3-Phase AC induction motors

Intro

For industrial and mining applications, 3-phase AC induction motors are the prime movers for the vast majority of machines. These motors can be operated either directly from the mains or from adjustable frequency drives. In modern industrialized countries, more than half the total electrical energy used in those countries is converted to mechanical energy through AC induction motors. The applications for these motors cover almost every stage of manufacturing and processing. Applications also extend to commercial buildings and the domestic environment. They are used to drive pumps, fans, compressors, mixers, agitators, mills, conveyors, crushers, machine tools, cranes, etc, etc.

It’s not surprising to find that this type of electric motor is so popular, when one considers its simplicity, reliability and low cost.

In the last decade, it has become increasingly common practice to use 3-phase squirrel cage AC induction motors with variable voltage variable frequency (VVVF) converters for variable speed drive (VSD) applications. To clearly understand how the VSD system works, it’s necessary to understand the principles of operation of this type of motor. Although the basic design of induction motors has not changed very much in the last 50 years, modern insulation materials, computer based design optimization techniques and automated manufacturing methods have resulted in motors of smaller physical size and lower cost per kW. International standardization of physical dimensions and frame sizes means that motors from most manufacturers are physically interchangeable and they have similar performance characteristics.

The reliability of squirrel cage AC induction motors, compared to DC motors, is high. The only parts of the squirrel cage motor that can wear are the bearings. Sliprings and brushes are not required for this type of construction. Improvements in modern pre lubricated bearing design have extended the life of these motors.

Although single-phase AC induction motors are quite popular and common for low power applications up to approx 2.2 kW, these are seldom used in industrial and mining applications. Single-phase motors are more often used for domestic applications.

The information in this section applies mainly to 3-phase squirrel cage AC induction motors, which is the type most commonly used with VVVF converters.

Basic construction

The AC induction motor comprises 2 electromagnetic parts:

• • Stationary part called the stator
• • Rotating part called the rotor, supported at each end on bearings
• The stator and the rotor are each made up of:
• • An electric circuit, usually made of insulated copper or aluminum, to carry current
• • A magnetic circuit, usually made from laminated steel, to carry magnetic flux

The stator

The stator is the outer stationary part of the motor, which consists of:

• • The outer cylindrical frame of the motor, which is made either of welded sheet steel, cast iron or cast aluminum alloy. This may include feet or a flange for mounting.
• • The magnetic path, which comprises a set of slotted steel laminations pressed into the cylindrical space inside the outer frame. The magnetic path is laminated to reduce eddy currents, lower losses and lower heating.
• • A set of insulated electrical windings, which are placed inside the slots of the laminated magnetic path. The cross-sectional area of these windings must be large enough for the power rating of the motor. For a 3-phase motor, 3 sets of windings are required, one for each phase.

====1: Stator and rotor laminations

The rotor

This is the rotating part of the motor. As with the stator above, the rotor consists of a set of slotted steel laminations pressed together in the form of a cylindrical magnetic path and the electrical circuit. The electrical circuit of the rotor can be either:

• • Wound rotor type, which comprises 3 sets of insulated windings with connections brought out to 3 sliprings mounted on the shaft. The external connections to the rotating part are made via brushes onto the sliprings. Consequently, this type of motor is often referred to as a slipring motor.
• • Squirrel cage rotor type, which comprises a set of copper or aluminum bars installed into the slots, which are connected to an end-ring at each end of the rotor. The construction of these rotor windings resembles a 'squirrel cage'. Aluminum rotor bars are usually die-cast into the rotor slots, which results in a very rugged construction. Even though the aluminum rotor bars are in direct contact with the steel laminations, practically all the rotor current flows through the aluminum bars and not in the laminations.

The other parts

The other parts, which are required to complete the induction motor are:

• • Two end-flanges to support the two bearings, one at the drive-end (DE) and the other at the non drive-end (NDE)
• • Two bearings to support the rotating shaft, at DE and NDE
• • Steel shaft for transmitting the torque to the load
• • Cooling fan located at the NDE to provide forced cooling for the stator and rotor
• • Terminal box on top or either side to receive the external electrical connections

====2: Assembly details of a typical AC induction motor

Principles of operation

When a 3-phase AC power supply is connected to the stator terminals of an induction motor, 3-phase alternating currents flow in the stator windings. These currents set up a changing magnetic field (flux pattern), which rotates around the inside of the stator. The speed of rotation is in synchronism with the electric power frequency and is called the synchronous speed.

