Regenerative Braking - Best Practices?

[F14Scott]

It is actually quite a tricky problem. When you are traveling at a constant speed, your power use is your friction losses (rolling + aero) and your accessories load (ie, car/radio/air con/heater etc). If we ignore the accessories, you have the situation:

speed = v
energy = 1/2v^2
Friction = f(X) - ie dependent on speed

You come to a stop when the energy has been used up by friction. If you are coasting, you use no energy to propel the car - but you regenerate none. When you keep going and brake (only regenerative) at the last moment, you will use energy to drive, but get say 75% of your kinetic energy back. If you are going 100kph (27.77m/s) in a car which weighs 1450kg (including driver), then the car has: 559413J (joules) of energy. If you (regen) brake, and get 75% back, you will get 419559J, or 0.116kWh.

At 100kph, the energy required to drive is about 14.5kWh/100km, so you are using 14.5kW propelling the car. You can drive for:

0.116/14.5*3600 = 28.9 seconds before using 0.116kWh. This means if you drive for less than 28.9 seconds before braking, you will use less energy. If you need to drive for longer than 28.9 seconds to cover the same distance as coasting for the same distance, you use more energy. Now in the real world, things may be different. You may only get back 60% of the energy (you are not only slowed by regen, but by friction as well), or efficiency/slope, wind etc changes the parameters, you may use more (or less) than 14.5kW etc., but it gives an idea.

I like your math, but can't tell, in your "60%" SWAG, if you included all the losses incurred from the regen process, itself. Without anything to back my guess up beyond some seat-of-the-pants guestimation, I think coasting out the Ek will always capture more E than trying to stuff it into a battery and then pull it out, again.

 

[vader]

Ok, so I was bored and wrote a quick finite element analysis of coasting vs regen just to see what happens. The scenario:

Coast to a stop and calculate distance traveled
Calculate the energy used if you keep going at constant speed and use max regen to travel the same distance
Work out how much more (or less) you use with each method.

Parameters:
weight = 1450 (car plus driver)
motor efficiency at constant speed = 95% (from i3 efficiency graph)
regen efficiency to battery = 75% (internet)
accessories = 2kW (air con/radio/car systems etc - from personal data)
air density/Cd/A from usual sources = 1.2kg/m^3, 0.3, 2.1
tyre rolling resistance = 0.01
dead flat road, no wind

Speed 150kph:
Coast for 3.305km, taking 214s to come to a stop.
Constant speed, max regen (0.19g) to travel 3.305km takes 90s
Difference in energy used: 0.35kWh more than coasting

Speed 100kph:
Coast for 2.135km, taking 180s to come to a stop.
Constant speed, max regen to travel 2.135km takes 84s
Difference in energy used: 0.105kWh more than coasting.

Speed 60kph:
Coast for 1.056km, taking 130s to come to a stop.
Constant speed, max regen for 1.056km takes 67s.
Difference in energy used: 0.02kWh more than coasting

At 30kph it was 0.005kWh, so basically the same.

So what does this mean? The faster you go, the more you lose to friction and the better coasting is. The slower you go, the less difference there is. At around 30kph there is effectively no difference. The next thing is how often do you get to coast for 1/2/3 km? If you can plan ahead for road works etc, and you don't mind annoying people behind you towards the end of the coast, then you will save a small, but measurable amount of energy. The slower you go, the less difference it makes.

I will note that if you are stopped at a traffic light, then the regen method will be sitting there waiting for the coaster to get there, and using accessory power, so it will get worse.

 

[Puppethead]

accessories = 2kW (air con/radio/car systems etc - from personal data)

I love your analysis, but did you get the 2kW number from HV battery drain? I think everything except air conditioner, resistive heater, and heat pump get power from the 12 V AGM battery.

 

[vader]

That was my calculation from my own efficiency results. I correlated it across different speeds to find the constant draw. It is actually a little low, but close enough.

 

[Texas22Step]

I will note that if you are stopped at a traffic light, then the regen method will be sitting there waiting for the coaster to get there, and using accessory power, so it will get worse.

I may be too dense to understand any of this, but why would there be any difference for the driver at a red light using regen "sitting there waiting for the coaster to get there, and using accessory power" when both will be using their accessories (a/c, radio, whatever) for the same amount of time? Both cars are on the road for the same amount of time (and drawing accessories power), so it seems to me that their consumption of power for accessory use would be the same in this case?

 

[F14Scott]

Ok, so I was bored and wrote a quick finite element analysis of coasting vs regen just to see what happens. The scenario:

Coast to a stop and calculate distance traveled
Calculate the energy used if you keep going at constant speed and use max regen to travel the same distance
Work out how much more (or less) you use with each method.

Parameters:
weight = 1450 (car plus driver)
motor efficiency at constant speed = 95% (from i3 efficiency graph)
regen efficiency to battery = 75% (internet)
accessories = 2kW (air con/radio/car systems etc - from personal data)
air density/Cd/A from usual sources = 1.2kg/m^3, 0.3, 2.1
tyre rolling resistance = 0.01
dead flat road, no wind

Speed 150kph:
Coast for 3.305km, taking 214s to come to a stop.
Constant speed, max regen (0.19g) to travel 3.305km takes 90s
Difference in energy used: 0.35kWh more than coasting

Speed 100kph:
Coast for 2.135km, taking 180s to come to a stop.
Constant speed, max regen to travel 2.135km takes 84s
Difference in energy used: 0.105kWh more than coasting.

Speed 60kph:
Coast for 1.056km, taking 130s to come to a stop.
Constant speed, max regen for 1.056km takes 67s.
Difference in energy used: 0.02kWh more than coasting

At 30kph it was 0.005kWh, so basically the same.

So what does this mean? The faster you go, the more you lose to friction and the better coasting is. The slower you go, the less difference there is. At around 30kph there is effectively no difference. The next thing is how often do you get to coast for 1/2/3 km? If you can plan ahead for road works etc, and you don't mind annoying people behind you towards the end of the coast, then you will save a small, but measurable amount of energy. The slower you go, the less difference it makes.

I will note that if you are stopped at a traffic light, then the regen method will be sitting there waiting for the coaster to get there, and using accessory power, so it will get worse.

We simple fighter pilots call guys like you "the 5,000 pound head guys." It is not an insult.

 

[vader]

Both cars are on the road for the same amount of time (and drawing accessories power), so it seems to me that their consumption of power for accessory use would be the same in this case?

The point is that the coasting car has an accessory draw for 214s, whereas the regen car only for 90s. I took that into account. The coasting car uses 124s (2 minutes) extra to get there. When you coast, your energy use isn"t zero, it is whatever the car is using on accessories.

The analysis was distance based, not time based. If the regen car waits, with the car on for 124s at the finish point, it has added to its energy use by using the accessories for another 124s.