# Module 7. Transformer. Version 2 EE IIT, Kharagpur

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Module 7 Transformer Version EE IIT, Kharagpur

2 Lesson 4 Practical Transformer Version EE IIT, Kharagpur

3 Contents 4 Practical Transformer 4 4. Goals of the lesson Practical transformer Core loss Taking core loss into account Taking winding resistances and leakage flux into account A few words about equivalent circuit Tick the correct answer. 4.7 Solve the problems Version EE IIT, Kharagpur

4 4. 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. 4. 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 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: V max = π fn Version EE IIT, Kharagpur

5 Hence maximum value of flux density BBmax is known from B max B = max, A i 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 NI mmax know H max =, where max is the maximum value of the magnetizing current. So rms l i max value of the magnetizing current will be =. 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. 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, The primary has to reacts by drawing extra current I (called reflected current) such that I N = I N and is to be satisfied at every instant. Which means that if at any instant i is leaving the dot terminal of secondary, 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 i and in ) will act in opposition as shown in figure 4.. 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 and the corresponding reflected current I Ni N i i i N N Figure 4.: MMf directions by I and I The net mmf therefore, acting in the magnetic circuit is once again N as mmfs IN and I N cancel each other. All these happens, because KVL is to be satisfied in the primary demanding max to remain same, no matter what is the status (i., open circuited or loaded) of the secondary. To create max, mmf necessary is N. Thus, net mmf provided by the two coils together must always be N under no load as under load condition. Better core material is used to make 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 into account. Consider first, the no load operation. We first draw the max phasor. Since the core is not ideal, a finite magnetizing current will be drawn from supply and it will be in phase with the flux phasor as shown in figure 4.(a). The induced voltages in primary E and secondary E are drawn 90º ahead (as explained earlier following convention ). Since winding resistances and the leakage flux are still neglected, terminal voltages V and V will be same as E and E respectively. Version EE IIT, Kharagpur

6 E =V V =E ' E =V I Ι θ V =E Ι If you compare this no load phasor diagram with the no load phasor diagram of the ideal transformer, the only difference is the absence of in the ideal transformer. Noting that lags V by 90º and the magnetizing current has to supplied for all loading conditions, common sense prompts us to connect a reactance, called the magnetizing reactance across the primary of an ideal transformer as shown in figure 4.3(a). Thus the transformer having a finite magnetizing current can be modeled or represented by an ideal transformer with a fixed magnetizing reactance connected across the primary. With S opened in figure 4.3(a), the current drawn from the supply is I = I m since there is no reflected current in the primary of the ideal transformer. However, with S closed there will be I, hence reflected current I = I / a will appear in the primary of the ideal transformer. So current drawn from the supply will be I = I + I. m O O Ι m Ι m (a) No load condition (b) Loaded condition Figure 4.: Phasor Diagram with magnetising current taken into account. θ I = I m Ideal Transformer S I Ideal Transformer S I I m I =0 I = 0 I V Z V Z (a) with secondary opened (a) with load in secondary Figure 4.3: Magnetising reactance to take into account. This model figure 4.3 correctly represents the phasor diagram of figure 4.. As can be seen from the phasor diagram, the input power factor angle θ will differ from the load power factor θ in fact power factor will be slightly poorer (since θ > θ ). Since we already know how to draw the equivalent circuit of an ideal transformer, so same rules of transferring impedances, voltages and currents from one side to the other side can be revoked here because a portion of the model has an ideal transformer. The equivalent circuits of the transformer having finite magnetizing current referring to primary and secondary side are shown respectively in figures 4.4(a) and (b). Version EE IIT, Kharagpur

