Toyota Prius Forum banner

1 - 20 of 36 Posts

·
Registered
Joined
·
220 Posts
Discussion Starter #1
I am interested in some definite figures on the efficiencey of the regenerative braking in the Prius, and theoretical maximums. For example:

- when you brake from 60 mph, if you were to apply the brake in the most efficient amount for the battery to absorb the charge, (i.e. relatively geltly), what is the maximum of the kinetic energy you could reclaim?

- what happens to the braking energy if the battery SOC is already at the highest acceptable level?

- in an ideal vehicle, with a battery with unlimited capacity and ability to absorb any amount of charge at any intensity, and a generator capable of providing enough resistance to brake the vehicle at any speed, what would be the practical upper limit of energy recovery? How much would be lost to normal rolling resistane, friction, heat, mechanical inefficiency, etc.?
 

·
Registered
Joined
·
35 Posts
Prius Braking and Power Generation

The operation and efficiency of the braking process on the 2004 Prius has been greatly enhanced due to lower internal resistance in the battery pack and higher operating RPM's and voltage on the motor/generator. The efficiency at any given time will vary depending on a lot of factors (temp, age, SOC, etc.) but around 80% would be doing well. Attached are full descriptions of the power generation and regeneration processes and another publication regarding the braking procedure that the Prius now incorporates. If the battery is already fully charged (which can happen in sustained downhill driving) the computer can reduce the amount of regeneration being produced and rely on standard friction braking. It can also spin the engine without fuel to aid in slowing or it can bleed off excess charge in the battery pack at any time by again, spinning the engine without fuel. Currently, the regenerative process is only occurring on the front wheels so part of the limitation (even with all conditions ideal) is maintaining driver control when braking. The more you attempt to theoretically retrieve, the more the front end dives and control is reduced. With more advanced 4 wheel drive systems coming, the need for friction braking can be reduced even further.
 

·
Registered
Joined
·
220 Posts
Discussion Starter #3
Thanks for the documents... I won't have time to read them til later, but I see they are comprehensive. Interested to know where you found them.

All the best...
 

·
Registered
Joined
·
4 Posts
energy estimates

For what it is worth, here are some estimates in Wh (Watt-hours), the
unit of energy used for the green leaf on the Prius display.

A gallon of oxygenated gas contains about 36,000 Wh, and a 30% engine
will convert that into 10,800 Wh.

Assuming 100% efficiency of the electric motor, 50 Wh of recovered
energy (one grean leaf) gives you the equivalent propulsive energy
of about 1 tablespoon of gas.

The kinetic energy of a Prius with 300 pounds cargo is about 150 Wh.

Further details are at
http://xray1.physics.sunysb.edu/~jacobsen/priusenergy.pdf
 

·
Registered
Joined
·
220 Posts
Discussion Starter #6
Re: energy estimates

Thanks for your input, physd102. This is the kind of info I was looking for, together with what Coastal Dave provided.

This really helps with an understanding of the actual efficiency.

Yesterday when I got home, I noticed that I had eight green leafs showing on the display over about 20 minutes. Taking your calculations in reverse, this should give me enough energy to go from 0 - 60 mph about three times. And of course, I'll get some of that energy back also. We would all want 100% efficiency, but this is way better than all other non-hybrid cars on the road. It is also promising for the future, because now that Toyota has the ball rolling, there will be competition to improve efficiency, which will become a major selling point.
 

·
Registered
Joined
·
220 Posts
Discussion Starter #7
More on this...

A green leaf representing a tablespoon of gas doesn't sound like much, but it depends on how you look at it.

There are 16 tablespoons in a cup, or 256 in a gallon. At 50 mpg, it takes only about five tablespoons (256/50) of gas (this is at actual efficiency) to propel the Prius a mile.

But you calculated the value of a green leaf as a tablespoon of utilized gas energy, which is only 30% of the actual of gas used (10,800 Wh/gal vs 35,960). The actual volume of gas represented by a green leaf would therefore be 3.3 tablespoons. So, when I get 8 green leafs over 20 minutes (maybe 10 miles at 30 mph), I'm reclaiming about 26 tablespoons worth of gas energy, or enough to go 5 miles. (You already accounted for the 20% loss of efficiency in delivering the 50 Wh 'leaf' to the tires)

OK, I must be wrong... where did I make my mistake?
 

