Transformer and Electrical Machines PDF

Transformer and Electrical Machines Transformer A transformer is a static electromagnetic device designed for the transformation of the alternating current (from primary) into another (secondary) one of the same frequency with other characteri...

Transformer and Electrical Machines Transformer A transformer is a static electromagnetic device designed for the transformation of the alternating current (from primary) into another (secondary) one of the same frequency with other characteristics, in particulars, voltage and current. Primary and secondary windings. The transformer winding to which the energy of the alternating current is delivered is called the secondary winding; the other winding from which energy is received is called the primary winding. If the secondary voltage is less than the primary one, the transformer is called a step-down transformer and if the secondary voltage is greater than the primary one, the transformer is called a step-up transformer. WORKING PRINCIPLE OF A TRANSFORMER A transformer operates on the principle of mutual inductance. The principle of mutual induction states that, when two coils are inductively couples and if current in one coil is changed uniformly then an e.m.f. gets induced in the other coil. This e.m.f. can drive a current, when a closed path is provided to it. The transformer works on the same principle. In its elementary form, it consist of two inductive coils which are electrically separated but linked through a common magnetic circuit. The two coils have mutual inductance. It consists of two windings in close proximity as shown in Fig. 1. The two windings are coupled by magnetic induction. (There is no conductive connection between the windings). One of the windings called primary is energised by a sinusoidal voltage. The second winding, called secondary feeds the load. The alternating current in the primary winding sets up an alternating flux (ϕ) in the core. The secondary winding is linked by most of this flux and e.m.f’s are induced in the two windings. The e.m.f. induced in the secondary winding drives a current through the load connected to the winding. Energy is transferred from the primary circuit to the secondary circuit through the medium of the magnetic field. In brief, a transformer is a device that : (i) transfers electric power from one circuit to another ; (ii) it does so without change of frequency ; (iii) it accomplishes this by electromagnetic induction (or mutual inductance). TRANSFORMER CONSTRUCTION All transformers have the following essential elements : 1. Two or more electrical windings insulated from each other and from the core (except in auto-transformers). 2. A core, which in case of a single-phase distribution transformers usually comprises cold rolled silicon-steel strip. The flux path in the assembled core is parallel to the directions of steel’s grain or ‘orientation’. This results in a reduction in core losses for a given flux density and frequency, or it permits the use of higher core densities and reduced size of transformers for given core losses. Other necessary parts are : A suitable container for the assembled core and windings. A suitable medium for insulating the core and its windings from each other and from the container. Suitable bushings for insulating and bringing the terminals of the windings out of the case. The two basic types of transformer construction are: 1. The core type. 2. The shell type. The above two types differ in their relative arrangements of copper conductors and the iron cores. In the ‘core type’, the copper virtually surrounds the iron core, while in the ‘shell type’, the iron surrounds the copper winding. 1. Core Type Transformer The complete magnetic circuit of the core-type transformer is in the shape of the hollow rectangle, as shown in Fig. 2 in which I0 is the no-load current and ϕ is the flux produced by it. N1 and N2 are the number of turns on the primary and secondary sides respectively. The core is made of silicon-steel laminations, which are, either rectangular or L-shaped. With the coils wound on two legs, the appearance is that of Fig. 3. If the two coils shown were the respective high and low-side coils as in Fig. 3, the leakage reactance would be much too great. In order to provide maximum linkage between windings, the group on each leg is made of both high-tension and low- tension coils. This may be seen in Fig. 4, where a cross-sectional cut is taken across the legs of the core. By placing the high-voltage winding around the low-voltage winding, only one layer of high-voltage insulation is required, that between the two coils. If the high-voltage coils were adjacent to the core, an additional high-voltage insulation layer would be necessary between the coils and the iron core. 2. Shell Type Transformer It has double magnetic circuit. The core has three limbs. Both the windings are placed on the central