The motor is operating at full load with a slip of 4%.
Determine:
1. The rotor current
2. The rotor copper loss
3. The air-gap power
4. The efficiency
Solution:
Given:
V=460V, f=60Hz, P=25hp, Poles=4, R1=0.641Ω, R2=0.332Ω, X1=1.106Ω, Slip(s)=4%
1. Rotor current
I2 = V/(R2 + jX2)
= 460/(0.332 + j1.106*0.04)
= 460/0.344
This document discusses direct current (DC) motors, including:
1) It introduces DC motors and explains their advantages over AC motors for certain applications.
2) It describes the basic working principle of DC motors, which involves a current-carrying conductor experiencing a force when placed in a magnetic field.
3) It discusses the different types of DC motors - shunt-wound, series-wound, and compound-wound - and explains their characteristics.
4) It provides equations for the voltage and power of DC motors and uses examples to demonstrate how to solve problems related to back EMF, speed, power input/output, and other motor parameters.
The armature winding is the main current-carrying winding in which the electromotive force or counter-emf of rotation is induced.
The current in the armature winding is known as the armature current.
The location of the winding depends upon the type of machine.
The armature windings of dc motors are located on the rotor, since they must operate in union with the commutator.
In DC rotating machines other than brushless DC machines, it is usually rotating.
The document discusses alternator construction and operation. It describes how alternators use a stationary armature winding and rotating magnetic field to generate alternating current. The key points are:
- Alternators have a stationary armature winding mounted on the stator and field windings on the rotating rotor. As the rotor spins, it induces an alternating current in the stationary armature coils.
- This arrangement allows the high-voltage AC output to be extracted directly from the stator terminals without brushes or slip rings. It also places the low-voltage DC field circuit on the rotor.
- The frequency of the generated AC is determined by the number of magnetic pole pairs on the rotor and the rotational speed according to the
1) For alternators to operate in parallel, they must be synchronized by having equal line voltage, frequency, phase sequence, phase angle, and waveform.
2) When alternators are synchronized and operating in parallel with no load, a circulating current will flow if their speeds or excitations differ slightly.
3) This circulating current acts to resynchronize the alternators by speeding up the slower one and slowing the faster one through their functioning as motor and generator respectively, until steady state is reached with no circulating current.
The document discusses induction motors, which are asynchronous AC motors that operate below synchronous speed. It describes the two main types - single phase and three phase induction motors. Three phase induction motors are commonly used in industry due to their ability to provide bulk power conversion from electrical to mechanical power. The document then discusses the construction and working principles of three phase induction motors in detail, including their stator, rotor, and how rotational motion is induced in the rotor via electromagnetic induction from the rotating stator magnetic field.
Induction motor modelling and applicationsUmesh Dadde
A three-phase induction motor is one of the most popular and versatile motor in electrical
power system and industries. It can perform the best when operated using a balanced three-phase
supply of the correct frequency. In spite of their robustness they do occasionally fail and their
resulting unplanned downtime can prove very costly. Therefore, condition monitoring of
electrical machines has received considerable attention in recent years.
This document provides information about induction motors. It describes the basic construction of an induction motor, including its stator and squirrel cage or wound rotor. It explains how a rotating magnetic field is produced from the three-phase stator windings and how this induces a voltage and current in the rotor. It defines key terms like synchronous speed and slip. It also presents the equivalent circuit model of an induction motor and discusses speed control methods and power losses in induction machines.
This document discusses direct current (DC) motors, including:
1) It introduces DC motors and explains their advantages over AC motors for certain applications.
2) It describes the basic working principle of DC motors, which involves a current-carrying conductor experiencing a force when placed in a magnetic field.
3) It discusses the different types of DC motors - shunt-wound, series-wound, and compound-wound - and explains their characteristics.
4) It provides equations for the voltage and power of DC motors and uses examples to demonstrate how to solve problems related to back EMF, speed, power input/output, and other motor parameters.
The armature winding is the main current-carrying winding in which the electromotive force or counter-emf of rotation is induced.
The current in the armature winding is known as the armature current.
The location of the winding depends upon the type of machine.
The armature windings of dc motors are located on the rotor, since they must operate in union with the commutator.
In DC rotating machines other than brushless DC machines, it is usually rotating.
The document discusses alternator construction and operation. It describes how alternators use a stationary armature winding and rotating magnetic field to generate alternating current. The key points are:
- Alternators have a stationary armature winding mounted on the stator and field windings on the rotating rotor. As the rotor spins, it induces an alternating current in the stationary armature coils.
- This arrangement allows the high-voltage AC output to be extracted directly from the stator terminals without brushes or slip rings. It also places the low-voltage DC field circuit on the rotor.
- The frequency of the generated AC is determined by the number of magnetic pole pairs on the rotor and the rotational speed according to the
1) For alternators to operate in parallel, they must be synchronized by having equal line voltage, frequency, phase sequence, phase angle, and waveform.
2) When alternators are synchronized and operating in parallel with no load, a circulating current will flow if their speeds or excitations differ slightly.
3) This circulating current acts to resynchronize the alternators by speeding up the slower one and slowing the faster one through their functioning as motor and generator respectively, until steady state is reached with no circulating current.
The document discusses induction motors, which are asynchronous AC motors that operate below synchronous speed. It describes the two main types - single phase and three phase induction motors. Three phase induction motors are commonly used in industry due to their ability to provide bulk power conversion from electrical to mechanical power. The document then discusses the construction and working principles of three phase induction motors in detail, including their stator, rotor, and how rotational motion is induced in the rotor via electromagnetic induction from the rotating stator magnetic field.
Induction motor modelling and applicationsUmesh Dadde
A three-phase induction motor is one of the most popular and versatile motor in electrical
power system and industries. It can perform the best when operated using a balanced three-phase
supply of the correct frequency. In spite of their robustness they do occasionally fail and their
resulting unplanned downtime can prove very costly. Therefore, condition monitoring of
electrical machines has received considerable attention in recent years.
This document provides information about induction motors. It describes the basic construction of an induction motor, including its stator and squirrel cage or wound rotor. It explains how a rotating magnetic field is produced from the three-phase stator windings and how this induces a voltage and current in the rotor. It defines key terms like synchronous speed and slip. It also presents the equivalent circuit model of an induction motor and discusses speed control methods and power losses in induction machines.
This document defines several basic concepts related to electric machines:
- The stator is the stationary part, and the rotor is the rotating part connected to the shaft. An air gap separates the stator and rotor.
- Machines can be DC or AC depending on the input/output current type. AC machines include synchronous and induction machines.