7 I a = N/N ' I I I' m V a Z V Z ' V X V m a a (a) Equivalent circuit referred to primary (b) Equivalent circuit referred to secondary 4.. Core loss Figure 4.4: Equivalent circuits with A transformer core is subjected to an alternating time varying field causing eddy current and hysteresis losses to occur inside the core of the transformer. The sum of these two losses is known as core loss of the transformer. A detail discussion on these two losses has been given in Lesson. Eddy current loss is essentially I R loss occurring inside the core. The current is caused by the induced voltage in any conceivable closed path due to time varying field. Obviously to reduce eddy current loss in a material we have to use very thin plates instead of using solid block of material which will ensure very less number of available eddy paths. Eddy current loss per unit volume of the material directly depends upon the square of the frequency, flux density and thickness of the plate. Also it is inversely proportional to the resistivity of the material. The core of the material is constructed using thin plates called lamination. Each plate is given a varnish coating for providing necessary insulation between the plates. Cold Rolled Grain Oriented, in short CRGO sheets are used to make transformer core. After experimenting with several magnetic materials, Steinmetz proposed the following empirical formula for quick and reasonable estimation of the hysteresis loss of a given material. P = k B f h h n max The value of n will generally lie between.5 to.5. Also we know the area enclosed by the hysteresis loop involving B-H characteristic of the core material is a measure of hysteresis loss per cycle. 4.3 Taking core loss into account The transformer core being subjected to an alternating field at supply frequency will have hysteresis and eddy losses and should be appropriately taken into account in the equivalent circuit. The effect of core loss is manifested by heating of the core and is a real power (or energy) loss. Naturally in the model an external resistance should be shown to take the core loss into account. We recall that in a well designed transformer, the flux density level BBmax practically remains same from no load to full load condition. Hence magnitude of the core loss will be practically independent of the degree of loading and this loss must be drawn from the supply. To take this into account, a fixed resistance R cl is shown connected in parallel with the magnetizing reactance as shown in the figure 4.5. Version EE IIT, Kharagpur

9 Mutual Flux I r x Ideal Transformer I' r x Leakage Flux V I c R c E E I Z Figure 4.7: Leakage flux and their paths. Equivalent circuit showing both sides Figure 4.8: Equivalent circuit of a practical transformer. The exact equivalent circuit can now be drawn with respective to various sides taking all the realities into account. Resistance and leakage reactance drops will be present on both the sides and represented as shown in the figures 4.8 and 4.9. The drops in the leakage impedances will make the terminal voltages different from the induced voltages. r x r' x' r' x' r x I 0 I' I' 0 I V I c Z' V' I' c I' m Z X' m R c R' c Equivalent circuit referred to primary Equivalent circuit referred to secondary Figure 4.9: Exact Equivalent circuit referred to primary and secondary sides. It should be noted that the parallel impedance representing core loss and the magnetizing current is much higher than the series leakage impedance of both the sides. Also the no load current I 0 is only about 3 to 5% of the rated current. While the use of exact equivalent circuit will give us exact modeling of the practical transformer, but it suffers from computational burden. The basic voltage equations in the primary and in the secondary based on the exact equivalent circuit looks like: V = E + I r + ji x V = E I r ji x It is seen that if the parallel branch of R cl and are brought forward just right across the supply, computationally it becomes much more easier to predict the performance of the transformer sacrificing of course a little bit of accuracy which hardly matters to an engineer. It is this approximate equivalent circuit which is widely used to analyse a practical power/distribution transformer and such an equivalent circuit is shown in the figure 4.. Version EE IIT, Kharagpur

