Three-Phase Induction Motor PDF

Three-Phase Induction Motor An electrical motor is an electromechanical device that converts electrical energy into mechanical energy. In the case of three-phase AC (Alternating Current) operation, the most widely used motor is a 3 phase induction motor, as this type...

Three-Phase Induction Motor An electrical motor is an electromechanical device that converts electrical energy into mechanical energy. In the case of three-phase AC (Alternating Current) operation, the most widely used motor is a 3 phase induction motor, as this type of motor does not require an additional starting device. These types of motors are known as self-starting induction motors. GENERATION OF ROTATING MAGNETIC FIELD Let the three-phase winding in the stator core is physically distributed in such a manner that winding of each phase is separated from other by 120o in space. Although the vector sum of three currents in a balanced three-phase system is zero at any instant, but the resultant of the magnetic fields produced by the currents is not zero rather it will have a constant non- zero value rotating in space in respect to time. The magnetic flux produced by the current in each phase can be represented by the equations given below. This is a similar representation of current is a three-phase system as the flux is cophasial with the current. Where, φR, φY and φB are the instantaneous flux of corresponding Red, Yellow and Blue phase winding, φm amplitude of the flux wave. The flux wave in the space can be represented as shown below. Now, on the above graphical representation of flux waves, we will first consider the point 0. Here, the value of φR is The value of φY is The value of φB is The resultant of these fluxes at that instant (φ r) is 1.5φm which is shown in the figure below. Now, on the above graphical representation of flux waves, we will consider the point 1, where ωt = π / 6 or 30o. Here, the value of φR is The value of φY is The value of φB is The resultant of these fluxes at that instant (φr) is 1.5φ m which is shown in the figure below. Here it is clear that the resultant flux vector is rotated 30o further clockwise without changing its value. Now, on the graphical representation of flux waves, we will consider the point 2, where ωt = π / 3 or 60o. Here, the value of φR is The value of φY is The value of φB is The resultant of these fluxes at that instant (φ r) is 1.5φ m which is shown in the figure below. Here it is clear that the resultant flux vector is rotated 30° further clockwise without changing its value. In this way we can prove that the due to balanced supply applied to the three phase stator winding a rotating or revolving magnetic fields is established in the space. CONSTRUCTION OF 3-PHASE INDUCTION MOTOR A 3-phase induction motor is constructed from two main parts, namely the rotor and stator: 1. Stator: As its name indicates stator is a stationary part of induction motor. A stator winding is placed in the stator of induction motor and the three phase supply is given to it. The stator of the three-phase induction motor consists of three main parts : Stator frame: It is the outer part of the three phase induction motor. Its main function is to support the stator core and the field winding. It acts as a covering, and it provides protection and mechanical strength to all the inner parts of the induction motor. Stator core: The main function of the stator core is to carry the alternating flux. In order to reduce the eddy current loss, the stator core is laminated. Stator winding or field winding: The slots on the periphery of the stator core of the three-phase induction motor carry three phase windings. We apply three phase ac supply to this three-phase winding. The three phases of the winding are connected either in star or delta depending upon which type of starting method we use. We start the squirrel cage motor mostly with star-delta starter and hence the stator of squirrel cage motor is delta connected. We start the slip ring three- phase induction motor by inserting resistances so, the stator winding of slip ring induction motor can be connected either in star or delta. The winding wound on the stator of three phase induction motor is also called field winding, and when this winding is excited by three phase ac supply, it produces a rotating magnetic field. 2. Rotor: The rotor is a rotating part of induction motor. The rotor is connected to the mechanical load through the shaft. The rotor of the three phase induction motor are further classified as Squirrel cage rotor Slip ring rotor or wound rotor or phase wound rotor. Squirrel cage rotor: The squirrel cage rotor consists of a cylindrical laminated core having slots on its outer periphery which are nearly parallel to the shaft axis or skewed. An uninsulated copper or aluminium bar (rotor conductor) is placed in each slot. At each end of the rotor, the rotor bar conductors are short-circuited by heavy end rings of the same material. This forms a permanently short circuited winding which is indestructible. This entire arrangement resembles a cage which was once commonly used for keeping squirrels and hence the name. This rotor is not connected electrically to the supply but has currents induced in it by the electromagnetic induction from the stator. Those 3-phase induction motors which