- Other concepts defined include the armature, field windings, load and magnetizing currents, slots/coils configuration, pole/slot pitch, and fractional vs full pitch coils.
- The torque produced in a current loop is proportional to the cross product of the magnetic field and current. The torque produced in a machine depends on the sine of the rotor position and
SINGLE PHASE INDUCTION MOTORS AND SPECIAL MACHINESRagulS61
Constructional details – Double revolving field theory – Equivalent circuit – Starting methods – Role of induction motor in industries and household appliances – Reluctance motor - Servo motor - Stepper motor - Universal motor - Switched reluctance motor - Linear induction motor – Linear Synchronous motor.
An AC motor uses an alternating current to generate a rotating magnetic field in the stator that interacts with the rotor. The two main types are induction and synchronous motors. Induction motors rely on electromagnetic induction to generate a current in the rotor from the stator's rotating magnetic field, causing the rotor to turn at a slower synchronous speed. Squirrel cage rotors have embedded conductors in a striped pattern and are simple, reliable, and cheaper but have poor starting torque. Wound rotors have coils connected through slip rings that allow reducing starting current and enabling speed control.
Solved Examples for Three - Phase Induction MotorsAli Altahir
This document provides solutions to two academic examples involving calculations related to induction motors. The first example calculates motor slip percentage, induced torque, operating speed if torque is doubled, and gross power if torque is doubled for a given induction motor setup. The second example calculates maximum torque, corresponding speed and slip, starting torque, effect of doubling rotor resistance, sketches torque-slip curves, and checks motor stability at different speeds. Review questions are also provided related to torque-speed characteristics, torque development, starting torque control, speed control, maximum torque conditions, full load torque, self-starting behavior, slip never being zero, effects of rotor resistance, reasons for high starting torque, and motors with high starting torque.
This document describes a project to control the speed of a single-phase induction motor using a TRIAC. It includes sections on the circuit description, induction motor working, SCR, TRIAC, DIAC, applications, advantages and disadvantages. The circuit uses a DIAC to trigger a TRIAC, allowing control of the firing angle to vary the voltage applied to the motor. This provides speed control of the induction motor for applications like pumps, fans and refrigeration.
1) The document describes the equivalent circuit model and power equations of a synchronous motor. It discusses how changes in shaft load, field excitation, and armature current affect the power angle, armature current, and power factor.
2) Increasing shaft load causes the power angle to increase and leads to a decrease in power factor. Increasing field excitation causes the power angle to decrease and can change the power factor from lagging to leading.
3) The document contains diagrams of the phasor relationships and how they change under different operating conditions, including under, normal, and over excitation levels.
Watch Video of this presentation on Link: https://youtu.be/bHKaPBgDk6g
For notes/articles, Visit my blog (link is given below).
For Video, Visit our YouTube Channel (link is given below).
Any Suggestions/doubts/reactions, please leave in the comment box.
Follow Us on
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An alternator is an electrical generator that converts mechanical energy to electrical energy in the form of alternating current. For reasons of cost and simplicity, most alternators use a rotating magnetic field with a stationary armature.
The document summarizes the operating principles and key components of an alternator. It operates on the principle of electromagnetic induction, with a stationary armature and rotating magnetic field. As the rotor rotates, voltage is induced in the stationary conductors. The induced emf is alternating current. Advantages of the stationary armature include reduced voltage drop from fixed terminals and easier insulation of windings. Key components include the stator frame, armature core, cylindrical or salient pole rotor, and damper windings. Ratings specified include voltage, KVA, power factor, and winding resistances. Regulation refers to the drop in terminal voltage from no load to full load conditions.
Synchronous generators operate on the principle of electromagnetic induction. They have a stationary armature winding and a rotating field winding supplied by a direct current source. It is advantageous to have the field winding on the rotor and armature winding on the stator because it allows for easier insulation of the high voltage winding and direct connection to the load. The frequency of the induced voltage depends on the number of rotor poles and its rotational speed. Armature reaction is the effect of the armature magnetic field on the main rotor field, distorting or strengthening it depending on the load power factor.
1. Three phase induction motors have a rotating magnetic field produced by a three phase stator winding that causes the rotor to turn.
2. The rotor can be either a squirrel cage (copper or aluminum bars short circuited by end rings) or wound construction.
3. Starters are used to reduce the starting current by lowering the supply voltage and improve starting torque by increasing rotor resistance during start up. Common starting methods include direct-on-line, star-delta, and auto transformer starters.
This document discusses DC motors. It begins with an introduction, explaining that a DC motor converts electrical energy to mechanical energy using electricity and a magnetic field to produce torque. It then discusses the principle, construction, types, and applications of DC motors. The principle section explains that a current-carrying conductor in a magnetic field experiences a Lorentz force, producing torque. The construction section states that DC motors have two windings: a stationary field winding and a rotating armature winding. The types section describes the three main types of DC motors: shunt, series, and compound. The applications section lists examples like lathes and fans using shunt motors, and electric traction using series motors.
3 phase half wave controlled converter with r Loadmechatronics jf
This document discusses three-phase converters that convert AC power to DC power for loads. It specifically describes three-phase half-wave controlled rectifiers, which are made up of three single-phase half-wave converters connected together. It provides the equation to calculate the average DC output voltage of a three-phase half-wave converter and discusses that the thyristor conducts from 30 degrees to 180 degrees for a resistive load. The document concludes by describing a problem to calculate firing angle, average/RMS load current, and efficiency for a 3-phase converter operating from a 230V 50Hz supply with a 10 ohm resistive load and 50% of maximum output voltage required.
The document describes two types of AC lap windings for electrical machines:
1) A single-phase, single-layer lap winding is developed for a 4-pole, 24-slot AC machine. The winding table is provided.
2) A double-layer lap winding is developed for a 3-phase, 4-pole, 24-slot AC machine. The slot distribution and winding table for the RYB phases are provided. A diagram of the complete main winding is included.
Synchronous generators are the majority source of commercial electrical energy. They are commonly used to convert the mechanical power output of steam turbines, gas turbines, reciprocating engines and hydro turbines into electrical power for the grid.
This document contains 5 numerical problems related to analyzing the operation of three-phase induction machines. Problem 1 involves calculating various speeds, frequencies, and voltages given machine specifications operating at rated slip. Problem 2 involves calculating power values given a 3-phase induction motor's rated power and windage/friction losses. Problem 3 involves calculating starting and full-load operating values like current, slip, and efficiency given motor parameters. Problem 4 involves determining the resistance value needed in the rotor circuit to reduce the motor speed from operating at a given speed and load to a lower speed. Problem 5 involves calculating torque values from the ratio of starting to full-load rotor current.