10 I r x Ideal Transformer I r x I c I I x V I r V R c E E Z -E I' I 0 Approximate Equivalent circuit showing both sides r' x' I r x θ I θ 0 I 0 I c V Z' R c I 0 I' θ I V I r I x E E Approximate Equivalent circuit referred to primary I' r' x' r x I 0 I' c I' m I V' Z R' c Figure 4.0: Phasor diagram of the transformer supplying lagging power factor load. Approximate Equivalent circuit referred to secondary Figure 4.: Approximate equivalent circuit. The exact phasor diagram of the transformer can now be drawn by drawing the flux phasor first and then applying the KVL equations in the primary and in the secondary. The phasor diagram of the transformer when it supplies a lagging power factor load is shown in the figure 4.0. It is clearly seen that the difference in the terminal and the induced voltage of both the sides are nothing but the leakage impedance drops of the respective sides. Also note that in the approximate equivalent circuit, the leakage impedance of a particular side is in series with the reflected leakage impedance of the other side. The sum of these leakage impedances are called equivalent leakage impedance referred to a particular side. Equivalent leakage impedance referred to primary re + jxe =( r+ a r) + j( x+ a x ) r x Equivalent leakage impedance referred to secondary re + jxe= r + j x + + a a N Where, a = N the turns ratio. 4.5 A few words about equivalent circuit Approximate equivalent circuit is widely used to predict the performance of a transformer such as estimating regulation and efficiency. Instead of using the equivalent circuit showing both the Version EE IIT, Kharagpur

11 sides, it is always advantageous to use the equivalent circuit referred to a particular side and analyse it. Actual quantities of current and voltage of the other side then can be calculated by multiplying or dividing as the case may be with appropriate factors involving turns ratio a. Transfer of parameters (impedances) and quantities (voltages and currents) from one side to the other should be done carefully. Suppose a transformer has turns ratio a, a = N /N = V /V where, N and N are respectively the primary and secondary turns and V and V are respectively the primary and secondary rated voltages. The rules for transferring parameters and quantities are summarized below.. Transferring impedances from secondary to the primary: If actual impedance on the secondary side be Z, referred to primary side it will become Z = az.. Transferring impedances from primary to the secondary: If actual impedance on the primary side be Z, referred to secondary side it will become = /. Z Z a 3. Transferring voltage from secondary to the primary: If actual voltage on the secondary side be V, referred to primary side it will become V = av. 4. Transferring voltage from primary to the secondary: If actual voltage on the primary side be V, referred to secondary side it will become V = V / a. 5. Transferring current from secondary to the primary: If actual current on the secondary side be I, referred to primary side it will become I = I / a. 6. Transferring current from primary to the secondary: If actual current on the primary side be I, referred to secondary side it will become I = ai. In spite of all these, gross mistakes in calculating the transferred values can be identified by remembering the following facts.. A current referred to LV side, will be higher compared to its value referred to HV side.. A voltage referred to LV side, will be lower compared to its value referred to HV side. 3. An impedance referred to LV side, will be lower compared to its value referred to HV side. 4.6 Tick the correct answer Version EE IIT, Kharagpur

13 Draw the equivalent circuit referred to [i] LV side and [ii] HV side and insert all the parameter values.. A 0 kva, 000 V / 00 V, 50 Hz, single phase transformer has HV and LV side winding resistances as. Ω and 0.05 Ω respectively. The leakage reactances of HV and LV sides are respectively 5. Ω and 0.5 Ω respectively. Calculate [i] the voltage to be applied to the HV side in order to circulate rated current with LV side shorted, [ii] Also calculate the power factor under this condition. 3. Draw the complete phasor diagrams of a single phase transformer when [i] the load in the secondary is purely resistive and [ii] secondary load power factor is leading. Version EE IIT, Kharagpur

### Open circuit and short circuit tests on single phase transformer

1 Aim Experiment No: 2 Open circuit and short circuit tests on single phase transformer To understand the basic working principle of a transformer. To obtain the equivalent circuit parameters from OC and

### Electrical Machines-I Prof. D. Kastha Department of Electrical Engineering Indian Institute of Technology, Kharagpur

Electrical Machines-I Prof. D. Kastha Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Voltage Regulation of Single Phase Transformers (Refer Slide Time: 00:59)

### Chapter 5 TRANSFORMERS

Chapter 5 TRANSFORMERS Objective Understand the transformer nameplate Describe the basic construction features of a transformer. Explain the relationship between voltage, current, impedance, and power

