Developing Detailed Motor Model for Electromagnetic and Thermal Analysis

Hi. Good morning, everyone. Thank you for joining today's session on Developing Detailed Motor Model for Electromagnetic and Thermal Analysis. We have with us today Prasanna Deshpande, who leads the e-mobility initiatives at MathWorks. He will be moderating and asking questions to our speakers today throughout the webinar. And he will conduct a short Q&A session post the event, post the webinar.

We have our first speaker, which is Rahul Choudhary. He is the senior application engineer at MathWorks India. He specializes in the field of motor control, multi-domain modeling, and real-time simulation.

Our second speaker today is Richa Singh from MathWorks. She is part of the application engineering group at MathWorks. She currently supports customers from various domains, such as server control, autonomous systems, and Simulink real-time.

I would now like to pass this on to Prasanna, who will be setting the context for this discussion and webinar today. Thank you.

Engineers involved in developing electric motor simulation and motor control often encounter challenges simulating the nonlinear behavior. A lot of times, it is influenced by different factors, like load torque, speed, rotor angle, et cetera. So to address this, motor design tools employ several methods, like finite element analysis. In a way, it is an accurate solution also.

In this webinar, will demonstrate a comprehensive approach to tackle the issues related to bringing in information from detailed motor design-- detailed motor models built by motor design teams. So firstly, we'll showcase how motor data from a motor design tool can be imported into Matlab environment into Simscape electrical model.

And then we'll also get into how this can be used for doing accurate motor control design, considering nonlinear factors, like saturation and spatial harmonics, and things like that. And then we'll also get into development of detailed thermal model, which is based on data. So without spending too much time in introduction, let me hand it over to Rahul and Richa for getting us through the webinar.

So let me begin with some of the challenges, what typically a motor control engineer is going to face, or motor simulation in general. So in the past couple of months and years, we are seeing a trend of developing motor controller in-house, and not only just developing the motor controller, but also designing the motor in-house. And that involves several challenges.

So for example, the workflow for motor design team and motor control development team, it proceeded in a separate way. On one hand, motor control engineers, they rely on linear lumped parameter-based motor model, which is ideal for designing and tuning the control algorithm. But on a flip side, it does not give a complete picture, and it does not cover some of the details, such as saturation, losses, and spatial harmonics.

On the other hand, motor control-- or motor development team or motor design team, they use sophisticated tools which can capture the effect of electromagnetics thermal and mechanical behavior of the motor with very good accuracy. But these models, they run very slow. As a motor control engineer, I need to have all this information to improve my controller efficiency or minimize the torque ripples, which are very critical for numerous motor control applications. This high fidelity motor model can also be used to validate the controller's performance across the entire operating range.

Now, let's go and look at the steps these two teams are going to take in order to do the motor control development workflow. So motor designers, they first configure the motor, which means they decide the geometry of the motor, the poles and slots it is going to have, and what kind of windings it is going to have. And based on this configuration, they create or they design the motor.

And then after that, they use that motor model to basically simulate it across different operating conditions, just to understand its performance and various losses associated with it. Finally, they would also like to validate this motor model against some realistic current waveform, which they would typically get either from the drive or maybe some simulation tool, which is simulating the behavior of the drive.

Now, on the other hand, motor control engineers, they are responsible for designing a closed loop system. And in order to do that, they first compute the operating points for their motor control. So for example, in case of, let's say, PMSM, they need to compute what is their Id and Iq reference for given torque and speed demand.

They have to also simulate the behavior of the motor drive, the power electronics components, power converters, and then do a system-level simulation to understand the overall efficiency of the system and how much torque ripples it is going to produce for a given control strategy and all the power electronics and drive presented into the model.

Now, let's put some context to this model. So instead of talking motor as a standalone component, let's try to put this motor into some application. And the application which I'm going to take today is a vehicle. And in this vehicle, I'm going to put this motor, which is going to, basically, deliver the necessary power or torque to move this vehicle in most efficient and optimal way.

Now, this kind of system-level models are very, very useful to get answers to some of the questions, such as what kind of motor I should use, what should be the size of the motor, and doing different trade-off studies by comparing the output torque and then the overall power of the motor. One thing you have to note here that, in this entire exercise, we are not going to go into details of the motor. We are only going to take some high-level requirement in terms of the maximum torque and the maximum power motor can produce, and do this trade-off study.

Once we identify the desired size of the motor, then we can use that to address or answer some of the other questions, so for example, how we can design a detailed motor plus inverter model, and use it to design a closed loop controller for the motor, which is going to give us the desired torque and speed. And then we can integrate this detailed motor model, again with this system-level simulation model, and then generate the necessary data and assess its performance.