Stepper motors are brushless DC motors that rotate in discrete steps. They have an external rotor divided into teeth that engages with internal electromagnets to rotate the shaft in steps. There are different types including permanent magnet, variable reluctance, and hybrid stepper motors that use different techniques to generate torque. Stepper motors are useful for applications requiring precise positional control like printers, factory automation equipment, and CNC machines.
The document discusses different types of electrical motors, including AC motors like induction motors and synchronous motors, and DC motors like shunt motors and series motors. It covers motor construction, cooling methods, load characteristics, starting methods, protection devices, and causes of motor failure. The key types of motors described are induction motors, synchronous motors, and DC motors. Methods of cooling discussed include TEFC, TETV, CACA and CACW. Bearing selection and motor protection are also summarized.
Three-phase induction motors are commonly used in industry due to their simple and rugged design. They run at a constant speed below synchronous speed due to the slip between the rotating magnetic field and the rotor. An induction motor contains a stationary stator and a revolving rotor. The stator produces a rotating magnetic field which induces a voltage and current in the rotor windings, generating torque. Torque and power equations are developed using the motor's equivalent circuit model, which relates the motor's electrical inputs and outputs.
This document defines several basic concepts related to electric machines:
- The stator is the stationary part, and the rotor is the rotating part connected to the shaft. An air gap separates the stator and rotor.
- Machines can be DC or AC depending on the input/output current type. AC machines include synchronous and induction machines.
- Other concepts defined include the armature, field windings, load and magnetizing currents, slots/coils configuration, pole/slot pitch, and fractional vs full pitch coils.
- The torque produced in a current loop is proportional to the cross product of the magnetic field and current. The torque produced in a machine depends on the sine of the rotor position and
SINGLE PHASE INDUCTION MOTORS AND SPECIAL MACHINESRagulS61
Constructional details – Double revolving field theory – Equivalent circuit – Starting methods – Role of induction motor in industries and household appliances – Reluctance motor - Servo motor - Stepper motor - Universal motor - Switched reluctance motor - Linear induction motor – Linear Synchronous motor.
An AC motor uses an alternating current to generate a rotating magnetic field in the stator that interacts with the rotor. The two main types are induction and synchronous motors. Induction motors rely on electromagnetic induction to generate a current in the rotor from the stator's rotating magnetic field, causing the rotor to turn at a slower synchronous speed. Squirrel cage rotors have embedded conductors in a striped pattern and are simple, reliable, and cheaper but have poor starting torque. Wound rotors have coils connected through slip rings that allow reducing starting current and enabling speed control.
Solved Examples for Three - Phase Induction MotorsAli Altahir
This document provides solutions to two academic examples involving calculations related to induction motors. The first example calculates motor slip percentage, induced torque, operating speed if torque is doubled, and gross power if torque is doubled for a given induction motor setup. The second example calculates maximum torque, corresponding speed and slip, starting torque, effect of doubling rotor resistance, sketches torque-slip curves, and checks motor stability at different speeds. Review questions are also provided related to torque-speed characteristics, torque development, starting torque control, speed control, maximum torque conditions, full load torque, self-starting behavior, slip never being zero, effects of rotor resistance, reasons for high starting torque, and motors with high starting torque.
This document describes a project to control the speed of a single-phase induction motor using a TRIAC. It includes sections on the circuit description, induction motor working, SCR, TRIAC, DIAC, applications, advantages and disadvantages. The circuit uses a DIAC to trigger a TRIAC, allowing control of the firing angle to vary the voltage applied to the motor. This provides speed control of the induction motor for applications like pumps, fans and refrigeration.
1) The document describes the equivalent circuit model and power equations of a synchronous motor. It discusses how changes in shaft load, field excitation, and armature current affect the power angle, armature current, and power factor.
2) Increasing shaft load causes the power angle to increase and leads to a decrease in power factor. Increasing field excitation causes the power angle to decrease and can change the power factor from lagging to leading.
3) The document contains diagrams of the phasor relationships and how they change under different operating conditions, including under, normal, and over excitation levels.
Watch Video of this presentation on Link: https://youtu.be/bHKaPBgDk6g
For notes/articles, Visit my blog (link is given below).
For Video, Visit our YouTube Channel (link is given below).
Any Suggestions/doubts/reactions, please leave in the comment box.
Follow Us on
YouTube: https://www.youtube.com/channel/UCVPftVoKZoIxVH_gh09bMkw/
Blog: https://e-gyaankosh.blogspot.com/
Facebook: https://www.facebook.com/egyaankosh/
An alternator is an electrical generator that converts mechanical energy to electrical energy in the form of alternating current. For reasons of cost and simplicity, most alternators use a rotating magnetic field with a stationary armature.
The document summarizes the operating principles and key components of an alternator. It operates on the principle of electromagnetic induction, with a stationary armature and rotating magnetic field. As the rotor rotates, voltage is induced in the stationary conductors. The induced emf is alternating current. Advantages of the stationary armature include reduced voltage drop from fixed terminals and easier insulation of windings. Key components include the stator frame, armature core, cylindrical or salient pole rotor, and damper windings. Ratings specified include voltage, KVA, power factor, and winding resistances. Regulation refers to the drop in terminal voltage from no load to full load conditions.
Synchronous generators operate on the principle of electromagnetic induction. They have a stationary armature winding and a rotating field winding supplied by a direct current source. It is advantageous to have the field winding on the rotor and armature winding on the stator because it allows for easier insulation of the high voltage winding and direct connection to the load. The frequency of the induced voltage depends on the number of rotor poles and its rotational speed. Armature reaction is the effect of the armature magnetic field on the main rotor field, distorting or strengthening it depending on the load power factor.
1. Three phase induction motors have a rotating magnetic field produced by a three phase stator winding that causes the rotor to turn.
2. The rotor can be either a squirrel cage (copper or aluminum bars short circuited by end rings) or wound construction.
3. Starters are used to reduce the starting current by lowering the supply voltage and improve starting torque by increasing rotor resistance during start up. Common starting methods include direct-on-line, star-delta, and auto transformer starters.
This document discusses DC motors. It begins with an introduction, explaining that a DC motor converts electrical energy to mechanical energy using electricity and a magnetic field to produce torque. It then discusses the principle, construction, types, and applications of DC motors. The principle section explains that a current-carrying conductor in a magnetic field experiences a Lorentz force, producing torque. The construction section states that DC motors have two windings: a stationary field winding and a rotating armature winding. The types section describes the three main types of DC motors: shunt, series, and compound. The applications section lists examples like lathes and fans using shunt motors, and electric traction using series motors.
