ADDIS ABABA SCIENCE and TECHNOLOGY UNIVERSITY SCHOOL of MECHANICAL and MANUFACTURING ENGINEERING DEPARTMENT of ELECTROMECHANICAL ENGINEERING LECTURE NOTE of INTRODUCTION to ELECTRICAL MACHINES (ECEG - 2261 ) OUTLINE 1. Magnetics 2. Transformers 3. AC 3-Phase Induction Machines (IM) 4. DC Machines 5. Synchronous Machines Chapter 1. Magnetics Magnetism and Electromagnetism Magnet:- is a material which has the property of attracting small bits of iron-containing objects. Magnets are generally classified in two categories Permanent magnets Electro-magnets 3 Permanent magnets Are magnets which have the inherence property of retaining their magnetism indefinitely and they don’t require electrical energy for retaining their magnetism. A permanent magnet will position itself in a north and south direction when freely suspended. The northseeking end of the magnet is called the North Pole, N, and the south-seeking end the South Pole, S. 4 Electromagnets Is the magnetization due to flow of an electric current through a coil. Electromagnets sometimes called as Artificial Magnets. Whenever an electric current flows through a conductor, a magnetic field is produced. 5 Electromagnets Hans Christian Oersted (1771-1851), who demonstrated in the year 1819 that a current-carrying conductor produced a magnetic field. The higher the current flow, the stronger the magnetic field produced. This is what we measure with a clamp on ammeter. The magnetic field produced in a conductor is proportional to the current moving through the conductor and the number of turns wound on the materials. 6 Magnetic Field Magnetic field:- is the area around a magnet and it is in this area that the effects of the magnetic force produced by the magnet can be detected. Michael Faraday suggested that the magnetic field could be represented pictorially, by imagining the field to consist of lines of magnetic flux, which enables investigation of the distribution and density of the field 7 Magnetic flux (magnetic line of force) Is total magnetic lines of force produced by a magnet The quantity of magnetism which exists in a magnetic field How much of magnetic force exist on the surface Magnetic fields may be produced by permanent magnets or electromagnets. Magnetic fields are created by alternating and directcurrent sources 8 Properties of Magnetic Lines of Force The direction of magnetic lines of force radiates from North Pole to South Pole outside the magnet and is from South to North Pole inside the magnet. Thus such lines of flux always form complete closed loops or paths; they never intersect and always have a definite direction. A magnetic field cannot be seen, felt, smelt or heard and therefore is difficult to represent. 9 Properties of Magnetic Lines of Force The laws of magnetic attraction and repulsion can be demonstrated by using two bar magnets. Unlike poles attract each other and like poles repel each other. This is indicated in the fig 1.1 below Figure 1.1 10 Electromagnetism A magnetic field is always associated with a currentcarrying conductor. Ampere's Right hand rule A magnetic field is always associated with a currentcarrying conductor. Field or flux line Current-carrying conductor The thumb pointing in the direction of the current Our fingers will point in the direction of magnetic field Another form of Ampere's right-hand rule Solenoid:- a cylindrical coil with large no of turns If we grasp the coil with our right hand the fingers pointing in the direction of the current, thumb will point in the direction of the north pole. Magnetic Properties of Materials Magnetic materials can be classified generally as Diamagnetic Paramagnetic Ferromagnetic Diamagnetic Materials Materials that experience a feeble or very weak force of repulsion by a magnetic field are called diamagnetic, such as bismuth, silver, and copper are diamagnetic materials. The permeability of a diamagnetic material is slightly 14 less than the permeability of free space. Magnetic Properties of Materials Paramagnetic Materials Materials that experience a feeble force of attraction by a magnetic field are called Paramagnetic materials but the permeability is slightly greater than the permeability of free space. Example Air, Aluminum, oxygen, Manganese, platinum and palladium Since the force experienced by a paramagnetic or a diamagnetic substance is quite feeble, for all practical purposes we can group them together and refer to them as nonmagnetic materials. Ferromagnetic materials These materials exhibit strong attraction and hence the permeability much greater than free space. Principal 15 ferromagnetic materials are Iron and various steel Is the magnetic flux per unit cross-sectional area. The total magnetic flux that comes out of the magnet is not uniformly distributed The magnetic flux density increases as we approach closer to the end of the magnet, as we move away the magnetic flux spreads out, and therefore the magnet flux density decreases. A greater amount of magnetic flux passing through an area that is nearer the magnet pole B A B = magnetic flux density, T = magnetic flux, Wb A = area through which penetrates perpendicularly, m2 16 Example 1. The total magnetic flux out of a cylindrical permanent magnet is found to be 0.032 mWb. If the magnet has a circular cross section and a diameter of 1 cm. what is the magnetic flux density at the end of the magnet? Solution 17 A driving force causing to establish magnetic flux. The magnetic flux is proportional to the products of amperes and turns. Ability of a coil to produce magnetic flux is magnetomotive force Fm NI Magneto motive force (MMF), AT N = number of turns of coil I = excitation current in coil, A Magneto motive force in the magnetic