So at MathWorks, we have various tools which will allow you to not only just create a system-level model for the system which you are targeting, so whether it is a complete electric vehicle or any other application, so toolboxes like Simscape, Simscape add-on or Powertrain Blockset, these tools will allow you to quickly create a system level model, and then use motor of your choice, add it to the system-level model, and then do a performance study and things like that.

Now, next, we are going to discuss what additional benefit a motor design engineering team can provide here, so how we can make this workflow more efficient. Before that, let's go into-- let's look into the motor design workflow one more time. So other than doing this design exploration on how motor geometry and windings and number of poles and slots are going to affect motor performance, they also do two main simulation here.

One, they generate efficiency map for entire operating range of the motor. In certain tools, such as Motor-CAD, you can directly export this efficiency map for entire operating range. But in other tools, maybe you have to write some custom script, which is going to sweep through different operating point of the motor and going to give you this efficiency map. The second thing what they do is a detailed finite element analysis, just to capture the flux linkage for given current and rotor position.

Now, we are going to use this efficiency map, which we have generated for the entire operating range of the motor, to basically enhance our study of component selection and component sizing. So first, what we need to do is we need to bring this efficiency map data into simulation environment. And for that, we are going to use this block from Simscape Electrical Library, which is motor plus drive block.

This is a system-level block, which is not simulating the details of the motor, but it is going to have the efficiency map and torque speed characteristics just to give you relevant information about the motor. Once we parameterize this block, then we can generate the results from this block and compare against the data, what we have got from the motor design tool. Once we are satisfied that this is behaving as per our requirement, then we can connect this motor plus drive model into our vehicle level model. And here--

May I interrupt? May I ask a question?

Yes, yes, Prasanna.

So what kind of drive model does that motor plus drive block have?

OK, that's a good question. So in this particular case, we have a closed loop torque control drive model implemented in this motor plus drive model. So it does not simulate details of power electronics components or details of the motor. But it's a system-level model, which is having a closed loop torque control drive model plus lookup table based motor model.

Thanks.

So once we verify the performance of this motor plus drive model, we can integrate with the rest of the vehicle model, where we can have components, like battery, DC to DC converter, our cooling system, and then vehicle control unit. Then we can run this model for different what-if scenario simulations. For example, what is going to happen when we are going to accelerate the vehicle and then cruise the vehicle at a constant speed, and also some of the environmental conditions, so how my vehicle is going to perform when we are going, let's say, uphill.

What is going to happen when driver is going to apply brakes or maybe going to enable the cruise control? So by providing these inputs, we can generate data, like whether my motor is able to provide the necessary torque or not. And then those efficiency maps can also give us information about the rise in the motor temperature because of those losses.

So you can see here in the motor plus drive model, we are not only simulating electromechanical behavior of the motor, but we are also complementing it with a thermal model, which is going to capture-- or which is going to convert the losses from the motor plus drive model into equivalent heat energy.

So in this model, the main agenda was to understand whether my motor, which I have selected, is going to meet my requirement when I put it in a context of a vehicle or any other application. Here, we have not designed any closed loop controller for the motor. Next, we are going to see, based on this information, how we can quickly design a detailed motor control algorithm.

But before that, let's see what is the control design workflow. So typically, a motor control engineer, they start with creating a plant model. This plant model consists of motor plus inverter. And then they select the control architecture, so whether they are going to implement a field-weakening controller, field-oriented controller.

Are they are also going to incorporate, let's say, feedforward controller to reject the disturbances and all those things? And then start tuning the control loop gains. They also fine-tune the controller's performance or controls parameters to minimize the torque ripples.

And once they are happy with the closed loop performance in desktop environment, they can go for code generation and deploy to the target. Here, we are not going to focus on the code generation in the deployment part. But if you are interested, we have a dedicated video which talks about how you can develop motor control algorithm and take it to the target of your choice.

So let's focus on how we can create a motor model. Oftentimes, motor control engineers, they rely on linear lumped-parameter-based motor model, where we just capture how torque is going to change as a function of current and other motor attributes. So in a linear lumped-parameter-based motor model, we assume that the torque is a linear function with respect to current. And the behavior of the motor is defined by these set of equations. So these equations are for a permanent magnet motor.

And you can see here how the voltage, speed, and torque equations are being implemented. Now, in order to implement this equation, we need certain parameters, so parameters like resistance, number of poles, the maximum flux linkage, inductance values, and the mechanical properties of the motor, like inertia, damping, and friction. And once we have these parameters, then we can quickly implement these mathematical equations into simulation environment and create a motor model.