employed squirrel cage rotor are known as squirrel cage induction motors. Most of the 3-phase induction motors in the industries use squirrel cage rotor because it has simple and robust construction enabling it to operate in the most adverse environment. Although, it suffers from a disadvantage of low starting torque. Advantages − The noise is reduced during operation. More uniform torque is produced. The cogging or magnetic locking tendency of the rotor is reduced. During cogging, the rotor and stator teeth locked with each other due to magnetic action. Slip ring rotor: In this type of three phase induction motor the rotor is wound for the same number of poles as that of the stator, but it has less number of slots and has fewer turns per phase of a heavier conductor. The rotor also carries star or delta winding similar to that of the stator winding. The rotor consists of numbers of slots and rotor winding are placed inside these slots. The three end terminals are connected together to form a star connection. As its name indicates, three phase slip ring induction motor consists of slip rings connected on the same shaft as that of the rotor. The three ends of three-phase windings are permanently connected to these slip rings. The external resistance can be easily connected through the brushes and slip rings and hence used for speed controlling and improving the starting torque of three phase induction motor. The brushes are used to carry current to and from the rotor winding. These brushes are further connected to three phase star connected resistances. An electrical diagram of a slip ring three phase induction motor is shown below: At starting, the resistance is connected to the rotor circuit and is gradually cut out as the rotor pick up its speed. When the motor is running the slip ring are shorted by connecting a metal collar, which connects all slip ring together, and the brushes are also removed. This reduces the wear and tear of the brushes. Due to the presence of slip rings and brushes the rotor construction becomes somewhat complicated therefore it is less used as compare to squirrel cage induction motor. Advantages - 1. It has high starting torque and low starting current. 2. Possibility of adding additional resistance to control speed. WORKING PRINCIPLE The stator of the motor consists of overlapping winding offset by an electrical angle of 120o. When we connect the primary winding, or the stator to a 3 phase AC source, it establishes rotating magnetic field which rotates at the synchronous speed. According to Faraday’s law an emf induced in any circuit is due to the rate of change of magnetic flux linkage through the circuit. As the rotor winding in an induction motor are either closed through an external resistance or directly shorted by end ring, and cut the stator rotating magnetic field, an emf is induced in the rotor copper bar and due to this emf a current flows through the rotor conductor. Here the relative speed between the rotating flux and static rotor conductor is the cause of current generation; hence as per Lenz’s law, the rotor will rotate in the same direction to reduce the cause, i.e., the relative velocity. But the rotor speed should not reach the synchronous speed produced by the stator. If the speeds become equal, there would be no such relative speed, so no emf induced in the rotor, and no current would be flowing, and therefore no torque would be generated. Consequently, the rotor cannot reach the synchronous speed. The difference between the stator (synchronous speed) and rotor speeds is called the slip. The rotation of the magnetic field in an induction motor has the advantage that no electrical connections need to be made to the rotor. Thus the three phase induction motor is: Self-starting. Robust in construction. Economical. Easier to maintain. Synchronous Speed In an induction motor, the speed at which the rotating magnetic field (RMF) rotates is known as synchronous speed (NS). The value of the synchronous speed depends upon the number of stator poles (P) in the motor and the supply frequency (f). Therefore, for a given motor of P-poles, the synchronous speed is, Slip in Induction Motor An induction motor cannot run at synchronous speed. If it runs at synchronous speed, there would be no cutting of the flux by the rotor conductors and there would be no induced EMF, no current and no torque. Therefore, the rotor of the induction motor rotates at a speed slightly less than the synchronous speed. For this reason, an induction motor is also known as asynchronous motor. The difference between the synchronous speed and the actual rotor speed is known as slip speed, i.e., Where, Nr is the actual rotor speed. Generally, the slip speed is expressed as a fraction of the synchronous speed is called the per-unit slip. The per-unit slip is usually called the slip and denoted by ‘s’. Thus, 3-Phase Induction Motor Rotor Frequency, EMF, Current and Power Factor Rotor Current Frequency The frequency of current and voltage in the stator of a 3-phase induction motor must be same as the supply frequency and is given by, But, the frequency of the current and EMF in the rotor circuit of the 3-phase induction motor is variable and depends upon the difference between the synchronous speed (NS) and the rotor speed (Nr), i.e., on the slip. Thus, the rotor