Three-Phase Induction Machines

Contents

**Describe the working principle of the Three-Phase Induction Motor** 1

**Describe the construction of Three-Phase Induction Motor** 3

**Compare Slip Ring and Squirrel Cage Induction Motor** 5

**Describe the Equivalent Circuit of Three-Phase Induction Motor** 7

**Draw the Power Flow Diagram of Three-Phase Induction Motor** 9

**Derive the equation for Torque developed in Three-Phase Induction Motor** 10

**Describe the Torque Speed/Torque Slip Characteristics of a Three-Phase Induction Motor** 10

**Derive the expression for the Maximum or the Breakdown Torque** 10

**Recall the Starting of a 3-φ Slip-ring Induction Motor** 10

**Recall the Losses in a Three-Phase Induction Motor** 10

**Recall the Efficiency in a Three-Phase Induction Motor** 10

**Recall No-Load Test in a Three-Phase Induction Motor** 10

**Recall Blocked Rotor Test in a Three-Phase Induction Motor** 10

**Recall the Circle Diagram of a Three-Phase Induction Motor** 10

**Construct the Circle Diagram of a Three-Phase Induction Motor** 10

**Describe the working of an Induction Generator** 10

**Recall the applications of an Induction Generator** 10

**Recall the Deep Bar Rotor in a Three-Phase Induction Motor.** 10

**Recall the Double Cage Rotor in a Three-Phase Induction Motor** 10

**Recall Cogging in a Three-Phase Induction Motor** 10

**Recall Crawling in a Three-Phase Induction Motor** 10

**Describe the working principle of the Three-Phase Induction Motor**

The three-phase induction motor is the most widely used type of motor in industrial and domestic applications. It works based on the principle of electromagnetic induction, where a rotating magnetic field is created by the stator windings, which induces an electric current in the rotor windings. The interaction between the magnetic fields of the stator and rotor produces torque, which causes the rotor to rotate.

The construction of a three-phase induction motor consists of a stator, rotor, and enclosure. The stator consists of three-phase windings arranged in a specific pattern to produce a rotating magnetic field when connected to a three-phase AC supply. The rotor can be either squirrel cage or wound type and is placed inside the stator. The enclosure protects the motor from dust, moisture, and mechanical damage.

The working principle of a three-phase induction motor can be explained as follows:

- When the three-phase AC supply is connected to the stator windings, a rotating magnetic field is produced.
- The rotating magnetic field induces an electric current in the rotor windings.
- Due to the induced current, a magnetic field is produced in the rotor.
- The interaction between the stator and rotor magnetic fields produces torque, causing the rotor to rotate.
- The rotor’s rotation speed is slightly less than the speed of the stator magnetic field. The difference in speed is called slip, and it is necessary for the rotor to produce torque.
- The amount of slip depends on the motor’s load, and it increases with an increase in load.

The torque produced by a three-phase induction motor is proportional to the square of the supply voltage and the difference in speed between the stator and rotor magnetic fields. The motor’s speed is determined by the frequency of the supply voltage and the number of poles in the stator winding.

In summary, the working principle of a three-phase induction motor involves the creation of a rotating magnetic field in the stator, which induces an electric current in the rotor. The interaction between the stator and rotor magnetic fields produces torque, causing the rotor to rotate. The speed of the motor is determined by the frequency of the supply voltage and the number of poles in the stator winding.

**Recall the concept of Slip**

In electrical engineering, slip refers to the difference between the synchronous speed of the rotating magnetic field in the stator of an AC motor and the rotor speed of the motor. It is denoted by the symbol “s” and is expressed as a percentage. The slip is an essential parameter in understanding the behavior and performance of an induction motor.

The synchronous speed of the rotating magnetic field in the stator is determined by the frequency of the AC power source and the number of poles of the motor. The rotor speed is determined by the number of poles and the slip. The slip is the ratio of the difference between the synchronous speed and the rotor speed to the synchronous speed, expressed as a percentage.

Mathematically, slip (s) is given by the formula:

s = (Ns – Nr) / Ns x 100%

Where Ns is the synchronous speed and Nr is the rotor speed.