3 phase half wave controlled converter with r Loadmechatronics jf
This document discusses three-phase converters that convert AC power to DC power for loads. It specifically describes three-phase half-wave controlled rectifiers, which are made up of three single-phase half-wave converters connected together. It provides the equation to calculate the average DC output voltage of a three-phase half-wave converter and discusses that the thyristor conducts from 30 degrees to 180 degrees for a resistive load. The document concludes by describing a problem to calculate firing angle, average/RMS load current, and efficiency for a 3-phase converter operating from a 230V 50Hz supply with a 10 ohm resistive load and 50% of maximum output voltage required.
The document describes two types of AC lap windings for electrical machines:
1) A single-phase, single-layer lap winding is developed for a 4-pole, 24-slot AC machine. The winding table is provided.
2) A double-layer lap winding is developed for a 3-phase, 4-pole, 24-slot AC machine. The slot distribution and winding table for the RYB phases are provided. A diagram of the complete main winding is included.
Synchronous generators are the majority source of commercial electrical energy. They are commonly used to convert the mechanical power output of steam turbines, gas turbines, reciprocating engines and hydro turbines into electrical power for the grid.
This document contains 5 numerical problems related to analyzing the operation of three-phase induction machines. Problem 1 involves calculating various speeds, frequencies, and voltages given machine specifications operating at rated slip. Problem 2 involves calculating power values given a 3-phase induction motor's rated power and windage/friction losses. Problem 3 involves calculating starting and full-load operating values like current, slip, and efficiency given motor parameters. Problem 4 involves determining the resistance value needed in the rotor circuit to reduce the motor speed from operating at a given speed and load to a lower speed. Problem 5 involves calculating torque values from the ratio of starting to full-load rotor current.
Stepper motors are brushless DC motors that rotate in discrete steps. They have an external rotor divided into teeth that engages with internal electromagnets to rotate the shaft in steps. There are different types including permanent magnet, variable reluctance, and hybrid stepper motors that use different techniques to generate torque. Stepper motors are useful for applications requiring precise positional control like printers, factory automation equipment, and CNC machines.
The document discusses different types of electrical motors, including AC motors like induction motors and synchronous motors, and DC motors like shunt motors and series motors. It covers motor construction, cooling methods, load characteristics, starting methods, protection devices, and causes of motor failure. The key types of motors described are induction motors, synchronous motors, and DC motors. Methods of cooling discussed include TEFC, TETV, CACA and CACW. Bearing selection and motor protection are also summarized.
Three-phase induction motors are commonly used in industry due to their simple and rugged design. They run at a constant speed below synchronous speed due to the slip between the rotating magnetic field and the rotor. An induction motor contains a stationary stator and a revolving rotor. The stator produces a rotating magnetic field which induces a voltage and current in the rotor windings, generating torque. Torque and power equations are developed using the motor's equivalent circuit model, which relates the motor's electrical inputs and outputs.
Three-phase induction motors are commonly used in industry due to their simple and rugged design. They run at a constant speed below synchronous speed due to the slip between the rotating magnetic field and the rotor. An induction motor contains a stationary stator and a revolving rotor. The stator produces a rotating magnetic field which induces a voltage and current in the rotor windings, generating torque. Torque and power relationships allow calculation of motor parameters such as speed, current, power factor, and efficiency based on the equivalent circuit model.
- Three-phase induction motors are commonly used in industry due to their simple and rugged design, low cost, and ability to operate at a nearly constant speed from no load to full load.
- An induction motor contains a stationary stator and a revolving rotor. When a balanced three-phase supply is applied to the stator, it produces a rotating magnetic field which induces voltages in the rotor windings and causes the rotor to turn.
- The rotor always runs at a slightly lower speed than the synchronous speed determined by the supply frequency. The difference between the two speeds is called the slip and is typically 1-5% at full load.
An induction motor is described with the following specifications:
- 480-V, 60 Hz, 50-hp, 3-phase
- Drawing 60A at 0.85 PF lagging
- Stator copper losses of 2 kW
- Rotor copper losses of 700 W
To determine the rotor frequency at full load, the slip is calculated using the given power rating, current, and power factor. The slip is then used to calculate the rotor frequency.
Three-phase induction motors are commonly used in industry due to their simple and rugged design. They operate by creating a rotating magnetic field from the three-phase stator windings which induces a voltage and current in the rotor windings. This induced current creates a torque from the interaction between the rotor and stator magnetic fields, causing the rotor to turn at a slightly lower speed than the synchronous speed set by the stator frequency. The difference between the synchronous and actual motor speeds is called the slip. Induction motors can operate at variable speeds by adjusting the frequency of the power supply using a variable frequency drive.
1) The document discusses the principles of rotating magnetic fields in induction motors and their production using a balanced three-phase winding fed by a balanced three-phase source.
2) It describes the construction and operation of induction motors, including squirrel cage and wound rotor types. The motor speed is always lower than the synchronous speed due to slip.
3) Equivalent circuits are derived for the induction motor using Thevenin's theorem, allowing calculation of torque, power, and efficiency based on motor parameters.
Three-phase induction motors are commonly used in industry due to their simple and rugged design. They have a wide power rating range and can run at nearly constant speed from no load to full load. An induction motor contains a stationary stator and a revolving rotor. The stator produces a rotating magnetic field which induces a voltage in the rotor windings, generating a torque. Induction motors always run slightly slower than synchronous speed due to slip. They are efficient machines but require a variable frequency drive for variable speed control.
Rotating Electrical Machines-AC & DC Machines,Induction Motor and DC MotorPrasant Kumar
Rotating electrical machines,induction machines,induction motor,construction working principle of ac machines,working of dc machines construction of DC motor,starting,torque speed relation,speed control mechanism of dc machines
This document provides information on three-phase induction motors:
- It discusses the construction, operation, and advantages/disadvantages of three-phase induction motors. The main components are the stationary stator and revolving rotor, which can be either a squirrel cage or wound type.
- A balanced three-phase supply to the stator produces a rotating magnetic field that induces voltage in the rotor windings, generating torque. The motor runs slightly slower than the synchronous speed due to slip.
- Equivalent circuits are presented for analyzing induction motors, accounting for variables like induced voltage and reactance that change with slip frequency. Power losses and relationships are also examined.
