Power Transformers. Energy Systems Research Laboratory, FIU

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1 Power Transformers By: Alberto Berzoy Energy Systems Research Laboratory Department of Electrical & Computer Engineering Florida International University Miami, Florida, USA

2 Overview 2 Introduction Transformer Construction Types of Transformers History about electromagnetism Ideal Transformer Real Model of the Transformer

Transformer A transformer is an static or stationary apparatus by means of which the electric power in one circuit is transformed into electrical of the same frequency in another circuit.

3 Transformer A transformer is an static or stationary apparatus by means of which the electric power in one circuit is transformed into electrical of the same frequency in another circuit. 3 Characteristics It can rise or lower the voltage and lower or rise the current respectively. The two circuits do not have electrical connection they are isolated. It works by magnetic induction Composition Two windings made of copper One magnetic core made of iron

4 Transformer Construction Other necessary part of the transformer are: Suitable container for assembled core and windings Suitable medium for insulating the core and its windings from the container. Suitable bushings (porcelain, oil-filled or capacitor-type) for insulating and bringing out the terminals of the winding from the tank. 4

Transformer Construction The core is constructed by sheet

The steel used has: High permeability Low hysteresis loss at

from each other by a light coat of core plate varnish or by

5 Transformer Construction The core is constructed by sheet steel laminations assembled. The steel used has: High permeability Low hysteresis loss at usual operating flux densities The laminations are insulated from each other by a light coat of core plate varnish or by an oxide layer on the surface. 5 The laminations are staggered together by joints. Shapes of the sheets

6 Transformer Types 6 There are two types of transformers: Core-type: The winding is around the core Shell-type: the core is around the winding

7 Core-Type Transformer 7 It has cylindrical coils wound in helical layers. Layers are insulated with each other by: Paper Mica Micarta board Cooling ducts Shell-Type Transformer Are wound in form of pancakes forming multilayers discs insulated form each others

Core Materials 8 The materials used for the

Hard Iron Laminated Silicon Steel Special Alloys

alloys are between Carbonyl iron nickel and iron in

8 Core Materials 8 The materials used for the fabrication of the core are: Solid Metals Soft iron Hard Iron Laminated Silicon Steel Special Alloys Mu-metal Permalloy Supermalloy Power Metals This alloys are between Carbonyl iron nickel and iron in different % Iron powder Ceramics Ferrite Ferrite normally used for high frequency

9 Cooling of the Transformer Another way to classify transformers it is by its cooling system (a) oil-filled self-cooled (b) oil-filled water-cooled (c) air-blast type 9

Electromagnetism History How is the father

relationship between electric currents and

10 Electromagnetism History How is the father of the electromagnetism? Hans Christian Oersted 1820 Danish physicist and chemist He discovered the relationship between electric currents and magnetic fields. He was searching for this relationship for several years 10

11 Electromagnetism History 11 After that: Andre Marie Ampere 1827 French physicist and mathematician In 1820 he saw the Oerted experiment He explained by the famous Ampere Law.

12 Electromagnetism History 12 After that: Michael Faraday 1831 English scientist Discovery of self-induction. He ask himself the reverse question that Oersted discover. Oersted discover that electric currents produce magnetic fields!!! Faraday ask Do magnetic fields can produce electric currents??? DON T FORGET ABOUT Len s Law

13 Why we need a core in the transformer? This question can be easily answer by understanding 13

14 Phasor and Time Notation 14 Time notation Notice the following: Voltage leading and current lagging Leading: happed before Lagging: happen after Past Now Future t

15 Phasor and Time Notation Phasor notation 15

16 Phasors Phasors are a complex numbers used to represent sinusoids. Complex Numbers Recall Euler's formula relating exponential and sinusoidal functions, 16 w = x + jy = Re j = R cos( ) + j R sin( ) where R is the magnitude and is the phase. R = sqrt(x 2 + y 2 ) Phasors Consider the sinusoidal function v(t) = A cos( t + ) A phasor representation is the complex number V with a magnitude A and a phase. V = A e j If we multiply V by e j t and apply Euler's formula, V e j t = A e j e j t = V e i( t + ) = A cos( t + ) + ja sin( t + ) The real part of V e j t is the desired sinusoidal function, v(t) = A cos( t + )

17 Phasors What is a Phasor? Voltage? Current? Impedance? Power? Complex Power? Apparent Power? 17 Voltage is a phasor Current is phasor Impedance is a complex number Power is a number Complex Power is a complex number Apparent Power is a number

18 Transformer Models 18 There are 4 types of models for the transformer: 1. Ideal Model: which is only a mathematical transformation that represents the voltage, current and impedance conversion from one side of the transformer to the other. 2. Model with no losses: which represents the physical phenomena of energy transfer through a magnetic flux. 3. Real Model: which represents the physical phenomena of energy transfer through a magnetic flux with all the considered losses. 4. Real Model with Hysteresis: which represents the physical phenomena of energy transfer through a magnetic flux with all the considered losses and the non-linear behavior of the core.

TRANSFORMERS PART A. 2. What is the turns ratio and transformer ratio of transformer? Turns ratio = N2/ N1 Transformer = E2/E1 = I1/ I2 =K

TRANSFORMERS PART A. 2. What is the turns ratio and transformer ratio of transformer? Turns ratio = N2/ N1 Transformer = E2/E1 = I1/ I2 =K UNIT II TRANSFORMERS PART A 1. Define a transformer? A transformer is a static device which changes the alternating voltage from one level to another. 2. What is the turns ratio and transformer ratio of