frequency is given by, Now, from the equations (1) and (2), we get, Hence, when the rotor is stationary, the frequency (fr) of the rotor current is the same as that of the supply frequency (f). When the rotor picks up speed, the relative speed between the rotating magnetic field and the rotor decreases. As a result of this, the slip (s) and hence the rotor current frequency decreases. At synchronous speed, i.e., Nr = NS, the frequency (fr) of the rotor current = 0 Rotor EMF When the rotor is stationary, the 3-phase induction motor behaves as a 3-phase transformer with secondary winding short circuited. Thus, the per phase induced EMF in the rotor (or secondary) is given by, Where, E1 = Per phase stator voltage. N1 = Number of turns in stator winding per phase. N2 = Number of turns in rotor winding per phase. When the rotor is running at slip ‘s’, then the relative speed between the rotating magnetic field of the stator and the rotor is (NS – Nr). Therefore, the rotor EMF is directly proportional to the (NS – Nr) or slip (s), i.e. Rotor EMF at slip s, E2′ = sKE1 = sE2... (4) Phase Rotor Current and Power Factor Consider a 3-phase induction motor at any slip value ‘s’ as shown in the figure below. Here, the rotor is assumed to be wound rotor and is connected in star. Therefore, Where, X2 is the rotor reactance per phase at standstill condition. The resistance of the rotor circuit is R2 per phase and is independent of the frequency and hence does not depend upon slip. Similarly, the resistance (R1) and reactance (X1) of the stator winding do not depend upon slip. Since the 3-phase induction represents a balanced 3-phase load, then we need to analyze one phase only and the conditions in the other two phases being similar. Case 1 – When the rotor is stationary When the rotor is stationary, the motor is at standstill (slip, s = 1) Case 2 – When the motor is running at slip ‘s’ Torque Equation of Three Phase Induction Motor The torque produced by three phase induction motor is proportional to flux per stator pole, rotor current and the power factor of the rotor. Combining all these factors, we get the equation of torque as- 𝑇 ∝ 𝜑𝐼2 cos 𝜃2 Where, T is the torque produced by the induction motor, φ is flux responsible for producing induced emf, I2 is rotor current, cosθ2 is the power factor of rotor circuit. The flux φ produced by the stator is proportional to stator emf E 1. i.e. φ ∝ E1 We know that transformation ratio K is defined as the ratio of secondary voltage (rotor voltage) to that of primary voltage (stator voltage). Rotor current I2 is defined as the ratio of rotor induced emf under running condition , sE2 to total impedance, Z2 of rotor side, and total impedance Z2 on rotor side is given by, Putting this value in above equation we get, Now the power factor is defined as ratio of resistance to that of impedance. The power factor of the rotor circuit is Putting the value of flux φ, rotor current I2, power factor cosθ2 in the equation of torque we get, Removing proportionality constant we get, Where, ns is synchronous speed in r. p. s, ns = Ns / 60. So, finally the equation of torque becomes, Torque Slip Characteristics of 3-Phase Induction Motor The graph plotted between the torque and slip for a particular value of rotor resistance and reactance is known as torque-slip characteristics of the induction motor. The torque of a 3-phase induction motor under running conditions is given by, From the eqn. (1), it can be seen that if R2 and X2 are kept constant, the torque depends upon the slip 's'. The torque-slip characteristics curve can be divided into three regions, viz. Low-slip region Medium-slip region High-slip region Low-Slip Region At synchronous speed, the slip s = 0, thus, the torque is 0. When the speed is very near to the synchronous speed, the slip is very low and the term (𝑠𝑋2)2 is negligible in comparison with R2. Therefore, If R2 is constant, then Eqn. (2) shows that the torque is proportional to the slip. Hence, when the slip is small, the torque-slip curve is straight line. Medium-Slip Region When the slip increases, the term (𝑠𝑋2)2 becomes large so that 𝑅22 may be neglected in comparison with (𝑠𝑋2)2. Therefore, If X2 is constant, then Thus, the torque is inversely proportional to slip towards standstill conditions. Hence, for intermediate values of the slip, the torque-slip characteristics is represented by a rectangular hyperbola. The curve passes through the point of maximum torque when R2 = 𝑠𝑋2. The maximum torque developed by an induction motor is known as pull-out torque or breakdown torque. This breakdown torque is a measure of the short time overloading capability of the motor. High-Slip Region The torque decreases beyond the point of maximum torque. As a result of this, the motor slows down and eventually stops. The induction motor operates for the values of slip between s = 0 and s = sm, where sm is the value of slip corresponding to maximum torque. For a typical 3-phase induction motor, the breakdown torque is 2 to 3 times of the full-load torque. Therefore, the motor can handle overloading for a short period of time without stalling. It may be seen from the torque-slip characteristics that addition of resistance to the rotor circuit does not change the value of maximum torque but it only changes the value of slip at which maximum torque occurs.