limb. The core encircles most part of the windings. The coil used generally multilayer disc type or sandwich coil. Each high voltage coil is in between two low voltage coils and low voltage coils are nearest to top and bottom of yokes. The core is laminated. While arranging the lamination of the core, care is taken that all joints at alternate layers are staggered. This is done to avoid narrow air gap at the joint, such joints are called overlapped joints. Generally for very high voltage transformers, shell type is preferred. As the core surrounds the windings, natural cooling does not exists. The schematic representation and construction of shell type transformer is shown below. Theory of an Ideal Transformer An ideal transformer, is one in which the resistance of the windings is negligible, there is no magnetic leakage and the core has no losses. An ideal transformer is an imaginary transformer, which has the following characteristics −  The primary and secondary windings have negligible (or zero) resistance.  No leakage flux, i.e., whole of the flux is confined to the magnetic circuit.  The magnetic core has infinite permeability, thus negligible mmf (magneto motive force) is require to establish flux in the core.  There are no losses due to winding resistances, hysteresis and eddy currents. Hence, the efficiency is 100 %. Ideal Transformer On No Load When load is not connected across the terminals of secondary winding of the ideal transformer, the transformer is said to be on no load. Let the secondary be open (Fig. 15), and let a sine wave of potential difference V 1 (Fig. 16) be applied to the primary. The potential difference causes an alternating current to flow in the primary winding. Since the primary resistance is negligible and there are no losses in the core, the effective resistance is zero and the circuit is purely reactive. Hence the current wave I m lags the applied voltage wave V1 by 90 degrees, as shown in Fig. 17. The reactance of circuit is very high and the magnetizing current is very small. This current in the N1 turns of the primary magnetizes the core and produces a flux ϕ that is at all times proportional to the current, and therefore in time phase with the current. The flux, by its rate of change, induces in the primary winding E1 which, at every instant of time is equal in value and opposite in direction to V1. It is called counter e.m.f. of the primary. The value attains by the primary current, must be such that the flux produced in the core is of sufficient value to induce in the primary the required counter e.m.f. Since the flux also links the secondary winding a voltage e2 is induced in the secondary. This voltage is proportional to the rate of change of flux and so is in time phase with e 1, but it may have any value depending upon the number of turns N2 in the secondary. Ideal Transformer On-Load When load is connected across the terminals of secondary winding of the ideal transformer, the transformer is said to be loaded and a load current flows through the secondary winding and the load. Circuit diagram On-Load condition Phasor Diagram. Consider an inductive load of impedance ZL is connected across the secondary winding of the ideal transformer (see the figure above). Then, the secondary EMF E2 will cause a current I2 to flow through the secondary winding and the load, which is given by, Since, for an ideal transformer, the EMF E2 is equal to secondary terminal voltage V2. Here, the load is inductive, therefore, the current I2 will lag behind the E2 (or V2) by an angle ϕ2. Also, the no-load current I0 being neglected because the transformer is ideal one. The current flowing in the secondary winding (I2) sets up an mmf (N2I2) which produces a flux ϕ2 in opposite direction to the main flux (ϕm). As a result, the total flux in the core changes from its original value, however, the flux in the core should not changes from its original value. Therefore, to maintain the flux in the core at its original value, the primary current must develop an mmf which can counter-balance the demagnetizing effect of the secondary mmf N2I2. Hence, the primary current I1 must flow such that, Therefore, the primary winding must draw enough current to neutralise the demagnetising effect of the secondary current so that the main flux in the core remains constant. Hence, when the secondary current (I2) increases, the primary current (I1) also increases in the same manner and keeps the mutual flux (ϕm) constant. It is clear from the phasor diagram of the ideal transformer on-load that the secondary current I 2 lags behind the secondary terminal voltage V2 by an angle of ϕ2. Practical Transformer A practical transformer is the one which has following properties −  The primary and secondary windings have finite resistance.  There is a leakage flux, i.e., whole of the flux is not confined to the magnetic circuit.  