Induction Machine electrical and electronicsprakashpacet
This document provides an overview of three-phase induction motors, including their construction, operation, and characteristics. It discusses the main components of induction motors, including the stator, squirrel cage rotor, and wound rotor. It explains how a rotating magnetic field is produced in the stator to induce voltage and current in the rotor. It also covers key concepts such as synchronous speed, slip speed, rotor frequency, torque production, and equivalent circuits. Power losses and relationships between input, output, and loss powers are also summarized.
Induction Machines electrical machines electrical and electronicsprakashpacet
This document summarizes the construction and operating principles of three-phase induction motors. It describes the main components of the stator and rotor, including squirrel cage and wound rotor designs. It explains how a rotating magnetic field is produced in the stator to induce voltage in the rotor windings. The motor runs at a speed slightly below synchronous speed due to slip. An equivalent circuit model is presented to analyze the motor. Power losses in different components are identified and power flow equations are provided.
This document discusses induction motors. It begins by explaining the basic construction and operation of 3-phase induction motors, including their squirrel cage and wound rotor types. It then describes how the rotating magnetic field is produced in the stator by the 3-phase currents and how this induces a voltage and current in the rotor. The document discusses how slip occurs and affects rotor speed and frequency. It also covers equivalent circuits, power losses, torque production, and provides an example problem calculating motor parameters.
This document provides information about synchronous motors and induction motors. It discusses the key characteristics and applications of synchronous motors, including their ability to maintain constant speed under varying loads. The document also explains the working principle of induction motors, how they develop torque through interaction between the stator and rotor magnetic fields. It analyzes the rotor currents and fluxes at different slip conditions like standstill, 5% slip, and no load. The summary compares the performance of synchronous and induction motors.
This document discusses three-phase induction motors. It describes their common use in industry due to their simple and rugged design. It explains that induction motors run at a constant speed from no-load to full-load. Variable speed control requires an adjustable frequency power supply. The motor has a stationary stator and a revolving rotor, which can have either wound or squirrel cage windings. A rotating magnetic field from the stator induces currents in the rotor to generate torque. Induction motors always run slightly slower than synchronous speed due to slip.
This document provides information about three-phase induction motors. It discusses the construction of induction motors including their stators and rotors. Squirrel cage and wound rotors are described. The document explains how a rotating magnetic field is produced in the stator to induce currents in the rotor. It discusses the principle of operation, slip speed, rotor current frequency, starting torque, and the relationship between torque and rotor power factor. Advantages and disadvantages of induction motors are also summarized.
3-φ induction motors operate based on the principles of electromagnetic induction. They contain a stationary stator with 3-phase windings connected to a 3-phase power supply. This produces a rotating magnetic field which cuts the rotor conductors and induces current in them. The interaction between the stator and rotor magnetic fields causes the rotor to rotate at a speed slightly less than synchronous speed. The amount the rotor speed is less than synchronous speed is called the slip. Torque characteristics are affected by the rotor resistance. Squirrel cage induction motors are used for fans, pumps and tools, while wound rotor motors are used for cranes and elevators due to their ability to control rotor resistance.
The document describes the construction and operating principles of induction motors. It discusses:
- The key components of induction motors including the stator, rotor, and rotating magnetic field generated by the stator windings.
- The two main types of rotors: squirrel cage and wound rotor. Squirrel cage rotors are simpler and more rugged while wound rotors can be used to adjust torque-speed characteristics.
- Concepts like synchronous speed, slip, and rotor frequency. Slip is defined as the difference between synchronous and actual rotor speed.
- The per-phase equivalent circuit model of induction motors and how it is used to analyze power flow and calculate performance parameters like torque.
The document discusses induction motors, also known as asynchronous motors. It describes their construction, including the stator, rotor, and rotating magnetic field produced. Squirrel cage and wound rotors are covered. Formulas for synchronous speed, slip, and rotor frequency are provided. Examples calculations are given to demonstrate determining speeds and frequencies under different operating conditions. The per-phase equivalent circuit of an induction motor is also mentioned.
This document discusses electric propulsion units used in electric vehicles and hybrid electric vehicles. It describes three main types of electric motors used: induction motors, permanent magnet brushless DC motors, and switched reluctance motors. For each motor type, the document covers basic operating principles, control methods, and applications in electric and hybrid vehicles. It also discusses losses in traction motors and inverters, as well as efficiency maps.
A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
2. Introduction
Three-phase induction motors are the most
common and frequently encountered machines in
industry
- simple design, rugged, low-price, easy maintenance
- wide range of power ratings: fractional horsepower to
10 MW
- run essentially as constant speed from no-load to full
load
- Its speed depends on the frequency of the power source
• not easy to have variable speed control
• requires a variable-frequency power-electronic drive for
optimal speed control
3. Construction
An induction motor has two main parts
- a stationary stator
• consisting of a steel frame that supports a hollow, cylindrical core
• core, constructed from stacked laminations (why?), having a
number of evenly spaced slots, providing the space for the stator
winding
Stator of IM
4. Construction
- a revolving rotor
• composed of punched laminations, stacked to create a series of rotor
slots, providing space for the rotor winding
• one of two types of rotor windings
• conventional 3-phase windings made of insulated wire (wound-rotor) »
similar to the winding on the stator
• aluminum bus bars shorted together at the ends by two aluminum rings,
forming a squirrel-cage shaped circuit (squirrel-cage)
Two basic design types depending on the rotor design
- squirrel-cage: conducting bars laid into slots and shorted at both
ends by shorting rings.
- wound-rotor: complete set of three-phase windings exactly as the
stator. Usually Y-connected, the ends of the three rotor wires are
connected to 3 slip rings on the rotor shaft. In this way, the rotor
circuit is accessible.
5. Construction
Squirrel cage rotor
Wound rotor
Notice the
slip rings
6. Construction
Slip rings
Cutaway in a
typical wound-
rotor IM.
Notice the
brushes and the
slip rings
Brushes
7. Rotating Magnetic Field
Balanced three phase windings, i.e.
mechanically displaced 120
degrees form each other, fed by
balanced three phase source
A rotating magnetic field with
constant magnitude is produced,
rotating with a speed
120 f e
nsync = rpm
P
Where fe is the supply frequency and
P is the no. of poles and nsync is called
the synchronous speed in rpm
(revolutions per minute)
14. Principle of operation
This rotating magnetic field cuts the rotor windings and
produces an induced voltage in the rotor windings
Due to the fact that the rotor windings are short circuited, for
both squirrel cage and wound-rotor, and induced current
flows in the rotor windings
The rotor current produces another magnetic field
A torque is produced as a result of the interaction of those
two magnetic fields
τ ind = kBR × Bs
Where τind is the induced torque and BR and BS are the magnetic
flux densities of the rotor and the stator respectively
15. Induction motor speed
At what speed will the IM run?
