As with any state-of-the-art technology, there tends to be a lot of misinformation about how new things work. Over the last few years as we’ve gotten into the EV space I have had a lot of difficulty finding relevant information about the control of AC motors in traction (i.e. automotive) applications. It wasn’t until we did a training session with Cascadia Motion (inverter suppliers for Formula 1 among other professional racing series), that some level of understanding developed.

It’s easy to find mounds of information on the internet about the fundamental operation of an electrical machine, but how about specific details that relate to operation in an EV? The goal of this article is to cover the basics to establish a bit of a foundation to avoid misinformation and rumors spreading (a classic gasoline-powered car rumor is that exhaust backpressure is needed to make torque, and that untruth has been alive and well for decades!) So let’s dive right into it.

#### What Does An AC Machine Need?

First, we need to understand what the motor needs to spin. If you’re familiar with the basics of an electrical motor then you likely know that when an electrical current is passed through the windings of a motor a magnetic field is created. The strength of that field is roughly proportional to the amount of current.

To put it simply, the motor needs this magnetic field to be positioned in such a way that the rotor of the motor (the rotor is the bit in the middle that spins) is inclined to turn. The more current that is applied, the greater the torque on the rotor to spin.

#### How Does The Inverter Give The AC Machine What It Needs?

With a very basic understanding of what the motor needs, let’s look at what the inverter must do to get the motor to spin smoothly and with precise control. This is where it gets a little bit more complicated.

The inverter needs to take a DC input voltage and convert it to an AC output of varying frequency and voltage while keeping the timing of those electrical currents in sync with the position of the motor. The inverter does this by using high power, high-speed transistors (switching the power on and off at a rate of 12,000 times per second or higher) to create rotating magnetic fields that are always just ahead (for forward motion) or just behind (for reverse) the poles of the motor. These transistors switch on and off to create what is effectively a sinusoidal AC voltage waveform.

The trick is in knowing exactly how to time these AC waveforms and how “large” to make them. The larger the waveform requested, the more current is needed to produce that waveform.

The methodology of looking at the currents applied to the motor from the perspective of the spinning rotor is called “field-oriented control.” Looking at the control from this perspective is the most intuitive way to think about it, as you can then set just one value as the target angle for the electromagnetic forces to be applied at. This is sometimes called the “advance” value. From there all that is required is a total current request value and the Field-Oriented control logic in the inverter backs this out (using two steps referred to as the Park Transformation and the Clarke Transformation – you can read more about field-oriented control (also called vector control) here.

This is somewhat akin to thinking of firing a sparkplug for a gasoline-powered motor at “30 degrees before top dead center” – in other words, you’re framing it in terms of the control value to produce the ideal output. The difference is with motor control, there is no “Top-Dead-Centre” – there is just a position ahead of or before the motor pole’s current location. Field-Oriented-Control lets you say, I want to always apply the maximum magnetic field strength X number of degrees ahead or before the pole.

When the inverter wants the motor to spin faster, it will apply that total current vector 90 electrical degrees ahead of the poles. This will create a field and a resultant force that will try to turn the motor. When the inverter wants the motor to spin slower, it will do the opposite and apply a current (or sink the back EMF back into the battery – more on that later), 90 electrical degrees behind the poles.

#### Current * Voltage = Power, right?

One thing to understand is that on either side of the motor, there are two sets of currents and voltages – and they are different! The output current (motor current) of an inverter is not the same as the input (battery) current of the inverter.

Knowing that **current** multiplied by **voltage** is **power**, you’ll see that this is a pretty confusing situation until you realize that the **voltage** on either side of the inverter is not the same. Let’s reconcile this.

On the input side of the inverter, the Voltage is obviously the DC voltage of the battery, which doesn’t change that much. During an acceleration run, the current going into the inverter will climb, and eventually level off at peak power, and then taper down as the motor runs into the field weakening range.

The input (battery) current is close to proportional to the input power as the battery voltage does not change very much. A log of the battery current and battery power (current * voltage) will roughly follow each other.

On the output of the inverter, motor voltage is proportional to the speed of the motor, and to a less extent the amount of torque of the motor. The motor current represents the torque that is produced as we mentioned earlier. More current = more torque. This is because in a permanent magnet motor the voltage of the motor is very close to the speed of the motor. It is worth noting that determining the power from the output current and voltage is a little more difficult than on the input to the inverter, as the power factor of the AC system comes into play.

When looking at the inverter’s output current, the “curve” of the output current closely matches the torque curve.

#### At Some Point, You Run Out Of Voltage.

This is where it gets interesting. If we had unlimited voltage, assuming it didn’t exceed the limits of the components inside the inverter, it would be possible to hold the inverter output current (and thus torque) as motor speed continued to rise. Since power is simply torque * rpm, the power would continue to rise as well.

