# Unit - I EE6401 Electrical Machines I Unit I Magnetic circuits and magnetic materials Magnetic circuits Laws governing magnetic circuits - Flux linkage, Inductance and energy Statically and Dynamically induced EMF Torque Properties of magnetic materials, Hysteresis and Eddy Current losses - AC excitation, introduction to permanent magnets-Transformer

as a magnetically coupled circuit. Unit II Transformers Construction principle of operation equivalent circuit parameters phasor diagrams, losses testing efficiency and voltage regulation-all day efficiency Sumpners test, per unit representation inrush current three phase transformers-connections Scott Connection Phasing of

transformer parallel operation of three phase transformers-auto transformer tap changing transformers tertiary winding. Unit III EMEC and Concepts in Rotating Machines Energy in magnetic system Field energy and coenergy force and torque equations singly and multiply excited magnetic field systems

mmf of distributed windings Winding Inductances, magnetic fields in rotating machines rotating mmf waves magnetic saturation and leakage fluxes. Unit IV DC Generators Construction and components of DC Machine Principle of operation Lap and wave windings EMF equations circuit model armature

reaction methods of excitation-commutation and interpoles compensating winding characteristics of DC generators. Unit V DC Motors Principle and operations types of DC Motors Speed Torque Characteristics of DC Motors starting and speed control of DC motors Plugging, dynamic and regenerative braking- testing and efficiency

Retardation test Swinburnes test and Hopkinsons test Permanent magnet dc motors(PMDC) DC Motor applications. Course Outcomes Statements

CO1 Realize the various concepts of magnetic-circuit analysis and magnetic materials. CO2 Explain the constructional details, principle of operation, prediction of

performance, methods of testing of transformers and three phase transformer connections. CO3 Apply the concepts of electromechanical energy conversion principles to derive expressions for generated voltage and torque developed in all Electrical Machines.

CO4 Describe the principles of DC machines as generators, determination of their no load/load characteristics, starting and methods of speed control of motors. CO5

Analyze the various losses taking place in D.C. Motor and to know the different testing methods to derive their performance. Unit I Magnetic Circuits and Magnetic Materials

Magnetic Circuit Electromagnetic system is an important element of all rotating electric machinery and static devices like transformer. Role is to create & control electromagnetic fields for EMEC process. EMEC happens with the help of magnetic field as a coupling medium. The closed path followed by the magnetic flux is called a magnetic

circuit. Made up of materials having high permeability such as iron, soft steel etc. Magnetic Circuit Electromagnetic system

Ferromagnetic core Exciting coil Coil has N turns

Coil carries a current of I amps Magnetic field established Magnetic flux flows through the core Small flux leaks through air Magnetic Circuit The magnetic field intensity produced in the core is H and from ampere

circuital law, Magnetic field intensity H causes a flux density B to be set up in the magnetic core. It is given by, Magnetic Circuit Sub equation 1 in equation 2, Flux flowing through the core is given by,

Where B is the average flux density and A is the area of cross section of the core. Substituting equation 3 in equation 4, we get, Magnetic Circuit and Electric Circuit Comparison of Magnetic and Electric Circuits

Magnetic Circuit Electric Circuit Hopkinsons Law Ohms Law

Flux ( Current (I) MMF ( EMF (V)

Permeability ( Conductivity ( Permeance () Conductance (G)

Direction of Current in a Conductor No current through the conductor. Conductor carries current away from the reader. Conductor carries current towards the reader. Right Hand Rule The direction of magnetic flux is found by using right hand rule.

Rule says that if one holds the conductor in such a way that the thumb points in the direction of current, then the closed fingers give the direction of flux produced. Faradays Law Whenever there is a variation of magnetic flux linking with a coil, an EMF is induced in that coil.

