Analysis of regen on an ebike

[fechter]

Great job Justin!
That's the best objective analysis I've seen with actual bike data to back it up. I stickified the thread.
There is really not much excuse for not having this feature in all brushless controllers as the additional hardware needed is practically zero. It's just logic. Using synchronous rectification both for regen and drive will improve efficiency and reduce heating as well (another feature commonly missing from most cheap controllers). One downside is the additional complexity may make the controller less "fault tolerant", but this can be addressed with proper design so that processor glitches can't cause shoot-through, etc.

[paultrafalgar]

Of course even better would be having relays that would dynamicaly switch batteries from series to parallel configurations, and even motor windings from delta to wye for a truly efficient system! This is in the dream real for now, but I just added it to my own controller features wish list!

Or variable gearing!

Hope this doesn't divert the topic, but what's your take on the NuVinci for that, Miles?

[Miles]

Hope this doesn't divert the topic, but what's your take on the NuVinci for that, Miles?

I should imagine the efficiency loss in the NuVinci would cancel out the gains in the regen

[dennis]

I think that regen on light ebikes is most usefull as a brake. Any extra range you get is just a bonus! Some folks will get more bonuses, and some will get less.

On the other hand, the positive aspects are:
- Much reduced wear on brakes
- Smoother braking action (when using current based regen with space-vector modulation)
- Some free extra range gained (proportional to hills and stops in route, along with total weight)

This sums up why I'm interested in regen, very well.

All of the above is true, except for the smooth part. With my Bionx system, I found that when braking the whole back wheel vibrates during regen and the back and forth torque placed on the rear axel will cause the nut to loosen over time. I always check my nuts now before each ride A good solution maybe a custom rear axel for electric hub motors...larger locking nut with a cotter pin with more surface area, similar to an off road motorcycle.... and if you like to track stand http://en.wikipedia.org/wiki/Track_stand, the way the hub sticks when regen kicks in, makes track standing much harder but is possible.

Regen, imo also reduces the useful life of the battery, in my case is LiMn which has a useful life of about 500 full cycle charges. With heavy use, my 9ah battery was only able to hold less than half a charge after 1.5 year. That is why I'm so interested in super capacitors. If someone can put it in a kit without adding too much weight. my 1/100 cent....

[ZapPat]

- Smoother braking action (when using current based regen with space-vector modulation)

All of the above is true, except for the smooth part. With my Bionx system, I found that when braking the whole back wheel vibrates during regen and the back and forth torque placed on the rear axel will cause the nut to loosen over time. I always check my nuts now before each ride A good solution maybe a custom rear axel for electric hub motors...larger locking nut with a cotter pin with more surface area, similar to an off road motorcycle.... and if you like to track stand http://en.wikipedia.org/wiki/Track_stand, the way the hub sticks when regen kicks in, makes track standing much harder but is possible.

I would agree with you on this point for regular regen, but as you see I did specify using SVM which reduces torque ripple both during drive and regen. This happens because a SVM capable controller will output a waveform that matches the motor's own back EMF, thus avoiding the uneven current flows that regular trapezoidal commutation produces. This of course does require more complexity mostly in firmware, more processing power, faster ADCs and phase current sensing. I must admit I have no idea what biox uses as a regen technique, but from what you say they must be using regular old commutation techniques.

Of course even with SVM we still have the bidirectionnal torque issue (although probably lessened with the smoother SVM) caused by regen. This will just be a matter of having good torque arms, along with some setup that will effectively lock your nuts to prevent them from loosening. I'm not a hardcore bike guy, so I'll leave this part for other great brains here to solve. Note that Justin just tighted the hell out of his nuts and that was already enough for his setup to not come loose, so I don't think that the solutions will be that complex.

Regen, imo also reduces the useful life of the battery, in my case is LiMn which has a useful life of about 500 full cycle charges. With heavy use, my 9ah battery was only able to hold less than half a charge after 1.5 year. That is why I'm so interested in super capacitors. If someone can put it in a kit without adding too much weight. my 1/100 cent....

Read Justin's posts, along with mine, then explain why you claim that regen inherantly reduces battery life when current limits and such are well thought out? In other words, explain what is the difference between regenerated current and regular charging current going into the battery? Also, what makes you sure that something else was not the cause of your packs premature demise? I know I might sound rash a bit here, but I strongly dislike unsubstantiated claims being posted by a few people and then repeated by many others...