### Module 7. Transformer. Version 2 EE IIT, Kharagpur

Module 7 Transformer Lesson 27 Auto-Transformer ontents 27 Auto-Transformer 4 27.1 Goals of the lesson. 4 27.2 Introduction 4 27.3 2-winding transformer as Autotransformer... 5 27.4 Autotransformer as

### ESO 210 Introduction to Electrical Engineering

ESO 210 Introduction to Electrical Engineering Lecture-22 Transformers 2 After going through this lecture students will be able to answer the following questions. 3 After developing the equivalent circuit

### STUDY OF IDEAL TRANSFORMER AND PRACTICAL TRANSFORMER

STUDY OF IDEAL TRANSFORMER AND PRACTICAL TRANSFORMER RUBY DHANKAR, SAPNA KAMRA,VISHAL JANGRA Abstract- This paper proposes the study of real and ideal transformer. It also explains load, no-load conditions

### Inductive and Capacitive Reactance

Inductive and Capacitive Reactance Course No: E04-005 Credit: 4 PDH A. Bhatia Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 322-5800 F: (877) 322-4774

### Electrical Fundamentals - Reactance and Impedance

PDHonline Course E239 (4 PDH) Electrical Fundamentals - Reactance and Impedance Instructor: A. Bhatia, B.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088

### Extra Questions - 1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A

Extra Questions - 1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated

### Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian Institute of Technology, Kharagpur. Lecture 2

Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture 2 (Refer Slide Time: 01:01) Welcome to lesson 2 on Power System Analysis.

### Reactance and Impedance

Reactance and Impedance Capacitance in AC Circuits Professor Andrew H. Andersen 1 Objectives Describe capacitive ac circuits Analyze inductive ac circuits Describe the relationship between current and

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT 4 Understand single-phase alternating current (ac) theory Single phase AC

### THE PER-UNIT SYSTEM. (2) The per-unit values for various components lie within a narrow range regardless of the equipment rating.

THE PER-UNIT SYSTEM An interconnected power system typically consists of many different voltage levels given a system containing several transformers and/or rotating machines. The per-unit system simplifies

### Chapter 12. RL Circuits. Objectives

Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine

### 7 Testing of Transformers

7 Testing of Transformers The structure of the circuit equivalent of a practical transformer is developed earlier. The performance parameters of interest can be obtained by solving that circuit for any

### 2. TRANSFORMERS. The main learning objectives for this chapter are listed below. Use equivalent circuits to determine voltages and currents.

. TRANSFORMERS Transformers are commonly used in applications which require the conversion of AC voltage from one voltage level to another. There are two broad categories of transformers: electronic transformers,

### Chapter 4. Magnetic Materials and Circuits

Chapter 4 Magnetic Materials and Circuits Objectives List six characteristics of magnetic field. Understand the right-hand rule for current and magnetic fluxes. Define magnetic flux, flux density, magnetomotive

### Experiment A5. Hysteresis in Magnetic Materials

HYSTERESIS IN MAGNETIC MATERIALS A5 1 Experiment A5. Hysteresis in Magnetic Materials Objectives This experiment illustrates energy losses in a transformer by using hysteresis curves. The difference betwen

### Full representation of the real transformer

TRASFORMERS EQVALET CRCT OF TWO-WDG TRASFORMER TR- Dots show the points of higher potential. There are applied following conventions of arrow directions: -for primary circuit -the passive sign convention

### Basic AC Reactive Components IMPEDANCE

Basic AC Reactive Components Whenever inductive and capacitive components are used in an AC circuit, the calculation of their effects on the flow of current is important. EO 1.9 EO 1.10 EO 1.11 EO 1.12

### BASIC ELECTRONICS AC CIRCUIT ANALYSIS. December 2011

AM 5-202 BASIC ELECTRONICS AC CIRCUIT ANALYSIS December 2011 DISTRIBUTION RESTRICTION: Approved for Pubic Release. Distribution is unlimited. DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM FORT

