Category: electrical Machines

Introduction to Induction Motor Induction motors are the most widely used electric motors in industrial applications. Almost all induction motors run at essentially constant speed from no-load to full-load conditions. The speed of induction motors depends on the supply frequency and hence these motors are not easily adapted to speed control. Induction motors are simple and rugged in construction, less expensive, easy to maintain, and can be designed and produced with characteristics to suit most industrial requirements. What is an Induction Motor? An induction motor is an asynchronous AC electric motor which converts alternating current electricity into the mechanical energy. It is called an induction motor because the electric current in the rotor circuit required to produce the deriving torque is obtained through electromagnetic induction from the rotating magnetic field of the stator winding. These motors are referred to as asynchronous motors because their rotor rotates at a speed less than the synchronous speed of the rotating magnetic field. The induction motor is an electromechanical energy conversion device, i.e. it converts electrical energy into mechanical energy in the form of rotation of shaft. Like any electric motor, an induction motor has two main parts namely stator and rotor. The stator carries a set of windings called stator winding. The stator winding may be single-phase winding or three-phase winding. The rotor carries a short-circuited winding called rotor winding. In case an induction motor, only the stator winding is fed from an AC supply, while the rotor winding derives its voltage and power from the stator winding through electromagnetic induction. Working Principle of Induction Motor The working of an induction motor is based on the principle of electromagnetic induction. In an induction, there are two windings namely, stator winding and rotor winding. The input AC supply is connected to the stator winding, the current flowing in the stator winding produces a magnetic flux. This magnetic flux is usually rotating, hence also called rotating magnetic field. The rotor winding of the induction motor is a short-circuit winding. The rotating magnetic flux from the stator cuts the short-circuited conductors of the rotor winding. According to Faraday’s law of electromagnetic induction, an EMF is induced in the rotor circuit which causes a current to flow through it. When the current flows through the rotor winding, another magnetic flux being produced in the machine. Therefore, there are two magnetic fluxes inside the induction motor, one is stator flux and the other is rotor flux. These two magnetic fluxes interact with each other. Because of that, the rotor will experience a torque which makes the rotor to rotate in the direction of the rotating magnetic field of the stator. In this way, an induction motor runs. Types of Induction Motors Depending on the type of input supply, induction motors are classified into the following two types − Single-Phase Induction Motors− An induction motor that works on single-phase AC supply is called as a single-phase induction motor. Three-Phase Induction Motors− An induction motor which requires three-phase AC supply to operate is called a three-phase induction motor. Advantages of Induction Motors The following are some major advantages of induction motors − Induction motors have simple and rugged construction. Induction motors are relatively less expensive. Induction motors have relatively high efficiency. Induction motors can be designed to have characteristics to meet the industrial requirements. Induction motors need little maintenance. Disadvantages of Induction Motors The main disadvantages of induction motors are as follows − The speed of induction motors cannot be changed easily because they are essentially constant speed motors. Induction motors draw a high inrush current at starting. Induction motors always operate at lagging power factor. Single-phase induction motors are not self-starting; hence we need provide some extra starting mechanism. Learning working make money

