Category: electrical Machines

Types of Transformers Depending on the number of turns in primary and secondary windings, the transformers may be classified into the following three types − Step-up transformer Step-down transformer One-to-one transformer Depending on the application, we may classify the transformers in the following three main types Power transformers Distribution transformers Instrument transformers Step-Up Transformer A transformer in which the number of turns in the secondary winding are greater than the number of turns in the primary winding, as a result its output voltage is greater than the input voltage is known as a step-up transformer. In power systems, the step-up transformer is used to increase the low voltages to a higher value for transmission purposes. Step-Down Transformer A transformer in which the number of turns in the secondary winding are less than that in the primary winding as a result the output voltage is less than the input voltage is known as a step-down transformer. In power systems, the step-down transformers are used to decrease the high-voltages to a lower value for distribution and utilization purposes. One-to-One (1:1) Transformer A transformer in which the number of turns in both primary winding and secondary winding are same so that it produces an output voltage equal to the input voltage is known as a one-to-one transformer. It is also known as isolation transformer. It finds application in such areas where two electrical circuits are required to be isolated electrically, but coupled magnetically for power transfer. Power Transformers A transformer with high volt-ampere (VA) rating, commonly of the order of Mega or Giga, is referred as a power transformer. The power transformers are designed to operate with an almost constant load which is equal to their rating. These transformers are used in generating stations, receiving stations and substations at ends of the power transmission lines for stepping-up or stepping-down the voltage. In practice, power transformers are put into operation during load periods while they are disconnected during light load periods. These transformers are designed to have maximum efficiency at or near full-load. However, power transformers are so designed that they have considerably high leakage reactance. Thus, for power transformers the current limiting effect of high leakage reactance is more important than the voltage regulation. Distribution Transformers The transformer which is used to reduce the high voltage to a low value for distribution purpose is known as a distribution transformer. Distribution transformers are designed to operate with variable load which is considerably less than their rating. Therefore, these transformers are designed to have maximum efficiency at the load between ½ and ¾ of the full-load. Distribution transformers are kept in operation all the 24 hours of a day whether they are carrying any load or not. Distribution transformers have a good voltage regulation, and are designed to have a small value of leakage reactance. Instrument Transformers It is very difficult to measure high alternating currents and voltages with simple measuring devices. Thus, to make the measurement of high alternating currents and voltages simple, we use specially designed transformers, called instrument transformers. By employing instrument transformers, we can measure high alternating quantities with low-range AC measurement devices. Depending on the type of quantity transformed, instrument transformers are of the following two types − Current Transformer (C.T.) Potential Transformer (P.T.) Current Transformer A current transformer is a type of instrument transformer which is used to decrease the high alternating current of power line to a measurable low value. Basically, a current transformer is a voltage step-up and current step-down transformer. It has a primary winding of a few turns of thick wire, and a secondary winding having more turns of fine wire. The primary winding of CT is connected in series with the line whose current is to be measured, and the secondary winding is connected across a low-range AC ammeter to measure and indicate the current. Potential Transformer A potential transformer is a voltage step-down transformer which is used to reduce the high line voltages to a measurable value. The primary winding of a PT has many turns while the secondary winding has few turns. The primary winding is connected across the power line whose voltage is to be measured and the secondary winding is connected across a low-range AC voltmeter to indicate the measured voltage value. Learning working make money