For example, consider a three-phase induction motor with four poles and a supply frequency of 50 Hz. The synchronous speed of the motor is given by:

Ns = (120 x f) / p = (120 x 50) / 4 = 1500 RPM

Suppose the rotor speed is 1450 RPM. Then the slip can be calculated as:

s = (Ns – Nr) / Ns x 100% = (1500 – 1450) / 1500 x 100% = 3.33%

This means that the rotor is rotating at 3.33% less than the synchronous speed. The slip determines the torque produced by the motor and the amount of current drawn from the power source. A higher slip indicates a higher torque but also results in higher current and lower efficiency.

**Describe the construction of Three-Phase Induction Motor**

This learning outcome focuses on the construction of a three-phase induction motor. A three-phase induction motor is a type of electric motor that converts electrical energy into mechanical energy. It works on the principle of electromagnetic induction, where a rotating magnetic field is created within the stator windings that induces a current in the rotor, resulting in rotation of the motor.

Construction of a Three-Phase Induction Motor:

The three-phase induction motor consists of two main parts: the stator and the rotor. The stator is the stationary part of the motor that houses the stator windings, while the rotor is the rotating part of the motor that consists of conductive bars or windings.

- Stator:

The stator is made up of laminated steel core that houses three-phase windings that are placed 120 degrees apart from each other. These windings are connected to three-phase AC supply, which creates a rotating magnetic field within the stator. The number of stator slots is equal to the number of winding phases, and each slot contains one phase winding. The stator core is made of a stack of laminations, which reduces eddy current losses.

- Rotor:

The rotor is also made up of laminated steel core and consists of conductive bars or windings that are placed parallel to the shaft axis. The conductive bars are short-circuited at both ends by end rings, which are made of copper or aluminum. The rotor windings are either wound type or squirrel cage type. The wound rotor has three-phase windings that are connected to slip rings, while the squirrel cage rotor has conductive bars that are permanently short-circuited.

- Bearings:

The motor shaft is supported by bearings, which are mounted on the motor frame. The bearings can be either sleeve bearings or ball bearings, depending on the application.

- Motor Frame:

The motor frame is the outer covering of the motor, which provides protection and support to the stator and rotor. The frame is made of cast iron or aluminum and provides a path for the magnetic flux.

Working Principle:

When the three-phase AC supply is given to the stator windings, a rotating magnetic field is created within the stator, which induces a current in the rotor. The current in the rotor produces a magnetic field that interacts with the stator magnetic field, resulting in the rotation of the rotor.

Examples:

- Industrial Applications: Three-phase induction motors are widely used in various industrial applications, such as conveyor systems, pumps, compressors, and machine tools, due to their rugged construction and high efficiency.
- Household Appliances: Three-phase induction motors are used in various household appliances, such as washing machines, air conditioners, and refrigerators, due to their reliability and low maintenance.
- Transportation: Three-phase induction motors are used in electric vehicles, trains, and other transportation systems, due to their high power density and efficiency.

In conclusion, the construction of a three-phase induction motor consists of two main parts, the stator and the rotor, which work together to convert electrical energy into mechanical energy. The motor is widely used in various applications due to its efficiency, reliability, and low maintenance.

**Compare Slip Ring and Squirrel Cage Induction Motor**

This learning outcome focuses on the comparison of two types of induction motors – Slip Ring and Squirrel Cage Induction Motors. Both these motors are widely used in various industrial and commercial applications. It is important to understand the differences between these two motors to determine which one is suitable for a particular application.

Comparison of Slip Ring and Squirrel Cage Induction Motor:

- Construction:

The construction of the two motors is different. The rotor of a Slip Ring Induction Motor consists of a wound rotor with three-phase windings that are connected to slip rings, while the rotor of a Squirrel Cage Induction Motor consists of a set of conducting bars that are short-circuited at both ends.

- Starting Torque:

The starting torque of the Slip Ring Induction Motor is higher compared to the Squirrel Cage Induction Motor. This is because the Slip Ring Induction Motor has a rotor with wound windings that can be connected to external resistors to increase the starting torque.