The magnitude of this EMF is proportional to the rate of change of flux linkages. Lenzs Law Lenzs law states that the induced EMF in a coil will induce a current whose direction is such that it opposes the cause producing the EMF. A ring is composed of three sections. The cross sectional area is 0.001 m2 for

each section. The mean arc lengths are la = 0.3 m, lb = 0.2 m and lc = 0.1 m. An air gap length of 0.1 mm is cut in the ring. Relative permeability for sections a, b and c are 5000, 1000 and 10000 respectively. Flux in the air gap is 7.5 X

10-4 Wb. Find (i) mmf, (ii) exciting current if the coil has 100 turns, (iii) reluctance of the sections.

Given Data Solution Air-gap and three sections form a series magnetic circuit. Flux in the air-gap is same as that of the three sections. Hence total mmf is the sum of mmf for each part of the magnetic circuit.

Solution Solution The magnetic circuit has dimensions: AC = 4 X 4 cm2, lg = 0.06 cm, lc = 40 cm and N = 600 turns. Assume the value of r = 6000 for iron. Find the exciting current for BC = 1.2 T and the corresponding flux and flux linkages.

Solution A wrought iron bar 30 cm long and 2 cm in diameter is bent into a circular shape as shown in figure below. It is then wound with 600 turns of wire. Calculate the current required to produce a flux of 0.5 mWb in the magnetic circuit in the following cases: (i) no air gap

(ii) with an air-gap of 1 mm (r of iron = 4000) (i) No Air-Gap =.

(ii) With Air-Gap =. The magnetic circuit shown below has steel core with dimensions as shown. Mean length from A to B through either outer limb = 0.5 m Mean length from A to B through central limb = 0.2 m

It is required to establish a flux of 0.75 mWb in the air-gap of the central limb. Determine the mmf of the exciting coil if the core material has Neglect fringing. ( ) = ( ) =

( ) = Self Inductance Consider a coil with N turns. When current i flows through it, a flux will be produced. As per Faradays law, Flux is produced by current i and hence any change in is

caused by changes in i. Therefore, The inductance L of the inductor is, This is called the Self Inductance of the coil. Mutual Inductance Consider 2 coils with self inductances L1 & L2 are kept close together.

Coil 1 has N1 turns and coil 2 has N2 turns. Current i1 creates a flux 1 in coil 1. This flux has got 2 components. 1 1 links with coil 1 only. 1 2 links with both the coils. Although both coils are physically separated, they are magnetically coupled.

Mutual Inductance Voltage induced in coil 1 is, L1 is the self inductance of the coil. Voltage induced in coil 2 is, M is the mutual inductance between the 2 coils.

Mutual Inductance Now consider a current i2 flows through coil 2 and produces a flux 2. This flux has got 2 components. 22 links with coil 1 only. 21 links with both the coils.

Mutual Inductance Voltage induced in coil 2 is, L2 is the self inductance of the coil. Voltage induced in coil 1 is, M is the mutual inductance between the 2 coils.

Mutual Inductance Mutual inductance is the ability of one inductor to induce a voltage across a neighboring inductor. It is measured in henrys (H). The polarity of mutual voltage is determined by using dot covention. A dot is placed at one end of each coupled coils to indicate the direction of the magnetic flux if current enters that dotted terminal of the coil.

Types of Induced EMF According to Faradays law of electromagnetic induction, an EMF is induced by changing the flux linkages in a coil. It can happen in two ways. EMF is induced either moving the coil and keeping the magnetic field stationary or moving the magnetic field and keeping the coil stationary. EMF is induced by changing the flux linking with a coil without moving either coil or magnetic field system.

Dynamically Induced EMF Moving the coil and keeping the magnetic field stationary or moving the magnetic field and keeping the coil stationary. EMF induced by this way is called dynamically induced emf. Dynamically Induced EMF

Since dx/dt=velocity Dynamically Induced EMF Now the conductor moves at an angle with the direction of magnetic field. Statically Induced EMF EMF induced in a coil when both the coil and magnetic field system are stationary but the magnetic flux linking with the coil changes is

called statically induced emf. Types of Statically Induced EMF Self Induced e.m.f. Mutually Induced e.m.f. Self Induced EMF Self-induced

e.m.f. is the e.m.f.

induced in a coil due to its own changing flux linked with it. Self Induced EMF Direction of induced voltage is such that it opposes the cause producing it.