The magnetic core has finite permeability, thus a considerable amount of mmf is require to establish flux in the core.  There are losses in the transformer due to winding resistances, hysteresis and eddy currents. Therefore, the efficiency of a practical transformer is less than 100 %. The figure shows a typical practical transformer, which possess all the characteristics that are described above.  Ideal Transformer Practical Transformer It has 100% efficiency. It has 100% below efficiency. It has no losses. It has losses. Purely inductive material is used. It is too purely inductive material used. It has no I2R losses. It has I2R losses. It has no iron loss. It has iron loss. There is no ohmic resistance drop. There is ohmic resistance drop. It has no leakage drop. It has leakage drop. In it ideal condition. In it practical condition. It is not used in practical condition. It is used in practical condition. E.M.F. Equation of a Transformer Equivalent Circuit of Transformer In transformers, the problems concerning voltages and currents can be solved by the use of phasor diagrams. However, it is more convenient to represent the transformer by an equivalent circuit. If an equivalent circuit is available the computations can be done by the direct application of circuit theory. An equivalent circuit is merely a circuit interpretation of the equations which describe the behaviour of the device. The transformer windings, in the equivalent circuit, are shown as ideal. The resistance and leakage reactance of the primary and secondary are shown separately in the primary and secondary circuits. The effect of magnetising current is represented by X0 connected in parallel across the winding. The effect of core loss is represented by a non-inductive resistance R 0 as shown in Fig. 35. Losses in Transformer, regulation and efficiency Losses in a Practical Transformer The different losses in the transformer are as follows Copper Losses (Winding Resistance) Current flowing through the windings causes resistive heating of the conductors. At higher frequencies, skin effect and proximity effect create additional winding resistance and losses. Core or Iron Losses There are two types of core or iron losses in a Transformer. a) Hysteresis Losses Power losses due to repeated change in magnetic polarity. Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core. For a given core material, the transformer losses are proportional to the frequency, and is a function of the peak flux density to which it is subjected. b) Eddy Current Losses AC current induced in iron core due to changing magnetic field. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness. Eddy current losses can be reduced by making the core of a stack of plates electrically insulated from each other, rather than a solid block; all transformers operating at low frequencies using laminated or similar cores. Eddy currents therefore circulate within the core in a plane normal to the flux, and are responsible for resistive heating of the core material. Stray losses (leakage Flux) Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer’s support structure will give rise to eddy currents and be converted to heat. There are also radiative losses due to the oscillating magnetic field, but these are usually small and negligible. Dielectric Loss In the solid insulation or transformer oil i.e. insulation material of the transformer, dielectric loss occurs when the solid insulation get damaged or the oil gets deteriorated or its quality decreases over the time. Hence, the overall efficiency of transformer may be affected due to this loss.  Electrical Machines DC Motor DC motors convert electrical energy into mechanical energy. This conversion of energy is based on the principle of the production of dynamically induced electromotive force (emf). The DC motors are very useful where wide range of speeds and perfect speed regulation is required such as electric traction. Electric motors are used for driving industrial machines, e.g., hammers, presses, drilling machines, lathes, rollers in paper and steel industry, blowers for furnaces, etc., and domestic appliances, e.g., refrigerators, fans, water pumps, toys, mixers, etc. The block diagram of energy conversion, when the electro-mechanical device works as a motor, is shown in Fig. 5.1. Principle of D.C. Motor A machine that converts d.c. power into mechanical power is known as a d.c. motor. Its operation is based on the principle that when a current carrying conductor is placed in a magnetic field, the conductor experiences a mechanical force. The direction of this force is given by Fleming’s left hand rule and magnitude is given by; F=BIl newtons F- Force. B- flux density. I- current flowing through conductor. l- Length of conductor. When the electric current passes through a coil in a magnetic field, a magnetic force will be generated, this produces a torque in the DC motor. Construction of DC motor A DC motor or machine consists of two