LECTURE NOTES ON ELECTRICAL MACHINE

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LECTURE NOTES ON ELECTRICAL MACHINE-II Subject Code - BEE 1401 th For B-Tech 4 SEM EE & EEE Part-II Module-III & IV VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Department of Electrical Engineering Burla, Sambalpur, Odisha 768018 www.vssut.ac.in L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 1 Syllabus of Bachelor of Technology in Electrical Engineering th (4 SEMESTER) ELECTRICAL MACHINES-II Subject Code: BEE 1401 Topics Page No. MODULE-III Three Phase Induction Motors: Types, Construction and principle of operation, 3 phase Induction Motor, general phasor diagram, equivalent circuit, power and torque relations, condition for maximum torque, circle diagram, 3-67 Performance characteristics, effect of rotor resistance on speed torque characteristics, stable & unstable region of operation, Operation with unbalanced supply voltage. Starting: Starting of 3 phase induction motors, high starting torque motors, speed control, rheostatic method, pole changing method, cascade control of speed, Double cage induction motor, Cogging and Crawling of Induction motor, Induction generator. MODULE-IV Single phase induction motor, theory of operation (Double revolving field theory, equivalent circuit, Determination of 68-99 parameters) Methods of starting, split phase starting, Repulsion starting, shaded pole starting, performance characteristics. Single phase series motor, theory of operation performance and application, Shcrage motor, Universal motor. EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 2 Disclaimer This document does not claim any originality and cannot be used as a substitute for prescribed textbooks. The information presented here is merely a collection by the committee members for their respective teaching assignments. Various sources as mentioned at the end of the document as well as freely available material from internet were consulted for preparing this document. The ownership of the information lies with the respective authors or institutions. Further, this document is not intended to be used for commercial purpose and the committee members are not accountable for any issues, legal or otherwise, arising out of use of this document. The committee members make no representations or warranties with respect to the accuracy or completeness of the contents of this document and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. The committee members shall not be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. EE DEPT. Veer Surendra Sai University of Technology, Burla SYLLABUS/ TOPICS COVERED Three Phase Induction Motors: Types, Construction and principle of operation, 3 phase Induction Motor, general phasor diagram, equivalent circuit, power and torque relations, condition for maximum torque, circle diagram, Performance characteristics, effect of rotor resistance on speed torque characteristics, stable & unstable region of operation, Operation with unbalanced supply voltage. Starting: Starting of 3 phase induction motors, high starting torque motors, speed control, rheostatic method, pole changing method cascade control of speed, MODULE-III Double cage induction motor, Cogging and Crawling of Induction motor, induction THREE PHASE INDCTION MOTOR generator Topics are arranged as per above sequence L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 4 Module-III 3.1 Three Phase Induction Motor The most common type of AC motor being used throughout the work today is the "Induction Motor". Applications of three-phase induction motors of size varying from half a kilowatt to thousands of kilowatts are numerous. They are found everywhere from a small workshop to a large manufacturing industry. The advantages of three-phase AC induction motor are listed below: • Simple design • Rugged construction • Reliable operation • Low initial cost • Easy operation and simple maintenance • Simple control gear for starting and speed control • High efficiency. Induction motor is originated in the year 1891 with crude construction (The induction machine principle was invented by NIKOLA TESLA in 1888.). Then an improved construction with distributed stator windings and a cage rotor was built. The slip ring rotor was developed after a decade or so. Since then a lot of improvement has taken place on the design of these two types of induction motors. Lot of research work has been carried out to improve its power factor and to achieve suitable methods of speed control. 