Experiment magnetic circuit all the contents is not 100% legit

1. FACULTY OF ELETRICAL ENGINEERING
UNIVERSITY TEKNOLOGI MARA
ELECTRICAL ENGINEERING LABORATORY 1
(EEE230)
EXPERIMENT 1
MAGNETIC CIRCUIT

2. TABLE OF CONTENT
CONTENT PAGE
ABSTRACT
Objective
Requirement
Introduction
Theory
EXPERIMENT PROCEDURE
EXPERIMENT RESULT
DISCUSSION
CONCLUSION
REFERENCE
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3. 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 Quantity
Single Phase Variac 20V(164) 1
Multimeter 4
Laminated core transformer 800 50Hz 1
Laminated core transformer 400 50Hz 1
Laminated 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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4. 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.
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5. 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
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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6. 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
with linear demagnetization curves first.
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7. 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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8. 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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9. 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 1.1
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 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.
Figure 1.1
PART B : APPLICATION OF ELECTRIC CIRCUIT ANALOGIES IN MAGNETIC CIRCUIT
1. The circuit was connected as in Figure 1.2
2. The variac voltage was increased in step from 100V to 200V and the voltmeter reading
was recorded in Table 1.2
3. The number of turn for all winding was recorded and the brach flux was calculated using
equation
Figure 1.2
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10. RESULTS
PART A : MAGNETIC CIRCUIT
Maximum Flux
Density, Bm
V1 Primary Secondary
Current, I1 Voltage, V2
220 0.69 96 1951.61 11.62m 4.738
210 0.63 92 1781.90 11.14m 4.975
200 0.58 88 1640.49 10.66m 5.171
190 0.54 84 1527.35 10.17m 5.299
180 0.49 80 1385.93 9.69m 5.564
170 0.45 76 1272.79 9.20m 5.752
160 0.41 72 1159.66 8.72m 5.984
150 0.38 67 1074.80 8.11m 6.005
140 0.35 64 981.95 7.75m 6.281
130 0.31 58 876.81 7.02m 6.371
120 0.28 54 791.96 6.54m 6.572
110 0.25 50 707.11 6.05m 6.809
100 0.23 45 650.54 5.45m 6.667
Table 1.1
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11. 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 1.730m
210 45 1.014m 49 0.522m 14 0.315m 0.867m
200 43 0.969m 47 0.529m 13 0.293m 0.822m
190 41 0.923m 45 0.507m 12 0.270m 0.777m
180 38 0.856m 43 0.484m 11 0.248m 0.732m
170 36 0.811m 41 0.462m 11 0.248m 0.710m
160 34 0.766m 38 0.428m 10 0.225m 0.653m
150 31 0.698m 36 0.405m 9 0.203m 0.608m
140 29 0.653m 33 0.372m 9 0.203m 0.575m
130 27 0.608m 31 0.349m 8 0.180m 0.525m
120 25 0.563m 28 0.315m 7 0.159m 0.473m
110 22 0.495m 26 0.293m 6 0.135m 0.428m
100 20 0.450m 22 0.248m 5 0.113m 0.361m
Table 1.2
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12. 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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