windings namely field winding and armature winding. The field winding is stationary and the armature winding can rotate. The field winding produces a magnetic flux in the air gap between the armature and field windings and the armature is placed in this magnetic field. The construction of DC motor or machine is shown in the following Figure. The main parts used in the construction of DC motor are the yoke, poles, field winding, commutator, carbon brushes bearings, etc. A brief description of the various parts is as follows:  DC Motor ANY ONE DIAGRAM FROM ABOVE 1.Yoke: The yoke acts as the outer cover of a DC motor and it is also known as the frame. The yoke is an iron body, made up of low reluctance magnetic material such as cast iron, silicon steel, rolled steel, etc. Yoke serves two purposes, firstly it provides mechanical protection to the outer parts of the machine secondly it provides a low reluctance path for the magnetic flux. 2. Poles and Pole Shoe: The pole and pole shoe are fixed on the yoke by bolts. These are made of thin cast steel or wrought iron laminations that are riveted together. Poles produce the magnetic flux when the field winding is excited. A Pole shoe is an extended part of a pole. Due to its shape, the pole area is enlarged and more flux can pass through the air gap to the armature. 3. Field Winding: The coils around the poles are known as field (or exciting) coils and are connected in series to form the field winding. Copper wire is used for the construction of field coils. When the DC is passed through the field windings, it magnetizes poles that produce magnetic flux. The connection of the field winding and the armature winding is done according to the type of the motor and decides the characteristics of the motor. 4. Armature Core: It is a cylindrical drum and keyed to the rotating shaft. A large number of slots are made all over its periphery, which accommodates the armature winding. Low reluctance, high permeability material such as silicon steel is used for armature core. The laminated construction is used to produce the armature core to minimize the eddy current losses. The air holes are also provided on the armature core for the air circulation which helps in cooling the motor. 5. Armature Winding: The armature winding plays a very important role in the construction of a DC motor because the conversion of power takes place in the armature winding. Based on connections, there are two types of armature windings named:  Wave Winding: In wave winding, all the armature coils are connected in series through commutator segments in such a way that the whole armature winding is divided into two parallel paths.  Lap Winding: In lap winding the armature conductors are divided into the groups equal to the number of poles of the motor. All the conductors in each group are connected in series and all such groups are connected in parallel. 6. Commutator: It is mounted on the shaft. It is made up of a large number of wedge-shaped segments of hard drawn copper, insulated from each other by a thin layer of mica. The commutator connects the rotating armature conductor to the stationary external circuit through carbon brushes. It converts alternating torque into unidirectional torque produced in the armature. 7. Carbon Brushes: The current is conducted from the voltage source to the armature by the carbon brushes which are held against the surface of the commutator by springs. They are made of high-grade carbon steel and are rectangular. 8. Bearings: The ball or roller bearings are fitted in the end housings. The friction between stationary and rotating parts of the motor is reduced by bearing. Mostly high carbon steel is used for making the bearings as it is a very hard material. 9. Interpoles: The brushes on the commutator short-circuit the armature coils when they are slipping from one commutator segment to the next. At this instant, EMF induced in those particular coils should be zero otherwise this EMF will create sparking on the commutator due to short-circuit. This is achieved by placing the carbon brushes at the MNA. (MNA is defined magnetic neutral axis, as the axis at the right angle to the main flux where armature conductors do not have any EMF in them). Working Principle of DC Motors The operation of a DC motor is based on the principle that when a current carrying conductor is placed in a magnetic field, a mechanical force is experienced by it. The direction of this force is determined by Fleming’s Left Hand Rule and its magnitude is given by the relation: F = Bil newton For simplicity, consider only one coil of the armature placed in the magnetic field produced by a bipolar machine [see Fig. 5.2(a)]. When DC supply is connected to the coil, current flows through it which sets up its own field as shown in Fig. 5.2(b). By the interaction of the two fields (i.e., field produced by the main poles and the coil), a resultant field is set up as