### 15-Non-Ideal Single Phase Transformers. ECEGR 450 Electromechanical Energy Conversion

15NonIdeal Single Phase Transformers ECEGR 450 Electromechanical Energy Conversion Magnetizing Reactance Core Resistance Leakage Reactance Winding Resistance Overview Dr. Louie 2 Questions What are the

### LCR Parallel Circuits

Module 10 AC Theory Introduction to What you'll learn in Module 10. The LCR Parallel Circuit. Module 10.1 Ideal Parallel Circuits. Recognise ideal LCR parallel circuits and describe the effects of internal

### Electrical Machines II. Week 1: Construction and theory of operation of single phase transformer

Electrical Machines II Week 1: Construction and theory of operation of single phase transformer Transformers Overview A transformer changes ac electric power at one frequency and voltage level to ac electric

### Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )

Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor Non-Ideal Inductor Dr. P.J. Randewijk

### Electromagnetic Induction

Electromagnetic Induction "Concepts without factual content are empty; sense data without concepts are blind... The understanding cannot see. The senses cannot think. By their union only can knowledge

### 1 Introduction. 2 The Symmetrical Component Transformation. J.L. Kirtley Jr.

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.06 Introduction to Power Systems Class Notes Chapter 4 Introduction To Symmetrical Components J.L. Kirtley

### 2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?

Extra Questions - 2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux

### Chapter 15 10/14/2014

Chapter 15 Analyze series and parallel ac circuits to find Voltage Current Power Total impedance, admittance Apply known circuit theories Kirchhoff s current, voltage laws Voltage or current divider rule

### Eðlisfræði 2, vor 2007

[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 31. Alternating Current Circuits Assignment is due at 2:00am on Wednesday, March 21, 2007 Credit for problems submitted late will decrease to 0% after the

### 13 ELECTRIC MOTORS. 13.1 Basic Relations

13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical actuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This

### Chapt ha e pt r e r 12 RL Circuits

Chapter 12 RL Circuits Sinusoidal Response of RL Circuits The inductor voltage leads the source voltage Inductance causes a phase shift between voltage and current that depends on the relative values of

### Digital Energy ITI. Instrument Transformer Basic Technical Information and Application

g Digital Energy ITI Instrument Transformer Basic Technical Information and Application Table of Contents DEFINITIONS AND FUNCTIONS CONSTRUCTION FEATURES MAGNETIC CIRCUITS RATING AND RATIO CURRENT TRANSFORMER

### Chapter 35 Alternating Current Circuits

hapter 35 Alternating urrent ircuits ac-ircuits Phasor Diagrams Resistors, apacitors and nductors in ac-ircuits R ac-ircuits ac-ircuit power. Resonance Transformers ac ircuits Alternating currents and

### LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module 9. What you'll learn in Module 9. Module 9 Introduction

Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing

THE ECONOMICS OF A TRANSFORMER DESIGNED WITH A LOW CURRENT, RESISTANCE BRIDGING LTC AND SERIES TRANSFORMER VERSUS A HIGH CURRENT, REACTANCE BRIDGING LTC AND NO SERIES TRANSFORMER By Steve Moore, SPX Transformer

### SYNCHRONOUS MACHINES

SYNCHRONOUS MACHINES The geometry of a synchronous machine is quite similar to that of the induction machine. The stator core and windings of a three-phase synchronous machine are practically identical

### Chapter 10. RC Circuits. Objectives

Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine

### Coupled Inductors. Introducing Coupled Inductors

Coupled Inductors From power distribution across large distances to radio transmissions, coupled inductors are used extensively in electrical applications. Their properties allow for increasing or decreasing

### Chapter 11. Inductors ISU EE. C.Y. Lee

Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive

### Power Quality Paper #3

The Effect of Voltage Dips On Induction Motors by: M D McCulloch 1. INTRODUCTION Voltage depressions caused by faults on the system affect the performance of induction motors, in terms of the production

### NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians

NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers

### Basics of Ferrite and Noise Countermeasures

TDK EMC Technology Basic Section Basics of Ferrite and Noise Countermeasures TDK Corporation Magnetics Business Group Shinichiro Ito 1 What is Ferrite? Ferrite was invented by Dr. Kato and Dr. Takei in

### Tutorial One: Calculation of leakage inductance of transformer using FEM. 31.5 MVA, 132 kv/33kv, Y/, Ampere-turns: 135024, No.