- Can the IM run at the synchronous speed, why?
- If rotor runs at the synchronous speed, which is the
same speed of the rotating magnetic field, then the rotor
will appear stationary to the rotating magnetic field and
the rotating magnetic field will not cut the rotor. So, no
induced current will flow in the rotor and no rotor
magnetic flux will be produced so no torque is
generated and the rotor speed will fall below the
synchronous speed
- When the speed falls, the rotating magnetic field will
cut the rotor windings and a torque is produced
16. Induction motor speed
So, the IM will always run at a speed lower than
the synchronous speed
The difference between the motor speed and the
synchronous speed is called the Slip
nslip = nsync − nm
Where nslip= slip speed
nsync= speed of the magnetic field
nm = mechanical shaft speed of the motor
17. The Slip
nsync − nm
s=
nsync
Where s is the slip
Notice that : if the rotor runs at synchronous speed
s=0
if the rotor is stationary
s=1
Slip may be expressed as a percentage by multiplying the above
eq. by 100, notice that the slip is a ratio and doesn’t have units
18. Induction Motors and Transformers
Both IM and transformer works on the principle of
induced voltage
- Transformer: voltage applied to the primary windings
produce an induced voltage in the secondary windings
- Induction motor: voltage applied to the stator windings
produce an induced voltage in the rotor windings
- The difference is that, in the case of the induction
motor, the secondary windings can move
- Due to the rotation of the rotor (the secondary winding
of the IM), the induced voltage in it does not have the
same frequency of the stator (the primary) voltage
19. Frequency
The frequency of the voltage induced in the rotor is
given by
P×n
fr =
120
Where fr = the rotor frequency (Hz)
P = number of stator poles
n = slip speed (rpm)
P × (ns − nm )
fr =
120
P × sns
= = sf e
120
20. Frequency
What would be the frequency of the rotor’s induced
voltage at any speed nm?
fr = s fe
When the rotor is blocked (s=1) , the frequency of
the induced voltage is equal to the supply frequency
On the other hand, if the rotor runs at synchronous
speed (s = 0), the frequency will be zero
21. Torque
While the input to the induction motor is electrical
power, its output is mechanical power and for that we
should know some terms and quantities related to
mechanical power
Any mechanical load applied to the motor shaft will
introduce a Torque on the motor shaft. This torque is
related to the motor output power and the rotor speed
Pout 2π nm
τ load = N .m and ωm = rad / s
ωm 60
22. Horse power
Another unit used to measure mechanical power is
the horse power
It is used to refer to the mechanical output power
of the motor
Since we, as an electrical engineers, deal with
watts as a unit to measure electrical power, there is
a relation between horse power and watts
hp = 746 watts
23. Example
A 208-V, 10hp, four pole, 60 Hz, Y-connected
induction motor has a full-load slip of 5 percent
1. What is the synchronous speed of this motor?
2. What is the rotor speed of this motor at rated load?
3. What is the rotor frequency of this motor at rated load?
4. What is the shaft torque of this motor at rated load?
24. Solution
120 f e 120(60)
1. nsync = = = 1800 rpm
P 4
2. nm = (1 − s )ns
= (1 − 0.05) ×1800 = 1710 rpm
3. f r = sf e = 0.05 × 60 = 3Hz
Pout Pout
4. τ load = =
ωm 2π nm
60
10 hp × 746 watt / hp
= = 41.7 N .m
1710 × 2π × (1/ 60)
25. Equivalent Circuit
The induction motor is similar to the transformer with
the exception that its secondary windings are free to
rotate
As we noticed in the transformer, it is easier if we can combine
these two circuits in one circuit but there are some difficulties
26. Equivalent Circuit
When the rotor is locked (or blocked), i.e. s =1, the
largest voltage and rotor frequency are induced in
the rotor, Why?
On the other side, if the rotor rotates at synchronous
speed, i.e. s = 0, the induced voltage and frequency
in the rotor will be equal to zero, Why?
ER = sER 0
Where ER0 is the largest value of the rotor’s induced voltage
obtained at s = 1(loacked rotor)
27. Equivalent Circuit
The same is true for the frequency, i.e.
fr = s fe
It is known that
X = ω L = 2π f L
So, as the frequency of the induced voltage in the
rotor changes, the reactance of the rotor circuit also
changes X = ω L = 2π f L
r r r r r
Where Xr0 is the rotor reactance
= 2π sf e Lr
at the supply frequency
(at blocked rotor) = sX r 0
28. Equivalent Circuit
Then, we can draw the rotor equivalent circuit as
follows
Where ER is the induced voltage in the rotor and RR is the
rotor resistance
29. Equivalent Circuit
Now we can calculate the rotor current as
ER
IR =
( RR + jX R )
sER 0
=
( RR + jsX R 0 )
Dividing both the numerator and denominator by s
so nothing changes we get
ER 0
IR =
RR
( + jX R 0 )
s
Where ER0 is the induced voltage and XR0 is the rotor
reactance at blocked rotor condition (s = 1)
31. Equivalent Circuit
Now as we managed to solve the induced voltage
and different frequency problems, we can combine
the stator and rotor circuits in one equivalent
circuit
Where
X 2 = aeff X R 0
2
R2 = aeff RR
2
IR
I2 =
aeff
E1 = aeff ER 0
NS
aeff =
NR
32. Power losses in Induction machines
Copper losses
- Copper loss in the stator (PSCL) = I12R1
- Copper loss in the rotor (PRCL) = I22R2
Core loss (Pcore)
Mechanical power loss due to friction and windage
How this power flow in the motor?
