Field Oriented Control of Induction Motors

Induction motors are everywhere. They're used in applications varying from vacuum pumps to cars. They're robust, simple to use, cheap, and efficient. In this video, I want to focus on field-oriented control of three-phase squirrel cage induction motors. There are many explanations online explaining how induction motors work, and how field-oriented control of permanent magnet motors works. However, I didn't find clear explanations online on field-oriented control of induction motors, even though it's commonly used in the industry. The explanations I did find mainly consist of equation throwing, with an exception to Dave Wilson's explanation on the subject, but I think there's still room for improvement. By the way, I'm probably going to do some equation throwing myself, but hopefully it won't hurt as much. I'll briefly cover how induction motors work, then go over some common control methods of induction motors, finishing with field-oriented control. So, how do induction motors work? If you haven't seen the video by Lessex, then come on, it's an awesome video, go see it. But in general, we have the stator, which consists of coils. If you pass a DC through a coil, it generates a constant magnetic field. If you pass AC through a coil, it'll generate an oscillating magnetic field. By having three coils separated by 120 degrees, we can generate a rotating magnetic field. Next, we have the rotor, which kind of looks like a squirrel cage, and it consists of the rotor bars, which are short-circuited at the ends. As the magnetic field rotates, the rotor bars experience a change in magnetic flux, and according to Faraday's law of inductance, a voltage will be induced on them. Since the rotor bars are short-circuited, a current will start flowing. Now, according to Fleming's left-hand rule, if there's a current flowing in a conductor while it's inside a magnetic field, a force will be exerted on the You might have heard induction motors being called asynchronous motors as well. That's because for voltage to be induced in the rotor bars, there has to be a speed difference, also known as a slip, between the speed of the rotor bars and the speed of the rotating magnetic field generated by the stator. Otherwise, no voltage will be induced on the rotor bars to generate the torque. Okay, now that we understand the operating principle of the induction motor, let's look at some common control methods. The goal of the voltage over frequency method is to maintain a constant torque at varying speeds. Let's see how the speed-torque curves change when changing only the frequency. We see that the faster the stator magnetic frequency is, the lower the peak torque. Let's look at some equations to understand why. Here's the torque equation of an induction motor. We can see that the torque is a function of the stator and rotor currents. The motor's magnetic fluxes also happen to be a function of the stator and rotor currents. Let's look at the stator circuit equation. If we assume steady state operation, and neglect the voltage drop on the stator coils, we're left with this equation. So, if we only increase the speed of the rotating magnetic field, the stator's magnetic flux would decrease, which would result in a lower torque output. So, if we made sure to keep the relation between the voltage and the speed of the stator's rotating magnetic field constant, we'd be able to move our speed-torque curve around to different speeds, while maintaining the same peak torque. There are a few caveats to the open-loop voltage over frequency control. In the equations above, we neglected the voltage drop across the stator resistance. At lower speeds, this part is no longer negligible, and needs to be taken into account. Additionally, at speeds exceeding the nominal speed, to keep the magnetic flux constant, we would need voltages which exceed the nominal value, so at higher speeds, the peak torque is reduced as the magnetic flux decreases. Let's move on to the closed-loop voltage over frequency control. In the open-loop method, we didn't actually control the rotor's speed, we controlled the rotation speed of the stator's magnetic field. The difference between the two is determined by the slip speed. Let's look back at the speed-torque curves. We can see the stator's magnetic rotation frequency, denoted as f. For a constant rotating magnetic frequency, the torque changes along the graph with different slip speeds, so the actual speed of the rotor varies with the load. For applications where the speed accuracy is more important, a closed-loop voltage over frequency control scheme can help. In addition to keeping the magnetic flux constant, we also measure the rotor's rotation speed. The control loop is fed back the rotor speed, and the rotating magnetic field is adjusted accordingly. Let's take an example. If the rotor speed is below the desired speed, how do you think we should change the speed of the rotating magnetic field? Should we increase it or decrease it? Looking at the constant voltage over frequency graph, it's easy to see that for a certain torque, if we want to rotate faster, we simply need to increase the speed of the rotating magnetic field. We could also perform torque control using the voltage over frequency control method. We saw that for a certain rotating magnetic frequency, the slip affects the torque, so the torque is a function of the slip speed, and we can command a certain slip speed based on the desired torque. So why is field-oriented control needed? Why can't we stay with the scale control methods? Well, we can, and a ton of applications do, but there are some applications where the benefits of the field-oriented control method are worth the extra necessary computation power. The field-oriented control method allows us to control two independent elements. The rotor magnetizing element, ID, to control the rotor's magnetic flux, and the torque generating element, IQ, which allows us to control the torque command. The main advantages of field-oriented control are a better dynamic response and the ability to decouple the torque and magnetizing elements. It also allows for a general control architecture, which supports both permanent magnet and induction motor