V.  Short-circuit  Current 

120.  If  a  short  circuit  occurs  at  the  secondary  terminals  of  a 
transformer,  and  the  power  supply  at  the  primary  is  sufficient  to 
maintain  the  primary  terminal  voltage,  the  primary  and  second- 
ary currents  of  the  transformer  are  limited  by  its  impedance  only. 
Thus,  if 

r  =  P  +  j* 

is  the  impedance  voltage,  as  fraction  of  full-load  voltage,  the  short- 
circuit  current  of  the  transformer  is 

1  1 

of  the  full-load  current,  thus  usually  is  very  large.  In  the  three 
instances  illustrated  in  Figs.  157,  159  and  160,  with 

f  =  0.02  +  0.02  j,  hence        f  =0.028 

0.01  +  0.04  j  0.04 

0.01  +  0.08  j  0.08 

the  short-circuit  current  thus  is  36,  25  and  12.5  times  full-load 
current,  respectively. 

As  seen,  with  the  exception  of  very  low  reactance  transformers, 
it  is  essentially  the  reactance  which  determines  the  total  im- 
pedance and  thus  the  short-circuit  current. 

121.  Primary  current  and  secondary  current  in  the  trans- 
former, being  opposite  in  phase,  repel  each  other.     This  repul- 
sion is  proportional  to  the  product  of  primary  and  secondary 
current,   thus,   since  primary  and  secondary  current  are   (ap- 

19 


294     ELEMENTS  OF  ELECTRICAL  ENGINEERING 

proximately)  proportional  to  each  other,  the  repulsion  is  pro- 
portional to  the  square  of  the  current.  The  repulsion  is  small 
at  full  load,  but  in  low-reactance  transformers,  with  'short-circuit 
currents  from  forty  to  fifty  times  full-load  current,  the  mechanical 
forces  have  increased  1600  to  2500  fold,  and  then,  with  large 
power  transformers,  reach  formidable  values,  amounting  to  many 
hundred  tons,  and  then  it  is  economically  difficult  to  build  trans- 
formers with  the  coils  supported  so  rigidly  as  to  stand  such  forces. 
Thus  far  very  few  generating  systems  exist  of  such  large  size 
as  to  be  capable  of  maintaining  full  voltage  at  the  primary  ter- 
minals of  a  large  transformer  at  secondary  short  circuit,  but  their 
number  is  increasing,  and  thus  the  necessity  of  limiting  the  short- 
circuit  current  of  large  power  transformers  to  a  mechanically 
safe  value  is  becoming  increasingly  important.  This  means  a 
construction  providing  for  considerable  internal  reactance.  As 
the  regulation  of  large  power  transformers  is  of  no  serious  impor- 
tance, the  desirability  of  low  reactance,  which  exists  in  the  small 
lighting  and  general  distribution  transformers,  does  not  exist  in 
large  power  transformers,  and  modern  practice  tends  toward  the 
use  of  internal  reactance  of  4  to  8  per  cent.,  to  secure  reasonable 
mechanical  safety.