Concept of Induced EMF According to principle of electromagnetic induction, when the magnetic flux linking to a conductor or coil changes, an EMF is induced in the conductor or coil. In practice, the following two ways are used to bring the change in the magnetic flux linkage. Method 1 − Conductor is moving in a stationary magnetic field We can move a conductor or coil in a stationary magnetic field in such a way that the magnetic flux linking to the conductor or coil changes in magnitude. Consequently, an EMF is induced in the conductor. This induced EMF is known as dynamically induced EMF. It is so called because the EMF induced in a conductor which is in motion. Example of dynamically induced EMF is the EMF generated in the AC and DC generators. Method 2 − A stationary conductor is placed in a changing magnetic field When a stationary conductor or coil is placed in a moving or changing magnetic field, an EMF is induced in the conductor or coil. The EMF induced in this way is known as statically induced EMF. It is so called because the EMF is induced in a conductor which is stationary. The EMF induced in a transformer is an example of statically induced EMF. Therefore, from the discussion, it is clear that the induced EMF can be classified into two major types namely, Dynamically Induced EMF Statically Induced EMF Dynamically Induced EMF As discussed in the above section that the dynamically induced EMF is one which induced in a moving conductor or coil placed in a stationary magnetic field. The expression for the dynamically induced EMF can be derived as follows − Consider a single conductor of length l meters located in a uniform magnetic field of magnetic flux density B Wb/m2 as shown in Figure-1. This conductor is moving at right angles relative to the magnetic field with a velocity of v m/s. Now, if the conductor moves through a small distance dx in time dt seconds, then the area swept by the conductor is given by, $$mathrm{mathit{A:=:ltimes dx:}mathrm{m^{mathrm{2}}}}$$ Therefore, the magnetic flux cut by the conductor is given by, $$mathrm{mathit{dphi }:=:mathrm{Flux:densitytimes Area: swept}}$$ $$mathrm{Rightarrow mathit{dphi }:=:mathit{Btimes ltimes dx}:mathrm{Wb}}$$ According to Faraday’s law of electromagnetic induction, the EMF induced in the conductor is given by, $$mathrm{mathit{e}:=:mathit{N}frac{mathit{dphi }}{mathit{dt}}:=:mathit{N}frac{mathit{Bldx}}{mathit{dt}}}$$ Since, we have taken only a single conductor, thus N = 1. $$mathrm{mathit{e}:=:mathit{Blv}:mathrm{volts}cdot cdot cdot (1)}$$ Where, v = dx/dt, velocity of the conductor in the magnetic field. If there is angular motion of the conductor in the magnetic field and the conductor moves at an angle θ relative to the magnetic field as shown in Figure-2. Then, the velocity at which the conductor moves across the magnetic field is equal to “vsinθ”. Thus, the induced EMF is given by, $$mathrm{mathit{e}:=:mathit{B:l:v}:mathrm{sinmathit{theta }}:mathrm{volts}cdot cdot cdot (2)}$$ Statically Induced EMF When a stationary conductor is placed in a changing magnetic field, the induced EMF in the conductor is known as statically induced EMF. The statically induced EMF is further classified into following two types − Self-Induced EMF Mutually Induced EMF Self Induced EMF When EMF is induced in a conductor or coil due to change of its own magnetic flux linkage, it is known as self-induced EMF. Consider a coil of N turn as shown in Figure-3. The current flowing through the coil establishes a magnetic field in the coil. If the current in the coil changes, then the magnetic flux linking the coil also changes. This changing magnetic field induces an EMF in the coil according to the Faraday’s law of electromagnetic induction. This EMF is known as self-induced EMF and the magnitude of the self-induced EMF is given by, $$mathrm{mathit{e}:=:mathit{N}frac{mathit{dphi }}{mathit{dt}}}$$ Mutually Induced EMF The EMF induced in a coil due to the changing magnetic field of a neighboring coil is known as mutually induced EMF. Consider two coils X and Y placed adjacent to each other as shown in Figure-4. Here, a fraction of the magnetic flux produced by the coil X links with the coil Y. This magnetic flux of coil X which is common to both coils X and Y is known as mutual flux ($mathit{phi _{m}}$). If the current in coil X is changed, then the mutual flux also changes and hence EMF is induced in both the coils. Where, the EMF induced in coil X is known as self-induced EMF and the EMF induced in coil Y is called mutually induced EMF. According to Faraday’s law, the magnitude of the mutually induced EMF is given by, $$mathrm{mathit{e_{m}}:=:mathit{N_{Y}}frac{mathit{dphi _{m}}}{mathit{dt}}}$$ Where,$mathit{N_{Y}}$ is the number of turns in coil Y and $frac{mathit{dphi _{m}}}{mathit{dt}}$ is rate of change of mutual flux. Learning working make money