34. Power relations
Pin = 3 VL I L cos θ = 3 V ph I ph cos θ
PSCL = 3 I12 R1
PAG = Pin − ( PSCL + Pcore )
PRCL = 3I 2 R2
2
Pconv = PAG − PRCL
Pconv
Pout = Pconv − ( Pf + w + Pstray ) τ ind =
ωm
35. Equivalent Circuit
We can rearrange the equivalent circuit as follows
Resistance
Actual rotor
equivalent to
resistance
mechanical load
36. Power relations
Pin = 3 VL I L cos θ = 3 V ph I ph cos θ
PSCL = 3 I12 R1
R2 PRCL
PAG = Pin − ( PSCL + Pcore ) = Pconv + PRCL = 3I 2
2 =
s s
PRCL = 3I 2 R2
2
PRCL (1 − s )
Pconv = PAG − PRCL = 3I 2 R2 (1 − s )
2
=
s s
Pconv = (1 − s ) PAG
Pconv (1 − s ) PAG
Pout = Pconv − ( Pf + w + Pstray ) τ ind = =
ωm (1 − s )ωs
37. Power relations
PAG Pconv
1 1-s
PRCL
s
PAG : PRCL : Pconv
1 : s : 1-s
38. Example
A 480-V, 60 Hz, 50-hp, three phase induction motor is
drawing 60A at 0.85 PF lagging. The stator copper
losses are 2 kW, and the rotor copper losses are
700 W. The friction and windage losses are 600
W, the core losses are 1800 W, and the stray losses
are negligible. Find the following quantities:
1. The air-gap power PAG.
2. The power converted Pconv.
3. The output power Pout.
4. The efficiency of the motor.
40. Solution
37.3
Pout = = 50 hp
0.746
Pout
4. η= × 100%
Pin
37.3
= × 100 = 88%
42.4
41. Example
A 460-V, 25-hp, 60 Hz, four-pole, Y-connected induction motor
has the following impedances in ohms per phase referred to
the stator circuit:
R1= 0.641Ω R2= 0.332Ω
X1= 1.106 Ω X2= 0.464 Ω XM= 26.3 Ω
The total rotational losses are 1100 W and are assumed to be
constant. The core loss is lumped in with the rotational losses.
For a rotor slip of 2.2 percent at the rated voltage and rated
frequency, find the motor’s 4. P and P
conv out
1. Speed
2. Stator current 5. τind and τload
3. Power factor 6. Efficiency
43. Solution
Z tot = Z stat + Z f
= 0.641 + j1.106 + 12.94∠31.1° Ω
= 11.72 + j 7.79 = 14.07∠33.6° Ω
460∠0°
Vφ 3
I1 = = = 18.88∠ − 33.6° A
Z tot 14.07∠33.6°
3. PF = cos 33.6° = 0.833 lagging
4. Pin = 3VL I L cos θ = 3 × 460 ×18.88 × 0.833 = 12530 W
PSCL = 3I12 R1 = 3(18.88) 2 × 0.641 = 685 W
PAG = Pin − PSCL = 12530 − 685 = 11845 W
44. Solution
Pconv = (1 − s ) PAG = (1 − 0.022)(11845) = 11585 W
Pout = Pconv − PF &W = 11585 − 1100 = 10485 W
10485
= = 14.1 hp
746
PAG 11845
5. τ ind = = = 62.8 N.m
ωsync 2π ×1800
60
Pout 10485
τ load = = = 56.9 N.m
ωm 2π ×1760
60
Pout 10485
6. η= ×100% = ×100 = 83.7%
Pin 12530
45. Torque, power and Thevenin’s
Theorem
Thevenin’s theorem can be used to transform the
network to the left of points ‘a’ and ‘b’ into an
equivalent voltage source VTH in series with
equivalent impedance RTH+jXTH
46. Torque, power and Thevenin’s
Theorem
jX M XM
VTH = Vφ | VTH |=| Vφ |
R1 + j ( X 1 + X M ) R12 + ( X 1 + X M )2
RTH + jX TH = ( R1 + jX 1 ) // jX M
47. Torque, power and Thevenin’s
Theorem
Since XM>>X1 and XM>>R1
XM
VTH ≈ Vφ
X1 + X M
Because XM>>X1 and XM+X1>>R1
2
XM
RTH ≈ R1 ÷
X1 + X M
X TH ≈ X 1
48. Torque, power and Thevenin’s
Theorem
VTH VTH
I2 = =
ZT R2
2
RTH + ÷ + ( X TH + X 2 ) 2
s
Then the power converted to mechanical (Pconv)
R2 (1 − s )
Pconv = 3I2
2
s
And the internal mechanical torque (Tconv)
2 R2
Pconv Pconv 3I
s = PAG
2
τ ind = = =
ωm (1 − s )ωs ωs ωs
49. Torque, power and Thevenin’s
Theorem
2
÷
3 VTH ÷ R2
τ ind = ÷ s ÷
ωs
÷
2
R + R2 + ( X + X ) 2
TH s ÷ TH 2 ÷
2 R2
3V ÷
TH
1 s
τ ind =
ωs R2
2
RTH + ÷ + ( X TH + X 2 ) 2
s
51. Comments
1. The induced torque is zero at synchronous speed.
Discussed earlier.
2. The curve is nearly linear between no-load and full
load. In this range, the rotor resistance is much
greater than the reactance, so the rotor current,
torque increase linearly with the slip.
3. There is a maximum possible torque that can’t be
exceeded. This torque is called pullout torque and
is 2 to 3 times the rated full-load torque.
52. Comments
4. The starting torque of the motor is slightly higher
than its full-load torque, so the motor will start
carrying any load it can supply at full load.
5. The torque of the motor for a given slip varies as
the square of the applied voltage.
6. If the rotor is driven faster than synchronous speed
it will run as a generator, converting mechanical
power to electric power.
54. Maximum torque
Maximum torque occurs when the power
transferred to R2/s is maximum.
This condition occurs when R2/s equals the
magnitude of the impedance RTH + j (XTH + X2)
R2
= RTH + ( X TH + X 2 ) 2
2
sTmax
R2
sTmax =
RTH + ( X TH + X 2 ) 2
2
55. Maximum torque
The corresponding maximum torque of an induction
motor equals
1 2
3VTH
τ max = ÷
2ωs R + R 2 + ( X + X )2 ÷
TH TH TH 2
The slip at maximum torque is directly proportional to
the rotor resistance R2
The maximum torque is independent of R2
56. Maximum torque
Rotor resistance can be increased by inserting
external resistance in the rotor of a wound-rotor
induction motor.
The
value of the maximum torque remains unaffected
but
the speed at which it occurs can be controlled.
57. Maximum torque
Effect of rotor resistance on torque-speed characteristic
58. Example
A two-pole, 50-Hz induction motor supplies 15kW to a
load at a speed of 2950 rpm.
1. What is the motor’s slip?
2. What is the induced torque in the motor in N.m under
these conditions?
3. What will be the operating speed of the motor if its
torque is doubled?
4. How much power will be supplied by the motor when
the torque is doubled?
