## The Magic of Tesla Roadster Regenerative Braking

In a battery-powered electric vehicle, regenerative braking (also called regen) is the conversion of the vehicle’s kinetic energy into chemical energy stored in the battery, where it can be used later to drive the vehicle. It is braking because it also serves to slow the vehicle. It is regenerative because the energy is recaptured in the battery where it can be used again.

The kinetic energy stored in a moving vehicle is related to the mass and speed of the vehicle by the equation E = ½mv². All else being equal, if your car is twice as heavy it has twice the kinetic energy and if it is moving twice as fast it has four times the kinetic energy. Any time your car slows down the kinetic energy stored in the vehicle has to go somewhere. Let’s take a look at where this energy goes. There is always some kinetic energy consumed by the rolling resistance, mechanical friction, and aerodynamics of your car. These bits of energy go into heating the road, the surrounding air, and various spinning parts in your car. But the vast majority of the kinetic energy is converted into heat by your brake pads when you stomp on the brakes. In the Tesla Roadster, regenerative braking recovers some energy that would otherwise have been wasted in the brakes.

How much energy does it recover?

Unfortunately, the adage “your mileage may vary” applies to regen as well. The amount of energy you can recover depends on how and where you drive. From the powertrain point of view it looks pretty good. The energy conversion efficiencies from chemical to electrical (battery), DC current to AC current (inverter), electrical to mechanical (motor), and torque to force (transmission and wheels) are all quite high and work just as efficiently returning energy into the battery. The bigger problem is aerodynamic losses and higher speeds and rolling friction of the tires. These both act to slow the car, but the energy dissipated cannot be recovered. We must also remember that, even though the battery-to-wheel conversion efficiency is pretty good (up to 80% or so), the energy makes a full circle back into the battery and it gets converted twice for a net efficiency of at most 80% * 80% = 64%.

Wie funktioniert das?

Due to the simplicity of the AC induction motor’s single moving part, the Tesla Roadster does not experience the engine compression braking of a traditional internal combustion engine (ICE). Instead, the advanced algorithms in the motor controller give it complete control of the motor torque for both driving and regenerative braking. A torque command is derived from the position of the throttle pedal. The motor controller converts this torque command into the appropriate 3-phase voltage and current waveforms to produce the commanded torque in the motor in the most efficient way. The torque command can be positive or negative. When the torque serves to slow the vehicle then energy is returned to the battery and presto - we have regenerative braking!

I should also note that the motor and controller can deliver the torque command at any operating speed, including 0 mph. This means that we can regen the car to a complete stop. But as a practical matter, the kinetic energy of a slowly moving car is low enough that very little energy is put back into the battery as the car comes to a stop. In fact, the last little bit of slowing the vehicle down generates such a small amount of energy that it does not even cover the fixed losses in the inverter and motor.

When does it work?

There are a number of goals and restrictions when using regenerative braking. Tesla Motors is still putting the final touches on the regen torque profile to achieve the goals within the constraints.

1. Safety: Negative torque applied to the rear wheels can cause a car to become unstable. Since regen braking is a source of negative torque, the Tesla Roadster uses the traction control system to limit regen if the rear wheels start to slip. I was part of the team that developed and verified this safety feature on a frozen lake in Arvidsjaur, Sweden.
2. Performance: Regenerative braking can enhance the driving experience in ways not available with a traditional internal combustion engine (ICE). Driving with regen is fun! Having that instant positive and negative torque command right at your toes really make you feel in control.
3. Limitations: Regenerative braking is necessarily limited when the batteries are fully charged. Because the additional charge from regenerative braking would cause the voltage of a full battery to rise above a safe level, our motor controller will limit regen torque in this case.

The future for regenerative braking

There are a number of subjective decisions we have to make concerning the regen profile. Some people like regen to work all the way to 0 mph, bringing the car to a complete stop. Others like to coast that last 2 to 3 mph. Almost everyone likes the car to regen when you take your foot off of the throttle pedal, but there are some who would prefer the car to coast when you do this. They would prefer the regen to be tied to the application of the brake pedal. Almost everyone likes the more aggressive regen available to the driver, but a few people are more comfortable with a traditional ICE-like compression braking and coast-down profile. Ultimately, the Tesla Roadster is a sports car and the regen profile will be fine tuned for sports car driving.

One day everyone will drive electric cars and regen will be a big part of what will make them fun to drive, efficient, and safe. The recent research and development to integrate the powertrain and brake systems to provide better traction and stability control can only be made easier by the use of electric drive systems. One thing I learned from the traction control work I did on the frozen lake is that traction control is a much simpler problem to solve when you have precise and instant control of torque through the AC induction motor controller. Further integration of antilock braking systems with the motor controller would allow the motor to take over more of the vehicle braking. It’s very exciting to be working at the forefront of these possibilities.

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