Three-Phase Induction Motor on Load In this chapter, we will explain the behavior of a three-phase induction motor on load. When we attach a mechanical load to the rotor shaft of the three-phase induction motor, it will begin to slow down and thus the rotating magnetic field (RMF) will cut the rotor conductors at a higher rate. Because of this, the induced EMF and resulting current in the rotor conductors will increase gradually, and producing a higher torque. This torque accelerates the rotor, and the rotor and mechanical load will soon reach a state of equilibrium when the rotor torque and load torque become equal. Once this state is reached, the speed of the motor stops to decrease further, and hence the motor will run at the new speed at a constant rate. However, the decrease in speed of a three-phase induction motor with increased load is small. It is because, impedance of its rotor circuit is low, and a small drop in the speed produces a large rotor current. This increased rotor current produces a higher torque to meet the increased load demand on the motor shaft. This is why the 3-phase induction motors are considered to be constant speed motors. However, these motors never run at synchronous speed, thus they are also called asynchronous motors. Technically, the change in load on the three-phase induction motor is met through the adjustment of slip (difference of synchronous speed and rotor speed). Which means, the slip increases slightly with the increase in load on the motor shaft. Due to this, the relative speed between the rotating magnetic field and rotor conductors is increased. Consequently, the rotor current is increased, producing a higher motor torque to meet the increased load demand. Also, with increasing mechanical load, the increased rotor current is in such a direction so as to decrease the rotating magnetic flux of the stator (according to Lenz’s law), thus decreasing the back EMF in the stator windings. The decreased back EMF allows the stator current to increase, and hence increasing the power input to the induction motor. Concept of Slip in Induction Motor In a three-phase induction motor, the rotor can never reach the speed of stator’s rotating magnetic field (called synchronous speed). If it did, there would be no relative motion between the rotating magnetic field and rotor conductors, no induced EMF in the rotor conductors, and hence no torque to rotate the rotor. Therefore, in practice, the speed of rotor of an induction motor is always less than the synchronous speed. This difference is known as slip speed, i.e., $$mathrm{mathrm{Slip:speed}:=:mathit{N_{s}-N_{r}}}$$ Where, $mathit{N_{s}}$ is the synchronous speed and $mathit{N_{r}}$ is the rotor speed. $$mathrm{mathrm{Synchronous:speed,}mathit{N_{s}}:=:frac{120mathit{f}}{mathit{P}}}$$ Where,f is the supply frequency and P is the number of poles in induction motor. The ratio of the slip speed to the synchronous speed is called the slip of the induction motor, i.e., $$mathrm{mathrm{Slip,}mathit{s}:=:frac{mathit{N_{s}-N_{r}}}{mathit{N_{s}}}}$$ Also, $$mathrm{mathrm{Percentage:Slip,}mathit{s}:=:frac{mathit{N_{s}-N_{r}}}{mathit{N_{s}}}times 100%}$$ In a practical three-phase induction motor, the change in the slip from no-load to full-load is around 0.1% to 3%. Numerical Example An 8-pole 3-phase induction motor is connected to a 60 Hz supply. If it is running at 880 RPM. Calculate the slip. Solution Given data, Poles,P = 8 Frequency,f = 60 Hz Rotor speed,Nr= 880 RPM $$mathrm{therefore mathrm{Synchronous:speed,}mathit{N_{s}}:=:frac{120times 60}{8}:=:900}$$ Therefore, the slip will be, $$mathrm{mathrm{Slip,}mathit{s}:=:frac{900-880}{900}times 100:=:2.22%}$$ Learning working make money