shown in Fig. 5.2(c). The tendency of this is to come to its original position i.e., in straight line due to which force is exerted on the two coil sides and torque develops which rotates the coil. Alternately, it can be said that the main poles produce a field Fm. Its direction is marked in Fig.5.3. When current is supplied to the coil (armature conductors), it produces its own field marked as Fr. This field tries to come in line with the main field and an electromagnetic torque develops in clockwise direction as marked in Fig. 5.3. It can be seen that to obtain a continuous torque, the direction of flow of current in each conductor or coil side must be reversed when it passes through the magnetic neutral axis (MNA). This is achieved with the help of a commutator. The function of a commutator in DC motors is to reverse the direction of flow of current in each armature conductor when it passes through the M.N.A. to obtain continuous torque. Back or Counter E.M.F. (Eb) When the armature of a d.c. motor rotates under the influence of the driving torque, the armature conductors move through the magnetic field and hence e.m.f. is induced in them. The induced e.m.f. acts in opposite direction to the applied voltage V(Lenz’s law) and in known as back or counter e.m.f. Eb. Eb= ( P Z ∅N/60 A) Eb – Back e.m.f. P - number of poles. N is the speed. A - number of parallel paths through the armature between the brushes of opposite polarity. Z is the total number of conductors in the armature and ϕ is the useful flux per pole. The back e.m.f. is always less than the applied voltage V, although this difference is small when the motor is running under normal conditions. A conventional circuit diagram of the machine working as motor, is shown in Fig. 5.6. In this case, the supply voltage is always greater than the induced or back emf (i.e., V > Eb). Therefore, current is always supplied to the motor from the mains and the relation among the various quantities will be; Eb = V – Ia Ra.  V applied voltage. Ra is the armature resistance. Ia is the armature current. Significance of Back emf The current flowing through the armature is given by the relation: When mechanical load applied on the motor increases, its speed decreases which reduces the value of Eb. As a result the value (V – Eb) increases which consequently increases Ia. Hence, motor draws extra current from the mains. Thus, the back emf regulates the input power as per the extra load. Voltage Equation of D.C. Motor Let in a d.c. motor V = applied voltage. Eb = back e.m.f. Ra = armature resistance. Ia = armature current Since back e.m.f. Eb acts in opposition to the applied voltage V, the net voltage across the armature circuit is V- Eb. The armature current Ia is given by; This is known as voltage equation of the d.c. motor. Types of DC Motors There are two types of d.c. motors characterized by the connections of field winding in relation to the armature viz.: 1. Separately excited DC motors: The supply is given separately to the field and armature windings. The conventional diagram of a separately excited DC motor is shown figure below. Its voltage equation will be; Eb = V – Ia Ra – 2Vb (where Vb is voltage drop per brush).  Separately excited DC motors 2. Self excited DC motors: In the Self Excited DC Motors, the field winding is linked to the armature winding in series, parallel, partly in series, or partly in parallel. These motors can be further classified as; (i) Shunt-wound motor in which the field winding is connected in parallel with the armature [See Fig. 4.4]. The current through the shunt field winding is not the same as the armature current. Shunt field windings are designed to produce the necessary m.m.f. by means of a relatively large number of turns of wire having high resistance. Therefore, shunt field current is relatively small compared with the armature current. (ii) Series-wound motor in which the field winding is connected in series with the armature [See Fig. 4.5]. Therefore, series field winding carries the armature current. Since the current passing through a series field winding is the same as the armature current, series field windings must be designed with much fewer turns than shunt field windings for the same m.m.f. Therefore, a series field winding has a relatively small number of turns of thick wire and, therefore, will possess a low resistance. (iii) Compound-wound motor which has two field windings; one connected in parallel with the armature and the other in series with it. There are two types of compound motor connections (like generators). When the shunt field winding is directly connected across the armature terminals [See Fig. 4.6], it is called short-shunt connection. When the shunt winding is so connected that it shunts the series combination of armature and series field [See Fig. 4.7], it is called long-shunt connection.  