3.2 Types and Construction of Three Phase Induction Motor Three phase induction motors are constructed into two major types: 1. Squirrel cage Induction Motors 2. Slip ring Induction Motors 3.2.1 Squirrel cage Induction Motors (a) Stator Construction The induction motor stator resembles the stator of a revolving field, three phase alternator. The stator or the stationary part consists of three phase winding held in place in the slots of a laminated steel core which is enclosed and supported by a cast iron or a steel frame as shown in Fig: 3.1(a). EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 5 The phase windings are placed 120 electrical degrees apart and may be connected in either star or delta externally, for which six leads are brought out to a terminal box mounted on the frame of the motor. When the stator is energized from a three phase voltage it will produce a rotating magnetic field in the stator core. Fig: 3.1 (b) Rotor Construction The rotor of the squirrel cage motor shown in Fig: 3.1(b) contains no windings. Instead it is a cylindrical core constructed of steel laminations with conductor bars mounted parallel to the shaft and embedded near the surface of the rotor core. These conductor bars are short circuited by an end rings at both end of the rotor core. In large machines, these conductor bars and the end rings are made up of copper with the bars brazed or welded to the end rings shown in Fig: 3.1(b).In small machines the conductor bars and end rings are sometimes made of aluminium with the bars and rings cast in as part of the rotor core. Actually the entire construction (bars and end-rings) resembles a squirrel cage, from which the name is derived. The rotor or rotating part is not connected electrically to the power supply but has voltage induced in it by transformer action from the stator. For this reason, the stator is sometimes called the primary and the rotor is referred to as the secondary of the motor since the motor operates on the principle of induction and as the construction of the rotor with the bars and end rings resembles a squirrel cage, the squirrel cage induction motor is used. The rotor bars are not insulated from the rotor core because they are made of metals having less resistance than the core. The induced current will flow mainly in them. Also the rotor bars are usually not quite parallel to the rotor shaft but are mounted in a slightly skewed position. This feature tends to produce a more uniform rotor field and torque. Also it helps to reduce some of the internal magnetic noise when the motor is running. EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 6 (c) End Shields The function of the two end shields is to support the rotor shaft. They are fitted with bearings and attached to the stator frame with the help of studs or bolts attention. 3.2.2 Slip ring Induction Motors (a) Stator Construction The construction of the slip ring induction motor is exactly similar to the construction of squirrel cage induction motor. There is no difference between squirrel cage and slip ring motors. (b) Rotor Construction The rotor of the slip ring induction motor is also cylindrical or constructed of lamination. Squirrel cage motors have a rotor with short circuited bars whereas slip ring motors have wound rotors having "three windings" each connected in star. The winding is made of copper wire. The terminals of the rotor windings of the slip ring motors are brought out through slip rings which are in contact with stationary brushes as shown in Fig: 3.2. Fig: 3.2 THE ADVANTAGES OF THE SLIPRING MOTOR ARE • It has susceptibility to speed control by regulating rotor resistance. • High starting torque of 200 to 250% of full load value. • Low starting current of the order of 250 to 350% of the full load current. Hence slip ring motors are used where one or more of the above requirements are to be met. EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 7 3.2.3 Comparison of Squirrel Cage and Slip Ring Motor Sl.No. Property Squirrel cage motor Slip ring motor 1. Bars are used in rotor. Winding wire is to be Rotor Construction Squirrel cage motor is used. very simple, rugged and Wound rotor required long lasting. No slip attention. rings and brushes Slip ring and brushes are needed also need frequent maintenance. 2. Starting Can be started by Rotor resistance starter D.O.L., star-delta, auto is required. transformer starters 3. Low Very high Starting torque 4. Starting High Low Current 5. Speed variation Not easy, but could be Easy to vary speed. varied in large steps by Speed change is possible pole changing or by inserting rotor through smaller resistance using incremental steps thyristors or by using through thyristors or by frequency variation frequency variation. injecting emf in the rotor circuit cascading. 