control. In the voltage over frequency method, all the equations assume the steady state response. There is no consideration for the transient response. In field-oriented control, we can estimate the response much more accurately. Just as an example, we know the relation between the rotor's magnetic flux and ID. It behaves like a low-pass filter. We can take that into consideration as we command our motor. Additionally, in the voltage over frequency method, the magnetic flux is kept constant all along the linear stage. This isn't necessarily the optimal magnetic flux for this entire operating range. In the field-oriented control method, we can separately control the rotor's magnetic flux using ID and the torque using IQ to more easily find the optimal values. The main disadvantage of the field-oriented control method is that it's more complicated, both to implement and to understand, and it might require a stronger controller because of some needed matrix transformations. Now, one of the basic assumptions of field-oriented control is that you know the position of the rotor's magnetic flux. In permanent magnet motors, that's relatively simple. You need to somehow find the permanent magnet's magnetic flux orientation and track it using some sensor, like an encoder or Hall sensors. With the induction motor, it's a bit more complicated. We can measure the rotor's position or speed, but how do we know where the rotor's magnetic flux is directed? After all, it depends on the motor's parameters and how we drive the motor. The two main methods for solving this problem are the direct and indirect field-oriented control. Both try to estimate the direction of the rotor's magnetic flux. Generally speaking, in the direct method, you try to estimate the rotor's flux using additional measurements. We know that when a magnetic field crosses a conductor, a voltage will be induced on the conductor. So you can measure the induced voltage on the sensors to estimate the flux in the air gap between the stator and the rotor. Sometimes you use additional coils as sensors, but you can also use the existing motor phases as was suggested in this article. After having an estimation of the air gap flux, you estimate the rotor's flux based on the motor parameters. As far as I know, this method is less commonly used in the industry due to the usual need of additional sensors and because of relatively high errors. The indirect method estimates the rotor's magnetic flux orientation based on the slip speed, which is a function of Iq, Id, and the motor parameters. Once we decide to align the magnetizing element Id with the rotor's magnetic flux, we get the following equation for the slip speed. So we first decide what we want the torque element Iq and the rotor flux generating element Id to be. And then, based on the motor's parameters and the rotor's speed, we can calculate the required slip speed to make sure that Id and the rotor's magnetic flux are aligned. The caveat here is that we're assuming we know the motor's parameters. Even if we measure them initially, they can change as we run the motor. For example, the rotor bar's resistance will change quite significantly as the temperature changes. These inaccuracies will lead us to choose a slip speed, which won't result in the rotor flux and Id being aligned, which will lead to suboptimal performance. There are some workarounds which try to estimate the motor's parameters in real time. How would you solve this problem? Leave a comment below. Okay, now let's assume we know the rotor's magnetic flux orientation and we align our reference frame correctly. There's still one missing piece in the puzzle we need to solve. Can you guess what it is? You're absolutely correct! Good job! We're still not sure how to divide the stator current vector. How much should we put into Iq and how much into Id? Well, that depends on what we're trying to achieve. Usually, people try to achieve the maximum torque output from a given stator current amplitude. This methodology is also known as MTPA, or maximum torque pair-on-pair. We can see in the image that when moving along this constant torque curve, there are many combinations of Iq and Id which can achieve a certain torque. When using the maximum torque pair-on-pair method, we want to use the smallest stator current amplitude possible to achieve the desired torque. We can see that point B will result in the smallest stator current amplitude while still outputting the desired torque. This point tells us the amplitude and angle of the stator current vector. That way, we know how to divide the vector between Id and Iq. Let's take a look at the torque equation of an induction motor. We can see it's made up of some constant followed by a multiplication of Iq and Id. To maximize it, we pretty much want the multiplication of Iq and Id to be the biggest. And this is the equation for the stator current amplitude, and we want to minimize it. So allegedly, the best way to achieve the maximum torque pair-on-pair is if Id and Iq are equal, meaning our stator current vector is pointing at a 45 degree angle between Iq and Id. Now let's look at the slip speed equation at steady state. We can see it's comprised of some constant multiplied by Iq and divided by Id. If Iq and Id are equal, we see that the maximum torque pair-on-pair slip speed is constant and is dependent on motor parameters. This however has some practical limitations. According to this article, the maximum torque pair-on-pair slip speed is much lower than the rated slip speed. So to operate at the rated torque using the maximum torque pair-on-pair slip speed, you would need a voltage higher than the rated voltage, which isn't practical. So when reaching the rated load, you would need to increase the slip speed and not operate at maximum torque pair-on-pair. An additional article also examined the optimal slip speed and found another observation. The optimal slip speed increases linearly based on torque and speed. So it's not as clear cut as I said earlier that Iq and Id should be equal. This opens a new door for finding ways to achieve the optimal slip speed for your application. Alright, that's it for this video. Hope you learned something. Thanks for watching and see you next time!