Construction of Three-Phase Induction Motor A three-phase induction motor consists of two main parts namely, Stator Rotor There is a small air gap between the stator and rotor which ranges from 0.4 mm to 4 mm depending on the power rating of the motor. Stator The stator of a three-phase induction motor is a stationary part, and it consists of a cylindrical-shaped frame made up of fabricated steel. This steel frame encloses a hollow cylindrical core made up of thin laminations of silicon steel. On the inner periphery of the core, a number of evenly spaced slots are provided to place the stator winding. The silicon-steel laminations are used to reduce the hysteresis and eddy current losses. Three windings are placed in the stator slots and are suitably connected to form a balanced three-phase delta or star connected circuit. As per the requirement of motor speed, these three-phase windings are wound for a definite number of poles. Where, greater is the number of poles, lesser is the speed of the induction motor and vice-versa. When we fed the three-phase stator winding from a balanced three-phase supply, a rotating magnetic field of constant magnitude is produced. This rotating magnetic induces EMF in the rotor circuit by electromagnetic induction. Rotor The rotor is a rotating or moving part of the three-phase induction motor. It consists of a rotor core made up of thin laminations of high grade silicon steel to reduce the hysteresis and eddy-current losses. The rotor core is a hollow cylinder, mounted on a shaft. On outer periphery of the rotor core, slots are provided to place the rotor winding. Based on the construction, the rotor of a three-phase induction motor can be of the following two types − Squirrel-cage rotor Wound rotor Let”s discuss these two types of rotors in detail. Squirrel Cage Rotor The squirrel-cage rotor consists of a laminated cylindrical core having parallel slots on its outer periphery. In case of squirrel-cage rotor, the rotor winding is made up of metal (copper or aluminium) bars. These metal bars are placed in the rotor slots and are short-circuited at each end by metal rings called end-rings as shown in Figure-2. From Figure-2, it can be observed that the construction of this rotor resembles a squirrel cage and hence the name. Here, it is also to be noted that the rotor is not connected electrically to the supply, but it derives its voltage and power by the electromagnetic induction from the stator. The three-phase induction motors that employ squirrel-cage rotor are known as squirrel-cage induction motors. Almost 70% to 80% three-induction motors used in industrial applications are squirrel-cage induction motors because of their simple and robust construction which enable them to operate in most adverse circumstances. Although, the induction motors that use squirrel-cage rotor have a low starting torque. Wound Rotor The wound rotor consists of a laminated cylindrical core made up of silicon steel. It carries a 3-phase rotor winding similar to the stator winding as shown in Figure-3. The rotor winding of the wound rotor is uniformly distributed in the slots and is connected in star fashion. The open ends of the star-connected rotor winding are brought out and connected to three slip rings mounted in the rotor shaft. A carbon brush is resting on each slip ring, and through these brushes, external resistances can be added to the rotor circuit. At starting, suitable values of external resistances are added into phases of the rotor winding to obtain a high starting torque. These external resistances are gradually removed from the circuit as the motor runs up to speed. The use of external resistances considerably reduces the starting current and increases the starting torque of the motor. Once the motor attains normal speed, the three carbon brushes are short-circuited so that the wound motor runs like a squirrel cage induction motor. Learning working make money

Electrical Machines Tutorial Job Search Electrical Machines is a core subject within electrical engineering discipline that deals with the design, operation and applications of energy conversion devices. A system that converts electrical energy into other forms of energy is known as an Electrical Machine. The purpose of the tutorial is to introduce and explain the fundamental concepts in Electrical Machines, which include Basic Concepts of Electromechanical Energy Conversion Devices, Transformers, DC Machines (Motor and Generator), Induction Motors, and Synchronous Machines (Alternator and Motor). Audience The target of this tutorial is electrical engineering students. It is good resource to help them gain knowledge on fundamentals of electrical machines. Prerequisites This tutorial is meant for novice readers. Almost anyone with a basic knowledge of elementary physics and electric circuits can make the most of this tutorial. It is difficult to avoid complex mathematics at some places, although we have tried to keep it at a minimum level. Therefore, it is expected that the readers are comfortable with mathematical equations. Learning working make money