In the simplest type of 3-phase induction motor, the rotating field is produced by 3 fixed stator windings, spaced 120 degrees apart around the perimeter of the stator. When the three stator windings are connected to the 3-phases power supply, the flux completes one rotation for every cycle of the supply voltage. On a 50 Hz power supply, the stator flux rotates at a speed of 50 revolutions per second, or 50 × 60 = 3000 rev per minute.

====3: Basic (simplified) principle of a 2 pole motor

A motor with only one set of stator electrical windings per phase, as described above, is called a 2 pole motor (2p) because the rotating magnetic field comprises 2 rotating poles, one North-pole and one South-pole. In some countries, motors with 2 rotating poles are also sometimes called a 1 pole-pair motor.

If there was a permanent magnet inside the rotor, it would follow in synchronism with the rotating magnetic field. The rotor magnetic field interacts with the rotating stator flux to produce a rotational force. A permanent magnet is only being mentioned because the principle of operation is easy to understand. The magnetic field in a normal induction motor is induced across the rotor air-gap as described below.

If the three windings of the stator were re-arranged to fit into half of the stator slots, there would be space for another 3 windings in the other half of the stator. The resulting rotating magnetic field would then have 4 poles (two North and two South), called a 4 pole motor. Since the rotating field only passes 3 stator windings for each power supply cycle, it will rotate at half the speed of the above example, 1500 rev/min.

Consequently, induction motors can be designed and manufactured with the number of stator windings to suit the base speed required for different applications:

• • 2 pole motors, stator flux rotates at 3000 rev/min
• • 4 pole motors, stator flux rotates at 1500 rev/min
• • 6 pole motors, stator flux rotates at 1000 rev/min
• • 8 pole motors, stator flux rotates at 750 rev/min
• • etc

====4: Flux distribution in a 4 pole machine at any one moment.

The speed at which the stator flux rotates is called the synchronous speed and, as shown above, depends on the number of poles of the motor and the power supply frequency.

Where no = Synchronous rotational speed in rev/min f = Power supply frequency in Hz p = Number of motor poles.

To establish a current flow in the rotor, there must first be a voltage present across the rotor bars. This voltage is supplied by the magnetic field created by the stator current. The rotating stator magnetic flux, which rotates at synchronous speed, passes from the stator iron path, across the air-gap between the stator and rotor and penetrates the rotor iron path. As the magnetic field rotates, the lines of flux cut across the rotor conductors. In accordance with Faraday's Law, this induces a voltage in the rotor windings, which is dependent on the rate of change of flux.

Since the rotor bars are short circuited by the end-rings, current flows in these bars will set up its own magnetic field. This field interacts with the rotating stator flux to produce the rotational force. In accordance with Lenz's Law, the direction of the force is that which tends to reduce the changes in flux field, which means that the rotor will accelerate to follow the direction of the rotating flux.

At starting, while the rotor is stationary, the magnetic flux cuts the rotor at synchronous speed and induces the highest rotor voltage and, consequently, the highest rotor current. Once the rotor starts to accelerate in the direction of the rotating field, the rate at which the magnetic flux cuts the rotor windings reduces and the induced rotor voltage decreases proportionately. The frequency of the rotor voltage and current also reduces.

When the speed of the rotor approaches synchronous speed at no load, both the magnitude and frequency of the rotor voltage becomes small. If the rotor reached synchronous speed, the rotor windings would be moving at the same speed as the rotating flux, and the induced voltage (and current) in the rotor would be zero. Without rotor current, there would be no rotor field and consequently no rotor torque. To produce torque, the rotor must rotate at a speed slower (or faster) than the synchronous speed.

Consequently, the rotor settles at a speed slightly less than the rotating flux, which provides enough torque to overcome bearing friction and windage. The actual speed of the rotor is called the slip speed and the difference in speed is called the slip.

Consequently, induction motors are often referred to as asynchronous motors because the rotor speed is not quite in synchronism with the rotating stator flux. The amount of slip is determined by the load torque, which is the torque required to turn the rotor shaft.

For example, on a 4 pole motor, with the rotor running at 1490 r/min on no-load, the rotor frequency is 10/1500 of 50 Hz and the induced voltage is approximately 10/1500 of its value at starting. At no-load, the rotor torque associated with this voltage is required to overcome the frictional and windage losses of the motor.

As shaft load torque increases, the slip increases and more flux lines cut the rotor windings, which in turn increases rotor current, which increases the rotor magnetic field and consequently the rotor torque. Typically, the slip varies between about 1% of synchronous speed at no-load to about 6% of synchronous speed at full-load.

…and actual rotational speed is ...

