7/29/2019 A.Exp 1

1/12

OBJECTIVES

1. To obtain the B-H curve for a single-phase transformer.

2. To obtain result for total magnetic flux.

LIST OF REQUIREMENTS

EQUIPMENT

1. Single phase variac 20V (164)

2. 2A a.c ammeter

3. 300V voltmeter

4. 150V voltmeter(x3)

5. Laminated core transformer 800/400, 50 Hz

THEORY:

For performance prediction of electromagnetic devices, magnetic field analysis is

required. Analytical solution of field distribution by the Maxwells equations, however, is

very difficult or sometimes impossible owing to the complex structures of practical devices.

Powerful numerical methods, such as the finite difference and finite element methods, are

out of the scope of this subject. In this chapter, we introduce a simple method of magnetic

circuit analysis based on an analogy to dc electrical circuits.

A Simple Magnetic Circuit

Consider a simple structure consisting of a current carrying coil ofNturns and a

magnetic core of mean length lc and a cross sectional areaAc as shown in the diagram

below. The permeability of the core material is mc. Assume that the size of the device and

the operation frequency are such that the displacement current in Maxwells equations are

negligible, and that the permeability of the core material is very high so that all magnetic

flux will be confined within the core. By Amperes law,

where Hc is the magnetic field strength in the core, and Nithe magnetomot ive force. The

magnetic flux through the cross section of the core can expressed as

7/29/2019 A.Exp 1

2/12

where fc is the flux in the core and Bc the flux density in the core. The constitutive equation

of the core material is

If we take the magnetic flux fc as the current, the magnetomotive force F=Nias the emf

of a voltage source, and Rc=lc/(cAc) (known as the magnetic reluctance) as the

resistance in the magnetic circuit, we have an analog ofOhms lawin electrical circuit

theory.

Magnetic Circuital Laws

Consider the magnetic circuit in the last section with an air gap of length lg cut in the

middle of a leg as shown in figure (a) in the diagram below. As they cross the air gap, the

magnetic flux lines bulge outward somewhat as illustrate in figure (b). The effect of the

f r ingingfield is to increase the effective cross sectional areaAg of the air gap. By Amperes

law, we can write

7/29/2019 A.Exp 1

3/12

That is, the above magnetic circuit with an air gap is analogous to a series electric circuit.

Further, if we regard Hclcand Hglgas the voltage drops across the reluctance of the core

and airgap respectively, the above equation from Amperes law can be interpreted as an

analog to the Kirchhoffs voltage law(KVL) in electric circuit theory, or

The Kirchhoffs current law(KCL) can be derived from the Gauss law in magnetics.

Consider a magnetic circuit as shown below. When the Gauss law is applied to the T joint

in the circuit, we have

Having derived the Ohms law, KVL

and KCL in magnetic circuits, we can solve very complex magnetic circuits by applying

these basic laws. All electrical dc circuit analysis techniques, such as mesh analysis and

nodal analysis, can also be applied in magnetic circuit analysis.

For nonlinear magnetic circuits where the nonlinear magnetization curves need to be

considered, the magnetic reluctance is a function of magnetic flux since the permeability is a

function of the magnetic field strength or flux density. Numerical or graphical methods are

required to solve nonlinear problems.

7/29/2019 A.Exp 1

4/12

Magnetic Circuit Model of Permanent Magnets

Permanent magnets are commonly used to generate magnetic fields for

electromechanical energy conversion in a number of electromagnetic devices, such as

actuators, permanent magnet generators and motors. As mentioned earlier, the

characteristics of permanent magnets are described by demagnetization curves (the part of

hysteresis loop in the second quadrant). The diagram below depicts the demagnetization

curve of five permanent magnets. It can be seen that the demagnetization curves of some

most commonly used permanent magnets: Neodymium Iron Boron (NdFeB), Samarium

Cobalt, and Ceramic 7 are linear. For the convenience of analysis, we consider the magnets

with linear demagnetization curves first.

Consider a piece of permanent magnet of a uniform cross sectional area ofAm and a

length lm. The demagnetization curve of the magnet is a straight line with a coercive force

ofHc and a remanent flux density ofBr as shown below. The demagnetization curve can beexpressed analytically as

which is a function of the magnetic field in the magnet. Notice that Hm is a negative value

since it is in the opposite direction ofBm. The derivation for the magnetic circuit model of a

nonlinear magnet is illustrated graphically by the diagram below.

7/29/2019 A.Exp 1

5/12

PROCEDURES:

PART A : MAGNETIC CIRCUIT

1. The Transformer was examined and the values of N1, N2, L and A was recorded.

2. The circuit was completed as figure below

3. The variac reading was setted to zero and switch the switch was turned on

4. A low input primary voltage use as start (started with 100V), The primary current I1

and the open circuited secondary voltage was measured and recorded.

5. Step 4 was repeated by increasing the primary voltage in step (start from 100V until

200V)

6. The Graph of Bm versus Hmand rVersus Hm.

7/29/2019 A.Exp 1

6/12

RESULTS:

PART A: MAGNETIC CIRCUIT.

