Practical Transformer - Module 7 Transformer Lesson 24 Notes | EduRev

: Practical Transformer - Module 7 Transformer Lesson 24 Notes | EduRev

 Page 1


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
Page 2


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
24 
 
Practical Transformer 
Version 2 EE IIT, Kharagpur 
Page 3


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
24 
 
Practical Transformer 
Version 2 EE IIT, Kharagpur 
Contents 
 
24 Practical Transformer 4 
       24.1  Goals of the lesson …………………………………………………………………. 4 
 24.2 Practical transformer  ………………………………………………………………. 4 
  24.2.1 Core loss………………………………………………………………….. 7 
 24.3 Taking core loss into account ……………………………………………………… 7 
 24.4 Taking winding resistances and leakage flux into account  ……………………….. 8 
 24.5 A few words about equivalent circuit  ……………………………………………... 10 
 24.6 Tick the correct answer  ……………………………………………………………. 11 
 24.7 Solve the problems  ………………………………………………………………… 12 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Version 2 EE IIT, Kharagpur 
Page 4


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
24 
 
Practical Transformer 
Version 2 EE IIT, Kharagpur 
Contents 
 
24 Practical Transformer 4 
       24.1  Goals of the lesson …………………………………………………………………. 4 
 24.2 Practical transformer  ………………………………………………………………. 4 
  24.2.1 Core loss………………………………………………………………….. 7 
 24.3 Taking core loss into account ……………………………………………………… 7 
 24.4 Taking winding resistances and leakage flux into account  ……………………….. 8 
 24.5 A few words about equivalent circuit  ……………………………………………... 10 
 24.6 Tick the correct answer  ……………………………………………………………. 11 
 24.7 Solve the problems  ………………………………………………………………… 12 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Version 2 EE IIT, Kharagpur 
 
24.1  Goals of the lesson 
 
In practice no transformer is ideal. In this lesson we shall add realities into an ideal transformer 
for correct representation of a practical transformer. In a practical transformer, core material will 
have (i) finite value of µ
r
 , (ii) winding resistances, (iii) leakage fluxes and (iv) core loss. One of 
the major goals of this lesson is to explain how the effects of these can be taken into account to 
represent a practical transformer. It will be shown that a practical transformer can be considered 
to be an ideal transformer plus some appropriate resistances and reactances connected to it to 
take into account the effects of items (i) to (iv) listed above.  
      Next goal of course will be to obtain exact and approximate equivalent circuit along with 
phasor diagram.  
Key words : leakage reactances, magnetizing reactance, no load current. 
 
      After going through this section students will be able to answer the following questions. 
 
• How does the effect of magnetizing current is taken into account? 
 
• How does the effect of core loss is taken into account? 
 
• How does the effect of leakage fluxes are taken into account? 
 
• How does the effect of winding resistances are taken into account? 
 
• Comment the variation of core loss from no load to full load condition. 
 
• Draw the exact and approximate equivalent circuits referred to primary side. 
 
• Draw the exact and approximate equivalent circuits referred to secondary side. 
 
• Draw the complete phasor diagram of the transformer showing flux, primary & 
secondary induced voltages, primary & secondary terminal voltages and primary & 
secondary currents. 
 
24.2 Practical transformer 
 
A practical transformer will differ from an ideal transformer in many ways. For example the core 
material will have finite permeability, there will be eddy current and hysteresis losses taking 
place in the core, there will be leakage fluxes, and finite winding resistances. We shall gradually 
bring the realities one by one and modify the ideal transformer to represent those factors. 
Consider a transformer which requires a finite magnetizing current for establishing flux in 
the core. In that case, the transformer will draw this current I
m
 even under no load condition. The 
level of flux in the core is decided by the voltage, frequency and number of turns of the primary 
and does not depend upon the nature of the core material used which is apparent from the 
following equation:      
max
f =
1
1
2
V
fN p
 
Version 2 EE IIT, Kharagpur 
Page 5


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
24 
 
Practical Transformer 
Version 2 EE IIT, Kharagpur 
Contents 
 
24 Practical Transformer 4 
       24.1  Goals of the lesson …………………………………………………………………. 4 
 24.2 Practical transformer  ………………………………………………………………. 4 
  24.2.1 Core loss………………………………………………………………….. 7 
 24.3 Taking core loss into account ……………………………………………………… 7 
 24.4 Taking winding resistances and leakage flux into account  ……………………….. 8 
 24.5 A few words about equivalent circuit  ……………………………………………... 10 
 24.6 Tick the correct answer  ……………………………………………………………. 11 
 24.7 Solve the problems  ………………………………………………………………… 12 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Version 2 EE IIT, Kharagpur 
 
24.1  Goals of the lesson 
 
In practice no transformer is ideal. In this lesson we shall add realities into an ideal transformer 
for correct representation of a practical transformer. In a practical transformer, core material will 
have (i) finite value of µ
r
 , (ii) winding resistances, (iii) leakage fluxes and (iv) core loss. One of 
the major goals of this lesson is to explain how the effects of these can be taken into account to 
represent a practical transformer. It will be shown that a practical transformer can be considered 
to be an ideal transformer plus some appropriate resistances and reactances connected to it to 
take into account the effects of items (i) to (iv) listed above.  
      Next goal of course will be to obtain exact and approximate equivalent circuit along with 
phasor diagram.  
Key words : leakage reactances, magnetizing reactance, no load current. 
 