When an inverter is commanded to deliver maximum torque it outputs the most current it is programmed to be able to deliver – and that is usually a constant amount limited by the switches and electronics inside the inverter. This constant amount of current equates to a fairly constant amount of torque at the motor even as RPM rises. So what stops the torque from carrying on flat all the way up to the motor’s maximum speed? Why do motor dyno graphs have a distinct “knee” in them where the torque suddenly drops off and the power goes flat?

#### A Bit About About Back-EMF

Before we can cover that, you need to understand Back-EMF – or Back Electromotive Force. You can read all about Back EMF on the internet, but the basics are that when you spin a magnet (the magnet is on the rotor of the motor) inside of a coil (the stator, or outside of the motor’s windings), a voltage is produced in those windings. The faster the motor spins, the higher this voltage becomes. Voltage is proportional to speed.

Keep that point in mind – that the higher the RPM, the higher the Back EMF voltage.

Interesting tidbit – with a permanent magnet motor (such as the Model 3’s rear motor) at some speeds this Back-EMF voltage is so high that it could actually damage the inverter if the inverter is suddenly powered off. This is why Tesla mandates that all cars are towed on a flat-bed – tow them by their rear wheels at highway speeds and you could fry the inverter!

#### Back to running out of Voltage

It takes a certain amount of current to produce a torque in a motor. We know this already. But what I haven’t mentioned, and what is the main key to all of this – is that in order to get that current there must be a voltage differential – i.e. a difference of voltage between the supply (the inverter) and the motor.

The more current that is commanded, the more voltage must be supplied from the inverter.

When the motor is spinning quickly, the motor voltage can be very high – in the hundreds of volts – even when no power is being applied. This means it requires at minimum that base level of voltage (and then some) to apply a positive torque.

At some combination of battery voltage, motor speed and requested torque, the voltage required exceeds the voltage available! And that is when you see the knee in the torque graph. It’s at that sad moment when you wished that your EV had an 800V battery!

The point where the torque begins to fall is called the “base speed.” There are many different ways of looking at base speed, as the “base speed” of a motor also depends on how much torque is being requested. In pure back EMF terms, the base speed might be very high, say 7,000 rpm. But when requesting 1000A the base-speed may be reached at only 5,000rpm, because of the voltage difference required to produce 1000A of current flow through the motor.

#### Enter Field Weakening

Luckily, motors are able to run above their base speed, and actually hold constant power over a pretty extensive speed range using something called Field Weakening. This is something most EVs employ a great deal of, as it allows for a motor to be tuned to have a massive amount of off-the-line torque while still having adequate power at high speeds.

The way Field Weakening works is by injecting a current to cancel out the magnetic field produced by the magnet of the rotor. This process weakens reduces the back EMF produced by the motor.

With lower Back EMF voltage there is now a larger difference between the battery’s input voltage and the voltage of the motor – allowing the inverter to apply more current without running out of voltage.

In the motorsport world, a motor would be wound differently, generally to provide less back-EMF to optimize the power for high-speed operation. In this case, you’d see lower torque down low, but the base speed would be higher, and thus the total power capability of the motor would be greater.

#### Making More Power

Now that you know how a motor produces power, it’s not too difficult to understand what needs to be done to get more of it. Without changing hardware, you can get more power either by increasing the current to the motor, or by increasing the voltage of the battery to increase the base speed.

Inverters are fairly expensive to make, so OEs generally run them at their maximum safe rated power. As the electronics inside the inverter get hot from running at this load, they will eventually de-rate. This is a big problem with the original Tesla Model S inverter for example. It can overheat after only half a lap on the racetrack in some cases! So running even more current on an inverter like that would be possible, but even further reduce the amount of time that peak power could be produced.

State of the art inverters, such as those found in the Model 3’s LR rear motor have more efficient switching technology which allows them to run at higher currents for longer without overheating – but they too are already tuned to just about their maximum output to keep them as small and cost-effective as possible.

Getting more voltage is difficult and requires entirely redesigning a battery pack. Different cell chemistries will have different levels of internal resistance – which affects how much the voltage sags when a large current is pulled from the battery. Less voltage sag is preferred for power, as more voltage under load equals more power.

The internal resistance of a battery generally goes down as the battery warms up, increasing power potential. That is why Tesla will pre-warm the battery in the Ludicrous cars before drag racing to help decrease battery voltage sag.

So you can see it’s very difficult to get more power from a production EV as they are generally already tuned to their limit, and changing parts is very difficult when the intention is to keep the car a road-going vehicle.

#### Wrapping Up

So those are the main points about how an inverter functions to control the motor. The important point and the purpose for this article was to give a start to finish overview of how motors and inverters work from a practical standpoint understanding the basics that voltage * current must equal power.

Most articles online about motor control hyper-focus on one point, or get extremely mathematical and are written by academics which makes it very difficult to get an understanding of what is actually going on.

So I hope this helps a little bit and perhaps in the future, we can dive in on more details of specific aspects of this incredibly interesting technology!

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