V.  Induction  Booster 

157.  In  the  induction  machine,  at  a  given  slip  s,  current  and 
terminal  voltage  are  proportional  to  each  other  and  of  constant 
phase  relation,  and  their  ratio  is  a  constant.  Thus  when  con- 
nected in  an  alternating-current  circuit,  whether  in  shunt  or  in 
series,  and  held  at  a  speed  giving  a  constant  and  definite  slip  s, 
either  positive  or  negative,  the  induction  machine  acts  like  a 
constant  impedance. 


350     ELEMENTS  OF  ELECTRICAL  ENGINEERING 

The  apparent  impedance  and  its  components,  the  apparent 
resistance  and  apparent  reactance  represented  by  the  induction 
machine,  vary  with  the  slip.  At  synchronism  apparent  impe- 
dance, resistance,  and  reactance  are  a  maximum.  They  decrease 
with  increasing  positive  slip.  With  increasing  negative  slip  the 
apparent  impedance  and  reactance  decrease  also,  the  apparent 


FIG.  191. — Effective  impedance  of  three-phase  induction  machine. 

resistance  decreases  to  zero  and  then  increases  again  in  negative 
direction  as  shown  in  Fig.  191,  which  gives  the  apparent  impe- 
dance, resistance,  and  reactance  of  the  machine  shown  in  Figs, 
176  and  177,  etc.,  with  the  speed  as  abscissas. 

The  cause  is  that  the  power  current  is  in  opposition  to  the  ter- 
minal voltage  above  synchronism,  and  thereby  the  induction 


INDUCTION  MACHINES  351 

machine  behaves  as  an  impedance  of  negative  resistance,  that  is, 
adding  a  power  e.m.f.  into  the  circuit  proportional  to  the  current. 

As  may  be  seen  herefrom,  the  induction  machine  when  inserted 
in  series  in  an  alternating-current  circuit  can  be  used  as  a  booster, 
that  is,  as  an  apparatus  to  generate  and  insert  in  the  circuit  an 
e.m.f.  proportional  to  the  current,  and  the  amount  of  the  boosting 
effect  can  be  varied  by  varying  the  speed,  that  is,  the  slip  at 
which  the  induction  machine  is  revolving.  Above  synchronism 
the  induction  machine  boosts,  that  is,  raises  the  voltage;  below 
synchronism  it  lowers  the  voltage;  in  either  case  also  adding  an 
out-of-phas.e  e.m.f.  due  to  its  reactance.  The  greater  the  slip, 
either  positive  or  negative,  the  less  is  the  apparent  resistance, 
positive  or  negative,  of  the  induction  machine. 

The  effect  of  resistance  inserted  in  the  secondary  of  the  induc- 
tion booster  is  similar  to  that  in  the  other  applications  of  the 
induction  machine;  that  is,  it  increases  the  slip  required  for  a 
certain  value  of  apparent  resistance,  thereby  lowering  the  effi- 
ciency of  the  apparatus,  but  at  the  same  time  making  it  less  de- 
pendent upon  minor  variations  of  speed ;  that  is,  requires  a  lesser 
constancy  of  slip,  and  thus  of  speed  and  frequency,  to  give  a 
steady  boosting  effect.