Pressure Drop – a detailed look at regenerative braking

Regenerative braking, or Brake Energy Recovery, is an important tool in the EV arsenal, and when implemented correctly, can add more than 25% electric range to a vehicle.

But what actually happens when you press the brake pedal (or pull the paddle or switch…)? In this article, I will explain step-by-step the process of regenerative braking, and work through an example brake manoeuvre in a vehicle.

Detailed look at the test vehicle

For the purposes of this article, we will use a Renault Zoe, which is a Front Wheel Drive Electric Vehicle, with front disc brakes, and rear drums.

Fig. 1: Zoe drive layout, and associated brake topology (yellow – electric torque, red – friction torque)

For the purposes of understanding the braking process, this is ideal. It’s got one gear ratio, a whole bunch of published data, and is pretty common in most EU markets. Lets have a quick list of the relevant specifications;

  • Motor max torque: 220Nm
  • Motor max power: 65kW
  • Motor max speed: 11,300 RPM
  • Vehicle max speed: 135km/h
  • Motor to wheel ratio: 9.32
  • Tyre size: 195/55/R16
  • Tyre dynamic diameter: 590mm
  • Tyre circumference: ~1.85m

Now let’s have a look a little closer at the motor itself – and particularly how it performs over speed.

Fig. 2: Electric Motor Spec

A few points are worth considering. Peak motor torque is available up to ~30km/h, with peak power starting from 30km/h up to ~100km/h. Between 100km/h and 135 km/h, power reduces. This is typical for electric motors – where field weakening (and similar strategies) are used to drive the motor to higher speeds than could be otherwise achieved. This has a negative impact on the motor efficiency, and consequently increases energy consumption (compounded by increased aerodynamic and rolling resistances at higher speeds, but we will cover EV efficiency in a later post).

Another important consideration for regenerative braking is how much electrical energy can be recovered to the battery, or in other words, how quickly the battery can accept charge. In our test vehicle, the on-board electronics limit regenerative charging to 40kW. The battery temperature and voltage also throw up their own limitations, and so it’s unlikely that the same brake event will always recover the same amount of energy.

For our brake manoeuvre we will brake the vehicle from 100km/h to 0km/h, over 9 seconds, which equates (roughly) to a 0.3g stop.

Power, Torque and Speed

Power can be described as the ability to do work over time. But to put it in more useful terms, Power can be seen as Torque multiplied by Speed – which is a much more useful definition for considering braking. Another useful thing to consider is that while torque and speed are affected by gearbox ratios, power remains constant. Therefore, if we know the power of our motor, and the speed of our vehicle, we can work out pretty much everything we need to know.

At 100km/h, the wheel speed is 900 RPM, and the motor speed is 8388 RPM. Since we can see the deployed power (up to 32kW – on the right of the screen above), and the reduction ratio (9.32), we can calculate the deployed torque at the motor, and regenerative torque at the wheel.

Fig. 3: Regenerative braking torque from two sources

Last time out, I discussed how the deceleration task is shared between the two brake systems. In our video, it’s clear that deceleration begins as soon as the brake pedal is depressed (signified by end of cruise control) , but it takes about a second before the deceleration reaches a steady state. The digital speedometer changes from 97 to 88, as the power changes from -2kW to -31kW).

As the vehicle speed decreases, the available motor torque rises, until at 37, the power indicated starts to reduce. From this point, there is a reduction in power as vehicle speed decreases (as the motor has now reached the torque limit), and finally a rapid drop off once speeds dip under 17km/h.

It is worth pointing out that the vehicle display has a delay in updating values, but it is clear that the deceleration and regenerative power remain constant for the majority of the stop.

Let’s have a look at the same stop, but slowed down to half speed.

Using the wheel speed and power as a guide, it’s possible to chart the torque progression through the stop, and show where the peak torque occurs.

  • Vehicle Speed : Power : Regen Torque @ wheel
  • 100km/h : 0kW : ONm
  • 97km/h : 2kW : 22Nm
  • 88km/h : 31kW : 374Nm
  • 77km/h : 31kW : 427Nm
  • 67km/h : 31kW : 490Nm
  • 57km/h : 32kW : 596Nm
  • 47km/h : 32kW : 722Nm
  • 37km/h : 31kW : 889Nm
  • 27km/h : 23kW : 904Nm
  • 17km/h : 6kW : 873Nm
  • 8km/h : 6kW : 795Nm
  • 0km/h : 0kW : 0Nm

The regenerative brake torque builds steadily, as the vehicle speed decreases. Then, between 37km/h and 27km/h the peak torque is reached, and the power starts to dissipate. As speeds approach zero, the regenerative brake torque drops off altogether, and friction brakes come back into play.

The vehicle deceleration remains (pretty close to) constant throughout, so while the regenerative torque changes, the brake hydraulics must meter pressure out and then back in to compensate. This is what is meant by brake blending – a seamless combination of two distinct braking mechanisms, to achieve a constant effect at the vehicle level.

Disregarding some details

In this analysis, I have concentrated on the front axle only. There is brake torque deployed on the rear axle at all times, but in this vehicle, regen is only happening on the front axle. Also, it is worth pointing out that deceleration is due to more than the braking torque – rolling and aerodynamic resistance play their part, as do external factors like wind, track condition and slope.