Types of DC Generators In practical DC generators, the magnetic field is produced by electromagnets rather than permanent magnets. The DC generators are then classified based on the connection of field winding in the generator circuit. On this basis, DC generators are classified into the following two types − Separately Excited DC Generators Self-Excited DC Generators Separately Excited DC Generator A DC generator whose magnetic field winding is excited from an independent source of DC electric supply like battery is called a separately excited DC generator. Figure-1 shows the connection diagram of a separately excited DC generator. The voltage generated by a separately excited DC generator depends upon the speed of the armature rotation and the field current (i.e. flux in the machine). The greater the speed of armature and field current, greater is the induced EMF in the generator. However, the separately excited DC generators are rarely used in practical applications because these require an external source of DC power for field excitation. Self-Excited DC Generators The type of DC generator whose magnetic field winding is excited from the output of the generator itself is known as a self-excited DC generator. Depending upon the manner in which the field winding is connected to the armature, self-excited DC generators are classified into the following three types − Series DC generator Shunt DC generator Compound DC generator Series DC Generator A dc generator whose field winding is connected in series with the armature so that whole armature current flows through the field winding as well as the load is called a series DC generator. Figure-2 shows the connection diagram of a series DC generator. In case of series dc generator, the field winding carries the whole load current, thus it is made up of thick wire with a few turns, so it possesses minimum resistance. The series DC generator is used in special applications like boosters, etc. The following are some important expressions for the series DC generator − $$mathrm{mathrm{Armature:current},mathit{I_{a}}:=:mathit{I_{se}}:=:mathit{I_{L}}}$$ Where,$mathit{I_{se}}$ is the series field current and $mathit{I_{L}}$ is the load current. $$mathrm{mathrm{Terminal:voltage},mathit{V_{t}}:=:mathit{E-I_{a}left ( mathit{R_{a}+R_{se}} right )}}$$ Where, E is the generated EMF, $mathit{R_{a}}$ is the armature circuit resistance,$mathit{R_{se}}$ is the series field resistance. Shunt DC Generator A DC generator whose field winding is connected in parallel with the armature winding so that terminal voltage of the generator is applied across it, is known as a shunt DC generator. Figure-3 shows the connection diagram of a shunt DC generator. In a shunt DC generator, the shunt field winding has a large number of turns of thin wire so it has high resistance, and therefore only a part of armature current flows through it and the rest flows through the load. The following are important expressions of a shunt DC generator − $$mathrm{mathrm{Armature:current,}mathit{I_{a}}:=:mathit{I_{L}+I_{sh}}}$$ $$mathrm{mathrm{Shunt:field:current,}mathit{I_{sh}}:=:frac{mathit{V_{t}}}{mathit{R_{sh}}}}$$ $$mathrm{mathrm{Terminal:voltage},mathit{V_{t}}:=:mathit{E-I_{a}R_{a}}}$$ Compound DC Generator A compound dc generator is one which has two sets of field windings on each magnetic pole – one is in series and the other is in parallel with the armature winding. The compound dc generators may further be divided into the following two types − Short-shunt compound DC generator Long-shunt compound DC generator A short-shunt compound DC generator is one in which only shunt field winding is in parallel with the armature winding as shown in Figure-4. A long-shunt compound DC generator is one in which shunt field winding is in parallel with both series field winding and armature winding as shown in Figure-5. The following are important expressions for compound DC generators − For short-shunt generator, $$mathrm{mathrm{Armature:current,}mathit{I_{a}}:=:mathit{I_{L}+I_{sh}}}$$ $$mathrm{mathrm{Series:field:current,}mathit{I_{se}}:=:mathit{I_{L}}}$$ $$mathrm{mathrm{Shunt:field:current,}mathit{I_{sh}}:=:frac{mathit{V_{t}}+mathit{I_{se}R_{se}}}{R_{sh}}}$$ $$mathrm{mathrm{Terminal:voltage},mathit{V_{t}}:=:mathit{E-I_{a}R_{a}-I_{se}R_{se}}}$$ For long-shunt generator, $$mathrm{mathrm{Armature:current,}mathit{I_{a}}:=:mathit{I_{L}+I_{sh}}}$$ $$mathrm{mathrm{Series:field:current,}mathit{I_{se}}:=:mathit{I_{a}}}$$ $$mathrm{mathrm{Shunt:field:current,}mathit{I_{sh}}:=:frac{mathit{V_{t}}}{mathit{R_{sh}}}}$$ $$mathrm{mathrm{Terminal:voltage},mathit{V_{t}}:=:mathit{E-I_{a}}left ( mathit{R_{a}+R_{se}} right )}$$ Learning working make money

