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Electrical Machines

Lecture 03: Magnetic Circuits and Transformers

(Textbook Chapter 4)

Instructor: Dr. Jung-Uk Lim

MWF 12:00 pm 12:50 pm

Corley, Room 268Class Website: http://faculty.atu.edu/jlim/machines.html

2013 Fall ELEG 3153 - Electrical Machines 1


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What is a Transformer? (Static Machine)

It is used to convert AC electric energy at one voltage and current levelto AC electric energy at another voltage and current level.

It is an electromagnetic system that consists of two or more windings

supported by a ferromagnetic structure.

It is a static machine. On the other hand, AC and DC machines such as

generators and motors are rotating machines.

Utilization of Transformers Change of voltage levels

Measurements of high voltages (PT) and high currents (CT)

Impedance matching:

In some audio systems, transformers are used to match theimpedance of a voltage source to the impedance of the load.

Impedance matching enables maximum power to be delivered fromthe source to the load.

Insulating one circuit from another or Insulating DC circuits from ACcircuits

Introduction (1)


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Introduction (2)

Connection of Transformers

Single-phase Transformers Consists of two or more windings coupled by a magnetic core

Three-phase Transformers Wye Wye Connection

Wye Delta Connection

Delta Wye Connection

Delta Delta Connection

The following necessary knowledge will be delivered to

understand the basic operation of a transformer. Some basic concepts of electromagnetic theory will be

reviewed.

Typical magnetic circuits will be analyzed.

Some parameters including flux linkages and inductances will be

defined.

ELEG 3153 - Electrical Machines 32013 Fall


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Magnetic Field of a Line Current

Magnetic Circuits Amperes Law (1)


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Magnetic Field of a Current-Carrying Coil (Solenoid)



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Magnetic Field in a Simple Magnetic Core

The magnetic core has a winding

carrying a current of Iamperes and Nturns.

2D


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What is happening in the core?

It generates a magnetomotive force (mmf) Fof N*iampere (A).

The mmfcreates a magnetic field in the core having an intensity

of H(ampere-turns/meter) along the length of the magnetic path.

Upon integrating the magnetic field intensity H along the closed

magnetic path, we get...

(Amperes Law).


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Magnetic Circuits (5)

Why do many transformers have ferromagnetic core materials? They are easily magnetized. They generate a high-density magnetic flux per unit area, a high B (Tesla or weber/m2).

The magnetic flux density B in the core is related to the magnetic fieldintensity H according to B-H curve as shown below.


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Magnetic Circuits (6)


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Electric Circuit VS Magnetic Circuit

(Electric Circuit) (Magnetic Circuit)


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Example 3.1


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Faradays Law

What is Faradays law?

A time-varying magnetic field induces an electromotive force,or emf ( = voltage) that produces a current in a closed circuit.



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Lenzs Law


Lenzs Law:

when an emf is generated by a change in magnetic flux according to

Faraday's Law, the polarity of the induced emf is such that it producesa current whose magnetic field opposes the change which produces it.


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Example 3.2


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Inductance and Magnetic Energy (1)



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Ideal Transformer (1)


How does it work?


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Example 3.3


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Example 3.4


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Example 3.5


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Non-ideal or Actual Transformer (1)



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Example 3.6


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Equivalent Circuit (Referred to the Primary Side)


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Phasor Diagram


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Approximate Equivalent Circuits (1)


: The Full Model

i i l i i ( )


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Approximate Equivalent Circuits (2)

ELEG 3153 - Electrical Machines 39

: The Simplest Models

2013 Fall

In many cases,

the parallel (or magnetizing, or excitation) branchcan be ignored.

V l R l i (1)


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Voltage Regulation (1)

Voltage Regulation (%)

To measure how much voltage magnitude will change as load is varied.

The change in the magnitude of the secondary voltage as the current

changes from full load to no load with the primary voltage held fixed.


V lt R l ti (2)


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Voltage Regulation (2)


Compare lengths of both the

blue and red line segments!!!

Efficiency


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Efficiency


Efficiency

The ration of the power output (Watt) to the power input (Watt)

2013 Fall


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Example 3.7


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Determination of


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Equivalent Circuit Parameters

Two simple tests are used to determine the values for theparameters of the transformer equivalent circuit:

Open-Circuit Test:

Short-Circuit Test:

* Details are usually discussed in the Electrical Machines Lab. Class.

Polarity


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Polarity


Autotransformer (1)


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Autotransformer (1)

On some occasions, it is desirable to change voltage levels byonly a small amount, for example, from 110 to 120V, vise

versa or from 13.2 to 13.8kV, vise versa. In such circumstances, it is wasteful and excessive to wind a

transformer with two full windings, each rated at about thesame voltage. Instead, an autotransformer is used.


Autotransformer (2)


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Autotransformer (2)


Lets move on to power transfers in the autotransformer!

Three-Winding Transformers


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Three Winding Transformers


Good VS. Bad

It can supply additional load providing insulation from secondary windings. Since two secondary windings and one primary winding are magnetically

connected, when a fault occurs at any of them, the impact must be takenon the other two.

Three-Phase Transformers (1)


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( )

3 Transformers are used

Between generators and transmission systems Between transmission and sub-transmission systems

Between sub-transmission and distribution systems

In most commercial and industrial loads

Two ways to construct a 3 Transformer

Connect three single transformers in a 3 bank.

Make a 3 transformer consisting of three sets of windingswrapped on a common core.




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( )

3 Transformer Connections

Wye-wye (Y-Y)




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( )

Wye-delta (Y-)




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Delta-wye (-Y)

2013 Fall

Three-Phase Transformers


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Delta-Delta (-)

2013 Fall


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Example 3.8


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Example 3.9


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