Induction Motor
What Is an Induction Motor?
About 90% of the motors running in industry today are induction motors. An induction motor is an AC motor that produces torque by inducing current in its rotor from a rotating magnetic field in the stator, with no brushes or commutator. It has powered everything from simple AC blowers to huge mine excavators since 1887, and thanks to modern Digital Signal Processing it can now be driven with advanced methods like Field Oriented Control (FOC).
Here in this article, we are discussing in detail the internal structure of the AC Induction motors and how they are controlled by VFDs and more explicitly how the Field Oriented Control is done with these Motors, we also show here a comprehensive dynamic modeling of an AC Induction motor with Squirrel case structure which can help in understanding them better.
As a matter of fact, There are different types of electric motors. Electric motors that are powered by either AC or DC power supply. An induction motor is an AC motor, mostly supplied with a three-phase AC power supply. This type of motor is the most popular, so that about 90 percent of motors used in the industry are induction motors.
Why Induction Motor Is Called Asynchronous Motor?
An induction motor is also called an asynchronous motor because the rotor always turns a little slower than the rotating field. That difference is called slip, and it is what makes torque possible: if the rotor ever reached the synchronous speed of the field, there would be no relative motion, no induced current, and therefore no torque. In other words, an induction motor must slip to pull.
Types of Induction Motors
Induction motors are grouped first by phase count and then by rotor construction.
Most motors in the field are three-phase squirrel cage machines, because they are robust and inexpensive.
Induction Motor Parts
An AC Induction Motor has two main parts:
– the Stator
– the Rotor
The stator contains a three-phase winding which consists of 3 phases displaced by 120 degrees from each other. These windings absorb power from the input power supply. There is a schematic down below which clarifies the positions of the windings in the stator. For example, a and a’ are two legs of the first winding.
Stator and rotor may have more windings for each phase. In that case, the electrical phase is different from mechanical displacement in space and is a coefficient of it. In a general rule, the electrical angle is p/2 of mechanical angle. ‘p’ is the number of windings for each phase and is called “pole”.
The second part is the rotor which is electrically isolated from the input power. There are two types of rotors that have different structures, called wounded rotor and squirrel cage rotor.
Wounded rotor type:
The rotor is a three-phase winding. The terminals are accessible in order to implement desired connections according to the application. They have a more complicated structure and are more expensive compared to squirrel cage rotors.
Squirrel cage type:
The rotor is made of conducting bars which are connected by rings to each other at both ends. It has a rigid and simple structure compared to a wounded rotor and is less expensive.
You can see an image of a three-phase squirrel cage rotor induction motor below.
How an Induction Motor Works: Rotating Field and Slip
When an induction motor is powered by a three-phase symmetric power supply, each phase draws sinusoidal current. These currents can be represented by the following equations:
f: frequency of power supply
According to Maxwell–Faraday equation, each of these currents produces a sinusoidal magnetic field. By using superposition for these three magnetic fields, we find there will be a net magnetic field which has a sinusoidal shape in space. This field rotates exactly with an angular speed of ω around the air gap. The following equation describes its behavior in time and space:
We can represent the field using space phasor:
As this magnetic field rotates, it induces a voltage in the rotor, which drives a current through its conductors. That current creates its own magnetic field, and the force between the two fields produces torque that drags the rotor along. The rotor chases the field but never catches it, and this slip is what sustains the torque. Because the field turns at a speed set by the supply frequency, changing the frequency changes the motor speed, which is exactly what a VFD does.
Dynamic Model of Induction Motors
We need a model to analyze dynamics of induction motors. The behavior can be studied using the mutually coupled circuits theory. So, we have a system of equations as below:.
K: one of the six windings,
R_k: resistance of the k-th winding,
p: time derivative operator
ϕ_k: flux linked with k-th winding
L_km: mutual inductance which is function of mechanical angle θ_m between the magnetic axes of the rotor and the stator
There is also a mechanical equation which determines energy balance in motor:
J: moment of inertia
The next step is to rewrite the equations for the stator and the rotor circuits. The space phasor method is used to have a more useful set of equations. It should be mentioned that the space phasor reference is fixed with the stator.
Now we have a model of the motor using five parameters Rs, Rr, Ls, Lr, and M. We can have a simpler model which uses four parameters to model the motor. Considering the fact that rotor is short-circuited and the definition of parameter L_ks=(L_s-M^2)/L_r, we end up the circuit below:
Now we have a set of equations which represent induction motor behavior:
v_s: stator voltage
v_r: rotor voltage
R_s: stator winding resistor
R_r: Rotor winding resistor
I_s: rotor current
I_r: stator current
n_p: number of pole pairs
L_ks: short circuit stator inductance
M: magnetization inductance
T_e: electromagnetic torque
T_r: load torque
We have got some intuition about induction motors so far. Accordingly, we are able to see whether they are suitable for our application or not. As you know two main important drawbacks of a dc motor are the use of a commutator and brushes. But, none of these parts exist in an induction motor. These parts cause more maintenance costs and also make the motor size larger. In addition, they lower the reliability at higher speeds. These two parts have their own losses which reduce the overall motor efficiency and also limit the maximum power capacity of electric motors available in the market.
Controlling an Induction Motor
You cannot control an induction motor by simply changing its voltage the way you would a brushed DC motor, because its speed is tied to the supply frequency. That is why induction motors are driven by a Variable Frequency Drive (VFD). There are two broad ways to do it:
V/f is the classic approach and is easy to set up, but it gives poor torque at low speed and slow response. Field Oriented Control treats the induction motor almost like a DC motor by separating the flux-producing current from the torque-producing current, which is why it delivers the accuracy modern applications expect. SOLO controllers run FOC on AC induction motors out of the box. The sections below detail how a VFD builds the drive voltage and how vector control closes the loop.