Applications of DC Machines At present, a large amount of electrical energy is generated in the form of alternating current. Consequently, the use of DC machines (motors or generators) has become limited. However, dc machines are still used in several applications like for supplying excitation systems of alternators, in electrolytic processes, welding processes, etc. Applications of DC Generators The applications of different kinds of DC generators are listed below − Separately-Excited DC Generator Generators are mainly used in laboratories for experiments and testing purposes. They are also used as a source of DC power for supplying DC motors. Series DC Generator Series DC generators are used in DC locomotives for regenerative braking for supplying field excitation current. Series DC generators are also used as a booster in distribution systems. Differentially compounded series generators are used for arc welding. Over compounded cumulative series generators are used for lighting and heavy power supplies. Flat compounded series generators are used for supplying power to offices, houses, and the other commercial buildings. Shunt DC Generator Shunt DC generators are mainly used for lighting purposes. Shunt DC generators are used for charging batteries. These generators are also used for supplying field excitation current to alternators. Applications of DC Motors The applications of different types of DC motors are given below − Series DC Motor Series DC motors are used in applications where high starting torque is required. Series DC motors are used in cranes and hoists. Series DC motors are used in electric tractions. They are used in air compressors. They are also used in vacuum cleaners. Series DC motors are also used in sewing machines, etc. Shunt DC Motor Shunt DC motors are used in applications that require constant speed. Shunt DC motors are used for driving lathe machines. These are also used in centrifugal pumps and blowers. These are used in fans, conveyors, and spinning machines. These DC motors are also used in lifts. Compound DC Motor Compound DC motors are used in those applications which require high starting torque and constant speed. Used in printing presses. They are also used in shears. They are used in elevators and lifts. Compound DC motors are also used in rolling mills and heavy planners, etc. Learning working make money

Working Principle of DC Motor The working principle of a DC motor is based on the law of electromagnetic interaction. According to this law, whenever a current carrying conductor or coil is placed in a magnetic field, the conductor or coil experiences an electromagnetic force. The magnitude of this force is given by, $$mathrm{mathit{F=BIL}}$$ Where, $mathit{B}$ is the magnetic flux density, $mathit{I}$ is the current flowing in the conductor or coil, and $mathit{l}$ is length of the conductor. The direction of this force can be determined by Fleming’s left-hand rule (FLHR) which we discussed in Module 1 (Basic Concepts) of this tutorial. In order to understand the working principle of dc motor, consider a two pole DC motor as shown in Figure-1. When terminals of this DC motor are connected to an external source of DC supply, the following two phenomenon happen inside the machine − The field electromagnets are excited developing alternate N and S poles. The armature conductors carry electric currents. Where, conductors under N-pole carry currents in one direction (say inside of the plane of the paper), while conductors under S-pole carry currents in the opposite direction (say outward of the plane of the paper). Since, in this case, each conductor is carrying a current and is placed in a magnetic field. Due to the interaction between the current and magnetic field, a mechanical force acts on the conductor. By applying Fleming’s left hand rule, it is clear that the mechanical force on each conductor is tending to move the conductor in the anticlockwise direction. The mechanical forces on all the conductors add together to produce a driving torque that sets the armature rotating. When the conductor moves from one pole side to the other, the current in that conductor is reversed due to commutation action, and at the same time, it comes under the influence of the next pole of opposite polarity. As a result, the direction of the force on the conductor remains the same. In this way, the armature of a DC motor rotates continuously in one direction. Armature Torque of DC Motor The armature of the dc motor rotates about its axis. Thus, the mechanical force acting on the armature is known as armature torque. It is defined as the turning moment of a force acting on the armature conductors, and is given by, $$mathrm{mathit{tau _{a}}/conductor:=:mathit{Ftimes r}}$$ Where, F is the force on each conductor and r is the average radius of the armature. If Z is the number of conductors in the armature, then the total armature torque is given by, $$mathrm{therefore mathit{tau _{a}}:=:mathit{ZFtimes r}:=:mathit{ZBILtimes r}}$$ Since, $$mathrm{mathit{B}:=:frac{mathit{phi }}{mathit{a}};:mathit{I:=:frac{I_{a}}{A}};mathit{a:=:frac{mathrm{2}pi rl}{P}}}$$ Where, $phi$ is flux per pole,$mathit{I_{a}}$ is armature current,l is the effective length of each armature conductor, A is the number of parallel paths, and P is the number of poles. Then, $$mathrm{mathit{tau _{a}}:=:frac{mathit{Zphi I_{a}}P}{mathrm{2}pi A}}$$ Since for a given dc motor, Z, P and A are fixed. $$mathrm{therefore mathit{tau _{a}}propto mathit{phi I_{a}}}$$ Hence, the torque in a DC motor is directly proportional to flux per pole and armature current. Learning working make money

