FACULTY OF ELETRICAL ENGINEERING

UNIVERSITY TEKNOLOGI MARA

ELECTRICAL ENGINEERING LABORATORY 1

(EEE230)

EXPERIMENT 1

MAGNETIC CIRCUIT

TABLE OF CONTENT

CONTENT PAGE

ABSTRACT Objective Requirement Introduction Theory

EXPERIMENT PROCEDURE

EXPERIMENT RESULT

DISCUSSION

CONCLUSION

REFERENCE

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ABSTRACT

The main Objectives of the experiment are :

1. To obtain the B-H curve for a single-phase transformer.2. To obtain result for total magnetic flux.

List Of Requirements:

Equipment QuantitySingle Phase Variac 20V(164) 1

Multimeter 4Laminated core transformer 800 50Hz 1Laminated core transformer 400 50Hz 1Laminated core transformer 200 50Hz 2

Theory :

For performance prediction of electromagnetic devices, magnetic field analysis is

required. Analytical solution of field distribution by the Maxwell’s 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 of N turns and a

magnetic core of mean length lc and a cross sectional area Ac 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 Maxwell’s 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 Ampere’s law,

we can write

where Hc is the magnetic field strength in the core, and Ni the magnetomotive force. The

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

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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=Ni as the “emf

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

“resistance” in the magnetic circuit, we have an analog of Ohm’s law in electrical circuit

theory.

Magnetic Circuital Laws

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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

fringing field is to increase the effective cross sectional area Ag of the air gap. By Ampere’s

law, we can write

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

Further, if we regard Hclc and Hglg as the “voltage drops” across the reluctance of the core

and airgap respectively, the above equation from Ampere’s law can be interpreted as an

analog to the Kirchhoff’s voltage law (KVL) in electric circuit theory, or

The Kirchhoff’s 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 Ohm’s 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.

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

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with linear demagnetization curves first.

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

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

of Hc and a remanent flux density of Br as shown below. The demagnetization curve can be

expressed analytically as

where μm=Br/Hc is the permeability of the permanent magnet, which is very close to μo, the

permeability of free space. For a NdFeB magnet, μm=1.05μo.

Demagnetization curves of permanent magnets

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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 of Bm. The derivation for the magnetic circuit model of a

nonlinear magnet is illustrated graphically by the diagram below.

It should also be understood that the operating point

(Hm,Bm) will not move along the nonlinear

demagnetization curve if a small (such that the magnet

will not be demagnetized) periodic external magnetic

field is applied to the magnet. Instead, the operating

point will move along a minor loop or simply a straight

line (center line of the minor loop) as illustrated in the

diagram on the right hand side.

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PROCEDURE

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 1.13. The variac reading was setted to zero and switch the switch was turned on4. 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 in Table 1.1.5. Step 4 was repeated by increasing the primary voltage in step (start from 100V until

200V)6. The Graph of Bm versus Hm and μr Versus Hm.

PART B : APPLICATION OF ELECTRIC CIRCUIT ANALOGIES IN MAGNETIC CIRCUIT

1. The circuit was connected as in Figure 1.22. The variac voltage was increased in step from 100V to 200V and the voltmeter reading

was recorded in Table 1.23. The number of turn for all winding was recorded and the brach flux was calculated using

equation

Ф= V4.44 fN

8Figure 1.2

Figure 1.1

RESULTS

PART A : MAGNETIC CIRCUIT

V1

Primary Current, I1

Secondary Voltage, V2

Hm=√2N 1 IL

Maximum Flux Density, Bm

Bm=V 2

4.44 f N2 A

μr=BμoH

220 0.69 96 1951.61 11.62m 4.738210 0.63 92 1781.90 11.14m 4.975200 0.58 88 1640.49 10.66m 5.171190 0.54 84 1527.35 10.17m 5.299180 0.49 80 1385.93 9.69m 5.564170 0.45 76 1272.79 9.20m 5.752160 0.41 72 1159.66 8.72m 5.984150 0.38 67 1074.80 8.11m 6.005140 0.35 64 981.95 7.75m 6.281130 0.31 58 876.81 7.02m 6.371120 0.28 54 791.96 6.54m 6.572110 0.25 50 707.11 6.05m 6.809100 0.23 45 650.54 5.45m 6.667

Table 1.1

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PART B : APPLICATION OF ELECTRIC CIRCUIT ANALOGIES IN MAGNETIC CIRCUIT

Vs V1(V) Ф1 V2(V) Ф2 V3(V) Ф3 Ф2+Ф3

220 47 1.059m 52 0.585m 15 0.338m 1.730m210 45 1.014m 49 0.522m 14 0.315m 0.867m200 43 0.969m 47 0.529m 13 0.293m 0.822m190 41 0.923m 45 0.507m 12 0.270m 0.777m180 38 0.856m 43 0.484m 11 0.248m 0.732m170 36 0.811m 41 0.462m 11 0.248m 0.710m160 34 0.766m 38 0.428m 10 0.225m 0.653m150 31 0.698m 36 0.405m 9 0.203m 0.608m140 29 0.653m 33 0.372m 9 0.203m 0.575m130 27 0.608m 31 0.349m 8 0.180m 0.525m120 25 0.563m 28 0.315m 7 0.159m 0.473m110 22 0.495m 26 0.293m 6 0.135m 0.428m100 20 0.450m 22 0.248m 5 0.113m 0.361m

Table 1.2

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REFERENCE

1. Matthew N.O sadiku, Charles K. Alexander(2009), Fundamental Of Electric Circuit 4(ed), Singapore:Mc Graw Hill.

2. Du Bois, H, The magnetic circuit in theory and practice, London : Longmans.

3. Rusnani Ariffin, Mohd Aminuddin Murad(2009), Laboratory Manual : Electrical Engineering Laboratory 1 EEE230, Shah Alam: University Publication Centre (UPENA) Universiti Teknologi Mara.

4. www1.mmu.edu.my/~wslim/lecture_notes/Chapter4.pdf

5. www.brighthub.com/engineering/electrical/articles/3829.aspx

6. media.wiley.com/product_data/excerpt/07/.../0471280607.pdf

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