Cheers!
Pat

[fechter]

Regen, imo also reduces the useful life of the battery, in my case is LiMn which has a useful life of about 500 full cycle charges. With heavy use, my 9ah battery was only able to hold less than half a charge after 1.5 year. That is why I'm so interested in super capacitors. If someone can put it in a kit without adding too much weight. my 1/100 cent....

I agree. Unless you have some kind of side-by-side test with careful controls, it would be hard to blame short cycle life on regen. My hybrid car has Nimh batteries and uses regen extensively. It has 89,000mi on it now and many thousands of cycles. If the regen current was too high and allowed the cells to get hot, then that would be a reason you could blame regen for shortened life.
No matter what the chemistry, the regen circuit must keep battery currents and voltages within the safe range for the batteries used.

[MitchJi]

Hi,

Regen, imo also reduces the useful life of the battery, in my case is LiMn which has a useful life of about 500 full cycle charges. With heavy use, my 9ah battery was only able to hold less than half a charge after 1.5 year. That is why I'm so interested in super capacitors. If someone can put it in a kit without adding too much weight. my 1/100 cent....

Read Justin's posts, along with mine, then explain why you claim that regen inherantly reduces battery life when current limits and such are well thought out? In other words, explain what is the difference between regenerated current and regular charging current going into the battery? Also, what makes you sure that something else was not the cause of your packs premature demise? I know I might sound rash a bit here, but I strongly dislike unsubstantiated claims being posted by a few people and then repeated by many others...

I think Dennis is concerned that one metric of cell life is charge/discharge cycles and with regen there are a lot more (small) charges. In other words I don't think his comment has anything to do with any "difference between regenerated current and regular charging current going into the battery".

I also think "unsubstantiated claims" might be a bit strong. He didn't actually state that his pack life was reduced by regen. He said with heavy use his pack only lasted 1.5 years and I think he is concerned that regen might reduce his pack life even further.

[solarbbq2003]

nice one justin!
another interesting thing is you can capture more regen when the batteries are more discharged, its quite noticeable, I guess the batts have lower resistance the more discharged they get and hence can capture more regen current, not sure if there is any practical way to utilise that, apart from having a spare pack which is discharged and put the regen back into that pack,

[solarbbq2003]

some advantages though for geared hub motors with no freewheel as can produce alot more amps in regen than a non geared

[ZapPat]

Hi,

Regen, imo also reduces the useful life of the battery, in my case is LiMn which has a useful life of about 500 full cycle charges. With heavy use, my 9ah battery was only able to hold less than half a charge after 1.5 year. That is why I'm so interested in super capacitors. If someone can put it in a kit without adding too much weight. my 1/100 cent....

Read Justin's posts, along with mine, then explain why you claim that regen inherantly reduces battery life when current limits and such are well thought out? In other words, explain what is the difference between regenerated current and regular charging current going into the battery? Also, what makes you sure that something else was not the cause of your packs premature demise? I know I might sound rash a bit here, but I strongly dislike unsubstantiated claims being posted by a few people and then repeated by many others...

I think Dennis is concerned that one metric of cell life is charge/discharge cycles and with regen there are a lot more (small) charges. In other words I don't think his comment has anything to do with any "difference between regenerated current and regular charging current going into the battery".

Hummm... There is no "cycle" counting mecanism in batteries, so smaller charge/discharges are not worse on them than fewer deeper cycles. In fact there seems to be evidence of the opposite, if all other conditions are kept equal. Read Sandia's lifebatt test report and you will see this is true. Fechter also seems to be of this opinion in the previous post (although his post is a bit confusing since he almost seems to be agreeing with denis until you really read what he says - you might want to clear that up, Fechter...).

I also think "unsubstantiated claims" might be a bit strong. He didn't actually state that his pack life was reduced by regen. He said with heavy use his pack only lasted 1.5 years and I think he is concerned that regen might reduce his pack life even further.

Well I might be misreading him, but what does "Regen, imo also reduces the useful life of the battery" sound like to you? Also, Denis talks about super caps helping his battery life when doing regen, which pretty much says he thinks that without them the pack's life is reduced. As discussed in earlier posts on this thread, you would need a fairly complex super-cap setup using an extra bi-directionnal DC-DC converter between the battery and the capacitor bank to have the capacitors help you at all. Just putting a parallel cap bank won't help you, since battery voltage goes up quite slowly while charging, but caps don't have that voltage plateau. So, as Justin says, caps in parallel will just smooth the current a bit, but will not be able to store any significant amount of energy since their voltage can't rise over the batterie's voltage plateau.