Working of 3-Phase Synchronous Motor A three-phase synchronous machine which converts three-phase electrical energy into mechanical energy is called a three-phase synchronous motor. A three-phase synchronous motor is a constant speed machine, and it runs at the synchronous speed. The synchronous speed of a three-phase synchronous motor is given by, $$mathrm{mathit{N_{s}}:=:frac{120mathit{f}}{mathit{p}}cdot cdot cdot (1)}$$ Where,f is the supply frequency andP is the number of field poles in the motor. Like any other electric motor, a 3-phase synchronous motor also consists of two main parts namely stator and rotor. The stator houses a 3-phase armature winding and receives power from a 3-phase ac supply source. The rotor is a rotating part and carries field winding which is excited from an external source of DC power. The most important drawback of a synchronous motor is that it is not self-starting and therefore an auxiliary mean has to be used for starting it. Working of 3-Phase Synchronous Motor Consider a three-phase synchronous motor having a salient-pole type rotor of two poles namely $mathit{N_{mathrm{2}}}$ and $mathit{S_{mathrm{2}}}$. Thus, the stator will also be wound for two poles which are $mathit{N_{mathrm{1}}}$ and $mathit{S_{mathrm{1}}}$. A direct voltage is applied to the rotor winding and a balanced three-phase ac voltage to the stator winding. The stator winding produces a rotating magnetic field which revolves around the stator at a speed called synchronous speed ($mathit{N_{mathit{s}}}$).The direct current flowing through the rotor winding produces two field poles in the rotor and the magnetic field due to these poles is stationary so long as the rotor is not running. Hence, in this case we have a pair of revolving armature poles $left ( mathit{N_{mathrm{1}}}-mathit{S_{mathrm{1}}} right )$ and a pair of stationary rotor poles $left ( mathit{N_{mathrm{2}}}-mathit{S_{mathrm{2}}} right )$. Now, consider an instant at which the stator poles are at positions A and B as shown in Figure-1. It is clear that poles $mathit{N_{mathrm{1}}}$ and $mathit{N_{mathrm{2}}}$ repel each other and so do the poles $mathit{S_{mathrm{1}}}$ and $mathit{S_{mathrm{1}}}$. Thus, the rotor tends to rotate in the anticlockwise direction. After a period of half-cycle of AC supply, the polarities of stator poles are reversed, but the polarities of the rotor poles remain the same as shown in Figure-2. In this situation, poles $mathit{S_{mathrm{1}}}$ and $mathit{N_{mathrm{2}}}$ attract each other and so do the poles $mathit{N_{mathrm{1}}}$ and $mathit{S_{mathrm{2}}}$. Thus, the rotor now tends to rotate in the clockwise direction. Since, the stator poles are changing their polarities rapidly, they tend to pull the rotor first in one direction and after half-cycle of ac in the other direction. Because of the bidirectional torque on the rotor and high inertia of the rotor, the synchronous motor fails to start. Therefore, a synchronous motor has no self-starting torque. Making a Synchronous Motor Self-Starting A synchronous motor cannot start by itself. To make the motor self-starting, a squirrel-cage winding, called damper winding, is provided on the rotor. The damper winding consists of copper bars embedded in the slots cut on in the pole faces of the salient poles of the rotor, as shown in Figure-3. These damper windings serve to start the synchronous motor by itself, which is explained below − Initially, a 3-phase supply is fed to the stator winding while the rotor winding is left open. The rotating magnetic field of the stator winding induces currents in the damper windings, and due to electromagnetic forces, the rotor starts moving. Thus, the synchronous motor is started as an induction motor. Once the motor attains a speed nearly equal to the synchronous speed, the rotor winding is excited from a source of dc supply. Now, the resulting poles on the rotor face the stators pole of opposite polarity, and a strong magnetic attraction is set up between them. Thus, the rotor poles are locked with the rotating poles of the stator. Consequently, the rotor revolves at the same speed of the stator poles, i.e. synchronous speed. Since the rotor is now rotating at the same speed as the stator field, the damper bars do not cut any flux, hence have no induced currents in them. Thus, the damper windings of the rotor are, in effect, removed from the operation of the motor. In this way, a synchronous motor is made self-starting. It must be noted that due to magnetic interlocking between the stator and rotor poles, the synchronous motor can only run at synchronous speed. Learning working make money

