the actual line the 



(6) 



FIG. 349. Delta capacitance of a 3-phase system replaced by an equivalent 



Y-capacitance. 



neutral may be the ground. The voltage across each of these 

 condensers c is E/-\/3 where E is the line voltage. 



Equation (87), page 384, may then be applied to finding the 

 capacitance c, and the voltage to neutral E/\/3 used for deter- 

 mining the charging current per conductor. 



Example. Assume that a third wire be added to the system of paragraph 

 160 to form a symmetrical spacing and that the system is operated three- 

 phase, 33,000 volts between conductors. Find the charging current per 

 conductor. 



r = 0.205 in. 

 D/r = 60/ 0.205 = 293 

 log, 293 = 2.47 



,=40Xy^ 8 = 0.628 mf. 



Volts to neutral = 33,000/\/3 = 19,070 volts. 

 The charging current per conductor 



L = 27r60 X 0.628 X 19,070 = 4.52 amp. Ans. 

 This may be checked by Appendix J, page 466. 