·
Registered
Joined
·
4 Posts
Canadian Prius said:
But you calculated the value of a green leaf as a tablespoon of utilized gas energy, which is only 30% of the actual of gas used (10,800 Wh/gal vs 35,960). The actual volume of gas represented by a green leaf would therefore be 3.3 tablespoons. So, when I get 8 green leafs over 20 minutes (maybe 10 miles at 30 mph), I'm reclaiming about 26 tablespoons worth of gas energy, or enough to go 5 miles. (You already accounted for the 20% loss of efficiency in delivering the 50 Wh 'leaf' to the tires)

OK, I must be wrong... where did I make my mistake?
Well, here's how I look at it. If I had a 100% efficient gas engine, I'd get 36,000 Wh of useful energy out of a gallon of gas. However, at 30% efficiency in turning heat energy to mechanical energy (typical of a gas engine, and thermodynamics sets a fundamental limit on this of maybe 35 or 40%), I really only get 10,800 Wh of usable mechanical energy out of the gallon of gas. If I had a 100% efficient electrical generator and battery, that's what I'd get in electrical energy as well. So, from a gallon of gas I've got at best 10,800 Wh of electrical energy. One 50 Wh unit of recovered energy is (50)/(10800) of that, or 1/220 of the maximum electrical energy I can get out of a gallon of gas. That's why I say it's about a tablespoon, which is about 1/256 of a gallon.

Of course it's difficult to know what is meant by a 50 Wh green leaf/car symbol. Does it refer to recovered energy we can deliver to the wheels with 100% efficiency? Does it refer to recovered energy we can deliver to the wheels with XXX efficiency? I'm sure some engineer in Japan could tell us...
 

·
Registered
Joined
·
4 Posts
Re: energy estimates

Taking your calculations in reverse, this should give me enough energy to go from 0 - 60 mph about three times. And of course, I'll get some of that energy back also.
Possibly, though if you cruise for very long at 60 mph you'll have dissipated a fair amount of energy into moving air around (turbulence), heating up bearings (friction), and so on. You can get a feel for how quickly the kinetic energy of moving at 60 mph is dissipated through turbulence by putting the car in neutral when you're at that speed. Friction is harder to get a feel for.
 

·
Registered
Joined
·
220 Posts
Discussion Starter #10
physd102 said:
That's why I say it's about a tablespoon, which is about 1/256 of a gallon.
Well, I'm sure you are right... I must have tripped myself up with my own logic. The bottom line is that the fraction of energy we are recovering from a gallon of gas equals the same fraction of the volume that we are recovering.

In this case I get to go a little less than two extra miles because of the regenerative braking - still not too shabby!
 

·
Registered
Joined
·
623 Posts
There was a thread once that discussed how much one green leaf represented, and I think (but I'm not at all certain) that it was stated that one green leaf was very roughly equivalent to one bar on the battery icon.

My experience is that I can drive about 1/4 mile in EV mode on one bar. This is very gentle acceleration on residential streets with stop signs every few blocks. Of course, buth acceleration and speed are greatly restricted in EV mode.

Your question relating green leaves to acceleration to 60 is complicated by the fact that the car will neither accelerate hard nor reach 60 in EV or electric mode, so you're always going to be using both gas and electricity when you accelerate to 60. Also, I presume that how hard you accelerate may make a difference.

I have always assumed (without any particular justification for it) that the 50 Wh of one green leaf means 50Wh stored back in the battery, after all the efficiency losses incurred, but before the losses that will be incurred getting it back out of the battery and using it in the motor.
 

·
Registered
Joined
·
220 Posts
Discussion Starter #12
Daniel said:
I have always assumed (without any particular justification for it) that the 50 Wh of one green leaf means 50Wh stored back in the battery, after all the efficiency losses incurred, but before the losses that will be incurred getting it back out of the battery and using it in the motor.
Yes, I think that's the logical way to look at it.

Regarding accelerating to 60 mph, I was thinking of this more as a yardstick than a practical possibility.

The whole concept of accelerating to 60 mph only to brake for the next traffic jam or stop light demonstrates the waste that is taken for granted in our society. While driving your Prius carefully to maximize mileage, how often does someone come up close behind you, pressuring you to go a little faster toward the upcoming red light? Driving the Prius you become more aware of this kind of waste, but probably most of us didn't think much of it until the Prius 'taught' us to think about it.

With regenerative braking, we can reclaim at least part of that wasted energy. I get a lot of satisfaction from this, and I want to understand how it works best, and how to maximize it.

The way I understand it now is that with the battery's charging characteristics, the most efficient way to reclaim your deceleration energy when you know you need to stop 300 yards ahead is to brake gradually, with about 20% brake pedal over the whole distance. This increases the overall charge to the battery, while staying within a charge level that the battery can absorb. Coasting most of the way and then braking more quickly would result in less charge while coasting, then too much charge during the quicker stop.

I know that the guy behind you won't like this much, but it really isn't an inconvenience for him because he is going to have to stop anyway, and there isn't much sense in rushing to the red light. But to keep stress levels down, I usually only do this when there is no one behind me.
 