Induction Motor 3-ϕ Induction Motor General Principle As a general rule, conversion of electrical power into mechanical power takes place in the rotating part of an electric motor. In d.c. motors, the electric power is conducted directly to the armature (i.e. rotating part) through brushes and commutator. Hence, in this sense, a d.c. motor can be called a conduction motor. However, in a.c. motors, the rotor does not receive electric power by conduction but by induction in exactly the same way as the secondary of a 2-winding transformer receives its power from the primary. That is why such motors are known as induction motors. In fact, an induction motor can be treated as a rotating transformer i.e. one in which primary winding is stationary but the secondary is free to rotate. Of all the a.c. motors, the polyphase induction motor is the one which is extensively used for various kinds of industrial drives. It has the following main advantages and also some dis-advantages: Advantages: 1. It has very simple and extremely rugged, almost unbreakable construction (especially squirrel cage type). 2. Its cost is low and it is very reliable. 3. It has sufficiently high efficiency. In normal running condition, no brushes are needed, hence frictional losses are reduced. It has a reasonably good power factor. 4. It requires minimum of maintenance. 5. It starts up from rest and needs no extra starting motor and has not to be synchronised. Its starting arrangement is simple especially for squirrel-cage type motor. Disadvantages: 1. Its speed cannot be varied without sacrificing some of its efficiency. 2. Just like a d.c. shunt motor, its speed decreases with increase in load. 3. Its starting torque is somewhat inferior to that of a d.c. shunt motor. Construction A 3-phase induction motor has two main parts (i) stator and (ii) rotor. The rotor is separated from the stator by a small air- gap which ranges from 0.4 mm to 4 mm, depending on the power of the motor. 1. Stator: It consists of a steel frame which encloses a hollow, cylindrical core made up of thin laminations of silicon steel to reduce hysteresis and eddy current losses. A number of evenly spaced slots are provided on the inner periphery of the laminations [Fig. (8.1)]. The insulated connected to form a balanced 3-phase star or delta connected circuit. The 3-phase stator winding is wound for a definite number of poles as per requirement of speed. Greater the number of poles, lesser is the speed of the motor and vice-versa. When 3-phase supply is given to the stator winding, a rotating magnetic field of constant magnitude is produced. This rotating field induces currents in the rotor by electromagnetic induction. 2. Rotor The rotor, mounted on a shaft, is a hollow laminated core having slots on its outer periphery. The winding placed in these slots (called rotor winding) may be one of the following two types: (i) Squirrel cage type (ii) Wound type. (i) Squirrel cage rotor. It consists of a laminated cylindrical core having parallel slots on its outer periphery. One copper or aluminum bar is placed in each slot. All these bars are joined at each end by metal rings called end rings [Fig. (8.2)]. This forms a permanently short-circuited winding which is indestructible. The entire construction (bars and end rings) resembles a squirrel cage and hence the name. The rotor is not connected electrically to the supply but has current induced in it by transformer action from the stator. Those induction motors which employ squirrel cage rotor are called squirrel cage induction motors. Most of 3-phase induction motors use squirrel cage rotor as it has a remarkably simple and robust construction enabling it to operate in the most adverse circumstances. However, it suffers from the disadvantage of a low starting torque. It is because the rotor bars are permanently short-circuited and it is not possible to add any external resistance to the rotor circuit to have a large starting torque.  Squirrel Cage rotor. (ii) Wound rotor or Slip Ring Rotor The slip ring rotor consists of a laminated cylindrical armature core. The slots are provided on the outer periphery and insulated conductors are put in the slots. The rotor conductors are connected to form a 3-phase double layer distributed winding similar to the stator winding. The rotor windings are connected in star fashion (see the figure). The open ends of the star circuit are taken outside the rotor and connected to three insulated slip rings. The slip rings are mounted on the rotor shaft with brushes resting on them. The brushes are connected to three variable resistors which are also connected in star. Here, the slip rings and brushes are used to provide a mean for connecting external resistors in the rotor circuit. The equivalent circuit of the wound rotor is shown in the figure below. Principle of Operation Consider a portion of 3-phase induction motor as shown in Fig. (8.13). The operation of the motor can be explained as under: (i) When 3-phase stator