Regenerative braking efficiency

As I drive along, I was always curious about regenerative braking efficiency. With Prius, there was small yellow tags on display to show 50 Wh (0.05 kWh) of energy regenerated. For a long down hill, I got multiple of these tags in any 5 minute window (Prius keeps track at 5 minute intervals). But the regeneration efficiency was always suspect. Prius regeneration is very weak, and brake pedal must be applied. Then how much of that is wasted as heat and how much to regen?

On SparkEV, there is no indication of how much energy was regenerated. However, it shows Watts in power being used and regenerated. It also has strong regen in L mode such that one does not need to apply the brakes for many hills. This makes it a good platform for testing regen efficiency.

Hilly road

My method is to take a hilly road of some length and drive down then up, both at same speed. Whatever regen power shown is compared against power to drive up the hill to come up with efficiency.

The key here is to pick the right road. The hill should be steep enough to allow only regen using L mode to slow the car on the way down while keeping up with traffic, yet not too steep that brakes must be applied. Once the brakes are applied, some energy may (or may not) waste as heat, so the experiment becomes invalid. The best is to have the hill long enough so that cruise control takes care of the speed.

Fortunately, I happen to drive on such road regularly: slope of about 8% and 4 miles long. Using cruise control at 50 MPH, I obtain the following.

Flat road: 9 kW to 10 kW
Up hill: 32 kW
Down hill: -9 kW

Power regenerated going down the hill is flat road power plus regen displayed, or 18 kW to 19 kW.

Power used to go up the hill is total power minus power going on flat road, or 22 kW to 23 kW.

Then the efficiencies are

18 / 23 = 78% (worst case)
19 / 22 = 86% (best case)

Power to the battery

These are power shown at the display. But exactly where is that power applied/coming from? Is it at the motor? At the electronics between motor and battery? At the battery terminal? Obviously, it's not inside the battery. We have to make some guesses.

When you step on the accelerator, displayed power goes beyond 100 kW, maybe even beyond 110 kW. Since the motor is rated for 104 kW, the power shown is not at the motor. It could be at the electronics or even the battery.

When you use DCFC, power shown is sometimes 48 kW, which makes SparkEV the quickest charging EV in the world. Given that the charger is capable of 50 kW, 48 kW would be 96%. It seems the power displayed is at the battery terminal.

Then we can adjust by considering the battery efficiency. Let's assume 96% is the estimate of battery efficiency. The result we get is

78% * 96% = 75% (worst case)

86% * 96% = 82% (best case)

Significant figures

SparkEV only gives integer values for power. Indeed, this is why I picked some high power speed and hill to do the experiment to minimize the errors. If I had done this test in slight hill that resulted in only 1 kW difference, I may not even see the difference and large errors would result. For example, 1 kW shown might be 0.5 kW or 1.5 kW, resulting in 100% error! But for 10 kW (roughly), the errors are about 10%.

However, it's not known how the rounding occurs. If 10 kW is shown, there are many possibilities. Some examples are 9.01 kW to 10.0kW, 9.5kW to 10.49 kW, 10.0 kW to 10.9 kW. Then which is it? Unfortunately, I don't dig that deep into this topic. I'll just assume 10% at nominal.

Then the new estimates are

75% * 90% = 68% (worst case)
82% * 110% = 91% (best case)

If I had to choose...

Well, there are lots of values, which one is correct? Probably none of them! We are trying to estimate the efficiency, not come up with absolutely correct value. My pick would be somewhere around 75%. Why? It's convenient to remember: 3/4 (three-fourth).

Ramifications

If one drives up a hill, one has to drive down a hill eventually. For a gas car, all that energy to drive up a hill would be lost as heat when coming down. In effect, that's money floating away as brake dust and heat.

For SparkEV, 75% of that energy gets put back into the battery. That's money in the pocket (or battery). In addition, it saves wear and tear on the brakes. Indeed, this is why my brakes had cross-hatch pattern on the rotors as if they're new even after 7000 miles of driving. Also the lack of heat would result in much longer life for brake components and fluid, although Chevy still has brake fluid change interval at 30K miles.

Combined, total monetary savings would be far more. Since gas car is 0%, it's meaningless to talk about percentage compared to those. But as energy cost savings and factoring in reduced brake wear, it could exceed 100% savings calculated as energy cost.

Alternative experiments

Above experiment was just on a hill. One could also perform an experiment on typical driving scenarios. If the regen efficiency I found hold throughout the speed range, one could think of low speed traffic (slow and go) range to be about 75% of what's shown in range polynomial blog post if one does not use the brake pedal to slow down. However, the efficiency may not hold at 75% throughout the speed range and regen power level. Also, one must apply the brakes to come to a stop or to stop rapidly. As such, 75% is meaningful only as one data point and nothing more. There should be more experiments to find out other values.

One such experiment would be to capture the video of the display as one's driving. Integrating over time would give data even without driving on hills. I asked my dog to hold the camera, but the result was camera with bite marks, and no usable video. Maybe you'll have better luck.

But even with video, one can only go so far. Display is still integer, and the update rate is about once a second and varying whereas hilly experiment was roughly constant power for many minutes. For slow acceleration and regen, this might be acceptable. But for high power regen (60 kW?) and acceleration (over 100 kW), there may not be enough to get much better data. As we all remember from second grade Simpson's rule, you need more boxes to get accurate result.

Beauty of SparkEV

As mentioned before, this test is not possible with Prius, even if it had power display. One reason is that regen is so weak that hilly road test would not be possible without using friction brakes. I suspect this is true with all cars that have regen always tied to brake pedal.

But there's another extreme. There are some cars that tout "one pedal driving" where releasing the accelerator pedal is used to bring the car to a stop. Since regen would get weaker at low speed, the car would expend energy from the battery to slow down. Some say BMW i3 and Tesla behave this way. In effect, this introduces the uncertainly similar to brake pedal induced braking (aka, blended brake); you wouldn't know if the car is using the power from the battery to slow down. That kind of car would be unsuited for this experiment.

The beauty of SparkEV is that regen in L is strong enough, yet knowing that it is only used for regen if the brake pedal is not applied. Supposedly, the new Volt and Bolt have even more modes of regen, but there's nothing like simplicity of SparkEV. In fact, if L is not max regen already, GM should do an update so that L result in max regen without using the battery or the brakes. You really only need D (regen like gas car for old timers), and L (strongest regen using accelerator pedal for most efficiency).