Working Principle of DC Generator The working principle of DC generator is based on the Faraday’s law of electromagnetic induction. According to this law, when the magnetic flux liked to a conductor or coil changes an EMF is induced in the conductor or coil. The magnitude of this induced EMF is given by, $$mathrm{mathit{e}:=:mathit{N}frac{mathit{dphi }}{mathit{dt}}:cdot cdot cdot (1)}$$ Where, $phi$ is the flux linkage of the coil and N is the number of turns in the coil. In case of a DC generator, the magnetic flux ($phi$) remains stationary and the coil rotates. The EMF induced where the coil is rotating and flux is stationary, is known as dynamically induced EMF. In order to understand the working principle of a DC generator, we consider a single loop DC generator (i.e. N = 1) as shown in above figure. Here, the coil is rotated by some prime mover (a source of mechanical energy), and there is a change in the magnetic flux linkage to the coil. Let $phi$ be the average magnetic flux produced by each magnetic pole of the machine, then the average induced EMF in the generator is given by, $$mathrm{mathit{E_{av}}:=:frac{mathit{dphi }}{mathit{dt}}:=:mathrm{Flux: cut: per:sec:by: the :coil}}$$ $$mathrm{Rightarrow mathit{E_{av}}:=:mathrm{Flux: cut: in :one :rotation:times :No.:of: rotations: per: sec}}$$ $$mathrm{Rightarrow mathit{E_{av}}:=:mathrm{left ( Flux:per:poletimes No.:of:poles right )}:times :mathrm{No.:of :rotations :per: sec}}$$ $$mathrm{therefore mathit{E_{av}}:=:mathit{phi :times P:times :n}:cdot cdot cdot (2)}$$ Where, P is the total number of poles in the generator and n is the speed of the coil in rotation per second. The expression in the Equation-(2) gives the average induced EMF in a single loop DC generator. The following points explain the working principle of a DC generator − Position 1 − The induced EMF is zero because, the movement of coil sides is parallel to the magnetic flux. Position 2 − The coil sides are moving at an angle to the magnetic flux, and hence a small EMF is generated in the loop. Position 3 − The coil sides are moving at right angle to the magnetic flux, therefore the induced EMF is maximum. Position 4 − The coil sides are cutting the magnetic flux at an angle, thus a reduced EMF is induced in the coil sides. Position 5 − No flux linkage with the coil side and the coil sides are moving parallel to the magnetic flux. Therefore, no EMF is induced in the coil. Position 6 − The coil sides move under a pole of opposite polarity and hence the polarity of induced EMF is reversed. The maximum EMF will induce in this direction at position 7 and zero when it is at position 1. This cycle repeats with rotation of the coil. In this way, EMF is induced in a DC generator. Though, this induced EMF is alternating in nature, which is then converted in the unidirectional EMF by using a device called commutator. The direction of induced EMF in the armature conductor of the DC generator is determined by the Fleming’ right hand rule (FRHR) which we discussed in the module-1 (basic concepts) of this tutorial. Learning working make money

Introduction to 3-Phase Synchronous Machines An electromechanical energy conversion device (or electrical machine) which operates on synchronous speed (i.e. speed of rotating magnetic field) is termed as a synchronous machine. A synchronous machine an AC machine, i.e., it requires AC supply to work. Based on the energy conversion, synchronous machines may be classified into two types − Synchronous Generator Synchronous Motor The synchronous machines are the most extensively used electrical machines in power system applications like power generator, power factor correction, driving constant speed mechanical load, etc. The synchronous machine which converts mechanical energy into alternating current electricity is called a synchronous generator or alternator. While the synchronous machine which converts alternating current electricity into mechanical energy is called a synchronous motor. The synchronous machines, used in most practical applications, are three-phase AC machines. However, there are single-phase synchronous machines also exist but they are used in special applications. A synchronous machine (generator or motor) always operate at a constant speed called synchronous speed. The synchronous speed is given by the following relation, $$mathrm{mathit{N_{s}}:=:frac{120mathit{f}}{mathit{p}}cdot cdot cdot (1)}$$ Where, f is the supply frequency, P is the number of poles in the machine. The synchronous speed is measured in revolution per minute (RPM). For satisfactory operation, a synchronous machine always maintains the expression given in Equation-1. If the synchronous machine fails to maintain the above relationship of Equation-1. The machine will stop to operated, and this condition is known as loss of synchronism or out of synchronism of the machine. Hence, this proves that the synchronous machine is designed to operate at a constant speed. Working