PETERSEN SYSTEM OF GROUNDING 



43 



voltage of the faulty wire to ground, viz., E?g = £30 + £0,, passes 

 gradually back to the normal value £30. At the same time the voltages 

 to ground of the two sound phases (£ig, E,g,) return to their normal 

 values £10, £20- The ends of the three vectors, £3^, £,,, £?,, may be 

 thought of as sliding at equal rates along the line £30 and the dotted 

 lines parallel to it. 



The efifectiveness of the action just sketched (it has been assumed 

 that the frequency of the series resonant circuit is accurately that of 

 the system fundamental), of course, depends on the accuracy of the 

 tuning and the amount of damping. If the free period of the resonant 

 circuit differs considerably from the fundamental period of the system, 

 the impressing on the faulty wire of a voltage to ground in excess of 

 normal may result, especially if the damping is small. The effect of 

 inexact tuning is discussed by Petersen in the article referred to above. 

 He describes some experiments in which the capacity of the power 

 system to ground was varied some 15 or 20%, each way from the 

 value corresponding to resonance, without apparent effect on the 

 quenching action of the reactor. 



2. Transient Overvoltage on Sound Phase at Time of Grounding 



To simplify the following theoretical discussion a single phase 

 system is treated. This is represented in Fig. 3. Referring to this 



Lac + l-zg 



'•ic-t-'-tg +'-2c^'-2g 



y E cos U3t (^^ t ItT 



I'lC+'-igt'-zc+'-zg+'-n 



Fig. 3 — Three-phase System with Neutral Grounded Through Reactor, with Fault 



to Ground on One Phase 



figure, when one phase is grounded (represented by the closing of the 

 switch S), the following equations, in which D denotes differentiation 

 with respect to time, must be satisfied: 