VFD
What is a VFD?
Variable Frequency Drive (VFD) is a type of motor drive used to control AC motor speed by varying motor input frequency and voltage.
As previously define the VFD drivers work on The Applied Frequency of the stator component of an Induction Motor.
Variable Frequency Drivers are mostly powered by a single or three-phase power supply and generate a three-phase sinusoidal voltage. These devices do this task in two main steps:
1- Converting input AC voltage to DC voltage,
2- Generating three-phase voltage at the desired frequency.
You can see the schematic of a variable frequency driver below.
The output AC is created by using PWM technique. In this technique every switch turns on or off in a specific pattern. Every switch receives a pulse through its gate and changes its state into short circuit or open circuit accordingly. We need to turn on and turn off the switches in a way that the created output has less possible harmonics. This method is called SPWM (Sinusoidal Pulse Width Modulation). The pattern is obtained from comparison of a triangle waveform which is called carrier, with a desired frequency sinusoidal waveform. For example, if frequency of 30 Hz is desired in output, we should compare a 30 Hz sinusoidal waveform with the carrier. You can see a picture of the procedure down below:
As you see when the pulses which are nearer to the minimum and maximum of the sinusoidal wave have longer duty cycles.
There is one more practical PWM technique to create sinusoidal waves called Bipolar SPWM. In this method, the carrier always varies between the positive and the negative values.
Although this method produces more harmonics compared to SPWM, it has a simpler switching pattern which makes it more practical and more favorable for industrial use.
When we want to implement this technique for a three-phase inverter we can generate a carrier with an MCU. The reference voltage of each phase has a 120-degree displacement compared to other phases. A comparator is needed for each phase to create pulses. You can see a schematic which describes the implementation of the procedure:
There are different types of electric motors. Electric motors are powered by either AC or DC power supply. An induction motor is an AC motor, mostly supplied with a three-phase AC power supply. This type of motor is the most popular, so that about 90 percent of motors used in industry are induction motors.
VFD Drives
The frequency of the power supply determines the rotation speed of the electric motor. This method has good steady-state stability, it doesn’t have a good dynamic response. Vector control is a newer approach which has been used since the 60s. This method makes it possible to decouple input current into two independent fictitious currents. One of these two currents determines flux and the other one determines the torque of the motor. This feature yields better control performance in transients. This control method needs more calculations, but nowadays digital processors make it possible to perform a big amount of calculations needed in this method.
By using space phasor, we can have a completely decoupled situation, from a magnetic point of view. So, we can precisely define two orthogonal axes:
– One is polar axes in the same direction of magnetic flux.
– The other one an interpolar axis for the armature current
The main purpose of vector control is two find a transform so that we have a fictitious machine which has two decoupled electromagnetic circuits. So, we define two ports for the fictitious machine. We call the first port direct port or ‘d’ on which the excitation acts. It’s an imaginary circuit for the creation of magnetic fields in the air gap. A current flows in this circuit to create a magnetic field as what happens in an induction motor. The other one is quadrature or ‘q’ on which armature current operates which is proportional to torque.
Now we have two fully decoupled types of dynamics in the motor. The first one is related to the magnetization of the motor and has a slower transient. The other one is related to electromechanical torque and has inherently faster transients.
The general approach in vector control is to measure real machine parameters and transfer them into fictitious machine parameters. Then fictitious command controls are created and changed into real machine commands using suitable inverse variable transforms. You can see the approach in the schematic below.
Choosing the axes ‘d’ and ‘q’ so that that ‘d’ is always at the same direction of ϕ_r and doing some algebra, yields to following equations:.
The third equation shows that the flux only depends on i_sd and the last equation indicates that torque only depends on i_sq .
Vector control of an induction motor is a closed loop control process. The parameters which should be measured are flux and rotor position. Detection rotor position/speed is straightforward and can be done using an encoder. But measuring flux is a bit tricky. To measure flux, currents drawn by stator phases are also measured and the flux is calculated using currents and speed. In the following picture, you can see a diagram which explains currents and speed loops.
According to this procedure and equations of induction motor, we have the following diagram:
As you see, the desired i_sq and i_sd which are respectively determined by desired torque and desired magnetic field are fed to the current controlled voltage source inverter. Then, VSI generates i_sq and i_sd in order to control the motor.
Mechanical rotation speed of the motor is measured and is used to calculate i_sq ref and i_sd ref. In the picture below, you can see a diagram of the control unit.
In this control loop, the rotor speed is measured and fed into the RΩ block. The output of this block is i_sq _ref which determines output torque. Also, Rϕ_r is used to calculate appropriate i_sd _ref. At low speeds, the motor should have a high torque regardless of speed itself. So, a filter is used to eliminate speed effects at low speeds. But at a higher speed, the flux should be calculated according to operation regions because the motor should work at its maximum power feedback.
Applications of Induction Motors
Wherever a robust, maintenance-light AC motor is needed, an induction motor is usually the default choice, and pairing it with a modern FOC drive extends it into precise, servo-like tasks.
Conclusion
Induction motors have many advantages over other types of electric motors which make them a suitable choice in many applications. As it is shown, their rotation speed can change by the power input frequency, a variable frequency power supply can be used to control the speed.These Devices generate three-phase voltages at their output using PWM techniques like SPWM USPWM or SVPWM. Vector Control is a method that simplifies an induction motor control by decoupling magnetization current and current which is needed to create torque. This decoupling is done by defining two vector currents named i_d and i_q. This method improves transient response and fastens its response to speed changes.
Want to run an AC induction motor with real FOC? SOLO controllers drive induction motors with Field Oriented Control, no external DSP required. See the step by step AC induction speed control tutorial, then pick the SOLO Uno or the SOLO Mega, or browse the full controller range.