Principle of Synchronous Machine The working principle of a synchronous machine is based on the law of electromagnetic interaction and law of magnetic interlocking. According to the law of electromagnetic interaction, when there is a relative motion between a conductor and a magnetic field, an EMF is induced in the conductor. On the other hand, when a current carrying conductor is placed in a magnetic field, a force acts on the conductor that tends to move it. According to the law of magnetic interlocking, two different magnetic fields (field of stator and field of rotor) are locked together and rotate at the same speed. This phenomenon is called magnetic interlocking. These two principles explain the working of a synchronous machine. The synchronous machine is first started by the electromagnetic interaction, and then the magnetic fields of rotor and stator are locked together to rotate at the synchronous speed. Three-Phase Synchronous Generator A synchronous machine that converts mechanical energy into 3-phase electrical energy through the process of electromagnetic induction is known as a 3-phase synchronous generator or alternator. A 3-phase alternator consists of an armature winding and a field winding, where the EMF is induced in the armature winding, while field winding produces the working magnetic field. In case of a 3-phase alternator, the armature winding is provided on the stator part of the machine while the field winding is provided on the rotor. The major advantage of stationary armature winding is that there is no need of commutator as required in the DC generators. The 3-phase synchronous generators are most widely used for generation of electric power in power generating plants. Three-Phase Synchronous Motor A synchronous machine that converts three-phase electricity into mechanical energy is known as three-phase synchronous motor. Like any other electric motor, a synchronous motor also consists of two major parts namely stator and rotor. The stator carries a three-phase armature winding, whereas the rotor carries a field winding which is excited from a dc supply to produce a certain number of fixed magnetic poles. A unique feature of a synchronous motor is that it can run at a constant speed, called synchronous speed. Although, the major disadvantage of a three-phase synchronous motor is that it does not have self-starting torque. Therefore, in order to start a 3-phase synchronous motor, it is brought up almost to its synchronous speed by some auxiliary mean. Being a constant speed motor, the load on the motor does not exceed the limiting value. If the load on the motor exceeds the limiting value, the motor will immediately stop. The three-phase synchronous motors are used for − driving mechanical loads at constant speed, improving power factor of a system, etc. Features of Synchronous Machines The following are the key features of synchronous machines (motor or generator) − Synchronous motors do not self-starting torque. Synchronous machine is a doubly-excited machine because it requires two input supplies – one on the stator and the other on the rotor. Synchronous machines operate at constant speed, called synchronous speed. Synchronous generators can produce a voltage of constant magnitude and frequency. A synchronous machine can be operated at lagging, leading or unity power factor just by changing the excitation. Synchronous motors have relatively high starting torque as compared to induction motors. Synchronous motors are suitable for driving constant and slow speed (usually less than 300 RPM) loads. Synchronous machines are expensive. Learning working make money

Characteristics of 3-Phase Induction Motor The operating performance of a three-phase induction motor can be explained with the help of the following two characteristics namely, Torque-Slip Characteristics Torque-Speed Characteristics Torque Slip Characteristics of 3 Phase Induction Motor The torque-slip characteristics of a three-phase induction motor is the curve drawn between the motor torque and slip for a particular value of rotor resistance. Figure-1 shows different torque-slip characteristics of a typical three-phase induction motor for a slip range from s = 0 to s= 1 for various values of rotor resistance. For a three-phase induction motor, the relation between the motor torque and slip under running condition is given by, $$mathrm{mathit{tau _{r}}:=:frac{mathit{KsR_{r}}}{mathit{R_{r}^{mathrm{2}}+s^{mathrm{2}}X_{r}^{mathrm{2}}}}:cdot cdot cdot (1)}$$ Where,K is a constant,s is the slip, $mathit{R_{r}}$ is the per phase rotor resistance, and $mathit{X_{r}}$ is the standstill rotor reactance per phase. From Equation-1, we may conclude the following points − Case 1 If s = 0, then $mathit{tau _{r}}:=:0$. Therefore, the torque-slip curve starts from the origin. Case 2 At normal speed of