- Efficiency:

The efficiency of the Squirrel Cage Induction Motor is higher compared to the Slip Ring Induction Motor. This is because the Squirrel Cage Induction Motor has a simpler rotor construction with no slip rings or brushes, which reduces losses and increases efficiency.

- Cost:

The cost of the Squirrel Cage Induction Motor is lower compared to the Slip Ring Induction Motor. This is because the Squirrel Cage Induction Motor has a simpler construction with no slip rings or brushes, which reduces the cost of manufacturing.

- Maintenance:

The maintenance of the Squirrel Cage Induction Motor is lower compared to the Slip Ring Induction Motor. This is because the Squirrel Cage Induction Motor has a simpler construction with no slip rings or brushes, which reduces the need for maintenance.

Examples:

- Slip Ring Induction Motor: A Slip Ring Induction Motor is suitable for applications that require high starting torque, such as cranes, hoists, and elevators. It is also used in applications where speed control is required, such as in textile mills and paper mills.
- Squirrel Cage Induction Motor: A Squirrel Cage Induction Motor is suitable for applications that require high efficiency and low maintenance, such as in fans, pumps, and blowers. It is also used in applications where constant speed is required, such as in machine tools and compressors.

In conclusion, both Slip Ring and Squirrel Cage Induction Motors have their advantages and disadvantages. The selection of the motor depends on the specific requirements of the application. If high starting torque or speed control is required, a Slip Ring Induction Motor may be suitable. If high efficiency and low maintenance are required, a Squirrel Cage Induction Motor may be suitable.

**Describe the Equivalent Circuit of Three-Phase Induction Motor**

This learning outcome focuses on the equivalent circuit of a three-phase induction motor. The equivalent circuit of an induction motor is a representation of the motor in terms of its electrical parameters. It is used to analyze the performance of the motor under various operating conditions.

**Equivalent Circuit of Three-Phase Induction Motor:**

The equivalent circuit of a three-phase induction motor consists of the following components:

- Stator Resistance (R1): The stator resistance represents the resistance of the stator winding.
- Stator Leakage Reactance (X1): The stator leakage reactance represents the leakage flux that links only the stator winding.
- Rotor Resistance (R2): The rotor resistance represents the resistance of the rotor winding.
- Rotor Leakage Reactance (X2): The rotor leakage reactance represents the leakage flux that links only the rotor winding.
- Magnetizing Reactance (Xm): The magnetising reactance represents the flux that links both the stator and rotor windings.
- Core Loss Resistance (Rc): The core loss resistance represents the resistance of the iron core losses.

The equivalent circuit of per phase induction motor is shown below:

Where:

V_{1LN} = Supply voltage

I_{1} = Stator current

I_{0} = Magnetizing current

I_{2} = Rotor current etc.

The equivalent circuit of a three-phase induction motor can be used to calculate various parameters such as the current, voltage, power factor, and efficiency of the motor under different operating conditions.

Examples:

- Calculation of Stator Current: The stator current can be calculated using the following formula:

I1 = (V1 – I2 X (R2 + jX2)) / (R1 + jX1)

- Calculation of Power Factor: The power factor can be calculated using the following formula:

cosφ = P / (|S| * √3 * V1 * I1)

where P is the active power, |S| is the apparent power, and φ is the phase angle between the voltage and current.

In conclusion, the equivalent circuit of a three-phase induction motor is an important tool for analyzing the performance of the motor under different operating conditions. It can be used to calculate various parameters such as the current, voltage, power factor, and efficiency of the motor.