59. Solution
120 f e 120 × 50
1. nsync = = = 3000 rpm
P 2
nsync − nm 3000 − 2950
s= = = 0.0167 or 1.67%
nsync 3000
2. Q no Pf +W given
∴ assume Pconv = Pload and τ ind = τ load
Pconv 15 ×103
τ ind = = = 48.6 N.m
ωm 2950 × 2π
60
60. Solution
3. In the low-slip region, the torque-speed curve is linear
and the induced torque is direct proportional to slip. So,
if the torque is doubled the new slip will be 3.33% and
the motor speed will be
nm = (1 − s )nsync = (1 − 0.0333) × 3000 = 2900 rpm
4. Pconv = τ ind ωm
2π
= (2 × 48.6) × (2900 × ) = 29.5 kW
60
61. Example
A 460-V, 25-hp, 60-Hz, four-pole, Y-connected wound-
rotor induction motor has the following impedances in
ohms per phase referred to the stator circuit
R1= 0.641Ω R2= 0.332Ω
X1= 1.106 Ω X2= 0.464 Ω XM= 26.3 Ω
1. What is the maximum torque of this motor? At what
speed and slip does it occur?
2. What is the starting torque of this motor?
3. If the rotor resistance is doubled, what is the speed at
which the maximum torque now occur? What is the
new starting torque of the motor?
4. Calculate and plot the T-s c/c for both cases.
62. Solution
XM
VTH = Vφ
R12 + ( X 1 + X M )2
460
× 26.3
= 3 = 255.2 V
(0.641) + (1.106 + 26.3)
2 2
2
XM
RTH ≈ R1 ÷
X1 + X M
2
26.3
≈ (0.641) ÷ = 0.590Ω
1.106 + 26.3
X TH ≈ X 1 = 1.106Ω
63. Solution
R2
1. sTmax =
RTH + ( X TH + X 2 ) 2
2
0.332
= = 0.198
(0.590) + (1.106 + 0.464)
2 2
The corresponding speed is
nm = (1 − s )nsync = (1 − 0.198) ×1800 = 1444 rpm
64. Solution
The torque at this speed is
1 2
3VTH
τ max = ÷
2ωs R + R 2 + ( X + X )2 ÷
TH TH TH 2
3 × (255.2) 2
=
2π
2 × (1800 × )[0.590 + (0.590) 2 + (1.106 + 0.464) 2 ]
60
= 229 N.m
65. Solution
2. The starting torque can be found from the torque eqn.
by substituting s = 1
2 R2
3VTH ÷
1 s
τ start = τ ind s =1 =
ωs R2
2
RTH + ÷ + ( X TH + X 2 ) 2
s s =1
2
3VTH R2
=
ωs [( RTH + R2 ) + ( X TH + X 2 ) 2 ]
2
3 × (255.2) 2 × (0.332)
=
2π
1800 × × [(0.590 + 0.332) 2 + (1.106 + 0.464) 2 ]
60
= 104 N.m
66. Solution
3. If the rotor resistance is doubled, then the slip at
maximum torque doubles too
R2
sTmax = = 0.396
RTH + ( X TH + X 2 ) 2
2
The corresponding speed is
nm = (1 − s )nsync = (1 − 0.396) × 1800 = 1087 rpm
The maximum torque is still
τmax = 229 N.m
68. Determination of motor parameters
Due to the similarity between the induction motor
equivalent circuit and the transformer equivalent
circuit, same tests are used to determine the values
of the motor parameters.
- DC test: determine the stator resistance R1
- No-load test: determine the rotational losses and
magnetization current (similar to no-load test in
Transformers).
- Locked-rotor test: determine the rotor and stator
impedances (similar to short-circuit test in
Transformers).
69. DC test
- The purpose of the DC test is to determine R1. A variable
DC voltage source is connected between two stator
terminals.
- The DC source is adjusted to provide approximately
rated stator current, and the resistance between the two
stator leads is determined from the voltmeter and
ammeter readings.
70. DC test
- then
VDC
RDC =
I DC
- If the stator is Y-connected, the per phase stator
resistance is
RDC
R1 =
2
- If the stator is delta-connected, the per phase stator
resistance is
3
R1 = RDC
2
71. No-load test
1. The motor is allowed to spin freely
2. The only load on the motor is the friction and windage
losses, so all Pconv is consumed by mechanical losses
3. The slip is very small
72. No-load test
4. At this small slip
R2 (1 − s ) R 2 (1 − s )
? R2 & ? X2
s s
The equivalent circuit reduces to…
74. No-load test
6. At the no-load conditions, the input power measured by
meters must equal the losses in the motor.
7. The PRCL is negligible because I2 is extremely small
because R2(1-s)/s is very large.
8. The input power equals
Pin = PSCL + Pcore + PF &W
= 3I12 R1 + Prot
Where
Prot = Pcore + PF &W
75. No-load test
9. The equivalent input impedance is thus approximately
Vφ
Z eq = ≈ X1 + X M
I1, nl
If X1 can be found, in some other fashion, the magnetizing
impedance XM will be known
76. Blocked-rotor test
In this test, the rotor is locked or blocked so that it
cannot move, a voltage is applied to the motor, and
the resulting voltage, current and power are
measured.
77. Blocked-rotor test
The AC voltage applied to the stator is adjusted so
that the current flow is approximately full-load
value.
The locked-rotor power factor can be found as
Pin
PF = cos θ =
3Vl I l
The magnitude of the total impedance
Vφ
Z LR =
I
78. Blocked-rotor test
Z LR = RLR + jX LR
'
= Z LR cos θ + j Z LR sin θ
RLR = R1 + R2
X LR = X 1' + X 2
' '
Where X’1 and X’2 are the stator and rotor reactances at
the test frequency respectively
R2 = RLR − R1
f rated '
X LR = X LR = X 1 + X 2
f test
79. Blocked-rotor test
X1 and X2 as function of XLR
Rotor Design X1 X2
Wound rotor 0.5 XLR 0.5 XLR
Design A 0.5 XLR 0.5 XLR
Design B 0.4 XLR 0.6 XLR
Design C 0.3 XLR 0.7 XLR
Design D 0.5 XLR 0.5 XLR
81. Example
The following test data were taken on a 7.5-hp, four-pole, 208-V, 60-
Hz, design A, Y-connected IM having a rated current of 28 A.
DC Test:
VDC = 13.6 V IDC = 28.0 A
No-load Test:
Vl = 208 V f = 60 Hz
I = 8.17 A Pin = 420 W
Locked-rotor Test:
Vl = 25 V f = 15 Hz
I = 27.9 A Pin = 920 W
(a) Sketch the per-phase equivalent circuit of this motor.
(b) Find the slip at pull-out torque, and find the value of the pull-out torque.