the motor, the slip is small, and thus $mathit{sX_{r}}$ is practically negligible as compared to $mathit{R_{r}}$. $$mathrm{therefore mathit{tau _{r}}propto mathit{frac{s}{R_{r}}}}$$ Since for a given motor, $mathit{R_{r}}$ is also constant. $$mathrm{therefore mathit{tau _{r}}propto mathit{s}}$$ Thus, the torque-slip curve is a straight line from zero slip to a slip that corresponds to full load. Case 3 If slip value exceeds the full-load slip, then torque increases and becomes maximum when $mathit{R _{r}}:=:mathit{s:X_{r}}$. This maximum torque in a three-phase induction motor is known as breakdown torque or pull-out torque. The value of the breakdown torque is at least double of the full-load torque when the induction motor is operated at rated voltage and frequency. Case 4 When the slip value becomes greater than that corresponding to the maximum torque, then the term $mathit{s^{mathrm{2}}:X_{r}^{mathrm{2}}}$ increases rapidly so that $mathit{R_{r}^{mathrm{2}}}$ may be neglected. $$mathrm{therefore mathit{tau _{r}}propto mathit{frac{s}{s^{mathrm{2}}X_{r}^{mathrm{2}}}}}$$ As $mathit{X_{r}^{mathrm{2}}}$ is practically constant, then $$mathrm{mathit{tau _{r}}propto mathit{frac{mathrm{1}}{s}}}$$ Hence, the torque is now inversely proportional to the slip. Thus, the torque-slip curve is a rectangular hyperbola. Therefore, from the above analysis of torque-slip characteristics of a three-phase induction motor it is clear that the 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 the maximum torque occurs. Torque-Speed Characteristic of 3-Phase Induction Motor For a three-phase induction motor, the motor torque depends upon the speed but we cannot express the relationship between them by a simple mathematical equation. Therefore, we use a torque-speed characteristic curve to show this relationship. Figure-2 shows a typical torque-speed characteristic curve of a three-phase induction motor. The following points may be noted from this characteristic curve − If the full-load torque is $tau$, then the starting torque is $1.5tau $ and the maximum torque (or breakdown torque) is $2.5tau $ At full-load, if speed of the motor is N, and if the mechanical load on the shaft increases, the speed of the motor will drop until the motor torque is again equal to the load torque. Once the two torques are equal, the motor will run at a constant speed but lower than the previous. Although, if the motor torque becomes greater than $2.5tau $(i.e. breakdown torque), the motor will suddenly stop. For a three-phase induction motor, the torque-speed curve is essentially a straight line between the points of no-load and full-load. The slope of the curve line depends upon the resistance of the rotor circuit, i.e., greater the resistance, the sharper the slope. Learning working make money

Rotating Electrical Machines Almost all electrical machines have several similar properties and features. The following discussion will explain the basic common features of rotating electrical machines. Where, a rotating electrical machine is one which has a moving (rotating) part, called rotor. The common examples of rotating electrical machines motors and generators. In a rotating electrical machine, the torque produced can be considered in terms of the instantaneous flux pattern. According to this concept, a torque is produced in an electrical machine when the net magnetic field has asymmetry or distortion. In any rotating electrical machine, the mechanical forces (torques) are produced due to the following two magnetic field effects − Alignment of magnetic field lines Interaction between magnetic fields and current-carrying conductors In practical electrical machine, magnetic fields are produced by energizing a coil system. It is because, this method of magnetic field production relatively versatile and economic. Basic Structure of Rotating Electrical Machines The basic construction and structure of all rotating electrical machines is similar. A typical rotating electrical machine consists of two main parts namely, Stator Rotor The stator and rotor are separated by an air gap. As the name implies, the stator is the stationary (non-movable) part of the electrical machine. In general, the stator is the outer frame of the machine. The rotor is the rotating (movable) part of the machine. Both stator and rotor are constructed by using laminated ferromagnetic materials to reduce the reluctance in the path of magnetic flux. All rotating electrical machines consist of two windings, one placed on the stator part and another on the rotor part. The winding of the machine in which voltage is induced is known as armature winding. The winding which is used to produce the main working magnetic flux in the machine is known as field winding. Sometimes, instead of field winding, permanent magnets are used to produce the main magnetic