·
Registered
Joined
·
623 Posts
I think there's a happy medium between the discourtesy of braking so slowly that you back up traffic, and slamming on the brakes. During the Carter administration, when we were all conscious of effecient driving, it was stated that if you simply coast to a stop at traffic lights you burn less gas, but the chain-reaction behind you causes the line of cars collectively to burn more gas, as they have to slow down more, and then burn gas to keep going.

I hate it when the person in front of me drives so slowly (well below the speed limit) that he, and only he, makes it through the light, and I don't.

Moderation in all things!
 

·
Registered
Joined
·
220 Posts
Discussion Starter #14
Daniel, you seem to be missing the point here. Just to be really, really clear about it, I'm talking about how regenerative braking works... not about driving like a moron slowing down other traffic unnecessarily, etc. Like I said, I avoid experimenting when other cars are behind me.

When I said previously the battery reclaims enough energy to accelerate to 60mph, it's a simple quantification, Daniel, not an impossible plan of action.

If I said the battery stored enough energy to elevate the Prius 200 feet off the ground, I have a feeling you might come back with the problems I would face trying to do that.

Have you ever had any interesting thoughts about the regenerative braking system on the Prius?
 

·
Registered
Joined
·
4 Posts
Daniel said:
Your question relating green leaves to acceleration to 60 is complicated by the fact that the car will neither accelerate hard nor reach 60 in EV or electric mode, so you're always going to be using both gas and electricity when you accelerate to 60. Also, I presume that how hard you accelerate may make a difference.
Ultimately all energy has to come from gas in the Prius. The battery is only a buffer to serve as a temporary store or source of energy. Therefore I think it is relatively immaterial whether you accelerate with gas or electric or both.

The energy needed to go from rest to 60 mph does not depend on the rate of acceleration if the engine has the same efficiency at all levels of power output - you just need to get that amount of kinetic energy. In reality all gas engines have sweet spots of RPM for maximum efficiency, which I suspect is usually below the RPM of maximum power. Because the Prius uses a continuously variable transmission, I would imagine that it would do better than many cars in making the engine spin at maximum efficiency for the required power much of the time. However, I would also imagine that the engine control system is programmed to abandon efficiency for power if you really stomp on the gas pedal.
 

·
Registered
Joined
·
623 Posts
Canadian Prius said:
Daniel, you seem to be missing the point here. Just to be really, really clear about it, I'm talking about how regenerative braking works... not about driving like a moron slowing down other traffic unnecessarily, etc. Like I said, I avoid experimenting when other cars are behind me.
But you also said:

Canadian Prius said:
The way I understand it now is that with the battery's charging characteristics, the most efficient way to reclaim your deceleration energy when you know you need to stop 300 yards ahead is to brake gradually, with about 20% brake pedal over the whole distance. <...snip...> I know that the guy behind you won't like this much, but it really isn't an inconvenience for him because he is going to have to stop anyway, and there isn't much sense in rushing to the red light. But to keep stress levels down, I usually only do this when there is no one behind me.
Emphasis mine. And I was disputing your assertion that "it really isn't an inconvenience for [the guy behind] because he is going to have to stop anyway." I was pointing out two different ways that it does affect the people behind you: it forces them to burn more gas and it will cause some of them to miss the light.

You gave mixed signals when you argue it's a good thing to do, and then said you "usually" only do this when there's no traffic.

I don't think your rude closing remark really requires comment.
 

·
Registered
Joined
·
220 Posts
Discussion Starter #19
Daniel said:
I don't think your rude closing remark really requires comment.
Daniel, I'm sorry I offended you with my comments. I was probably a little irked by what I saw as your superior attitude.

I am actually really quite interested in regenerative braking, and that is my focus here. Although I think proper behaviour on the road is extremely important, it's hard to discuss the optimum way of driving a Prius concerning its energy efficiency without suggesting ways of driving that a person wouldn't necessarily use in normal driving. Since driving the Prius does suggest different driving behaviour, and this is an interesting subject, I'm going to open a different thread so that it won't be mixed with this thread: http://www.priusonline.com/viewtopic.php?p=15125&sid=a67c9a61309e62dd00a3e94a8f39cfa9#15125
 

·
Registered
Joined
·
220 Posts
Discussion Starter #20
clett said:
My calculations on the bottom of page one suggest you'll only ever get back three-quarters of what you gave out to accelerate, even under optimum conditions.
That is fairly encouraging. Toyota has done a great job, but as you say, they probably haven't achieved the optimum regeneration yet. However, you did your calculations are based on a 21 kw generator. I believe that during braking, the 50 kw motor/generator comes into play, and this would bring you a lot closer to the optimum.

When I descend a long hill with a stop sign at the end of it, I brake at about 20% pressure all the way down, guaging it so that my speed drops evenly until I stop at the stop sign. I find I get much more regeneration than by coasting and a more sudden stop at the end.
 
1 - 20 of 36 Posts
Top