Tutorial One: Calculation of leakage inductance of transformer using FEM Consider a transformer with the following rating: 31.5 MVA, 132 kv/33kv, Y/, Ampere-turns: 135024, No. of HV turns = 980 Although

### Application Note. So You Need to Measure Some Inductors?

So You Need to Measure Some nductors? Take a look at the 1910 nductance Analyzer. Although specifically designed for production testing of inductors and coils, in addition to measuring inductance (L),

### EE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits

EE Circuits II Chapter 3 Magnetically Coupled Circuits Magnetically Coupled Circuits 3. What is a transformer? 3. Mutual Inductance 3.3 Energy in a Coupled Circuit 3.4 inear Transformers 3.5 Ideal Transformers

### ELEC-E8407 Electromechanics. Laboratory exercise 1: Transformer

ELEC-E8407 Electromechanics Laboratory exercise 1: Transformer ELEC-E8407 Electromechanics 2 In the exercise, the properties of a core-type transformer are tested by carrying out the following measurements

### IEEE C IEEE Standard General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers

July, 2012 This goal for this month s paper is to provide a basic understanding of tests performed on each liquid filled transformer. The following standards detail the general construction requirements

### April 8. Physics 272. Spring Prof. Philip von Doetinchem

Physics 272 April 8 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 218 L-C in parallel

### Functions, variations and application areas of magnetic components

Westring 18 3314 Büren Germany T +49 951 60 01 0 F +49 951 60 01 3 www.schaffner.com energy efficiency and reliability 1.1 Transformers The transformer is one of the traditional components of electrical

### 8 Speed control of Induction Machines

8 Speed control of Induction Machines We have seen the speed torque characteristic of the machine. In the stable region of operation in the motoring mode, the curve is rather steep and goes from zero torque

### 45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across?

PHYS Practice Problems hapters 8- hapter 8. 45. The peak value of an alternating current in a 5-W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,

### Alternating Current. Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin

Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin 30.10.2012 Contents Alternating Voltage Phase Phasor Representation of AC Behaviors of Basic Circuit Components under AC Resistance, Reactance

### Mutual Inductance and Transformers F3 3. r L = ω o

utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil

### Module 10. Measuring Instruments. Version 2 EE IIT, Kharagpur

Module 1 Measuring Instruments Lesson 44 Study of Single Phase Induction Type Energy Meter or Watt-hour Meter Objectives To understand the basic construction and different components of a single phase

### DIMENSIONING OF CURRENT TRANSFORMERS FOR PROTECTON APPLICATION

ÿþ üûúùø öõöôùóùõò CT Dimensioning DIMENSIONING OF CURRENT TRANSFORMERS FOR PROTECTON APPLICATION Application note GER3973 1 CT Dimensioning ÿþ üûúùø öõöôùóùõò GER-3973 Application note ÿþ üûúùø öõöôùóùõò

### Chapter 22: Alternating current. What will we learn in this chapter?

Chapter 22: Alternating current What will we learn in this chapter? Contents: Phasors and alternating currents Resistance and reactance Series R L C circuit Power in ac-circuits Series resonance Parallel

### Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large

### Capacitors in Circuits

apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively

### W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören

W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018 - Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and

### RESISTANCE, REACTANCE AND IMPEDANCE A Primer. Douglas Brooks, PhD UltraCAD Design, Inc. PART 2, REACTANCE

RESISTANCE, REACTANCE AND IMPEDANCE A Primer Douglas Brooks, PhD UltraCAD Design, Inc. PART 2, REACTANCE This is part 2 of a 3-part series on resistance, reactance and impedance. Most of us are familiar

### Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

### Keywords: Distribution Transformer, Step Core, Core Type, Round And Rectangular, Tank And Temperature Rise.

www.semargroup.org, www.ijsetr.com ISSN 2319-8885 Vol.03,Issue.15 July-2014, Pages:3176-3181 Design Comparison of Round and Rectangular Wire Winding Transformer SOE NAING 1, MYO THET TUN 2 1 Dept of Electrical

### APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY. EE100 Basics of Electrical

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY EE100 Basics of Electrical SAMPLE QUESTION PAPER Maximum Marks 100 Part- A (10 questions) Attempt all the questions 10*4=40 1. We have two identical 10 V electromotive

### DIRECT CURRENT GENERATORS

DIRECT CURRENT GENERATORS Revision 12:50 14 Nov 05 INTRODUCTION A generator is a machine that converts mechanical energy into electrical energy by using the principle of magnetic induction. This principle

### Power measurement in balanced 3 phase circuits and power factor improvement. 1 Power in Single Phase Circuits. Experiment no 1

Experiment no 1 Power measurement in balanced 3 phase circuits and power factor improvement 1 Power in Single Phase Circuits Let v = m cos(ωt) = cos(ωt) is the voltage applied to a R-L circuit and i =

### Electrical Circuit Calculations

Electrical Circuit Calculations Series Circuits Many circuits have more than one conversion device in them (i.e. toaster. heater. lamps etc.) and some have more than one source of electrical energy. If

### Selecting Current Transformers Part 1 By Darrell G. Broussard, P.E.

By Darrell G. Broussard, P.E. Introduction: As engineers, we are aware that electrical power systems have grown. How much have they grown? When was the last time you specified a 2400-volt system, a 4160-volt

### Lecture 5: Transformers(continued)

Lecture 5: Transformers(continued) Equivalent circuit of a transformer Figure (1) shows an equivalent circuit of a transformer. R 1 and R 2 represent the resistances of the primary and secondary windings

### UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE206 - Electrical Circuits and Systems II Laboratory.

UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE06 - Electrical Circuits and Systems II Laboratory. Objectives: Transformer Lab. Comparison of the ideal transformer versus

### EE 221 AC Circuit Power Analysis. Instantaneous and average power RMS value Apparent power and power factor Complex power

EE 1 AC Circuit Power Analysis Instantaneous and average power RMS value Apparent power and power factor Complex power Instantaneous Power Product of time-domain voltage and time-domain current p(t) =

### Inductors & Inductance. Electronic Components

Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered

### 3 Synchronous Generator Operation

3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine xa xl ra xa E xl ra E Load A (a) (b)phasor diagram for R load xs ra Zs Xs Zs Load (c) φ (d)phasor diagram for R-L load Ι Figure 30: Equivalent

### PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA

PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid

### LCR Meter Measurement Accuracy

LCR Meter Measurement Accuracy Introduction LCR meters make taking L, C and R measurements very easy. One can simply hook up the test component between the clip terminals and get the reading on the display

### The Synchronous Machine

Experiment No. 5 The Synchronous Machine Synchronous ac machines find application as motors in constant speed applications and, when interfaced to the power source with a variable-frequency converter system,

### Design of Planar Power Transformers

Design of Planar Power Transformers Contents Introduction 3 Design procedure 4 Design examples -flyback 8 -forward 10 Formulas 13 Layer design 14 1 Exploded view of a planar transformer 2 Introduction

### Unified Lecture # 4 Vectors

Fall 2005 Unified Lecture # 4 Vectors These notes were written by J. Peraire as a review of vectors for Dynamics 16.07. They have been adapted for Unified Engineering by R. Radovitzky. References [1] Feynmann,

