Controlling the "amount" of regenerative braking (variable back torque?)

Question

I have a question I have been wondering about for a while regarding regenerative braking on electric vehicles.

If my understanding of electrical motors is correct

In a perfect world with no friction or noise, the amount of power put into a motor should equal the amount of power that can then be taken from the motor. That is to say, if you accelerate to 60 mph in an electric vehicle, and then take your foot off the gas and come to a complete stop, the amount of power generated should be the same as the power spent (again assuming no loss in this perfect world).

Does this concept work the same with torque? Would the maximum amount of torque that a motor can output, be equal to the max amount of torque that the motor can generate?

If this is the case, how can electric vehicles brake "more" with regenerative braking? What is the electrical system that controls how much power is allowed to be generated by the motor?

I would imagine that taking your foot completely off the gas would be the maximum back torque and maximum regenerative braking (obviously putting negative charge through the motor to slow it down makes no sense for regenerative braking!). And yet, electric vehicles allow you to brake harder or softer, charging the battery more or less.

Any insight on this is greatly appreciated! This is a difficult question to word given my limited knowledge, please ask for clarification if I have not articulated enough.

Answer 1

The amount of torque a motor generates is dependent on the current flowing through it. Control the current, and you control the torque.

You can control the current when accelerating using your standard acceleration controller.

When regenerative braking, the controller that charges the battery from the motor generated power is programmed to draw a small or large current from the motors, generating a small or large braking torque.

The maximum torque a motor can generate depends on the maximum current you are prepared to put through it. There are several limits on motor current. Amongst the limits that directly limit the current are we must not demagnetise the motor, tear the windings out or break the shaft. An indirect limit is the maximum temperature of the motor. It will have a continuous rated current, which it can run at all day without overheating, losing heat continuously through its ventilation. This current will be an order of magnitude lower than the other direct limits, so it can be run at more than that for a limited time. For example, it might be able to run at continuous+50% for a few minutes, +100% for one minute, absorbing the excess heat by raising the motor temperature.

I don't know whether commercially available systems make use of this, but if I was an electric automotive designer, I certainly would. When motoring, especially if going up a hill, there is no limit to how long that would be required, so you must limit at the motor's continuous rated current. When braking, we know the maximum amount of energy we are going to have to handle, so can afford to operate the motor in a time-limited overload, and stop with a higher power than we'd use to motor.

How 'taking your foot off the gas' is programmed to control the vehicle is simply a software/usability issue, it will work however it's been programmed to work. As a driver, I'd prefer foot off the gas to equate to no applied power, no applied braking, which some folks call coasting. Pressure on the brake pedal should control the braking torque, so that it drives like all other vehicles drive. Obviously there would be significant safety and UX engineering to happen into exactly how the brake pedal was mechanically linked to the friction brakes, and controlled the regen brakes, but that doesn't change the physics of the motor and its current control.

Answer 2

Your understanding of power is incorrect. Energy is stored inside a moving mass, not power. Power is energy divided by time. So, you can de-accelerate either quickly (high power) or slowly (low power).

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Let's take a simple example: a 1920ies streetcar. One of the most simple arrangements driving electrical. It has a series DC motor and some resistors on the roof top for braking.

Let's say we have an energy of 50kWs stored in the moving mass of the car. The resistive brakes can take up to 10kW without overheating. So, using the electrical brake at full power, we should be able to bring the car to standstill in five seconds. Okay, but: can we employ that?

Mechanical power is torque times drive speed

$$P \sim M \cdot n$$

but what is the torque/speed relation? Luckily, the drive of such a 1920ies streetcar has a torque/speed characteristic which is roughly a hyperbolic curve.

$$M \sim \frac{1}{n}$$

Torque is very high at low speeds and low at higher speeds. This is very practical for both accelerating and braking. So, the power we can brake at is

$$P \sim \frac{1}{n} \cdot n = 1$$

So, yes: we can brake the streetcar with constant power, while the torque is the inverse of the momentary drive speed. And that's true for any power. The only thing we do by changing the braking resistance is scaling the de-acceleration curve.

For another drive, you had to look at the M/n characteristic first, then deduce the power to speed relation from that. But this curve is very common for electrical vehicles because it's so favourable, making it possible to make full use of the power rating of the equipment at all speeds.