1. • Windings have definite resistance values
• Primary & Secondary Leakage Flux
• Occurrence of Losses
 Copper Loss (Pry & Sec)
 Core Loss (Hysteresis Loss & Eddy current Loss)
Working: Practical Transformer
101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal

2. Working: Practical Transformer - No
Load
mco IˆIˆIˆ +=
101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
N1 N2
V2V1
Io
E1 E2
• Primary draws a current IO called No-load current
• IO has two components:
IC = iron loss component – supplies eddy current loss
Im = magnetization component – sets up magnetic field
• Primary winding impedance Z1 = R1+jX1
• E1 = V1 – IOZ1
• A part of primary flux links with secondary
• E2 is induced
• I2 = 0. Therefore, E2 = V2

3. Working: Practical Transformer - On
Load
2
1
2'
2 Iˆ
N
N
Iˆ






=
101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
LOAD
N1 N2
V2V1
I1
E1 E2
I2
• Primary draws a current IO=IC+Im
• Secondary supplies I2 to load
• A current I2
1
is drawn by primary to balance the load current
• Total primary current I1 = IO+I2
1
• E1 = V1 – I1Z1
• Z2 = R2+jX2 = secondary winding impedance
• V2 = E2 – I2Z2

4. 101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
Equivalent circuit
RC XM
Ic
Im
Io
Core:
Io = No load current component
Ic = Core loss current component
Im = Magnetizing current component
RC = core loss equivalent
XM = magnetization equivalent
Primary Side:
R1 X1
Secondary Side:
R2 X2

5. 101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
• Resistances & Reactances are can be transferred to either side
• All quantities are referred to either primary side or secondary side
Ideal Transformer
V1
E1
I1
R1 X1
Rc Xm
Ic Im
Io
R2 X2
I2
ZL
E2
V2
I'2
N1 N2
Equivalent circuit representation

6. 101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
Equivalent circuit as referred to
secondary
Equivalent primary winding resistance as
referred to secondary 1
2
1
2
1
N
N
RR 





=′
Equivalent primary winding reactance as
referred to secondary
1
2
1
2
1
N
N
XX 





=′
E2
I1
1
R1
1 X1
1
V1
1 R1
C X1
m
I1
c I1
m
I1
o
R2 X2
ZLV2
I2
K
N
N
==
1
2
1
1
1
V
V

7. 101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
Approximate equivalent circuit
• No load current Io is quite small as compared to rated primary current
• Therefore, Voltage drops in primary due to Io is negligibly small
• Shunt branch circuit is shifted towards the supply side
R2 X2
E2
I1
1
V1
1
R1
c X1
m
I1
c I1
m
I1
o
ZLV2
I2
R1
1 X1
1

8. 101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
Approx. equivalent circuit referred to
secondary
I1
1
V1
1
R1
c X1
m
I1
c I1
m
I1
o
ZLV2
I2 R2e X2e
Equivalent winding resistance
2
1
12 R+= RR e
Equivalent winding reactance 2
1
12 XXX e +=
Equivalent winding impedance eee jXRZ 222 +=

9. 101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal
Approx. equivalent circuit referred to primary
Equivalent winding resistance 1
211 R+= RR e
Equivalent winding reactance 1
211 XXX e +=
Equivalent winding impedance eee jXRZ 111 +=
I1
V1
Rc Xm
Ic Im
Io
Z1
LV1
2
I1
2 R1e X1e

10. Exercise
A 15 kVA, 2200 / 110 V, 50 Hz, 1φ transformer has pry & sec winding
resistances of 1.75 Ω & 0.0045 Ω and pry & sec winding reactances of 2.6
Ω & 0.0075 Ω respectively. Determine (a) equivalent resistance, reactance
& impedance as referred to pry (b) equivalent resistance, reactance &
impedance as referred to sec (c) total copper loss
Ans: (a) 3.55 Ω, 5.6 Ω, 6.63 ∠57.63o
(b) 0.008875 Ω, 0.014 Ω, 0.0166 ∠57.56o
(c)
165 W
101 / 102 Basic Electrical Technology Dept of E & E, MIT Manipal