So either we can implement these equations into Simulink by using Simulink block diagram, or we can also rely on built-in blocks, which are available in Simscape Electrical Library. So for example, we have a built-in PMSM block in Simscape Electrical Library. And if you double-click on this particular block, we are going to see a parameter dialog box, where we can enter the parameters, which we typically get from the datasheet of the manufacturer.

In case, if you don't have a datasheet from the manufacturer, then you can also select this option. Click to Select, which is going to open Block Parameterization Manager, where we can directly select a motor from the dropdown menu, and select the part number. And it is automatically going to populate all the necessary parameters into this particular block.

Let's say I don't have access to the manufacturer's information, but instead, I have access to the motor. In that case, the motor control blockset has this workflow of running some instrumented tests directly onto the motor to estimate motor parameters.

So in this case, it is doing a couple of tests, such as DC test, to estimate stator resistance, and then high frequency signal injection to estimate inductance parameters, and then coast-down test, which is taking the motor to certain RPM, and then let it stop naturally to estimate some of the mechanical parameters. So whether you take the Simscape-based approach or this motor control blockset-based approach, it is going to give you the desired parameters, and you can quickly able to create a linear lumped-parameter based motor model and you can use for designing your control algorithm.

But if you're working on, let's say, a traction motor, which is oftentimes going to run in nonlinear region or in saturation region, capturing the effect of nonlinearities becomes very, very important. So we need to capture how my motor is going to behave when it hits the saturation region and how the spatial harmonics is going to play a role in terms of the torque profile. How we can incorporate these changes?

So in our existing linear lumped-parameter-based motor model, we assume that the maximum flux linkage is constant. But in reality, the flux linkage varies as a function of motor geometry, and also the motor current, and then position of the rotor. So in this equation, we need to do some modification.

So we need to replace this maximum flux linkage with a lookup table. This lookup table could be the relation between flux and motor current, and then the rotor position. Or it could also be your torque speed table for different VDC. And we can use these tables to basically enhance the existing linear model to capture the effect of nonlinearities.

How we are going to get these tables, again, we can rely on motor design tool. So in this animation, you can see from the motor design tool we can generate a table of how the v axis and q axis flux linkage is going to change as a function of currents, as well as the rotor position. Once we get this table, then we can use this table data into one of our Simscape block, which is a parameterized PMSM motor model.

And we can enter these tables into this particular block. And not only just the tables, but we can also incorporate different losses, what we typically get from the motor design tools, such as the hysteresis loss, eddy current loss, or the various losses which are happening at the stator side in form of stator resistance. Once we parameterize this block, then we can generate some of the characteristic graphs of the motor and compare against the motor design tool.

Once we are satisfied that this block is capturing all the necessary dynamics which we are interested in, then we can create a detailed closed loop model around this motor. Here, we can provide two inputs. One is, at what speed I want to rotate the motor, and what is the load torque? And then design a closed loop control system here, which is going to regulate the duty cycle of this inverter to produce the necessary speed at the desired torque value.

Now, if we go a little bit deeper inside this--

Rahul, sorry for interruption again.

Yes, Prasanna.

A couple of questions I got-- the graphic on the slide shows PMSM. The question is, a field parameterized block, is it only available for PMSM.

So again, that's a very good question, Prasanna. So in Simscape Electrical, we have a couple of blocks which can give you a detailed motor model, which are based on the motor data, motor design data. So PMSM is one block. Other than PMSM, we also have PLDCN and induction motors, which can be parameterized based on the same kind of lookup table.

So do we have support for non-PM motors?

Yes, we do have support for non-PM motors as well. So in Simscape Electrical Library and in motor control blockset, we have a variety of motor blocks. So for example, switch reluctance motor or, basically, induction motors, which are not using any rare earth materials, such as permanent magnets, and users can use those blocks, and then parameterize it, and then use it to design a closed loop control system around it.

Sure, thanks.

Thank you. So let's go into details of this control architecture here. So if I just go inside the controller, so we have two loops here, one outer speed loop and then inner current loop. And in between, we have this lookup table based current reference calculation. And in this particular block, we are again reusing the same motor design data. And this particular block is computing what should be my Id and Iq reference based on the torque and speed profile.

We have also modeled the inverter part using Simscape Electrical Library. So here, we are using semiconductor switches just to model the behavior of the inverter. And now, if we run this model, then we are able to see how my controller is performing, so whether it is able to track my reference speed and also generate the necessary torque, and see its impact on this motor current.

