Transcript “Real” Transformer

“Real” Transformer
EP = 4.44NPfΦP
ES = 4.44NSfΦS
ΦP = ΦM + Φlp
ΦS = ΦM – Φls
EP = E’P + Elp
ES = E’S - Els
“Real” Transformer (continued)
KVL @ primary
VT = EP + IPRP = E’P+ Elp +IPRP
IP = Ife + IM + IP LOAD
Equivalent Circuit of a Real Transformer
VT = EP + IPRP = E’P+ Elp +IPRP
“Real” Transformer (continued)
KVL @ secondary ES = ISRS + VLOAD = E’S – Els
E’S = Els + ISRS + VLOAD
Equivalent Circuit of a Real Transformer
VT = EP + IPRP = E’P+ Elp +IPRP
E’S = Els + ISRS + VLOAD
Flux in the “Leakage coils”
 ls 
 lp 
N pI p
Rlp
Ns Is
Rls
Ns Is
 ls 
Rls
Voltage generated by flux through the
window of a coil
e  2 fN  max cos(2 ft )
Emax  2 fN  max
 N p I p max
Elp ,max  2 fN p 
 R
lp

 N p2 
Elp ,max  2 f 
I
 R  p max
 lp 
 N p2 
Elp ,rms  2 f 
I
 R  p ,rms
 lp 
N2
L
R
Elp  (2 fLlp )( I p )
Elp  I p X lp



Similar expression for the secondary
Equivalent Circuit using Leakage Reactance
Equivalent Impedance of a Transformer
'
E
Zin'  a 2 S
IS
ES'
IS 
RS  jX ls  Z load
ES'
 RS  jX ls  Z load
IS
Z in'  a 2 ( RS  jX ls  Z load )
Z in'  a 2 RS  ja 2 X ls  a 2 Z load
Equivalent Circuit
Parameters Referred to the Primary
Z eq , P  RP  a 2 RS  j ( X lp  a 2 X ls )
Z eq , P  Req , P  jX eq , P
Define ZeqP = The “equivalent impedance” with all
parameters referred to the primary
Z eq , P  RP  a 2 RS  j ( X lp  a 2 X ls )
Z eq , P  Req , P  jX eq , P
Equivalent Circuit
Parameters Referred to Secondary
Z eq , S
Z eq , S
X lp
RP
 RS  2  j ( X ls  2 )
a
a
 Req , S  jX eq ,S
Note that the excitation branch has been moved to the left!
It’s OK as long as the transformer is operated near rated
conditions!
Equivalent Circuit for Step-Down Operation
Using High-Side Values
Use this equivalent circuit to determine the input
impedance of the transformer and load.
Equivalent Circuit for Step-Down Operation
Using Low-Side Values
Use this equivalent circuit to determine the no-load
voltage and the voltage regulation.
Equivalent Circuit for Step-Up Operation
Using Low-Side Values
Use this equivalent circuit to determine the input
impedance of the transformer and load.
Equivalent Circuit for Step-Up
High-Side Values
Use this equivalent circuit to determine the no-load
voltage and the voltage regulation.