At any rate, Denis can respond to defend his claim. All I can say is that the numbers I've seen don't support the claims of reduced cell life being linked directly to regen. A badly done regen setup would shorten cell life for sure, and I think that this is the real problem with almost all present ebike regen systems (note that hybrid cars already have full regen protection, and for good reasons too!)

What is missing almost always in regen setups? Most people using good regen controllers set a max regen current limit, so that will protect the battery from heat-related charging problems caused by too much charge current. This leaves over-voltage protection (over charge protection), but this protection right now is only done on a pack level in the controller, which as we well know can be quickly fatal to the first cell reaching it's end of charge voltage. This is why we have BMS circuits used while charging that offer cell-level protection for charge termination. As far as I know, most regen setups don't go though the BMS, and as such this very, very important protection feature is not present during regen, but only during regular charging. This I think is the real culprit behing the present widely-repeated belief that regen inherantly reduces cell life.

And now what's the solution to the cell over charge problem? I'm looking into having some basic link between the BMS and the regen-capable controller, so that the controller knows as soon as the first cell hits full charge and disables regen in a safe way for the user. What most people rely on right now to avoid this destructive situation is to not use regen when their battery might be close to full charge - but only one error, only once, and blam there goes a cell!

Does this help explain my slight annoyance when reading such claims about regen reducing battery life, but with no explanations to prove the point? If anyone can prove the opposite, please post numbers and I will gladly learn from them! I know I can find numbers to prove my points here... So before dissing something (such as regen here), please understand it first!

Cheers!
Pat

[fechter]

In general, the deeper the cycle, the fewer cycles the battery will last. For Nimh, if the state of charge is kept between 20%- 80% there seems to be no practical limit to the number of cycles the battery will last. Most other chemistries are similar. Cell damage tends to occur when the cells are over charged or over-discharged. In a Nimh pack with lots of cells and no BMS, it would be easy for one cell to get weak and be reverse charged during a discharge cycle, destroying it.

Since the best you can get out of regen is way less than 50%, unless you live at the top of a hill, it would be nearly impossible to get a situation where the batteries couldn't absorb the regen charge. To make things idiot proof, you would still need to manage this possibility. You can either stop regen if the batteries get too high, or use some kind of dump load resistor to dissipate the excess. Either of these could be triggered by a BMS circuit if one was present.

[ZapPat]

Since the best you can get out of regen is way less than 50%, unless you live at the top of a hill, it would be nearly impossible to get a situation where the batteries couldn't absorb the regen charge. To make things idiot proof, you would still need to manage this possibility. You can either stop regen if the batteries get too high, or use some kind of dump load resistor to dissipate the excess. Either of these could be triggered by a BMS circuit if one was present.

Methinks idiot-proof is what is needed for the masses! For people not understanding what's involved with regen, this situation could happen all too often. Imagine someone pulls their ebike off the charger with the pack not well balanced, then rolls down their driveway using regen to brake them. With no cell-based over-voltage signal available to the controller, one cell's voltage may rise enough to damage it very badly very fast - specially if the hill is big enough to generate strong regen currents.

I suppose that a simple battery level over-voltage protection would be enough to protect all the cells in the battery under many circumstances, but it's not idiot-proof. Setting the controller's over-voltage regen cutoff limit lower than total full charge might be good enough too, since the cell's voltage rises quite fast at the end of charge. I would still be nervous about one unbalanced cell being overcharged in such a situation though, specially if the pack is getting older and is prone to having it's cells fall out of balance.

Do you think a cell-triggered OVP going to the controller signal would be overkill? It would be pretty simple and would make regen more robust IMO. We are talking about very expensive batteries here after all...

[billvon]

nice one justin!
another interesting thing is you can capture more regen when the batteries are more discharged, its quite noticeable, I guess the batts have lower resistance the more discharged they get and hence can capture more regen current

Is that really the reason? I think many batteries increase in ESR as they are discharged.

Perhaps you might be seeing one of these:

1) When a cold battery warms up, often its ESR goes down. Discharging a battery at a good rate will warm it.
2) At a given pulse width, a low voltage battery will take more current than a high voltage one, since the voltage differential will be higher between back EMF and battery.
3) Most controller designs start to self-regen above base speed, and thus will start sooner the lower the battery voltage is.

[justin_le]

Would a lower system voltage (36v or 48v), be more effective % wise, when using regen?
Blessings, Snow Crow

Since a regen controller inherently does synchronous rectification, the answer is basically no. The difference in regen efficienty with a 36V pack vs a 48V pack would be too small to measure, since the switching losses would be more or less the same, and the conduction losses on the motor->controller side would be the same as well.