6. Almost ZERO Requires frequent Maintenance maintenance maintenance 7. Cost Low High 3.3 Principle of Operation The operation of a 3-phase induction motor is based upon the application of Faraday Law and the Lorentz force on a conductor. The behaviour can readily be understood by means of the following example. Consider a series of conductors of length l, whose extremities are short-circuited by two bars A and B (Fig.3.3 a). A permanent magnet placed above this conducting ladder, moves rapidly to the right at a speed v, so that its magnetic field B sweeps across the conductors. The following sequence of events then takes place: EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 8 1. A voltage E = Blv is induced in each conductor while it is being cut by the flux (Faraday law). 2. The induced voltage immediately produces a current I, which flows down the conductor underneath the pole face, through the end-bars, and back through the other conductors. 3. Because the current carrying conductor lies in the magnetic field of the permanent magnet, it experiences a mechanical force (Lorentz force). 4. The force always acts in a direction to drag the conductor along with the magnetic field. If the conducting ladder is free to move, it will accelerate toward the right. However, as it picks up speed, the conductors will be cut less rapidly by the moving magnet, with the result that the induced voltage E and the current I will diminish. Consequently, the force acting on the conductors wilt also decreases. If the ladder were to move at the same speed as the magnetic field, the induced voltage E, the current I, and the force dragging the ladder along would all become zero. Fig: 3.3 In an induction motor the ladder is closed upon itself to form a squirrel-cage (Fig.3.3b) and the moving magnet is replaced by a rotating field. The field is produced by the 3-phase currents that flow in the stator windings. 3.4 Rotating Magnetic Field and Induced Voltages Consider a simple stator having 6 salient poles, each of which carries a coil having 5 turns (Fig.3.4). Coils that are diametrically opposite are connected in series by means of three jumpers EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 9 that respectively connect terminals a-a, b-b, and c-c. This creates three identical sets of windings AN, BN, CN, which are mechanically spaced at 120 degrees to each other. The two coils in each winding produce magneto motive forces that act in the same direction. The three sets of windings are connected in wye, thus forming a common neutral N. Owing to the perfectly symmetrical arrangement, the line to neutral impedances are identical. In other words, as regards terminals A, B, C, the windings constitute a balanced 3-phase system. For a two-pole machine, rotating in the air gap, the magnetic field (i.e., flux density) being sinusoidally distributed with the peak along the centre of the magnetic poles. The result is illustrated in Fig.3.5. The rotating field will induce voltages in the phase coils aa', bb', and cc'. Expressions for the induced voltages can be obtained by using Faraday laws of induction. Fig: 3.4 Elementary stator having terminals A, B, C connected to a 3-phase source (not shown). Currents flowing from line to neutral are considered to be positive. Fig: 3.5 Air gap flux density distribution. EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 10 Let us consider that the phase coils are full-pitch coils of N turns (the coil sides of each phase are 180 electrical degrees apart as shown in Fig.3.5). It is obvious that as the rotating field moves (or the magnetic poles rotate) the flux linkage of a coil will vary. The flux linkage for coil aa' will be maximum. Hence, Where f is the frequency in hertz. Above equation has the same form as that for the induced voltage in transformers. However, Ø represents the flux per pole of the machine. P EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 11 The above equation also shows the rms voltage per phase. The N is the total number of series turns per phase with the turns forming a concentrated full-pitch winding. In an actual AC machine each phase winding is distributed in a number of slots for better use of the iron and copper and to improve the waveform. For such a distributed winding, the EMF induced in various coils placed in different slots are not in time phase, and therefore the phasor sum of the EMF is less than their numerical sum when they are connected in series for the phase winding. A reduction factor K , W called the winding factor, must therefore be applied. For most three-phase machine windings K W is about 0.85 to 0.95. Therefore, for a distributed phase winding, the rms voltage per phase is Erms = 4.44fNφ K ph p W Where N is the number of turns in series per phase. ph 3.5 Alternate Analysis for Rotating Magnetic Field When a 3-phase winding is energized from a 3-phase supply, a