V1 PrimaryCurrent, I1

SecondaryVoltage, V2

Maximum FluxDensity, Bm

100 0.20 50 560.08 0.63 895.12

110 0.20 55 560.08 0.69 980.37

120 0.20 60 560.08 0.75 1065.62

130 0.20 65 560.08 0.81 1150.87

140 0.22 70 616.09 0.88 1136.65150 0.28 72 784.12 0.90 913.38

160 0.30 74 840.13 0.93 880.9

170 0.34 75 952.14 0.94 785.63

180 0.38 78 1064.16 0.98 732.84

190 0.40 80 1126.17 1.0 706.62

200 0.42 85 1176.18 1.06 717.17

210 0.48 88 1344.20 1.1 651.21

220 0.52 94 1456.22 1.18 644.83

7/29/2019 A.Exp 1

7/12

Example of calculation:

Formula using:-

Hm=

, Bm = , r =

, N1 = 800T , N2 = 400T , L = 0.404meter , A = 0.899mm , o =

Find Hm using I = 0.20 A,

Hm=

=()()()

= 560.08

Find Bm using V2 = 50V,

Bm =

=

()()()()= 0.63

Find r using B = 0.63, H = 560.08,

r =

=

()() = 895.12

7/29/2019 A.Exp 1

8/12

DISCUSSION:

PART A: MAGNETIC CIRCUIT

B-H curve is the graph to show the permeability of the materials. Permeability (m) is a

material property that describes the ease with which a magnetic flux is established in a

component. It is the ratio of the flux density (B) created within a material to the magnetizing

field (H). The strength of magnetic will vary in accordance with the core used. This variation

in strength is due to the number of flux lines passing through the core.The maximum

permeability is the point where the slope of the B/H curve for the non magnetized material is

the greatest. This point is often taken as the point where a straight line from the origin is

tangent to the B/H curve. From the graph, when the value of magnetizing force is increase

the value of the magnetic flux (B) also increase until it value is constant The value of flux

density (B) remains constant because it is achieve the saturation. Saturation is most clearly

seen in the magnetization curve (also called BH curve or hysteresis curve) of a substance,

as a bending to the right of the curve. Saturation occurs because the random haphazard

arrangement of the molecule structure within the core material changes as the tiny molecular

7/29/2019 A.Exp 1

9/12

magnets within the material become "lined-up". As the magnetic field strength, (H) increases

these molecular magnets become more and more aligned until they reach perfect alignment

producing maximum flux density and any increase in the magnetic field strength due to an

increase in the electrical current flowing through the coil will have little or no effect. The lower

the transformer design frequency, the worse the DC saturation can be. This is because

achieving good low frequency response calls for a high permeability core. The smaller the

core is physically, the less the current required for saturation.

Ferrous-magnetic material in transformer is the transformers work by coupling the magnetic

fields of two electrical coils .Ferrous metal is magnetic and made of iron but Non Ferrous

metal is not Ferrous material will allow for better coupling of the magnetic flux allowing for a

smaller more efficient transformer than one made with non ferrous materials. Adding a

ferrous material confines the vast majority of the magnetic flux to the core, thus greatly

increasing the coupling efficiency and reducing losses. The advantages of ferrous-magnetic

material in transformer application are one which is a bivalent iron compound. It is more

common to refer to materials as non-ferrous for example metals that do not contain iron.

CONCLUSION:

PART A : MAGNETIC CIRCUIT

What can be concluded from part A of the experiment is we can obtain the B-H curve for a

single-phase transformer and the value of Hm is proportional to the value of Bm obtain from

the graph. Based on the graph we obtain in comparison to the B-H curve provided. It shows

that the graph we obtain is very similar to sheet steel graph with just slight different that

might be occur because of error in experiment. To get the value of graph, we must repeat

the step 4 by increasing the primary voltage in step, starting from 100V until 220V.

7/29/2019 A.Exp 1

10/12

REFERENCES:

ELECTRICAL AND ELECTRONICS ENGINEERING STUDIES FORM 5. SALWANI BINTI MOHD

DAUD. FARIZA BINTI SAID HASSAN. LIZA BINTI ABD LATIFF. MORINA BINTI ABDULLAH.KAMARUDDIN BIN TAWI. RASLI BIN ABD GHANI. DEWAN BAHASA DAN PUSTAKA KUALA

LUMPUR 2007.

NEWNES ELECTRICAL POCKET BOOK, 22nd EDITION,E.A REEVES.

LABORATORY MANUAL. ELECTRICAL ENGINEERING LABORATORY 1. RUSNANI ARIFFIN,

MOHD AMINUDIN MURAD. WINNER OF THE PRIME MINISTERS QUALITY AWARD Q 2008.

ALEXENDER, C.K & SADIKU, M.N.O.(2007). FUNDAMENTALS OF ELECTRIC CIRCUITS (3rd ed).

New York: MCGRAW HILL.

COLLEGE PHYSICS.(3rd ed). GIAMBATTISTA, RICHARDSON. MCGRAW.HILL INTERNATIONAL

EDITION.

http://www.blurtit.com/q6103121.html (30 July 2011)

http://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/

Permeability.htm( 30 July 2011)

http://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/

Permeability.htm (30 July 2011)

http://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htmhttp://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htmhttp://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htmhttp://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htmhttp://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htmhttp://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htmhttp://www.ndt.ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Permeability.htm

7/29/2019 A.Exp 1

11/12

PART A:

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Bm versus Hm

Bm versus Hm

0

200

400

600

800

1000

1200

1400

560.

08

560.

08

560.

08

560.

08

616.

09

784.

12

840.

13

952.

14

1064.

16

1126.

17

1176.

18

1344.

2

1456.

22

r versus Hm

r versus Hm

7/29/2019 A.Exp 1

12/12

TABLE OF CONTENT

CONTENT PAGE

OBJECTIVESLIST OF REQUIREMENTS

THEORY

PROCEDURES PART A: MAGNETIC CIRCUITRESULT

DISCUSSIONCONCLUSION

PROCEDURES PART B: APPLICATION OF ELECTRIC CICUITANALOGIES IN MAGNETIC CIRCUIT.

RESULTDISCUSSIONCONCLUSION