Justin

[justin_le]

nice one justin!
another interesting thing is you can capture more regen when the batteries are more discharged, its quite noticeable, I guess the batts have lower resistance the more discharged they get and hence can capture more regen current,

This is not something that I have observed in the regen controller that I was using, although I could see it being the case if either a) the controller has an upper voltage limit on the regen, and it will scale back the peak regen amperage so as not to exceed this voltage, or b) it is implemented to go down to a fixed PWM duty cycle so that with a lower battery voltage you'd naturally wind up with a lot more regen current.

On the tests I was doing, the controller firmware is designed such that the regen throttle is directly regulating the magnitude of the regen phase current through the motor, so direct braking torque control, and it will dump the ensuing energy into your battery regardless of the state of charge or voltage of the pack. You do get more regen amp-hours when the battery is flat than when it is charged, simply because at a lower voltage the same amount of regen energy is transfered at a higher current but a smaller voltage.

But the idea of a battery being able to 'capture' regen current is not a term I would use and is a bit misleading. If the controller feeds regen energy to the battery, the battery will have no choice but to take it.

Justin

[justin_le]

Justin, could you improve the regen capture by using an ultracapacitor as intermediary, with an ultracapacitor such as JCG uses here:
viewtopic.php?f=6&t=7511&start=0&st=0&sk=t&sd=a&hilit=JCG

I think that my first reply perhaps didn't quite address what I think you were getting at so I'll try again here. One of the main reasons that ultracapacitors are touted is because of their ability to absorb very large currents that a battery couldn't safely handle. For instance, an ebike and a rider (~100kg) together moving at say 40 kph have a kinetic energy of about 6kJ, and if you wanted to come to a stop in say 2 seconds, then that means absorbing some 3 kW of power on average. No ebike battery could take 3kW of charge current, so better absorb that with an ultracap right?!

But what I was showing with parabolic regen battery current curves is that for high rates of regen braking, the amount of regen current that actually flows back into the battery starts to decrease with higher braking forces. If you want to come to a fast stop, then just short all the windings, and you don't have to worry about any excessive recharge currents damaging the battery. This also illustrates how if you do want to come to a fast stop, the efficiency of the regen is quite poor, simply because high regen torque means massive amounts of I^2R losses in the motor winding, so increasing the rate at which you can recapture energy (as supposedly an ultracap would allow) actually decreases the total energy you end up getting. On the curve that showed the % of kinetic energy recaptured, you can see that beyond 12 amps of regen current, sure I could come to a stop faster and waste less energy to wind and rolling drag, but I would actually get fewer watt-hours back in the source because the generating efficiency is pretty low at these kinds of currents.

So even if an ultracap would allow me to do a maximum regen current of say 20 amps. Yes, I would be able to do more regen and come to a faster stop, but no, I would not get any more energy back. In fact, I would recover quite a bit less energy than had I come to a more gradual stop at 6 amps regen using just a battery to absorb the energy. So the idea that an ultracap could help 'improve' the percentage of recaptured energy is quite false in this case.

It is interesting to note that for similar reasons, if you have both mechanical brakes and regen brakes and need to come to a quick stop, you can actually get more energy back to the battery by using both the mechanical and a more modest regen together, than you would coming to that stop purely on regen alone.

Justin

[paultrafalgar]

Thanks a lot Justin for that erudite exposition. Slight off topic, but I notice from your sig that you're installing a NuVinci on your new bike; I was very interested in that kit but various people have convinced me that they are inefficient including Miles whom I have great respect for (eg. viewtopic.php?f=2&t=7891&p=119269&hilit=NuVinci#p119269). I'd love to hear your opinion on that. Perhaps the way to do it would be in a build-thread on your new bike.
Thanks again,
Paul

[Toorbough ULL-Zeveigh]

But what I was showing with parabolic regen battery current curves is that for high rates of regen braking, the amount of regen current that actually flows back into the battery starts to decrease with higher braking forces.

When seeing those current curves I was thinking of another kind of generator, a PV solar cell which will also will give you max current at short circuit but zero power out.
You want to pick an operating point at the I/V knee maximum power point.
As with any generator, an audio amp being another example, max power transmission occurs when the load impedance is matched.
It seems like an ultracap would be much lower impedance & relatively speaking, like dumping the power into a short.

