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ABSTRACTThe 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 2Theory :For performance prediction of electromagnetic devices, magnetic field analysis isrequired. Analytical solution of field distribution by the Maxwell’s equations, however, isvery difficult or sometimes impossible owing to the complex structures of practical devices.Powerful numerical methods, such as the finite difference and finite element methods, areout of the scope of this subject. In this chapter, we introduce a simple method of magneticcircuit analysis based on an analogy to dc electrical circuits.A Simple Magnetic CircuitConsider a simple structure consisting of a current carrying coil of N turns and amagnetic core of mean length lc and a cross sectional area Ac as shown in the diagrambelow. The permeability of the core material is mc. Assume that the size of the device andthe operation frequency are such that the displacement current in Maxwell’s equations arenegligible, and that the permeability of the core material is very high so that all magneticflux will be confined within the core. By Ampere’s law,we can writewhere Hc is the magnetic field strength in the core, and Ni the magnetomotive force. Themagnetic flux through the cross section of the core can expressed as 2
where fc is the flux in the core and Bc the flux density in the core. The constitutive equationof the core material isIf we take the magnetic flux fc as the “current”, the magnetomotive force F=Ni as the “emfof 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 circuittheory. 3
Magnetic Circuital LawsConsider the magnetic circuit in the last section with an air gap of length lg cut in themiddle of a leg as shown in figure (a) in the diagram below. As they cross the air gap, themagnetic flux lines bulge outward somewhat as illustrate in figure (b). The effect of thefringing field is to increase the effective cross sectional area Ag of the air gap. By Ampere’slaw, we can write 4
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 coreand airgap respectively, the above equation from Ampere’s law can be interpreted as ananalog to the Kirchhoff’s voltage law (KVL) in electric circuit theory, orThe 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 jointin the circuit, we haveHaving derived the Ohm’s law, KVLand KCL in magnetic circuits, we can solve very complex magnetic circuits by applyingthese basic laws. All electrical dc circuit analysis techniques, such as mesh analysis andnodal analysis, can also be applied in magnetic circuit analysis.For nonlinear magnetic circuits where the nonlinear magnetization curves need to beconsidered, the magnetic reluctance is a function of magnetic flux since the permeability is afunction of the magnetic field strength or flux density. Numerical or graphical methods arerequired to solve nonlinear problems.Magnetic Circuit Model of Permanent MagnetsPermanent magnets are commonly used to generate magnetic fields forelectromechanical energy conversion in a number of electromagnetic devices, such asactuators, permanent magnet generators and motors. As mentioned earlier, thecharacteristics of permanent magnets are described by demagnetization curves (the part ofhysteresis loop in the second quadrant). The diagram below depicts the demagnetizationcurve of five permanent magnets. It can be seen that the demagnetization curves of somemost commonly used permanent magnets: Neodymium Iron Boron (NdFeB), SamariumCobalt, and Ceramic 7 are linear. For the convenience of analysis, we consider the magnetswith linear demagnetization curves first. 5
Consider a piece of permanent magnet of a uniform cross sectional area of Am and alength lm. The demagnetization curve of the magnet is a straight line with a coercive forceof Hc and a remanent flux density of Br as shown below. The demagnetization curve can beexpressed analytically aswhere μm=Br/Hc is the permeability of the permanent magnet, which is very close to μo, thepermeability of free space. For a NdFeB magnet, μm=1.05μo. Demagnetization curves of permanent magnets 6
which is a function of the magnetic field in the magnet. Notice that Hm is a negative valuesince it is in the opposite direction of Bm. The derivation for the magnetic circuit model of anonlinear magnet is illustrated graphically by the diagram below.It should also be understood that the operating point(Hm,Bm) will not move along the nonlineardemagnetization curve if a small (such that the magnetwill not be demagnetized) periodic external magneticfield is applied to the magnet. Instead, the operatingpoint will move along a minor loop or simply a straightline (center line of the minor loop) as illustrated in thediagram on the right hand side. 7
PROCEDUREPART 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 1.1PART 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 8
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 11