rotating magnetic field is produced. This field is such that its poles do no remain in a fixed position on the stator but go on shifting their positions around the stator. For this reason, it is called a rotating Held. It can be shown that magnitude of this rotating field is constant and is equal to 1.5 m where m is the maximum flux due to any phase. To see how rotating field is produced, consider a 2-pole, 3-phase winding as shown in Fig. 3.6 (i). The three phases X, Y and Z are energized from a 3-phase source and currents in these phases are indicated as Ix, Iy and Iz See Fig. 3.6 (ii). Referring to Fig. 3.6 (ii), the fluxes produced by these currents are given by: Here φm is the maximum flux due to any phase. Above figure shows the phasor diagram of the three fluxes. We shall now prove that this 3-phase supply produces a rotating field of constant magnitude equal to 1.5 φm. At instant 1 See Fig. 3.6 (ii) and Fig. 3.6 (iii), the current in phase X is zero and currents in phases Y and Z are equal and opposite. The currents are flowing outward in the top conductors and inward EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 12 in the bottom conductors. This establishes a resultant flux towards right. The magnitude of the resultant flux is constant and is equal to 1.5 φm as proved under: So, At instant 2 Fig: 3.7 (ii), the current is maximum (negative) in φ phase Y and 0.5 maximum y (positive) in phases X and Y. The magnitude of resultant flux is 1.5 φ as proved under: m At instant 2, ωt = 30°. Therefore, the three fluxes are given by; EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 13 Fig: 3.6 At instant 3Fig: 3.7 (iii), current in phase Z is zero and the currents in phases X and Y are equal and opposite (currents in phases X and Y arc 0.866 × max. value). The magnitude of resultant flux is 1.5 φ as proved under: m EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 14 Fig: 3.7 At instant 4 Fig: 3.7 (iv), the current in phase X is maximum (positive) and the currents in phases V and Z are equal and negative (currents in phases V and Z are 0.5 × max. value). This establishes a resultant flux downward as shown under: EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 15 It follows from the above discussion that a 3-phase supply produces a rotating field of constant value (= 1.5 φ , where φ is the maximum flux due to any phase). m m 3.5.1 Speed of rotating magnetic field The speed at which the rotating magnetic field revolves is called the synchronous speed (Ns). Referring to Fig. 3.6 (ii), the time instant 4 represents the completion of one-quarter cycle of alternating current Ix from the time instant 1. During this one quarter cycle, the field has rotated through 90°. At a time instant represented by 13 Fig. 3.6 (ii) or one complete cycle of current Ix from the origin, the field has completed one revolution. Therefore, for a 2-pole stator winding, the field makes one revolution in one cycle of current. In a 4-pole stator winding, it can be shown that the rotating field makes one revolution in two cycles of current. In general, fur P poles, the rotating field makes one revolution in P/2 cycles of current. The speed of the rotating magnetic field is the same as the speed of the alternator that is supplying power to the motor if the two have the same number of poles. Hence the magnetic flux is said to rotate at synchronous speed. EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 16 3.5.2 Direction of rotating magnetic field The phase sequence of the three-phase voltage applied to the stator winding in Fig. 3.6 (ii) is X- Y-Z. If this sequence is changed to X-Z-Y, it is observed that direction of rotation of the field is reversed i.e., the field rotates counter clockwise rather than clockwise. However, the number of poles and the speed at which the magnetic field rotates remain unchanged. Thus it is necessary only to change the phase sequence in order to change the direction of rotation of the magnetic field. For a three-phase supply, this can be done by interchanging any two of the three lines. As we shall see, the rotor in a 3-phase induction motor runs in the same direction as the rotating magnetic field. Therefore, the direction of rotation of a 3-phase induction motor can be reversed by interchanging any two of the three motor supply lines. 