### Linear DC Motors. 15.1 Magnetic Flux. 15.1.1 Permanent Bar Magnets

Linear DC Motors The purpose of this supplement is to present the basic material needed to understand the operation of simple DC motors. This is intended to be used as the reference material for the linear

### MOTIONLESS ELECTRIC GENERATOR DESIGN BASED ON PERMANENT MAGNETS AND MAGNETIC AMPLIFIER

12/28/2009 MOTIONLESS ELECTRIC GENERATOR DESIGN BASED ON PERMANENT MAGNETS AND MAGNETIC AMPLIFIER FEDERALLY SPONSOR RESEARCH Not Applicable BACKGROUND - Field [0001] This application relates to motionless

### RLC Resonant Circuits

C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document

### 7.1 POWER IN AC CIRCUITS

C H A P T E R 7 AC POWER he aim of this chapter is to introduce the student to simple AC power calculations and to the generation and distribution of electric power. The chapter builds on the material

### VOLTAGE REGULATOR AND PARALLEL OPERATION

VOLTAGE REGULATOR AND PARALLEL OPERATION Generator sets are operated in parallel to improve fuel economy and reliability of the power supply. Economy is improved with multiple paralleled generators by

### Before we proceed with a study of electric machinery, it is desirable to discuss

CHAPTER 2 Transformers Before we proceed with a study of electric machinery, it is desirable to discuss certain aspects of the theory of magnetically coupled circuits, with emphasis on transformer action.

### DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE2302 - ELECTRICAL MACHINES II UNIT-I SYNCHRONOUS GENERATOR

1 DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING Constructional details Types of rotors EE2302 - ELECTRICAL MACHINES II UNIT-I SYNCHRONOUS GENERATOR PART A 1.

### The Ideal Transformer. Description and Circuit Symbol

The Ideal Transformer Description and Circuit Symbol As with all the other circuit elements, there is a physical transformer commonly used in circuits whose behavior can be discussed in great detail. However,

### A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3 - MAGNETISM and INDUCTION

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 3 - MAGNETISM and INDUCTION 3 Understand the principles and properties of magnetism Magnetic field:

### Lecture - 4 Diode Rectifier Circuits

Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture - 4 Diode Rectifier Circuits

### Chapter 14. Transformers ISU EE. C.Y. Lee

Chapter 14 Transformers Objectives Explain mutual inductance Describe how a transformer is constructed and how it works Explain how a step-up and -down transformer works Discuss the effect of a resistive

### Direction of current flow through conductor. Fig. 1 Magnetic field generated by current flow

ingle Conductor Cable Copper heathed Cable heath Currents ingle conductor cables present certain application considerations that do not arise in multiconductor cable installations. These considerations

### Student Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics

Student Name Instructor Name High School or Vocational Center Grade COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Please check below each skill the student has mastered as described,

### Level 2 Physics: Demonstrate understanding of electricity and electromagnetism

Level 2 Physics: Demonstrate understanding of electricity and electromagnetism Static Electricity: Uniform electric field, electric field strength, force on a charge in an electric field, electric potential

### Solution Derivations for Capa #11

Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the

### Magnetic Field of a Circular Coil Lab 12

HB 11-26-07 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment- coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,

### AS91526: Demonstrate understanding of electrical systems Level 3 Credits 6

AS956: Demonstrate understanding of electrical systems Level 3 redits 6 This achievement standard involves demonstrating understanding of electrical systems. Achievement riteria Achievement Achievement

### Three phase circuits

Three phase circuits THREE PHASE CIRCUITS THREE-PHASE ADVANTAGES 1. The horsepower rating of three-phase motors and the kva rating of three-phase transformers are 150% greater than single-phase motors

### The Transformer. Technical information. is applied to the transformer s primary winding, an AC voltage U 2. If an AC voltage U 1

Technical information The Transformer A transformer is an electrical machine without moving parts. It works on the induction principle and can only be connected to alternating current. Its main task is