      After going through this section students will be able to answer the following questions. 
 
• How does the effect of magnetizing current is taken into account? 
 
• How does the effect of core loss is taken into account? 
 
• How does the effect of leakage fluxes are taken into account? 
 
• How does the effect of winding resistances are taken into account? 
 
• Comment the variation of core loss from no load to full load condition. 
 
• Draw the exact and approximate equivalent circuits referred to primary side. 
 
• Draw the exact and approximate equivalent circuits referred to secondary side. 
 
• Draw the complete phasor diagram of the transformer showing flux, primary & 
secondary induced voltages, primary & secondary terminal voltages and primary & 
secondary currents. 
 
24.2 Practical transformer 
 
A practical transformer will differ from an ideal transformer in many ways. For example the core 
material will have finite permeability, there will be eddy current and hysteresis losses taking 
place in the core, there will be leakage fluxes, and finite winding resistances. We shall gradually 
bring the realities one by one and modify the ideal transformer to represent those factors. 
Consider a transformer which requires a finite magnetizing current for establishing flux in 
the core. In that case, the transformer will draw this current I
m
 even under no load condition. The 
level of flux in the core is decided by the voltage, frequency and number of turns of the primary 
and does not depend upon the nature of the core material used which is apparent from the 
following equation:      
max
f =
1
1
2
V
fN p
 
Version 2 EE IIT, Kharagpur 
Hence maximum value of flux density BB max
 is known from B
max 
B =
 
max
,
i
A
f
where A
i
 is the net cross 
sectional area of the core. Now H
max 
is obtained from the B – H curve of the material. But we 
know H
max 
= 
1max
,
m
i
NI
l
where I
mmax
 is the maximum value of the magnetizing current. So rms 
value of the magnetizing current will be I
m
 = 
max
.
2
m
I
Thus we find that the amount of magnetizing 
current drawn will be different for different core material although applied voltage, frequency 
and number of turns are same. Under no load condition the required amount of flux will be 
produced by the mmf N
1
I
m
. In fact this amount of mmf must exist in the core of the transformer 
all the time, independent of the degree of loading.  
Whenever secondary delivers a current I
2
, The primary has to reacts by drawing extra 
current I’
2
 (called reflected current) such that I’
2
N
1
 = I
2
N
2
 and is to be satisfied at every instant.  
Which means that if at any instant i
2
 is leaving the dot terminal of secondary, 
2
i ' will be drawn 
from the dot terminal of the primary.  It can be easily shown that under this condition, these two 
mmfs (i.e, N
2
i
2
 and 
21
iN ' ) will act in opposition as shown in figure 24.1.  If these two mmfs also 
happen to be numerically equal, there can not be any flux produced in the core, due to the effect 
of actual secondary current I
2
 and the corresponding reflected current 
2
I '  
 
Figure 24.1: MMf directions by I
2
 and '
2
I 
N
1 
'
12
Ni
N
2 
N
2 
i
2 
 
i
2 
'
2
i 
 
 
 
 
 
 
 
 
 
  
The net mmf therefore, acting in the magnetic circuit is once again I
m
N
1
 as mmfs 
21
IN ' and I
2
N
2
 
cancel each other.  All these happens, because KVL is to be satisfied in the primary demanding 
f
max
 to remain same, no matter what is the status (i., open circuited or loaded) of the secondary.  
To create f
max
, mmf necessary is N
1
I
m
.  Thus, net mmf provided by the two coils together must 
always be N
1
I
m
 – under no load as under load condition.  Better core material is used to make I
m
 
smaller in a well designed transformer. 
 Keeping the above facts in mind, we are now in a position to draw phasor diagram of the 
transformer and also to suggest modification necessary to an ideal transformer to take 
magnetizing current 
m
I into account.  Consider first, the no load operation.  We first draw the 
max
f phasor.  Since the core is not ideal, a finite magnetizing current 
m
I will be drawn from 
supply and it will be in phase with the flux phasor as shown in figure 24.2(a).  The induced 
voltages in primary 
1
E and secondary
2
E are drawn 90º ahead (as explained earlier following 
convention 2).  Since winding resistances and the leakage flux are still neglected, terminal 
voltages 
1
V and 
2
V will be same as 
1
E and 
2
E respectively. 
 
Version 2 EE IIT, Kharagpur 
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