flux. Rotating Magnetic Field The resultant magnetic field which revolve in the space and is produced by a system of windings (coils) symmetrically placed and supplied with poly-phase currents is known as rotating magnetic field (RMF). The rotating magnetic field is such as that its magnetic poles do not remain in a fixed position, but go on shifting their positions. The speed of rotation of the magnetic field is known as synchronous speed and is denoted by NS. Mathematically, the synchronous speed is given by, $$mathrm{mathit{N_{s}}:=:frac{120mathit{f}}{mathit{P}}}$$ Where, f is the supply frequency in Hz and P is the number of poles. It is measured in RPM (Revolution per Minute). Machine Torques Torque is defined as the turning movement of force. The torque is the main factor which rotates the rotor of the machine. In electromechanical devices, there are two types of torques developed − Electromagnetic Torque Reluctance Torque Electromagnetic Torque The electromagnetic torque is one which produced due to interaction of the magnetic fields produced by the currents in two coils which may move relative to each other. In a rotating electrical machine, under normal operating conditions, there are two magnetic fields present – a magnetic field from the stator circuit and another magnetic field from the rotor circuit. The interaction between these two magnetic fields produces the torque in the machine. This torque is known as electromagnetic torque. The electromagnetic torque is also known as induced torque. Reluctance Torque When an object made up of a ferromagnetic material is placed in an external magnetic field experiences a force (torque) which causes the object to align it with the external magnetic field, it is known as reluctance torque. The reluctance torque occurs because the external magnetic field induced an internal magnetic field in the ferromagnetic object, and a torque is produced by interaction of the two magnetic fields moving the object to align with the external magnetic field. Since, the reluctance torque on the object tries to position it to give minimum reluctance (or saliency) for the magnetic flux. Therefore, the reluctance torque is also known as alignment torque or saliency torque. Learning working make money

Energy Stored in a Magnetic Field In the previous chapter, we discussed that in an electromechanical energy conversion device, there is a medium of coupling between electrical and mechanical systems. In most of practical devices, magnetic field is used as the coupling medium. Therefore, an electromechanical energy conversion device comprises an electromagnetic system. Consequently, the energy stored in the coupling medium is in the form of the magnetic field. We can calculate the energy stored in the magnetic field of an electromechanical energy conversion system as described below. Consider a coil having N turns of conductor wire wound around a magnetic core as shown in Figure-1. This coil is energized from a voltage source of v volts. By applying KVL, the applied voltage to the coil to given by, $$mathrm{mathit{V:=:e:+:iR}cdot cdot cdot (1)}$$ Where, e is induced EMF in the coil due to electromagnetic induction. R is the resistance of the coil circuit. $mathit{i}$ is the current flowing the coil. The instantaneous power input to the electromagnetic system is given by, $$mathrm{mathit{p}:=:mathit{Vi:=:ileft ( e+iR right )}}$$ $$mathrm{Rightarrow mathit{p}:=:mathit{ie+ i^{mathrm{2}}}mathit{R}cdot cdot cdot (2)}$$ Now, let a direct voltage is applied to the circuit at time t = 0 and that at end of t = t1 seconds, and the current in the circuit has attained a value of I amperes. Then, during this time interval, the energy input the system is given by, $$mathrm{mathit{W}_{in}:=:int_{0}^{t_{mathrm{1}}}:mathit{p:dt}}$$ $$mathrm{Rightarrow mathit{W}_{in}:=:int_{0}^{t_{mathrm{1}}}:mathit{ie:dt}:+:int_{0}^{t_{mathrm{1}}}mathit{i^{mathrm{2}}R:dt}cdot cdot cdot (3)}$$ From Equation-3, it is clear that the total input energy consists of two parts − The first part is the energy stored in the magnetic field. The second part is the energy dissipated due to electrical resistance of the coil. Thus, the energy stored in the magnetic field of the system is, $$mathrm{mathit{W}_{mathit{f}}:=:int_{0}^{t_{mathrm{1}}}:mathit{ie:dt}:cdot cdot cdot (4)}$$ According to Faraday’s law of electromagnetic induction, we have, $$mathrm{mathit{e}:=:frac{mathit{dpsi }}{mathit{dt}}:=:frac{mathit{d}}{mathit{dt}}left ( mathit{Nphi } right ):=:mathit{N}frac{mathit{dphi }}{mathit{dt}}cdot cdot cdot (5)}$$ Where, $psi$ is the magnetic flux linkage and it is equal to $mathit{psi :=:Nphi }$. $$mathrm{therefore mathit{W_{f}}:=:int_{0}^{mathit{t_{mathrm{1}}}}frac{mathit{dpsi }}{mathit{dt}}mathit{i:dt}}$$ $$mathrm{Rightarrow mathit{W_{f}}:=:int_{0}^{psi_{mathrm{1}}}mathit{i:dpsi }cdot cdot