winding is energized from a 3-phase supply, a rotating magnetic field is set up which rotates round the stator at synchronous speed Ns (= 120 f/P). (ii) The rotating field passes through the air gap and cuts the rotor conductors, which as yet, are stationary. Due to the relative speed between the rotating flux and the stationary rotor, e.m.f.’s are induced in the rotor conductors. Since the rotor circuit is short-circuited, currents start flowing in the rotor conductors. (iii) The current-carrying rotor conductors are placed in the magnetic field produced by the stator. Consequently, mechanical force acts on the rotor conductors. The sum of the mechanical forces on all the rotor conductors produces a torque which tends to move the rotor in the same direction as the rotating field. (iv) The fact that rotor is urged to follow the stator field (i.e., rotor moves in the direction of stator field) can be explained by Lenz’s law. According to this law, the direction of rotor currents will be such that they tend to oppose the cause producing them. Now, the cause producing the rotor currents is the relative speed between the rotating field and the stationary rotor conductors. Hence to reduce this relative speed, the rotor starts running in the same direction as that of stator field and tries to catch it. Slip In practice, the rotor never succeeds in ‘catching up’ with the stator field. If it really did so, then there would be no relative speed between the two, hence no rotor e.m.f., no rotor current and so no torque to maintain rotation. That is why the rotor runs at a speed which is always less than the speed of the stator field. The difference in speeds depends upon the load on the motor. The difference between the synchronous speed Ns and the actual speed N of the rotor is known as slip. Though it may be expressed in so many revolutions/second, yet it is usual to express it as a percentage of the synchronous speed. Actually, the term ‘slip’ is descriptive of the way in which the rotor ‘slips back’ from synchronism. Sometimes, Ns− N is called the slip speed. Obviously, rotor (or motor) speed is N = Ns (1 − s). It may be kept in mind that revolving flux is rotating synchronously, relative to the stator (i.e. stationary space) but at slip speed relative to the rotor. 1-ϕ Induction Motor A single phase induction motor is very similar to a 3-phase squirrel cage induction motor. It has (i) a squirrel-cage rotor identical to a 3-phase motor and (ii) a single-phase winding on the stator. Unlike a 3-phase induction motor, a single- phase induction motor is not self starting but requires some starting means. The single-phase stator winding produces a magnetic field that pulsates in strength in a sinusoidal manner. The field polarity reverses after each half cycle but the field does not rotate. Consequently, the alternating flux cannot produce rotation in a stationary squirrel-cage rotor. However, if the rotor of a single-phase motor is rotated in one direction by some mechanical means, it will continue to run in the direction of rotation. As a matter of fact, the rotor quickly accelerates until it reaches a speed slightly below the synchronous speed. Once the motor is running at this speed, it will continue to rotate even though single-phase current is flowing through the stator winding. This method of starting is generally not convenient for large motors. Nor can it be employed fur a motor located at some inaccessible spot. Fig. (9.1) shows single-phase induction motor having a squirrel cage rotor and a single phase distributed stator winding. Such a motor inherently docs not develop any starting torque and, therefore, will not start to rotate if the stator winding is connected to single-phase a.c. supply. However, if the rotor is started by auxiliary means, the motor will quickly attain me final speed. This strange behavior of single-phase induction motor can be explained on the basis of double-field revolving theory. Construction of Single Phase Induction Motor Like any other electrical motor it also have two main parts namely rotor and stator. Stator: As its name indicates stator is a stationary part of induction motor. A single phase AC supply is given to the stator of single phase induction motor. The stator core carries the stator windings connected across a single phase ac supply which produces a rotating magnetic field. The stator of the single-phase induction motor has laminated stamping to reduce eddy current losses on its periphery. The slots are provided on its stamping to carry stator or main winding. Stampings are made up of silicon steel to reduce the hysteresis losses. When we apply a single phase AC supply to the stator winding, the magnetic field gets produced, and the motor rotates at speed slightly less than the synchronous speed N s. Synchronous speed Ns is given by Where, f = supply voltage frequency, P = No. of poles of the motor. The construction of the stator of the single-phase induction motor is similar to that of three phase induction motor except there are two dissimilarities in the winding part of the single phase induction motor. 