Rate of change of flux depends on rate of change of current. L is the self inductance of the coil. Mutually Induced EMF Mutually induced e.m.f. is the e.m.f. induced in a coil due to the change of flux produced by another coil

(kept close) linking with it. Magnetisation Curve The curve that shows the variation in magnetic flux density B with respect to the variation in magnetic field intensity H in a ferromagnetic material. Hysteresis Loop A hysteresis loop shows the variation of the magnetic flux density (B) with respect to

the variation in magnetizing force (H). It is often referred to as the B-H loop. Hysteresis Loop Retentivity It is the ability of a material to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. Residual Magnetism or Residual Flux The magnetic flux density that

remains in a material when the magnetizing force is zero. Coercive Force The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero. Hysteresis and Eddy Current Loss When a magnetic material is subjected to cyclic magnetization, two kinds of power losses occur in it.

Hysteresis loss and Eddy current loss together called core loss. Hysteresis Loss Magnetic circuit is subjected to magnetic field reversals as it passes under successive poles. Hysteresis Loss Some amount of power has to be spent to reverse the molecular magnets

in the armature core continuously. It is considered as loss. The loss of power in the core due to hysteresis effect is called hysteresis loss. Hysteresis Loss

It is given by Steinmetz formula. Where To reduce this loss, the magnetic core is made of such materials which have a low value of Steinmetz hysteresis co-efficient e.g., silicon steel. Eddy Current Loss

In addition to the voltages induced in the conductors, there are also voltages induced in the magnetic core. These voltages produce circulating currents in the core. Eddy Current Loss It is given by

Where The core loss (hysteresis + eddy current loss) for a given specimen of magnetic material is found to be 2000 W at 50 Hz. Keeping the flux density constant, the frequency of the supply is raised to 75 Hz resulting in a core loss of 3200 W. Compute separately hysteresis and eddy current losses at

both the frequencies. Leakage Flux The stray flux, which does not take part in the energy conversion process, is called leakage flux. This leakage flux can never be eliminated. The effect of leakage flux is incorporated in

machine models through the concept of the leakage inductance. Fringing The flux in a magnetic circuit bulges (or fringes) outwards while passing through an air-gap. This results in non-uniform flux density in the airgap, enlargement of air-gap area and reduction in flux density in air-gap.

This phenomenon is called fringing. The effect of fringing increases with the increase in air-gap length. Stacking Factor Magnetic cores are made up of thin, lightly insulated (coated with varnish) laminations to reduce eddy current loss. As a result, the net cross sectional area of the core occupied by the magnetic material is less than its gross cross section.

Hence the ratio of net cross sectional area to the gross cross sectional area of the core is called Stacking factor. The field winding of DC electromagnet is wound with 800 turns and has a resistance of 40 when exciting voltage is 230 V and the magnetic flux around the coil is 0.004 Wb. Calculate self-inductance and energy stored in magnetic field.

Two coils A and B are wound on same iron core. There are 600 turns on A and 3600 turns on B. 4 amps of current through the coil A produces a flux of 500 X 10-6 Wb in the core. If this current is reversed in 0.02 seconds, calculate average emf induced in coils A and B. Current reversal means that the current changing from +4A to -4A. Actual change in current is 8A. Hence change in flux is 1000 X 10-6 wb Properties of Magnetic

Materials All materials are classified according to their relative permeability. Paramagnetic r slightly greater than 1 Diamagnetic

r slightly lesser than 1 Ferro & Ferrimagnetic r much higher than that of free space

Properties of Magnetic Materials Ferromagnetic materials are further subdivided into hard and soft.

Hard (Per. Magnet) Soft Alnico

Chromium steel Copper nickel alloys Metal alloys Iron and its alloys with nickel, cobalt, tungsten and aluminium