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

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.

• I think this comes down to conservation of energy. In this perfect world, If you wanted an immediate braking effect, and still recover all your energy, the back torque from the motor would have to be much higher than the torque you put in, when you accelerated slowly. This variable torque can be done by gearing Commented Jul 27, 2017 at 23:53
• Also look at how alternators work in cars. Their magnetic field is produced by the excitation current; this current is regulated up and down, increasing or decreasing the magnetic field's strength, thus putting more or less resistance (torque) on the driving side in order to output the amount of electrical power required at each moment irrespective of RPM &c. Commented Jul 28, 2017 at 11:13

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.

• But pressure on the brake pedal controls the actual brakes so your suggestion looses the regen braking - unless you implement a multi-stage brake pedal.... Also, foot of the gas in an ordinary car is not coasting, it is deceleration (aka engine braking) coasting is taking it out of gear. Commented Jul 28, 2017 at 5:37
• @SolarMike Pressure on the brake pedal is whatever the designer of the vehicle intends it to be. If I had a vehicle with regen braking, I would expect it to have an intelligent brake pedal. So pressure would map to deceleration force, with an active system to 'not apply' friction brakes until the requested braking excededed the regen that could be applied. That way, if the active system failed, friction brakes would be applied, I don't like the idea of relying on an active system to stop the car. Obviously, there's plenty of safety engineering to go into that. Commented Jul 28, 2017 at 6:29
• I don't know about your car, but I have to change down to get significant engine braking on mine. Whatever the actual acceleration is with no throttle in top gear, it's an order of magnitude different from full throttle or gentle braking, so I call it coasting. I'll modify the answer to address the pedantry. Commented Jul 28, 2017 at 6:32
• I drove an electric car and coming off the throttle caused regen - using the brakes was the friction option. As for my current car there is sufficient engine braking in 6th to gently slow for traffic changes - heavier braking requires the use of the brakes. Commented Jul 28, 2017 at 6:45
• @SolarMike In the first instance, I wouldn't buy an electric car that drove like that. Eventually, if that's all the market provided, I suppose I'd have to get used to the idea, grumbling resentfully. I suppose it means you have to keep your foot on the loud pedal when you want to go forward. When I've engaged cruise, I take my foot off anyway, so it's not like a dead-mans-handle. There's always deceleration with no throttle, it's only deciding what to call the magnitudes. Nobody drops into neutral to coast, but with electric you can get nearer to that effect safely. Commented Jul 28, 2017 at 6:56

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).

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.

• Right this makes sense, thanks for the clarification of power. Energy is definitely what I should have used. However, what I am interested in is how the electric motor (while acting as a generator) can change the braking resistance and generate more power? Commented Jul 28, 2017 at 18:06
• I used the streetcar example because it's so dead simple. To change the braking power, you have to adjust the electrical power. And that you can do by adjusting the resistance on the rooftop. The lower the resistance is, the more power is turned into heat. This is done with the huge switch in front of the driver. It has a number of "drive" settings, which do not matter here, and two or three "brake" settings. These change the series/parallel arrangement of the resistors to the motor/generator terminals. Commented Jul 28, 2017 at 19:08
• Generative braking has another obstacle. The voltage coming from a generator isn't constant but a function of the speed. So you have to use a mechanism to adjust this voltage (it has to be higher than the grid/battery voltage). This can for example be done by connecting the field winding to some regulator instead of putting it in series; the drawback of this approach is it bends the M/n characteristic. A modern idea is using electronics to step-up the output voltage at low speeds. Commented Jul 28, 2017 at 19:19