1. Firstly, the single-phase induction motors are mostly provided with concentric coils. We can easily adjust the number of turns per coil can with the help of concentric coils. The m.m.f. (magneto motive force) distribution is almost sinusoidal. 2. Except for shaded pole motor, the asynchronous motor has two stator windings namely the main winding and the auxiliary winding. These two windings are placed in space quadrature to each other. Rotor: The rotor is a rotating part of an induction motor. The rotor connects the mechanical load through the shaft. The rotor in the single-phase induction motor is of squirrel cage rotor type. The rotor has aluminium or copper bars which are permanently circuited at both ends by conducting end rings. The construction of the rotor of the single-phase induction motor is similar to the squirrel cage three-phase induction motor. The rotor is cylindrical and has slots all over its periphery. The slots are not made parallel to each other but are a little bit skewed as the skewing prevents magnetic locking of stator and rotor teeth and makes the working of induction motor more smooth and quieter (i.e. less noisy). The squirrel cage rotor consists of aluminum, brass or copper bars. These aluminum or copper bars are called rotor conductors and placed in the slots on the periphery of the rotor. The copper or aluminum rings permanently short the rotor conductors called the end rings. To provide mechanical strength, these rotor conductors are braced to the end ring and hence form a complete closed circuit resembling a cage and hence got its name as squirrel cage induction motor. As end rings permanently short the bars, the rotor electrical resistance is very small and it is not possible to add external resistance as the bars get permanently shorted. The absence of slip ring and brushes make the construction of single phase induction motor very simple and robust. The construction of single phase induction motor is almost similar to the squirrel cage three-phase induction motor. But in case of a single phase induction motor, the stator has two windings instead of one three-phase winding in three phase induction motor. Working Principle of Single Phase Induction Motor We know that for the working of any electrical motor whether its AC or DC motor, we require two fluxes as the interaction of these two fluxes produced the required torque. When we apply a single phase AC supply to the stator winding of single phase induction motor, the alternating current starts flowing through the stator or main winding. This alternating current produces an alternating flux called main flux. This main flux also links with the rotor conductors and hence cut the rotor conductors. According to the Faraday’s law of electromagnetic induction, emf gets induced in the rotor. As the rotor circuit is closed one so, the current starts flowing in the rotor. This current is called the rotor current. This rotor current produces its flux called rotor flux. Since this flux is produced due to the induction principle so, the motor working on this principle got its name as an induction motor. Now there are two fluxes one is main flux, and another is called rotor flux. These two fluxes produce the desired torque which is required by the motor to rotate. Comparison between Single Phase and Three Phase Induction Motors Characteristics Single Phase induction Motor Three Phase Induction Motor Power Source Single Phase (1-phase) Only. Generally requires more than a single phase power source (like 3-phase supply). Starting Mechanism They are NOT self-starting. They are self-starting. Efficiency Low as only one winding has to carry all the High because three winding are available to carry current. the current Types Shaded pole. Split Phase. Squirrel cage type. Capacitor Start Inductor Run. Slip ring type or wound induction motor. Capacitor Start Capacitor Run. Cost Cheaper. Quite Expensive. Slip (s) There are two slips: It has only forward slip 1. Forward slip (s). 2. Backward slip (2-s) Size (for same power Larger in size. Smaller in size. rating) Power Factor Low. High. Repair & Maintenance Easier to repair. Difficult to repair and maintain. Structure Simple and easy to manufacture. More complicated to construct because of extra components involvement. Starting Torque Low. High. Operational Reliability More Reliable. Less Reliable. Motor Rotation There is no mechanism to change the rotation. Can be changed easily by changing the phase sequence in stator. Uses Frequently used for lighter loads. Blowers. Extensively employed in industrial and commercial Vacuum cleaner fans. Centrifugal pump. drives since they are more rugged and economical Washing machine. Grinder. Compressor. in terms of operational efficiency.