Where n0 = Synchronous rotational speed in rev/min

n = Actual rotational speed in rev/min

s = Slip in per-unit

The direction of the rotating stator flux depends on the phase sequence of the power supply connected to the stator windings. The phase sequence is the sequence in which the voltage in the 3-phases rises and reaches a peak. Usually the phase sequence is designated A-B-C, L1-L2-L3 or R-W-B (Red-White-Blue). In Europe this is often designated as U V-W and many IEC style motors use this terminal designation. If two supply connections are changed, the phase sequence A-C-B would result in a reversal of the direction of the rotating stator flux and the direction of the rotor.

The equivalent circuit

To understand the performance of an AC induction motor operating from a VVVF converter, it’s useful to electrically represent the motor by an equivalent circuit. This clarifies what happens in the motor when stator voltage and frequency are changed or when the load torque and slip are changed.

There are many different versions of the equivalent circuit, which depend on the level of detail and complexity. The stator current IS, which is drawn into the stator windings from the AC stator supply voltage V, can then be predicted using this model.

====5: The equivalent circuit of an AC induction motor

Where:

V = Stator supply voltage

E_S = Stator induced voltage

E_R = Rotor induced voltage

N_S = Stator turns

N_R = Rotor turns

I_S = Stator current

IR = Rotor current; IM = Magnetizing current; RC = Core losses, bearing friction, windage losses, etc; R_S = Stator resistance; XS = Stator leakage reactance at 50 Hz; R_R = Rotor resistance; XR = Rotor leakage reactance; XM = Magnetizing inductance

The main components of the motor electrical equivalent circuit are:

• Resistances represent the resistive losses in an induction motor and comprise:

- Stator winding resistance losses (RS).

- Rotor winding resistance losses (RR).

- Iron losses, which depend on the grade and flux density of the core steel.

- Friction and windage losses (RC).

• Inductances represent the leakage reactance. These are associated with the fact that not all the flux produced by the stator windings cross the air-gap to link with the rotor windings and not all of the rotor flux enters the air-gap to produce torque.

- Stator leakage reactance (XS shown in figure below).

- Rotor leakage reactance (XR shown in figure below).

- Magnetizing inductance (XM which produces the magnetic field flux).

In contrast with a DC motor, the AC induction motor does not have separate field windings. As shown in the equivalent circuit, the stator current therefore serves a double purpose:

• It carries the current (IM) which provides the rotating magnetic field.

• It carries the current (IR) which is transferred to the rotor to provide shaft torque.

The stator voltage ES is the theoretical stator voltage that differs from the supply voltage by the volt drop across XS and RS. XM represents the magnetizing inductance of the core and RC represents the energy lost in the core losses, bearing friction and windage losses. The rotor part of the equivalent circuit consists of the induced voltage s. ER, which as discussed earlier is proportional to the slip and the rotor reactance s. XR, which depends on frequency and is consequently also dependent on slip.

This equivalent circuit is quite complex to analyze because the transformer, between the stator and rotor, has a ratio that changes when the slip changes. Fortunately, the circuit can be simplified by mathematically adjusting the rotor resistance and reactance values by the turns ratio N2 = (NS/NR) 2, i.e. 'transferring' them to the stator side of the transformer. Once these components have been transferred, the transformer is no longer relevant and it can be removed from the circuit. This mathematical manipulation must also adjust for the variable rotor voltage, which depends on slip. The equivalent circuit can be re-arranged and simplified as shown in the figure below.

====6: The simplified equivalent circuit of an AC induction motor.

Where X'R = N2 × XR R'R = N2 × RR

N = NS/NR, the stator/rotor turns ratio

In this modified equivalent circuit, the rotor resistance is represented by an element that is dependent on the slip s. This represents the fact that the induced rotor voltage and consequently current depends on the slip. Consequently, when the induction motor is supplied from a power source of constant voltage and frequency, the current IS drawn by the motor depends primarily on the slip.

The equivalent circuit can be simplified even further to represent only the most significant components, which are:

• Magnetizing inductance (XM)

• Variable rotor resistance (R'R/s)

All other components are assumed to be negligibly small and have been left out.

====7: The very simplified equivalent circuit of an AC induction motor

As illustrated above, the total stator current IS largely represents the vector sum of:

• The reactive magnetizing current IM, which is largely independent of load and generates the rotating magnetic field. This current lags the voltage by 90 deg. and its magnitude depends on the stator voltage and its frequency. To maintain a constant flux in the motor, the V/f ratio should be kept constant.

[...]

• The active current IR, which produces the rotor torque depends on the mechanical loading of the machine and is proportional to slip. At no-load, when the slip is small, this current is small. As load increases and slip increases, this current increases in proportion. This current is largely in phase with the stator voltage.

The figure below shows the current vectors for low-load and high-load conditions.

====8: Stator current for low-load and high-load conditions.