LOW-FREQUENCY INDUCTION 595 



represents the same exposure conditions as in the preceding set-up 

 and the telephone circuit is soHdly grounded at both ends, but the fault 

 current instead of flowing through the entire exposure flows through 

 only half of it. In this case the telephone circuit impedances are 

 the same as in the preceding case, but only half of the induced voltage 

 is present. Consequently, the amount of current through the longi- 

 tudinal circuit is only half of that in the preceding case. Now if the 

 net voltage drop from either end to the middle is taken, it will be found 

 that it is equal to one-half of the total longitudinal voltage induced 

 under the conditions shown. Figure 14 also shows the set-up for 

 demonstrating this condition. In this case the longitudinal voltage is 

 smaller than in the preceding demonstration, but if both ends are 

 grounded and the voltage measuring device is moved along the line, 

 the voltage-to-ground increases from one end to the middle and then 

 falls off from the middle to the opposite end. 



In the last two demonstrations, the fault current on the power line 

 was fed from one end only, i.e., "single-end feed." It sometimes 

 happens that the fault current may be supplied to a power line, at 

 least during the initial stage of a disturbance, from both ends, i.e., 

 "double-end feed." The double-end feed condition tends to reduce 

 the overall longitudinal induction when the fault occurs inside the 

 exposure. In the demonstration shown in Fig. 15 it may be observed 

 that for the set-up with a fault at the middle of the exposure the 

 symmetry is so good that the total longitudinal voltage is very small. 

 However, with the telephone circuit grounded at both ends, a sub- 

 stantial voltage-to-ground exists at a point in the telephone circuit 

 opposite the fault and this voltage-to-ground reduces to zero at the 

 ends. As the fault is moved toward either end of the exposure, there 

 is a tendency for the longitudinal voltage to increase and for the voltage- 

 to-ground, with both ends of the line grounded, to decrease until the 

 limiting condition brought out in Fig. 13 is reached. 



The analysis of voltage-to-ground can be carried out for any com- 

 bination of impedances and induced voltage distributions by totaling 

 vectorially the voltage drops (including any voltage drop over pro- 

 tector ground resistance) and the induced voltages between a grounded 

 point and the point at which the voltage-to-ground is desired. The 

 same analysis can also be carried out regardless of whether one or 

 numerous wires are involved as long as all of the wires are grounded 

 directly or through arrestors at the same points. If some of the wires 

 on a line are not grounded, i.e., the protectors are not operated, the 

 analysis for these wires must be carried out on the basis of their 

 admittance-to-ground as discussed previously. In such a case, the 



