Ideal Transformer - Electrical Engineering - Notes - Electrical Engineering (EE)

 Page 1


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
Page 2


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
23 
 
Ideal Transformer 
Version 2 EE IIT, Kharagpur 
Page 3


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
23 
 
Ideal Transformer 
Version 2 EE IIT, Kharagpur 
Contents  
 
 
23 Ideal Transformer (Lesson: 23)  4 
 23.1 Goals of the lesson …………………………………………………………… 4 
 23.2 Introduction  ………………………………………………………………….. 5 
  23.2.1 Principle of operation ……………………………………………….. 5 
 23.3 Ideal Transformer…………………………………………………………….. 6 
  23.3.1 Core flux gets fixed by voltage and frequency ……………………… 6 
  23.3.2 Analysis of ideal transformer………………………………………... 7 
  23.3.3 No load phasor diagram …………………………………………….. 8 
 23.4 Transformer under loaded condition  ………………………………………… 9 
  23.4.1 Dot convention ……………………………………………………… 10 
  23.4.2 Equivalent circuit of an ideal transformer ………………………… 11 
 23.5 Tick the correct answer ……………………………………………………… 12 
 23.6 Solve the following …………………………………………………………... 14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Version 2 EE IIT, Kharagpur 
Page 4


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
23 
 
Ideal Transformer 
Version 2 EE IIT, Kharagpur 
Contents  
 
 
23 Ideal Transformer (Lesson: 23)  4 
 23.1 Goals of the lesson …………………………………………………………… 4 
 23.2 Introduction  ………………………………………………………………….. 5 
  23.2.1 Principle of operation ……………………………………………….. 5 
 23.3 Ideal Transformer…………………………………………………………….. 6 
  23.3.1 Core flux gets fixed by voltage and frequency ……………………… 6 
  23.3.2 Analysis of ideal transformer………………………………………... 7 
  23.3.3 No load phasor diagram …………………………………………….. 8 
 23.4 Transformer under loaded condition  ………………………………………… 9 
  23.4.1 Dot convention ……………………………………………………… 10 
  23.4.2 Equivalent circuit of an ideal transformer ………………………… 11 
 23.5 Tick the correct answer ……………………………………………………… 12 
 23.6 Solve the following …………………………………………………………... 14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Version 2 EE IIT, Kharagpur 
23.1 Goals of the lesson  
 
In this lesson, we shall study two winding ideal transformer, its properties and working 
principle under no load condition as well as under load condition. Induced voltages in 
primary and secondary are obtained, clearly identifying the factors on which they depend 
upon. The ratio between the primary and secondary voltages are shown to depend on 
ratio of turns of the two windings. At the end, how to draw phasor diagram under no load 
and load conditions, are explained.  Importance of studying such a transformer will be 
highlighted. At the end, several objective type and numerical problems have been given 
for solving. 
Key Words: Magnetising current, HV & LV windings, no load phasor diagram, reflected 
current, equivalent circuit. 
 
After going through this section students will be able to understand the following. 
 
1. necessity of transformers in power system. 
2. properties of an ideal transformer. 
3. meaning of load and no load operation. 
4. basic working principle of operation under no load condition. 
5. no load operation and phasor diagram under no load. 
6. the factors on which the primary and secondary induced voltages depend. 
7. fundamental relations between primary and secondary voltages. 
8. the factors on which peak flux in the core depend. 
9. the factors which decides the magnitude of the magnetizing current. 
10. What does loading of a transformer means? 
11. What is reflected current and when does it flow in the primary? 
12. Why does VA (or kVA) remain same on both the sides? 
13. What impedance does the supply see when a given impedance Z
2
 is connected 
across the secondary? 
14. Equivalent circuit of ideal transformer referred to different sides. 
 
23.2 Introduction  
 
Transformers are one of the most important components of any power system. It basically 
changes the level of voltages from one value to the other at constant frequency. Being a 
static machine the efficiency of a transformer could be as high as 99%. 
 Big generating stations are located at hundreds or more km away from the load 
center (where the power will be actually consumed). Long transmission lines carry the 
power to the load centre from the generating stations. Generator is a rotating machines 
and the level of voltage at which it generates power is limited to several kilo volts only – 
Version 2 EE IIT, Kharagpur 
Page 5


 
 
 
 
 
 
 
 
 
Module 
7 
 
Transformer 
Version 2 EE IIT, Kharagpur 
 
 
 
 
 
 
 
 
 