circuit is analogous to electromotive force 18 Example 2. The coil below has 1000 turns wound on a cardboard toroid. The mean diameter D of the toroid is 10 cm, and the cross section is 1 cm. The total magnetic flux in the toroid is 3Wb when there is an excitation current of 10 mA in the coil. a. What is the magnetic flux when the current is increased to 20 mA? b. What is the magnetic flux density within the coil when the current is 20 mA 19 Solution 20 Magnetic Reluctance It is Opposition of the material to establish magnetic flux. Fm m The MMF, AT = magnetic flux, Wb m= reluctance of the magnetic circuit. At/Wb Transposing, we have Fm m ………………..Ohm's law of magnetic circuits. m l μA Doubling the MMF in the circuit results in a doubling of the flux 21 Permeability Permeability (μ) – the magnetic property of a material to allow itself to be magnetized. It determines the characteristics of magnetic materials and nonmagnetic materials. 0 4 10 7 H / m The reluctance of magnetic materials is much lower than that of air or nonmagnetic material. The permeability of magnetic materials is much greater than that of air or non magnetic material Magnetic materials (iron steel cobalt nickel ) 22 Example 3. In Figure below we assume that the magnetic flux is practically uniform in the cross-sectional area of the toroid. The mean path length is 0.314 m and the cross-sectional area through which the flux exists is 78.5 x 10-6 m2. Calculate the number of ampere-turns required to set up magnetic flux of 1 Wb. 23 Solution This is obviously a very large number and we may conclude that the path reluctance is very high. This means that it is comparatively difficult to establish a large magnetic flux in air. 24 Relative Permeability Compares the permeability of magnetic materials with that of air r 0 B H Where = absolute permeability of the material. H/m 0 = 410-7H/m = permeability of free space r = relative permeability 25 Magnetic Field Intensity Magnetizing force or magnetic field strength. It is the magneto motive force gradient per unit length of magnetic circuit Fm H = l The magnetic field intensity for the air path is much larger than for the iron path 26 Magnetization (B-H) Curve The nonlinear relationship between magnetic flux density and magnetic field intensity The magnetic flux density increases almost linearly with an increase in the magnetic field intensity up to the knee point Beyond the knee a continued increase in the magnetic field intensity results in a relatively small increase in the magnetic flux density A slight increase in magnetic flux density for a relatively large increase in magnetic field intensity the materials are said to be saturated 27 Magnetization (B-H) Curve 28 Magnetization (B-H) Curve Magnetic material theory Magnetic materials are composed of many tiny magnets (magnetic domains) that are randomly positioned when the material is totally demagnetized Application of a magnetizing force the tiny magnets will tend to align themselves in the direction of this force The aligned tiny magnets increase proportionally until the knee of the curve. Beyond the knee fewer tiny magnets remain to be aligned When there are no more tiny magnets to be aligned, the ferromagnetic material is completely saturated. Saturation region practical implications in the operation of electrical 29 machines Hysteresis loop Hysteresis is lagging of flux density B behind the magnetizing force H If the specimen has been completely demagnetized and the magnetizing force H is increased oa is the normal magnetization curve The trace of B is higher than oa A residual flux density referred to as remnant flux (retentivity) density ob. In order to reduce B to zero, a negative field strength oc must be applied. The magnetic field intensity oc required to wipe out the residual magnetism ob is called coercive force (coercive) -H to +H, the path defa is similar to the curve abcd. The closed loop abcdefa thus traced out is called the hysteresis loop 30 HYSTERESIS is the dependence on the preceding flux history and the resulting failure to retrace flux paths. When mmf is removed, the flux does not go to zero – Residual Flux. To force the flux to zero, extra energy must be applied in the opposite direction. This extra energy requirement is known as hysteresis loss. 31 Hysteresis loop Conclusions A. Flux density B always lags with respect to the magnetizing force H. B. An expenditure of energy is essential to get a complete cycle of magnetization. C. Energy loss is proportional to the area of hysteresis loop and depends upon the quality of the magnetic material. 32 Eddy current loss A time-changing flux induces voltage within a ferromagnetic core. These voltages cause swirls of current to flow within the core – eddy currents. Energy is dissipated (in the form of heat) because these eddy currents are flowing in a resistive material (iron) The amount of energy lost to eddy currents is proportional to the size of the paths they follow within the core. To reduce energy loss, ferromagnetic core should be broken up into small strips, or laminations, and build the core up out of these strips. An insulating oxide or resin is used between the strips, so that the current paths for eddy currents are limited to small areas 33 Conclusion: Core loss analysis is extremely important in practice, since it greatly affects operating temperatures, efficiencies, and ratings of magnetic devices. 34 A current-carrying wire produces a magnetic field in the area around it. H dl I net where H is the magnetic field intensity produced by the current I𝒏𝒆𝒕 and dl is a differential element of length along the path of integration. H is measured in Ampere-turns per meter. 