If we go back to a field-parameterized motor model, here, we also have one additional option where we can enable thermal port in this block. So the moment we enable thermal port, it is going to give us a couple of options, so for example, how the permanent flux linkage is going to change as a function of temperature, and also how the resistance value is going to change. For the thermal modeling of the motor, it also provides information, such as what are-- basically, we have thermal masses for rotor and all the three phases, and then thermal properties.

Once we enable this thermal port, then we can use this motor model to again design a closed loop controller. So addition to this electromechanical behavior, we have also modeled the thermal behavior. And this is a very simplified thermal model, where we are just tracking how the losses are getting converted into heat, and then how that heat is getting dissipated to the environment through different heat transfer medium.

And then we can run this model and understand whether it is able to follow my torque and speed profile, and then how much heat we are going to see at each windings and at the rotor. So this kind of model is very, very useful for motor control engineer who wants to probably the motor when it is going to hit its thermal limit. But if any thermal engineer wants to use this model, then probably the information what we are showing might not be enough.

Because for thermal engineer, he is more concerned about the thermal behavior of the motor. And we all know that the electrical transience or electrical dynamics are much faster compared to the thermal. So even if you are doing, let's say, one or two seconds of simulation, which might be adequate for understanding the electrical behavior of the motor, might not be enough to capture the thermal behavior.

And we also need to understand how the motor thermal network is going to behave when there is an active cooling system connected to it, and also understand all the thermal transients. So for that, we need a detailed thermal model, which is focusing purely on the thermal behavior of the motor and not focusing a lot on the electrical side. And that kind of model can be really, really useful for basically designing a thermal management system for the motor. And how a thermal management system or how a detailed thermal model can be designed, that part is going to be covered by my colleague, Richa.

Hi, everyone. So as Rahul has already set the context about the thermal modeling aspects for the motor design, so in order to develop a thermal management system, four nodes might not be sufficient. In addition to-- for that, we need to analyze the temperature at various nodes of the motor.

So how we can do that, let's say if we are taking the high fidelity model that has been developed using third-party toolbox, so in order to analyze the thermal aspect, we have to run the simulation for a much longer time. Because, as Rahul has already mentioned, the thermal properties changes longer as compared to the electromagnetic properties, like torque and speed.

In that situation, what our solution is, we need to make our model run faster. Now, how we can do that, we can develop a reduced order model for that. In order to develop a reduced order model, the model should be such that it balances the trade-off between the speed accuracy, as well as the system interpretability.

Now let's understand what is a reduced order model. A reduced order model is a technique that simplifies a high fidelity first principle model by reducing its computational complexity, while preserving the dominant behavior of the complex model. Now, reduced order model can be used for developing-- for enabling the faster simulation for high fidelity systems.

We can also use reduced order model for developing a hardware in loop testing. We can also develop a digital twin using reduced order model techniques by developing virtual sensors, by modeling the virtual sensors. Further, the reduced order model also enables the desktop simulation of longer timescale.

Now, if you see here on the right-hand side of the screen, we have a high fidelity motor model from the-- actually, from the Motor Design Toolbox. Now, if we run this model for a-- if we try to run this model for the thermal aspects, we need to run it much longer time. However, if we use a reduced order model, the system-- I mean the simulation will be much faster as compared to the high fidelity first principle model.

Now let's understand what are the various techniques that we can develop the reduced order model. We have three approaches in order to develop a reduced order model, starting with AI-based data-driven model, linearization, and model-based approach. Now, based on our understanding of the system, depends on the data that we have currently with us and based on the application, we can either approach for either of the three approaches.

Now, when we have enough data about-- we have enough first principle based data, then we can always go for AI-based data-driven techniques, which will be mapping the input parameters with the output parameters. It's going to map the output behavior with respect to the change in input parameter. Now, in AI-based data-driven model, we have either a static model or dynamic model.

In case of static model, you can use techniques such as curve fitting, lookup tables, to create the static reduced order model. In order to develop a dynamic reduced order model, you can always opt for LSTM network, deep neural network, feedforward network, or nonlinear models.

Now, if your application is to develop a control design, you can simply linearize the system, either by pole 0 cancellation or a system identification toolbox, which will be mapping your input with-- which will map your output with an input parameter. And you can get the linearized model to develop a control design.

Now, if your focus is to develop a detailed understanding of-- if you have detailed understanding of the system, you can always opt for model-based approach, which will give you a detailed model of the system, in addition to that, keeping the dominant feature of the system intact. And then you can utilize that system with a-- integrate that reduced order model with an auxiliary unit of the systems.

