66 SYNCHRONOUS MOTORS 



(or reactive) currents are practically constant at all loads and can even 

 be predetermined, at least roughly, according to the output of the 

 appliances, without knowing exactly what these are. Let J d be the 

 total value of the reactive currents, and J w be the total corresponding 

 active current, at any given instant. 



To neutralize completely the lag of the line, it would be necessary 

 to produce, by means of the synchronous motors in- that part of the 

 line, a reactive current which is leading in phase and equal to 



j=Jd, 



(in absolute units). But it is not usually necessary to fulfill strictly 

 this condition, because it may be, as a rule, considered sufficient to 

 have a power-factor 0.95 to 0.97, corresponding to reactance-factors 

 (tan f) ranging in value from to ^, respectively. Let us take, 

 for example, tan f %. It is then sufficient to satisfy the equation 



Jw+i 



in which i equals the active current absorbed by the synchronous 



motors, and which must be added to that of the apparatus, J w (useful 



load). 



From this we have 



This means that the reactive current which the synchronous motors must 

 produce to render the reactance-effects of neighboring motors practically 

 negligible need not be equal to the current actually consumed by these 

 appliances, but may be reduced more and more as their useful load 

 is increased. Owing to this circumstance, one or more relatively small 

 synchronous motors will suffice, in practice, to neutralize the harmful 

 effects of reactance on the line. 



Let us suppose, for simplicity, that there is only one such compensa- 

 tor-motor, and that it is also serving, at the same time, as a motor 

 doing mechanical work. Its total armature-current will be equal to 

 the resultant 



The current / being limited by the heating of the motor, the useful 

 current i and, consequently, the useful corresponding power P 2 , will 



