II.  Excitation 

112.  The    primary    current    i\    is    not    strictly    proportional 
to  the  secondary  current,  i2  by  the  ratio  of  transformation, 


TRANSFORMER 
Excitation  and  Iron  Losses 


Vo 


tage 


fower 
factor 


50 


30 


FIG.  153. — Excitation  and  core  loss  of  transformer. 

and  does  not  become  zero  at  no  load  or  open  circuit,  but  a  small 
and  lagging  current  ^o  remains  at  no  load,  which  is  called  the 
exciting  current.  It  produces  the  magnetic  flux  and  supplies 
the  losses  in  the  iron,  so-called  "core  loss."  Its  reactive  com- 
ponent, imj  is  called  the  magnetizing  current,  and  is  usually 
greatly  distorted  in  wave  shape,  while  the  energy  component, 


280     ELEMENTS  OF  ELECTRICAL  ENGINEERING 

ih,  does  not  much  differ  from  a  sine  wave,  and  is  the  hysteresis 
energy  current: 

/o  =  ih  -  Jim- 

Under  load,  the  primary  current  then  consists  of  two  com- 
ponents: the  load  current  7'2  which  is  the  transformed  second- 

ary current  7'2  =  —  >  and  the  exciting,  current  IQ.     The  total 
«i 

primary  current  thus  is: 

Ji  =  /'2  +  /o  =  ^+  (ih-jim). 

In  general,  /0  rarely  exceeds  5  per  cent,  of  the  full-load  primary 
current. 

Core  loss  and  exciting  current,  with  its  two  components,  are 
determined  by  measuring  volts,  amperes  and  watts  input  into 
the  primary  of  the  transformer  at  open  secondary.  It  is  ob- 
vious that  either  of  the  transformer  coils  can  for  this  purpose  be 
used  as  primary,  and  usually  the  low  voltage  coil  is  employed 
as  more  convenient. 

Such  excitation  and  core-loss  curves  are  given  in  Fig.  153, 
with  the  impressed  volts  as  abscissae,  and  the  total  exciting 
current,  and  core  loss  as  ordinates. 

The  exciting  current  is  usually  not  proportional  to  the  voltage, 
due  to  the  use  of  a  closed  magnetic  circuit,  and  for  the  same 
reason,  the  power-factor  of  the  exciting  current  is  fairly  high, 
from  40  to  60  per  cent.,  except  at  high  voltages,  where  magnetic 
saturation  causes  an  abnormal  increase  of  the  magnetizing 
current. 

The  power-factor  is  shown  on  Fig.  153. 

IE.  Losses  and  Efficiency 

113.  The  losses  in  the  transformer  are 

(a)  The  core  loss,  comprising  the  loss  by  hysteresis  and 
eddy  currents  in  the  iron.  This  depends  on  the  maximum 
magnetic  flux,  and  thus  on  the  induced  voltage: 


and  as  the  induced  voltage  is  practically  equal  to  the  impressed 
voltage  61,  at  constant  impressed  voltage,  the  core  loss  is  practi- 
cally constant,  and  is  often  assumed  as  constant,  that  is,  the 


ALTERNATING-CURRENT  TRANSFORMER       281 

core  loss  is  a  constant  or  no-load  loss,  and  is  supplied  by  the 
exciting  current  i0. 

(b)  The  i2r  losses  in  the  primary  and  secondary  coils.     These 
are  load  losses,  increasing  with  the  square  of  the  load. 

(c)  Spurious  load  losses,  as  eddy  currents  in  the  conductors 
and  other  metal  parts.     With  proper   design  these  should  be 
negligible. 

(d)  In   very   high   voltage   transformers,   electrostatic   losses 
in  the  insulation  appear.     These  usually  are  small  in  large  well- 
designed  transformers. 

In  large  transformers,  the  total  &r  loss  may  be  less  than  1 
per  cent.,  and  so  also  the  core  loss,  resulting  in  efficiencies  of 
over  98  per  cent. 

As  instance  are  shown,  in  Figs.  154  and  155,  the  loss  curves 
and  the  efficiency  curves  of  two  transformers,  of  the  respective 
constants,  at  full  load  of  20  kw.