**Draw the Power Flow Diagram of Three-Phase Induction Motor**

The power flow diagram of a three-phase induction motor is a graphical representation that shows the flow of power between different components of the motor. This diagram helps in understanding the energy conversion process in the motor and how the various components of the motor are interconnected. The following are detailed notes on how to draw the power flow diagram of a three-phase induction motor with suitable examples:

- Power Input: The power input to the three-phase induction motor is given by the three-phase AC supply. The supply voltage is typically 415 V in India and 480 V in the USA. The power input is given to the stator windings of the motor.
- Stator Windings: The stator windings are the stationary part of the motor that receives the power input. The stator windings are arranged in a specific pattern, such as a star or delta connection. The stator windings produce a rotating magnetic field that rotates at synchronous speed.
- Rotating Magnetic Field: The rotating magnetic field produced by the stator windings interacts with the rotor to produce torque. The rotating magnetic field is responsible for inducing a current in the rotor windings.
- Rotor Windings: The rotor windings are the conductors that are placed on the rotor surface. The rotor windings are either in the form of a squirrel cage or a wound rotor. The rotor windings produce a magnetic field that interacts with the rotating magnetic field of the stator to produce torque.
- Torque: The interaction between the rotor and stator magnetic fields produces torque. This torque is responsible for rotating the rotor and driving the load connected to the motor.
- Shaft: The shaft is the rotating part of the motor that connects the rotor to the load. The shaft rotates at a speed slightly less than the synchronous speed of the rotating magnetic field.
- Load: The load is the device that is driven by the three-phase induction motor. The load can be a pump, fan, conveyor, compressor, or any other device that requires a rotational motion.

Example: Let us consider a 10 HP three-phase induction motor with a rated voltage of 415 V and a rated speed of 1440 RPM. The motor is connected to a centrifugal pump that requires a rotational speed of 1420 RPM. The power flow diagram of the motor can be drawn as follows:

- Power Input: The power input to the motor is 10 HP, which is equivalent to 7.46 kW.
- Stator Windings: The stator windings are connected in a star configuration and receive the power input from the AC supply.
- Rotating Magnetic Field: The stator windings produce a rotating magnetic field that rotates at 1440 RPM.
- Rotor Windings: The rotor windings are in the form of a squirrel cage and produce a magnetic field that interacts with the stator magnetic field to produce torque.
- Torque: The interaction between the rotor and stator magnetic fields produces torque that drives the pump.
- Shaft: The shaft connects the rotor to the pump and rotates at a speed slightly less than the synchronous speed of the rotating magnetic field.
- Load: The load is a centrifugal pump that requires a rotational speed of 1420 RPM.

In conclusion, the power flow diagram of a three-phase induction motor shows the flow of power between the various components of the motor. The diagram helps in understanding the energy conversion process in the motor and how the motor drives the load.

**Derive the equation for Torque developed in Three-Phase Induction Motor**

The torque developed in a three-phase induction motor is an essential parameter that determines the motor’s ability to drive the load. The torque produced in the motor is a result of the interaction between the magnetic fields of the stator and the rotor. The following are detailed notes on how to derive the equation for torque developed in a three-phase induction motor with suitable examples:

- Magnetic Fields: The interaction between the magnetic fields of the stator and rotor is the primary cause of torque development in a three-phase induction motor. The stator windings produce a rotating magnetic field that rotates at synchronous speed. The rotor windings produce a magnetic field that interacts with the rotating magnetic field of the stator to produce torque.
- Slip: The difference between the synchronous speed of the rotating magnetic field and the rotor speed is known as slip. The slip determines the torque developed in the motor. The greater the slip, the greater the torque developed.
- Electromagnetic Induction: The magnetic fields produced by the stator and rotor windings induce an electromotive force (EMF) in the windings. The EMF produces an electric current in the windings that interact with the magnetic fields to produce torque.
- Lenz’s Law: According to Lenz’s law, the direction of the induced EMF opposes the change in magnetic flux that produces it. This means that the rotor windings’ magnetic field will always try to oppose the rotating magnetic field of the stator.
- Torque Equation: The torque developed in a three-phase induction motor can be derived using the following equation:

T = (3 * V^2 * R2 * s) / (ω2 * ((R1 + R2^2/s^2)^2 + (X1 + X2)^2))

Where:

T = Torque developed in the motor

V = Voltage supplied to the motor

R1 = Stator resistance

R2 = Rotor resistance

X1 = Stator reactance

X2 = Rotor reactance

s = Slip of the motor

ω2 = Angular frequency of the rotor magnetic field

Example: Let us consider a 10 HP, 415 V, 1440 RPM, three-phase induction motor with a rotor resistance of 0.2 Ω, rotor reactance of 0.3 Ω, stator resistance of 0.1 Ω, and stator reactance of 0.2 Ω. The slip of the motor is 0.05. We can calculate the torque developed in the motor using the above equation as follows:

T = (3 * 415^2 * 0.2 * 0.05) / (2π * 1440/60 * ((0.1 + 0.04)^2 + (0.2 + 0.3)^2))

T = 12.63 N-m

In conclusion, the torque developed in a three-phase induction motor is a result of the interaction between the magnetic fields of the stator and the rotor. The torque equation can be derived using the stator and rotor resistances and reactances, slip, voltage supplied, and angular frequency of the rotor magnetic field. The torque developed determines the motor’s ability to drive the load and is a critical parameter for motor selection and design.

**Describe the Torque Speed/Torque Slip Characteristics of a Three-Phase Induction Motor**

The torque-speed (or torque-slip) characteristics of a three-phase induction motor illustrate the relationship between the torque and speed (or slip) of the motor. Understanding this relationship is essential for selecting the right motor for a specific application and for determining the motor’s operating characteristics. The following are detailed notes on how to describe the torque-speed/torque-slip characteristics of a three-phase induction motor with suitable examples:

- Torque-Speed Characteristics: The torque-speed characteristics of a three-phase induction motor describe how the motor’s torque varies with the motor’s speed. The torque-speed characteristics can be divided into two regions: the starting region and the running region.

- Starting Region: When the motor is starting, the rotor is not rotating, and the slip is maximum. The torque developed in this region is high but drops rapidly as the rotor begins to rotate. This region is also called the breakdown torque region.
- Running Region: Once the motor starts rotating, the slip decreases, and the motor moves into the running region. In this region, the torque developed decreases linearly with the speed (or slip) of the motor.

- Torque-Slip Characteristics: The torque-slip characteristics of a three-phase induction motor describe how the motor’s torque varies with the motor’s slip. The torque-slip characteristics of the motor can be divided into three regions: the starting region, the pull-up torque region, and the stable region.

- Starting Region: The starting region of the torque-slip curve is the same as the starting region of the torque-speed curve. In this region, the torque developed is high, but the slip is also high.
- Pull-Up Torque Region: As the motor accelerates, the slip decreases, and the torque developed by the motor increases. The point at which the motor reaches its maximum torque is called the pull-up torque. The pull-up torque is higher than the starting torque and is an essential parameter for motor selection.
- Stable Region: Once the motor reaches the pull-up torque, the torque developed decreases linearly with the slip. This region is called the stable region, and the motor operates in this region during normal operation.

- Example: Let us consider a three-phase induction motor with the following parameters:

- Rated power = 5 kW
- Rated voltage = 415 V
- Rated frequency = 50 Hz
- Stator resistance = 0.2 Ω
- Stator reactance = 0.4 Ω
- Rotor resistance = 0.3 Ω
- Rotor reactance = 0.5 Ω

The torque-speed and torque-slip characteristics of the motor can be plotted using the motor’s parameters and the torque equation (derived in ALO:

The graph shows that the motor has a starting torque of 1.5 times the full-load torque and a pull-up torque of 2.5 times the full-load torque. The motor’s operating point is in the stable region, where the torque developed by the motor decreases linearly with the slip.

In conclusion, the torque-speed/torque-slip characteristics of a three-phase induction motor illustrate the relationship between the motor’s torque and speed (or slip).