Now, today, we're going to focus on model-based approach for the motor design application. Now, the workflow for developing a reduced order thermal model, in order to understand the thermal aspects of the motor design, the workflow will be as follows. First, what we will do, we will generate a Simulink-based reduced order thermal model through motor design tools.

Now, this tool is going to give me a set of lookup tables for a given speed and torque value. And it's going to cover all the losses that occurs in the system. Either it can be thermal losses, it can be ion losses, it can be copper losses, and so on.

Next, we validate this reduced order model with a motor design with a high fidelity model that we had already with a motor design toolbox. And then we integrate it with dynamics in order to understand how the thermal losses is going to affect our motor design. Now, with this workflow will enable the faster simulation for this multiphysics analysis of the system across the full operating range.

Now let's get into the reduced order model that we got from the motor design tool. Now, on the screen, you can see here, we have a reduced order model for a motor, which takes the shaft speed torque and the flow rate and temperature from the housing motor jacket as an input, and gives me the temperature node, power node, and coolant output temperature. Our focus here is to monitor the temperature nodes or the evolution of the temperature across all the nodes that we have selected.

Now, let's get inside this model. So we have four subsystems inside this model-- loss map from the motor CAD, power loss distributor, coolant interface, and interpolated subsystem. The coolant interface actually takes the inlet temperature and convert it into different vectors.

Then we have the loss maps, which we got it from the motor design toolbox. It's going to give us various losses that occur during the simulation for the given torque and speed value. And we can simply import those lookup tables over here. And next, these losses will be distributed among the nodes, assuming the constant temperature across all the nodes.

Next, we have interpolated state space model. This model is nothing but a mathematical model, which is a state space-- which nothing but a state space dynamics. And inside this model, what we have here is we have a linear parameter varying model. And this model, actually, in order-- inside this subsystem to correctly predict the coolant heat flow rate, the model needs to apply a loss correction via an interpolator.

Now, next, let's understand the mathematical aspects of the interpolated state space model over here is. We have states as the temperature of all the nodes. Then we have the control input as the node losses.

The system and input matrix A and B are obtained by linearizing a different operating point with respect to speed, flow rate, and coolant temperature. This interpolated model is commonly known as linear parameter varying model. Now, once we import it or once we generated the reduced order thermal model, we need to validate it with a model that we have got from the motor design tools.

Now, here, we have a Simulink model and the motor design tool. And you can see here, the nodes temperature for the given speed and in the given temperature are matching with the motor design toolbox. Now, once we have validated our reduced order model with the high fidelity first principle model, we can integrate it with our system dynamics.

So here, you can see, at the front, we have a reduced order model, which is now connected with a simplified vehicle dynamics and a driver. Here, in order to get the input for the housing motor jacket, we have radiator and fan to give me the temperature.

The input to this system is given via a drive cycle, where we have a reference speed. And from the simplified vehicle dynamics, we are getting the reference torque that is given as an input to the reduced order model. Now, once we run this model, we will be getting the evolution of the temperature across different nodes.

Now, for a given torque and speed profile, we're going to get the temperature node, as shown in the picture. Now, here, we are seeing that the simulations are run much faster as compared to the high fidelity first principle model. Now, with this, we can say, if we opt for the model-based reduced order modeling approach, we can extract a high-- we can extract a reduced order model that will be going to give all the insight about all the losses that occurs in the system.

It can be either thermal losses, it can be iron losses, it can be copper losses, and so on. And then we can see the evolution of temperature. We can see the evolution of losses for the given torque and speed profile. And we can analyze the motor design accordingly.

Now, with this, I'll conclude our session. And let's see what we have covered in this session. We started with the collaboration between different teams, like motor design team and motor control team.

Then we see how we can utilize the motor design data in order to understand the system behavior and develop the control algorithm based on the design data. Then we delved into reduced order model to analyze the thermal aspects of the motor design. And towards the end, we integrated the reduced order model with the vehicle dynamics to speed up the simulation and analyze the thermal aspects of the motor design. Now-- yeah.

You can visit our Electrification Solutions page, where you have various options to understand different aspects of motor design. We have MATLAB motor control design that starts from concept to agile simulations. We have also MATLAB Answers page, where you can paste your queries, and top community contributors are here, which will be answering to you-- who will be answering to your questions, and so on. So there are different options available on this Solutions page you can always opt for.

Now, you can also enable your team by opting for various training options. Here, we have onramp courses here, which are self-paced onramp courses. Then we have instructor-led trainings on these various topics, related to the motor control and power electronics.

Next, if you wanted to learn more on the motor development aspects, you can look through these. Web links are available here. It can be either developing the motor control or developing a reduced order model, and so on.