35 Consider a current currying conductor is wrapped around a ferromagnetic core; I CSA N turns mean path length, lc Applying Ampere’s law, the total amount of magnetic field induced will be proportional to the amount of current flowing through the conductor wound with N turns around the ferromagnetic material as shown above. 36 The path of integration in Ampere’s law is the mean path length of the core, lc. The current passing within the path of integration I𝒏𝒆𝒕 is then Ni, since the coil of wires cuts the path of integration N times while carrying the current i. Hence Ampere’s Law becomes, Hlc Ni Ni H lc 37 In a core such as in the above figure, B = H = Ni lc Now, to measure the total flux flowing in the ferromagnetic core, BdA A where A - cross sectional area throughout the core - total flux flowing in the ferromagnetic core (webers) Assuming B is constant throughout hence constant A, the equation simplifies to be: NiA BA lc 38 ELECTROMAGNETIC INDUCTION Faraday's laws of electromagnetic induction 1) Whenever the magnetic flux is changed or when a conductor is cut by the magnetic flux an emf is induced 2) The magnitude of the induced emf generated in a coil is directly proportional to the rate of change of magnetic flux. The change of flux can be produced in two different ways: I. Dynamically induced emf :-By the motion of the conductor or the coil in a magnetic field II. Statically induced emf :-By changing the current (either increasing or decreasing) Statically induced emf can be further subdivided into (a) self-induced emf and (b) mutually induced emf. 39 Self induced emf Any electrical circuit in which the change of current is accompanied by the change of flux, and therefore by an induced emf is said to be inductive or to possess self inductance. The property of the coil which enables to induce an emf in it, whenever the current changes is called self-induction d e N dt di e L dt A coil with changing current and flux 40 Mutually induced emf (Transformer) The phenomenon of generation of induced emf in a circuit by changing the current in a neighboring circuit is called mutual induction. When the switch K is closed to start current in the coil P the galvanometer gives a sudden "kick" in one direction. when K is opened, the galvanometer again shows a deflection but in the opposite direction. di e M 12 2 dt M 12 1 2 M N N 21 2 I 1 I 41 Lenz’s Law The voltage built up in the coil will tend to establish a flux that will oppose the change in the original flux. The induced current opposes the cause that produced it used to fix the direction of statically induced emf. The direction of the induced emf is always opposite to the change of flux responsible for producing that emf. 42 Induced Voltage on a Conductor Moving in a Magnetic Field (ELECTRIC GENERATOR) If a conductor moves or ‘cuts’ through a magnetic field, voltage will be induced between the terminals of the conductor. eind = (v x B) l Ein = (VX B)l cos θ Where: θ - angle between the conductor and the direction of (v x B) The magnitude of the induced voltage is dependent upon the velocity of the wire assuming that the magnetic field is constant. 43 Direction of Induced emf Fleming's right hand rule To obtain direction dynamically induced emf of Stretch the right hand fingers in three mutually perpendicular directions If the forefinger points in the direction of the magnetic flux the thumb points in the direction of motion of the conductor relative to the magnetic field then the middle finger represents the direction of the induced emf. 44 A current carrying conductor present in a uniform magnetic field of flux density B, would produce a force to the conductor/wire. F i l B F ilB sin Where: - angle between the conductor and the direction of the magnetic field. Direction of the force depends on the direction of current flow and the direction of the surrounding magnetic field 45 and is given by the Flemings left-hand rule. Left-hand rule. Thumb (resultant force) Index Finger (current direction) Middle Finger (Magnetic Flux Direction) (a) (b) Figure(b) shows a conductor moving with a velocity v to the right and the direction of the flux density is into the page. 46 Magnet circuit is the path followed by magnetic flux. In fact the laws of magnetic circuit are almost similar (but not exactly same) to those of the electric circuit. A + V - Electric Circuit Analogy R F=Ni (mmf) + - Reluctance, R Magnetic Circuit Analogy F R (similar to V=IR) 47 Composite Series Magnetic Circuits A magnetic circuit of varying length of different materials of different parameters through which the same flux flows is known as a series magnetic circuit. This is also called composite magnetic circuit. Hence the total reluctance is the sum of reluctance of individual parts or magnetic path. (Rm)= (L1/1o A1) + (L2/2o A2) + (L3/3o A3) 48 Leakage Flux in Magnetic Circuit Leakage flux is the flux which does not follow the designed path intended to be followed in a magnetic circuit. The flux passing through the air gap is known as useful flux. However, as air is not perfect magnetic insulator, hence a part of the total flux returns by paths(outside the designed magnetic path) is leakage flux. The total flux =flux in air gap(useful flux) + leakage flux. Leakage factor ==Total fux ( flux through iron path) useful flux flux through air gap For electrical machine vary between 1.1 to 1.25 49 Comparison between Electrical and Magnetic Circuit 50 The major applications of magnets They are used in Transformers, motors and generators, old telephones, relays, loudspeakers, computer hard drives and floppy disks, anti-lock brakes, cameras, fishing reels, electronic ignition systems, keyboards, T.V and radio components and in transmission equipments 51