Transcript “Ideal Transformer”

“Ideal Transformer”
E’P , E’S = Voltages induced in the primary, secondary
E’HS , E’LS = Voltages induced at High-side, Low-Side
VHS , VLS = Nameplate voltages
ECE 441 of High-side, Low-Side
1
“Ideal Transformer” (continued)
• Define the turns ratio as “a”
E
E
N
a


E
E
N
'
'
P
HS
'
'
S
LS
HS
LS
V

V
HS
LS
– If the primary is the High-Side,
E
N
a

E
N
'
P
P
'
S
ECE 441
S
2
Input Impedance, Z’in
Z’in = Impedance looking into the primary = E’P / IP
Turns ratio a = E’P / E’S >>>>> E’P = aE’S
ECE 441
3
Input Impedance, Z’in (continued)
•
•
•
•
For an IDEAL transformer, VAin =VAout
E’PI*P = E’SI*S
I*P = E’SI*S / E’P = I*S / a
IP = IS / a
E
aE
E
Z 

a
aZ
1
I
I
I
a
'
'
'
P
S
'
2
S
in
P
2
LOA D
S
S
ECE 441
4
“Real” Transformer
EP = 4.44NPfΦP
ES = 4.44NSfΦS
ΦP = ΦM + Φlp
ΦS = ΦM – Φls
EP = E’P + Elp
ECE 441
ES = E’S - Els
5
“Real” Transformer (continued)
KVL @ primary
VT = EP + IPRP = E’P+ Elp +IPRP
IP = Ife + IM + IP LOAD
ECE 441
6
Equivalent Circuit of a Real Transformer
VT = EP + IPRP = E’P+ Elp +IPRP
ECE 441
7
“Real” Transformer (continued)
KVL @ secondary ES = ISRS + VLOAD = E’S – Els
E’S = Els + ISRS + VLOAD
ECE 441
8
Equivalent Circuit of a Real Transformer
VT = EP + IPRP = E’P+ Elp +IPRP
E’S = ElsECE
+ 441
ISRS + VLOAD
9
Equivalent Circuit using Leakage Reactance
ECE 441
10
Looking into the primary of the
Ideal Transformer
Z’in = a2ZLOAD = a2(E’S / IS)
IS = E’S /(RS +jXls + ZLOAD) >>> E’S / IS = RS + jXls + ZLOAD
ECE 441
Z’in = a2RS + ja2Xls + a2ZLOAD
11
Equivalent Circuit
Parameters Referred to Primary
Define ZeqP = The “equivalent impedance” with all
parameters referred to the primary
ZeqP = RP + a2RS +jXlp +ja2Xls
ECE 441
12
Equivalent Circuit
Parameters Referred to Secondary
ZeqS = RS + RP/a2 +j(Xls + Xlp/a2)
ECE 441
13