Lesson 
23 
 
Ideal Transformer 
Version 2 EE IIT, Kharagpur 
Contents  
 
 
23 Ideal Transformer (Lesson: 23)  4 
 23.1 Goals of the lesson …………………………………………………………… 4 
 23.2 Introduction  ………………………………………………………………….. 5 
  23.2.1 Principle of operation ……………………………………………….. 5 
 23.3 Ideal Transformer…………………………………………………………….. 6 
  23.3.1 Core flux gets fixed by voltage and frequency ……………………… 6 
  23.3.2 Analysis of ideal transformer………………………………………... 7 
  23.3.3 No load phasor diagram …………………………………………….. 8 
 23.4 Transformer under loaded condition  ………………………………………… 9 
  23.4.1 Dot convention ……………………………………………………… 10 
  23.4.2 Equivalent circuit of an ideal transformer ………………………… 11 
 23.5 Tick the correct answer ……………………………………………………… 12 
 23.6 Solve the following …………………………………………………………... 14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Version 2 EE IIT, Kharagpur 
23.1 Goals of the lesson  
 
In this lesson, we shall study two winding ideal transformer, its properties and working 
principle under no load condition as well as under load condition. Induced voltages in 
primary and secondary are obtained, clearly identifying the factors on which they depend 
upon. The ratio between the primary and secondary voltages are shown to depend on 
ratio of turns of the two windings. At the end, how to draw phasor diagram under no load 
and load conditions, are explained.  Importance of studying such a transformer will be 
highlighted. At the end, several objective type and numerical problems have been given 
for solving. 
Key Words: Magnetising current, HV & LV windings, no load phasor diagram, reflected 
current, equivalent circuit. 
 
After going through this section students will be able to understand the following. 
 
1. necessity of transformers in power system. 
2. properties of an ideal transformer. 
3. meaning of load and no load operation. 
4. basic working principle of operation under no load condition. 
5. no load operation and phasor diagram under no load. 
6. the factors on which the primary and secondary induced voltages depend. 
7. fundamental relations between primary and secondary voltages. 
8. the factors on which peak flux in the core depend. 
9. the factors which decides the magnitude of the magnetizing current. 
10. What does loading of a transformer means? 
11. What is reflected current and when does it flow in the primary? 
12. Why does VA (or kVA) remain same on both the sides? 
13. What impedance does the supply see when a given impedance Z
2
 is connected 
across the secondary? 
14. Equivalent circuit of ideal transformer referred to different sides. 
 
23.2 Introduction  
 
Transformers are one of the most important components of any power system. It basically 
changes the level of voltages from one value to the other at constant frequency. Being a 
static machine the efficiency of a transformer could be as high as 99%. 
 Big generating stations are located at hundreds or more km away from the load 
center (where the power will be actually consumed). Long transmission lines carry the 
power to the load centre from the generating stations. Generator is a rotating machines 
and the level of voltage at which it generates power is limited to several kilo volts only – 
Version 2 EE IIT, Kharagpur 
a typical value is 11 kV. To transmit large amount of power (several thousands of mega 
watts) at this voltage level means large amount of current has to flow through the 
transmission lines. The cross sectional area of the conductor of the lines accordingly 
should be large. Hence cost involved in transmitting a given amount of power rises many 
folds. Not only that, the transmission lines has their own resistances. This huge amount of 
current will cause tremendous amount of power loss or I
2
r loss in the lines. This loss will 
simply heat the lines and becomes a wasteful energy. In other words, efficiency of 
transmission becomes poor and cost involved is high. 
 The above problems may addressed if we could transmit power at a very high 
voltage say, at 200 kV or 400 kV or even higher at 800 kV. But as pointed out earlier, a 
generator is incapable of generating voltage at these level due to its own practical 
limitation. The solution to this problem is to use an appropriate step-up transformer at the 
generating station to bring the transmission voltage level at the desired value as depicted 
in figure 23.1 where for simplicity single phase system is shown to understand the basic 
idea. Obviously when power reaches the load centre, one has to step down the voltage to 
suitable and safe values by using transformers. Thus transformers are an integral part in 
any modern power system. Transformers are located in places called substations. In cities 
or towns you must have noticed transformers are installed on poles – these are called pole 
mounted distribution transformers. These type of transformers change voltage level 
typically from 3-phase, 6 kV to 3-phase 440 V line to line. 
 
Long Transmission line 
400 kV
To 
loads 
Step down 
transformer
Step up 
transformer
11 
kV 
G 
Figure 23.1:  A simple single phase power system. 
 
 
 
 
 
 
 
 
 In this and the following lessons we shall study the basic principle of operation 
and performance evaluation based on equivalent circuit. 
 
23.2.1 Principle of operation  
A transformer in its simplest form will consist of a rectangular laminated magnetic 
structure on which two coils of different number of turns are wound as shown in Figure 
23.2. 
 
 The winding to which a.c voltage is impressed is called the primary of the 
transformer and the winding across which the load is connected is called the secondary of 
the transformer. 
 
23.3 Ideal Transformer  
 
To understand the working of a transformer it is always instructive, to begin with the 
concept of an ideal transformer with the following properties. 
Version 2 EE IIT, Kharagpur