[ZapPat]

But what I was showing with parabolic regen battery current curves is that for high rates of regen braking, the amount of regen current that actually flows back into the battery starts to decrease with higher braking forces.

When seeing those current curves I was thinking of another kind of generator, a PV solar cell which will also will give you max current at short circuit but zero power out.
You want to pick an operating point at the I/V knee maximum power point.
As with any generator, an audio amp being another example, max power transmission occurs when the load impedance is matched.
It seems like an ultracap would be much lower impedance & relatively speaking, like dumping the power into a short.

They call that MPPT for maximum power point traking, in the solar scene.

Having the controller itself programmed for this type of regen optimization is exactly what I want to do. I decribed it as "- Regen on demand (with some automatic current adjustment done by the controller to optimize efficiency)" in my controller feature thread, but I think I'll change the wording to something similar to regen MPPT. This is pretty much what Justin was doing manually during his excellent regen analysis - not setting the duty cycle too high nor too low, depending on the instantaneous ratio of motor voltage to battery voltage. This should help in getting better regen efficiency no matter what the user does (or overdoes) with the regen throttle.

As for the ultracap vs motor impedance issue, I don't think it's really like dumping into a short. The controller is actually doing the impedance matching between the motor and the battery / capacitors (by using PWM with motor inductance and battery capacitance). This is what the MPPT controllers used for solar are actually doing already. As a side note, the few ultracaps for which I've read the datasheets seem to have not-so great ESR, not really any better than LiFePO4 batteries it seemed to me at the time. Please correct me on this if I'm out of date with the cap situation!

[fechter]

As for the ultracap vs motor impedance issue, I don't think it's really like dumping into a short. The controller is actually doing the impedance matching between the motor and the battery / capacitors (by using PWM with motor inductance and battery capacitance). This is what the MPPT controllers used for solar are actually doing already. As a side note, the few ultracaps for which I've read the datasheets seem to have not-so great ESR, not really any better than LiFePO4 batteries it seemed to me at the time. Please correct me on this if I'm out of date with the cap situation!

You can't argue with Justin's curves. At one end of the spectrum, the duty cycle of the braking switch gets high enough for the inductors to reach steady state. Whatever the opposite of discontinuous is? If you restrict yourself to the efficient range, the braking force will drop off as you slow down and may result in too much charge current under fast braking.

A MPPT-like scheme could work and would maximize energy recovery under some conditons, but I think it would result in less than ideal driveability characteristics. I would rather sacrafice some efficiency to get optimum driveability. Improved, safer braking takes priority over energy recovery. The overall energy recovery is so low that even if it was optimized it would still be pretty low.

I found constant motor current braking to be nearly ideal in terms of driveability and it limits the drivetrain torque to prevent damage. On my Zappy (synchronous switching), the braking force would remain constant until the speed was almost zero.

[TylerDurden]

On my Zappy (synchronous switching), the braking force would remain constant until the speed was almost zero.

For clarity, was the force constant or the rate of deceleration? (less force being needed as the vehicle slows)

[fechter]

For clarity, was the force constant or the rate of deceleration? (less force being needed as the vehicle slows)

The force was constant.

Braking force is directly proportional to motor current. By keeping the motor current constant, the braking force remains constant. If the braking force was too high on my setup, it would cause the belt to skip teeth. I normally adjusted the limit to just below where the teeth would start skipping. If I adjusted the limit to zero, it would behave like very low resistance free wheeling.

[ZapPat]

You can't argue with Justin's curves. At one end of the spectrum, the duty cycle of the braking switch gets high enough for the inductors to reach steady state. Whatever the opposite of discontinuous is? If you restrict yourself to the efficient range, the braking force will drop off as you slow down and may result in too much charge current under fast braking.
A MPPT-like scheme could work and would maximize energy recovery under some conditons, but I think it would result in less than ideal driveability characteristics. I would rather sacrafice some efficiency to get optimum driveability. Improved, safer braking takes priority over energy recovery. The overall energy recovery is so low that even if it was optimized it would still be pretty low.
I found constant motor current braking to be nearly ideal in terms of driveability and it limits the drivetrain torque to prevent damage. On my Zappy (synchronous switching), the braking force would remain constant until the speed was almost zero.