3.5.3 Slip We have seen above that rotor rapidly accelerates in the direction of rotating field. In practice, the rotor can never reach the speed of stator flux. If it did, there would be no relative speed between the stator field and rotor conductors, no induced rotor currents and, therefore, no torque to drive the rotor. The friction and windage would immediately cause the rotor to slow down. Hence, the rotor speed (N) is always less than the suitor field speed (Ns). This difference in speed depends upon load on the motor. The difference between the synchronous speed Ns of the rotating stator field and the actual rotor speed N is called slip. It is usually expressed as a percentage of synchronous speed i.e. 3.5.4 Rotor Current Frequency The frequency of a voltage or current induced due to the relative speed between a vending and a magnetic field is given by the general formula; EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 17 (ii) As the rotor picks up speed, the relative speed between the rotating flux and the rotor decreases. Consequently, the slip s and hence rotor current frequency decreases. 3.6 Phasor Diagram of Three Phase Induction Motor In a 3-phase induction motor, the stator winding is connected to 3-phase supply and the rotor winding is short-circuited. The energy is transferred magnetically from the stator winding to the short-circuited, rotor winding. Therefore, an induction motor may be considered to be a transformer with a rotating secondary (short-circuited). The stator winding corresponds to transformer primary and the rotor finding corresponds to transformer secondary. In view of the similarity of the flux and voltage conditions to those in a transformer, one can expect that the equivalent circuit of an induction motor will be similar to that of a transformer. Fig. 3.8 shows the equivalent circuit per phase for an induction motor. Let discuss the stator and rotor circuits separately. Fig: 3.8 EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 18 Stator circuit. In the stator, the events are very similar to those in the transformer primary. The applied voltage per phase to the stator is V1 and R1and X1 are the stator resistance and leakage reactance per phase respectively. The applied voltage V1 produces a magnetic flux which links the stator winding (i.e., primary) as well as the rotor winding (i.e., secondary). As a result, self- induced e.m.f. E1 is induced in the stator winding and mutually induced e.m.f. E'2(= s E = s K E1 where K is transformation ratio) is induced in the rotor winding. The flow of 2 stator current I causes voltage drops in R and X . 1 1 1 ∴ V = −E + I (R + j X ) ...phasor sum 1 1 1 1 1 When the motor is at no-load, the stator winding draws a current I0. It has two components viz., (i) which supplies the no-load motor losses and (ii) magnetizing component Im which sets up magnetic flux in the core and the air gap. The parallel combination of Rc and Xm, therefore, represents the no-load motor losses and the production of magnetic flux respectively. ∴ I0 = Iw + Im Rotor circuit. Here R2 and X2 represent the rotor resistance and standstill rotor reactance per phase respectively. At any slip s, the rotor reactance will be X The induced voltage/phase in the 2 . rotor is E' = s E2 = s K E . Since the rotor winding is short-circuited, the whole of e.m.f. E' is 2 1 2 used up in circulating the rotor current I' . 2 ∴ E' = I' (R + j s X2) 2 2 2 The rotor current I'2 is reflected as I" (= K I' ) in the stator. The phasor sum of I" and I gives the 2 2 2 0 stator current I . 1 It is important to note that input to the primary and output from the secondary of a transformer are electrical. However, in an induction motor, the inputs to the stator and rotor are electrical but the output from the rotor is mechanical. To facilitate calculations, it is desirable and necessary to replace the mechanical load by an equivalent electrical load. We then have the transformer equivalent circuit of the induction motor. EE DEPT. Veer Surendra Sai University of Technology, Burla L e c t u r e N ot e s – E le c t r ic a l M a c h in e - I I B E E 1401 P a ge 19 Fig: 3.9 It may be noted that even though the frequencies of stator and rotor currents are different, yet the magnetic fields due to them rotate at synchronous speed Ns. The stator currents produce a magnetic flux which rotates at a speed Ns. At slip s, the speed of rotation of the rotor field relative to the rotor surface in the direction of rotation of the rotor is But the rotor is revolving at a speed of N relative to the stator core. Therefore, the speed of rotor field relative to stator core Thus no matter what the value of slip s, the stator and rotor magnetic fields are synchronous with each other when seen by an observer stationed in space. Consequently, the 3-phase induction motor can be regarded as being equivalent to a transformer having an air-gap separating the iron portions of the magnetic circuit carrying the primary and secondary windings. Fig. 3.9 shows the phasor diagram of induction motor. EE DEPT. Veer Surendra Sai University of Technology, Burla

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