cdot (6)}$$ Therefore, the equation (6) shows that the energy stored in the magnetic field is equal to the area between the ($psi -i$) curve (i.e., magnetization curve) for the electromagnetic system and the flux linkage ($psi$) axis as shown in Figure-2. For a linear electromagnetic system, the energy stored in the magnetic field is given by, $$mathrm{mathit{W_{f}}:=:int_{0}^{mathit{psi _{mathrm{1}}}}mathit{idpsi }:=:int_{0}^{psi_{mathrm{1}} }frac{psi }{mathit{L}}mathit{dpsi }}$$ Where, $psi:=:mathit{Nphi }:=:mathit{Li}$ and L is the self-inductance of the coil. $$mathrm{therefore mathit{W_{f}}:=:frac{psi ^{mathrm{2}}}{2mathit{L}}:=:frac{1}{2}mathit{Li^{mathrm{2}}}cdot cdot cdot (7)}$$ Concept of Coenergy Coenergy is an imaginary concept used to derive expressions for torque developed in an electromagnetic system. Thus, the coenergy has no physical significance in the system. Basically, the coenergy is the area between the $psi -i$ curve and the current axis and is denoted by $mathit{W_{f}^{”}}$ as shown above in Figure-2. Mathematically, the coenergy is given by, $$mathrm{mathit{W_{f}^{”}}:=:int_{0}^{i}psi mathit{di}:=:int_{0}^{i}mathit{Li:di}}$$ $$mathrm{Rightarrow mathit{W_{f}^{”}}:=:frac{1}{2}mathit{Li^{mathrm{2}}}cdot cdot cdot (8)}$$ From equations (7) and (8), it is clear that for a linear magnetic system, the energy stored in the magnetic field and the coenergy are equal. Learning working make money

Electromechanical Energy Conversion Today, electrical energy is the most widely used form of energy for performing several industrial, commercial and domestic functions such as pumping water, fans, coolers, air conditioning, refrigeration, etc. Since, most of processes require the conversion of electrical energy into mechanical energy. Also, the mechanical energy is converted into electrical energy. Hence, this clears that we need a mechanism to convert the electrical energy into mechanical energy and mechanical energy into electrical energy and such a mechanism is known as electromechanical energy conversion device. Electromechanical Energy Conversion Device Thus, a device which can convert electrical energy into mechanical energy or mechanical energy into electrical energy is known as electromechanical energy conversion device. The electric generators and electric motors are the examples of electromechanical energy conversion device. In any electromechanical energy conversion device, the conversion of electrical energy into mechanical energy and vice-versa takes place through the medium of an electric field or a magnetic field. Though, in most of the practical electromechanical energy conversion devices, magnetic field is used as the coupling medium between electrical and mechanical systems. The electromechanical energy conversion devices can be classified into two types − Gross motion devices (like motors and generators) Incremental motion devices (such as electromagnetic relays, measuring instruments, loudspeakers, etc.) The device which converts electrical energy into mechanical energy is known as electric motor. The device which converts mechanical energy into electrical energy is known as electric generator. In an electric motor, when a current carrying conductor is placed in a changing (or rotating) magnetic field, the conductor experiences a mechanical force. In case of a generator, when a conductor moves in a magnetic field, an EMF is induced in the conductor. Although, these two electromagnetic effects occur simultaneously, when the energy conversion takes place from electrical to mechanical and vice-versa in all the electromechanical energy conversion devices. Energy Balance Equation The energy balance equation is an expression which shows the complete process of energy conversion. In an electromechanical energy conversion device, the total input energy is equal to the sum of three components − Energy dissipated or lost Energy stored Useful output energy Therefore, for an electric motor, the energy balance equation can be written as, Electrical energy input = Energy dissipated + Energy stored + Mechanical energy output Where, The electrical energy input is the electricity supplied from the main supply. Energy stored is equal to sum of the energy stored in the magnetic field and in the mechanical system in the form of potential and kinetic energies. The energy dissipated is equal to sum of energy loss in electric resistance, energy loss in magnetic core (hysteresis loss + eddy current loss) and mechanical losses (windage and friction losses). For an electric generator, the energy balance equation can be written as, Mechanical energy input = Electrical energy output + Energy stored + Energy dissipated Where, the mechanical energy input is the mechanical energy obtained from a turbine, engine, etc. to turn the shaft of the generator. Learning working make money