You're probably right about the driveability being under par for this type of controlled regen... but I'll have to try it out anyways! Justin did observe that by using a combination of regen and regular breaks together, we could actually get more energy back than with regen alone. I guess an MPPT-like regen used along with the regular breaks would illustrate exactly this situation! Anyways, maybe some type of compromise could be found, and if I do decide to keep an MPPT-like regen mode it would definitely be optional only via user-interface software, with constant motor side current regen being the standard mode. And of course it would be city users (stop and go) and hilly area users that would benefit from this mostly, making efficient regen a no-brainer when this mode of regen would be selected.

[justin_le]

Don't forget ZapPat that maximum power-point regen is almost by definition only 50% efficient on the electrical side, it's not really where you want to be. A controller that defaults to this state wouldn't deliver as much back to the battery as a proportional regen system that is generally well to the right of the max power point where the regen efficiency is much higher (even if the braking force is somewhat less). Ideally the rider anticipates stopping far enough in advance that they can come to a stop on regen alone, while keeping the duty cycle somewhere between 75-85% of what it would be to match the back-emf voltage.

If you are operating anywhere to the left of the MPPoint on that curve, then you are better off reducing the regen so it moves right to the MPPT point and making up for the difference in stopping power with mechanical brakes. This way you would come to stop just as fast but you would get more amp-hours back into the battery.

-Justin

You're probably right about the driveability being under par for this type of controlled regen... but I'll have to try it out anyways! Justin did observe that by using a combination of regen and regular breaks together, we could actually get more energy back than with regen alone. I guess an MPPT-like regen used along with the regular breaks would illustrate exactly this situation! Anyways, maybe some type of compromise could be found, and if I do decide to keep an MPPT-like regen mode it would definitely be optional only via user-interface software, with constant motor side current regen being the standard mode. And of course it would be city users (stop and go) and hilly area users that would benefit from this mostly, making efficient regen a no-brainer when this mode of regen would be selected.

[ZapPat]

[...]Justin did observe that by using a combination of regen and regular breaks together, we could actually get more energy back than with regen alone. I guess an MPPT-like regen used along with the regular breaks would illustrate exactly this situation! Anyways, maybe some type of compromise could be found, and if I do decide to keep an MPPT-like regen mode it would definitely be optional only via user-interface software, with constant motor side current regen being the standard mode. And of course it would be city users (stop and go) and hilly area users that would benefit from this mostly, making efficient regen a no-brainer when this mode of regen would be selected.

Don't forget ZapPat that maximum power-point regen is almost by definition only 50% efficient on the electrical side, it's not really where you want to be. A controller that defaults to this state wouldn't deliver as much back to the battery as a proportional regen system that is generally well to the right of the max power point where the regen efficiency is much higher (even if the braking force is somewhat less). Ideally the rider anticipates stopping far enough in advance that they can come to a stop on regen alone, while keeping the duty cycle somewhere between 75-85% of what it would be to match the back-emf voltage.
If you are operating anywhere to the left of the MPPoint on that curve, then you are better off reducing the regen so it moves right to the MPPT point and making up for the difference in stopping power with mechanical brakes. This way you would come to stop just as fast but you would get more amp-hours back into the battery.
-Justin

I think we are actually saying the same thing here Justin - I guess I am not being very clear. My idea of the MPPoint, or maybe more rightly called the M.P. Area, is as seen from the battery side of the controller, not the motor side. The "MP Area" will change with travelled speed, so as the bike slows down the controller would be dynamicaly changing the duty cycle to stay in this efficiency area. Here is one of your gifs I moded to give you an example:

Maximum Power Area example

Kinetic Recapture Efficiency (regen - MPPoint).gif (8 KiB) Viewed 2131 times

As I see it, the red area would be the MP Area at a given speed.
I don't quite get your statement "Don't forget ZapPat that maximum power-point regen is almost by definition only 50% efficient on the electrical side, it's not really where you want to be.". According to your own gif here, you did not go much over 50% recaptured even with the best duty cycle setting. It seems to me that the principal of MPPT is to maximize energy transfer between a source and load, and as such would be our goal, no?
*EDIT*
I re-read your posts again, and maybe now have a better idea of what you mean. Here's another of your pictures from this thread (edited also).

Highest efficiency regen throttle settings vs speed

Regen Current vs Throttle (high efficiency regen setting).gif (16.4 KiB) Viewed 2124 times

The green lines give maximum battery current during regen for each speed, but if I understand you correctly, maximum efficiency would be more like where the blue arrows point to... is this right?
And if I understand correctly, the maximum efficiency regen throttle setting would be situated midway between the max current setting and another point that is limited by the bike's frictionnal losses (air+rolling). Any idea of how this could be calculated in firmware?
I appreciate your patience!
Pat