Three-Phase Transformer In practice, electrical power is generated, transmitted and distributed by using three-phase system. Therefore, we require a three-phase transformer to step-up or step-down the voltage at various stages of a power system network. We can construct a three-phase transformer in one of the following two ways − We can connect three separate single-phase transformers for 3-phase operation. This arrangement is known as a three-phase bank of transformers. We can construct a single three-phase transformer which consists of a magnetic core and having windings for all the three phases. This whole assembly is combined in a single structure. The windings of a three-phase transformer may be connected in the following ways − Star-Star Connection − In this case, both primary and secondary windings are connected in star connection. Delta-Delta Connection − In this case, both primary and secondary windings are connected in delta connection. Delta-Star Connection − In this case, the primary winding is connected in delta, while the secondary winding is connected in star. Star-Delta Connection − In this case, the primary winding is connected in star while the secondary winding is connected in delta. Construction of Three Phase Transformer A three phase transformer can be constructed in two ways namely core-type construction and shell-type construction. Core Type Construction In the core type construction of 3-phase transformer, the magnetic core has three vertical limbs and two horizontal sections as shown in Figure-1. Here, one pair of primary and secondary windings is placed on each limb. The low voltage (lv) winding is placed next to the core while the high-voltage (hv) winding is wound around the lv winding. Shell Type Construction A shell type three-phase transformer can be constructed by stacking three single-phase shell-type transformers together as shown in Figure-2. In this case, both primary and secondary windings are placed on the central limb and the two outer limbs serve the path for flux. The behavior of a shell-type three-phase transformer is almost similar to that of a bank of three single-phase transformers. Advantages of a Bank of Three Single Phase Transformers The following are the major advantages that a bank of three single-phase transformers have over a three-phase unit transformer − When one 1-phase transformer of a bank of transformers is damaged and isolated from the service, the remaining two transformers may be used to supply power in open-delta connection. In the bank of transformers, we can provide a single-phase transformer with higher kVA rating than the others to supply an imbalance load. For a bank of three single-phase transformers, the standby requirement is lesser. It is more convenient to transport a 1-phase transformer than a 3-phase transformer. Advantages of a Three Phase Unit Transformer For the same kVA rating, a three-phase unit transformer has the following advantages over a bank of three single-phase transformers − A three-phase unit transformer is smaller in size, light in weight and cheaper. It is more efficient than bank of transformers. Its installation is simple. Depending upon the requirements, we use both bank of transformers and a three-phase unit transformer. However, it is a common practice to use a three-phase unit transformer. Learning working make money

Three-Phase Induction Motor As the name suggests, a three-phase induction motor is one which works on three-phase AC supply, and converts three-phase AC electricity into mechanical energy. Three-phase induction motors are the most extensively used electric motors in industries. These motors run at almost a constant speed from no-load to full-load, i.e., they have good speed regulation. Although the speed of three-phase induction motors depends on the supply frequency and number of poles in the machine and therefore, it is quite difficult to change their speed. Just like any other electric motor, a typical three-phase induction motor also consists of two main parts namely stator and rotor. The stator is a stationary part and carries a three-phase winding, called stator winding. The rotor is a rotating part of the motor and carries a short-circuited winding, called rotor winding. The stator winding of a three-phase induction motor is fed from a three-phase balanced AC supply, while the rotor winding derives its working voltage and power from the stator winding via electromagnetic induction. This is why, it is named so. A three-phase induction motor may be considered to be a three-phase transformer with a rotating secondary winding. Therefore, it could be described