**Derive the expression for the Maximum or the Breakdown Torque**

The maximum or the breakdown torque is an essential parameter of a three-phase induction motor. The maximum torque is the maximum amount of torque that the motor can develop while starting, and it usually occurs at the start of the motor’s operation. The following are detailed notes on how to derive the expression for the maximum or the breakdown torque with suitable examples:

- Torque Equation: The torque equation of a three-phase induction motor relates the motor’s torque to the stator current, rotor current, and rotor slip. The torque equation can be written as:

T = (3 * V1^2 * R2 / ωs) * [(R1 / R2)^2 + (X1 / X2)^2] * s / [(R1 / R2 + s^2 * (X1 / X2))^2 + (X1 / X2)^2]

where,

- T: Torque developed by the motor
- V1: Supply voltage
- R1: Stator resistance
- R2: Rotor resistance
- X1: Stator reactance
- X2: Rotor reactance
- s: Slip
- ωs: Synchronous speed of the motor

- Maximum or Breakdown Torque: The maximum or the breakdown torque is the maximum amount of torque that the motor can develop while starting. The maximum torque occurs at a slip value where the denominator of the torque equation is minimum. Therefore, to determine the maximum torque, we need to differentiate the denominator of the torque equation with respect to slip and equate it to zero.

The denominator of the torque equation is given by:

(R1 / R2 + s^2 * (X1 / X2))^2 + (X1 / X2)^2

Differentiating the denominator with respect to slip, we get:

2(R1 / R2 + s^2 * (X1 / X2)) * 2s * (X1 / X2) – 2s * (R1 / R2 + s^2 * (X1 / X2))^2 = 0

Simplifying the equation, we get:

s^3 – (R1 + R2) / (X1 + X2) * s^2 + (R1 * R2 – X1 * X2) / (X1 + X2)^2 = 0

Solving this cubic equation for s, we get three values of s. Out of these three values, the one that satisfies the condition of 0 < s < 1 is the maximum torque.

The expression for the maximum or the breakdown torque is given by:

T_max = (3 * V1^2 * R2 / ωs) * [(R1 / R2)^2 + (X1 / X2)^2] / (2 * (R1 + R2) / (X1 + X2))

- Example: Let us consider a three-phase induction motor with the following parameters:

- Rated power = 5 kW
- Rated voltage = 415 V
- Rated frequency = 50 Hz
- Stator resistance = 0.2 Ω
- Stator reactance = 0.4 Ω
- Rotor resistance = 0.3 Ω
- Rotor reactance = 0.5 Ω

The synchronous speed of the motor can be calculated as:

ωs = 2 * π * f / p = 2 * π * 50 / 2 = 157.1 rad/s

**Recall the Starting of a 3-φ Squirrel-Cage Induction Motor a) Direct-on-line start b) Reduced voltage start c) Star-Delta Start**

Starting a 3-phase squirrel-cage induction motor involves the process of providing electrical power to the motor’s stator windings in a controlled manner. This helps to gradually increase the motor’s torque and speed while minimizing any electrical disturbances. There are several methods used for starting these motors, including direct-on-line start, reduced voltage start, and star-delta start.

a) Direct-on-line start:

This method involves directly connecting the motor to the power source at full voltage. It is the simplest and most common starting method used for smaller motors. When the motor is connected to the power source, a large inrush current is drawn, which can lead to voltage dips and possible damage to other electrical equipment connected to the same power source. Therefore, this method is not suitable for larger motors.

Example: Suppose we want to start a 3-phase squirrel-cage induction motor with a rated voltage of 440V and a rated power of 10 kW. A direct-on-line starter can be used for this motor. Once the starter is turned on, the motor will draw a large inrush current, causing a voltage dip in the power supply. This method is best suited for smaller motors and is not recommended for larger motors.

b) Reduced voltage start:

This method involves reducing the voltage supplied to the motor during the starting process. This helps to reduce the inrush current and torque, which in turn reduces any mechanical stresses on the motor. There are several types of reduced voltage starters, including autotransformer starters, reactor starters, and soft starters.

Example: Suppose we want to start a 3-phase squirrel-cage induction motor with a rated voltage of 440V and a rated power of 50 kW. A reduced voltage starter, such as a soft starter, can be used for this motor. The soft starter gradually increases the voltage supplied to the motor, minimising the inrush current and torque. This method is suitable for larger motors and helps to reduce any mechanical stresses on the motor during the starting process.

c) Star-Delta Start:

This method involves connecting the motor windings in a star configuration during the starting process, and then switching to a delta configurati