as a transformer-type AC machine. The only difference is that the induction motor converts electricity into mechanical energy. Types of Three-Phase Induction Motors According to the rotor construction, three-phase induction motors are classified into the following two basic types − Squirrel-Cage Induction Motor Slip-Ring Induction Motor Advantages of Three-Phase Induction Motors Here is a list of some of the major advantages of three-phase induction motors − The design and construction of three-phase induction motors are quite simple. They have robust construction. Three-phase induction motors require less maintenance. Three-phase induction motors have self-starting property. These motors have reasonably good power factor. Three-phase induction motors are more economical. They have high efficiency. Disadvantages of Three-Phase Induction Motors The major disadvantages of three-phase induction motors are listed below − Three-phase induction motors are essentially constant speed motors, and require complex mechanism to change the speed. Three-phase induction motors always work on lagging power factor. These motors draw very high starting current. Applications of Three-Phase Induction Motors The major applications of three-phase induction motors are given below − The squirrel-cage type three-phase induction motors are suitable for driving blowers, fans, machine tools, centrifugal pumps, etc. Three-phase induction motors are also used for driving different industrial load like compressors, crushers, conveyors, reciprocating pumps, etc. The slip-ring induction motors are best suited for driving loads that require high starting toque like crushers, plungers, cranes, elevators, hoists, conveyors, etc. Learning working make money

Types of DC Motors In practical DC motors, the magnetic field is produced by electromagnets rather than permanent magnets. DC motors are then classified based on the connection of field winding in the motor circuit. On this basis, DC motors are classified into the following two types − Separately Excited DC Motors Self-Excited DC Motors Separately Excited DC Motor A DC motor whose magnetic field winding is excited from an independent source of DC electric supply like a battery is called a separately excited DC motor. Figure-1 shows the connection diagram of a separately excited DC motor. The speed of a separately excited DC motor depends upon the supply voltage and field current, i.e. magnetic flux in the machine. However, the separately excited DC motors are rarely used in practical applications because these require an external source of DC power for field excitation. Self-Excited DC Motors The type of DC motor whose magnetic field winding is excited from the same power supply from which the armature is supplied, is known as a self-excited DC motor. Depending upon the manner in which the field winding is connected with the armature winding, self-excited DC motors are classified in the following three types − Series DC motor Shunt DC motor Compound DC motor Series DC Motor A DC motor whose field winding is connected in series with the armature winding so that whole armature current passes through the field winding is called a series DC motor. Figure-2 shows the connection diagram of a series DC motor. In case of a series DC motor, the field winding carries the whole armature current, thus it is made up of thick wire with less number of turns so that it possesses minimum resistance. The following are some important expressions for the series DC motor − $$mathrm{mathrm{Armature:current},mathit{I_{a}}:=:mathit{I_{se}}:=:mathit{I_{s}}}$$ Where, $mathit{I_{se}}$ is the series field current and $mathit{I_{s}}$ is the supply current. $$mathrm{mathrm{Supply:voltage},mathit{V_{s}}:=:mathit{E_{b}+I_{a}left ( mathit{R_{a}+R_{se}} right )}}$$ Where, $mathit{E_{b}}$ is the back EMF, $mathit{R_{a}}$ is the armature circuit resistance, $mathit{R_{se}}$ is the series field resistance. Shunt DC Motor A DC motor whose field winding is connected in parallel with the armature winding so that total supply voltage is applied across it, is known as a shunt DC motor. Figure-3 shows the connection diagram of a shunt DC motor. In a shunt DC motor, the shunt field winding has a large number of turns of thin wire so that it has high resistance, and therefore only a part of supply current flows through it and the rest flows through the armature winding. Following are the important expressions of a shunt DC motor − $$mathrm{mathrm{Armature:current,}mathit{I_{a}}:=:mathit{I_{s}-I_{sh}}}$$ $$mathrm{mathrm{Shunt:field:current,}mathit{I_{sh}}:=:mathit{frac{V_{s}}{R_{sh}}}}$$ $$mathrm{mathrm{Supply:Voltage,}mathit{V_{s}}:=:mathit{E_{b}+I_{a}R_{a}}}$$ Compound DC Motor A compound DC motor is one which has two sets of field windings on each magnetic pole – one is in series and the other is in parallel with the armature winding. Compound DC motors are sub-divided into the following two types − Short-shunt compound DC motor Long-shunt compound DC motor A short-shunt compound DC motor is one in which only shunt field winding is in parallel with the armature winding as shown in Figure-4. A long-shunt compound DC motor is one in which shunt field winding is in parallel with both series field winding and armature winding as shown in Figure-5. The following are the important expressions for compound DC motors − For short-shunt motor, $$mathrm{mathrm{Armature:current,}mathit{I_{a}}:=:mathit{I_{s}-I_{sh}}}$$ $$mathrm{mathrm{Series:field:current,}mathit{I_{se}}:=:mathit{I_{a}}}$$ $$mathrm{mathrm{Shunt:field:current,}mathit{I_{sh}}:=:frac{mathit{V_{s}}-mathit{I_{se}R_{se}}}{R_{sh}}}$$ $$mathrm{mathrm{Supply:voltage},mathit{V_{s}}:=:mathit{E_{b}+I_{a}R_{a}+I_{se}R_{se}}}$$ For long-shunt motor, $$mathrm{mathrm{Armature:current,}mathit{I_{a}}:=:mathit{I_{s}-I_{sh}}}$$ $$mathrm{mathrm{Series:field:current,}mathit{I_{se}}:=:mathit{I_{s}}}$$ $$mathrm{mathrm{Shunt:field:current,}mathit{I_{sh}}:=:frac{mathit{V_{s}}}{R_{sh}}}$$ $$mathrm{mathrm{Supply:voltage},mathit{V_{s}}:=:mathit{E_{b}+I_{a}left ( R_{a}+R_{se} right )}}$$ Learning working make money

Faraday’s Laws of Electromagnetic Induction When a changing magnetic field links to a conductor or coil, an EMF is produced in the conductor or coil, this phenomenon is known as electromagnetic induction. The electromagnetic induction is the most fundamental concept used to design the electrical machines. Michael Faraday, an English scientist, performed several experiments to demonstrate the phenomenon of electromagnetic induction. He concluded the results of all experiments into two laws, popularly known as Faraday’s laws of electromagnetic induction. Faraday’s First Law Faraday’s first law of electromagnetic induction provides information about the condition under which an EMF is induced in a conductor or coil. The first law states that − When a magnetic flux linking to a conductor or coil changes, an EMF is induced in the conductor or coil. Therefore, the basic need for inducing EMF in a conductor or coil is the change in the magnetic flux linking to the conductor or coil. Faraday’s Second Law Faraday’s second law of electromagnetic induction gives the magnitude of the induced EMF in a conductor or coil and it may be states as follows − The magnitude of the induced EMF in a conductor or coil is directly proportional to the time rate of change of magnetic flux linkage. Explanation Consider a coil has N turns and magnetic flux linking the coil changes from $mathit{phi _{mathrm{1}}}$ weber to $mathit{phi _{mathrm{2}}}$ weber in time t seconds. Now, the magnetic flux linkage ($mathit{psi }$) to a coil is the product of magnetic flux and number of turns in the coil. Therefore, $$mathrm{mathrm{Initial: magnetic: flux: linkage,}mathit{psi _{mathrm{1}}}:=:mathit{Nphi _{mathrm{1}}}}$$ $$mathrm{mathrm{Final: magnetic: flux: linkage,}mathit{psi _{mathrm{2}}}:=:mathit{Nphi _{mathrm{2}}}}$$ According to Faraday’s law of electromagnetic induction, $$mathrm{mathrm{Induced: EMF,}mathit{e}propto frac{mathit{Nphi _{mathrm{2}}}-mathit{Nphi} _{mathrm{1}}}{mathit{t}}cdot cdot cdot (1)}$$ $$mathrm{Rightarrow mathit{e}:=:mathit{k}left ( frac{mathit{Nphi _{mathrm{2}}}-mathit{Nphi} _{mathrm{1}}}{mathit{t}} right )}$$ Where, k is a constant of proportionality, its value is unity in SI units. Therefore, the induced EMF in the coil is given by, $$mathrm{mathit{e}:=:frac{mathit{Nphi _{mathrm{2}}}-mathit{Nphi} _{mathrm{1}}}{mathit{t}}cdot cdot cdot (2)}$$ In differential form, $$mathrm{mathit{e}:=:mathit{N}frac{mathit{dphi }}{mathit{dt}}cdot cdot cdot (3)}$$ The direction of induced EMF is always such that it tends set up a current which produces a magnetic flux that opposes the change of magnetic flux responsible for inducing the EMF. Therefore, the magnitude and direction of the induced EMF in the coil is to be written as, $$mathrm{ mathit{e}:=:mathit{-N}frac{mathit{dphi }}{mathit{dt}}cdot cdot cdot (4)}$$ Where, the negative (-) sign shows that the direction of the induced EMF is such that it opposes the cause that produces it, i.e., the change in the magnetic flux, this statement is known as Lenz’s law. The equation (4) is the mathematical representation of Lenz’s law. Learning working make money