PWM current multiplication effect

[Mathurin]

nlc did a similar test here, except the motor was held immobile.
This were his results for battery volts/amps & amps in the phase cables:

36V 20A 45A
48v 20A 52A
72V 20a 65A


What voltage were you running at, fechter?

 

[safe]

This chart from Wikipedia does a good job of making the "Buck Converter" (PWM) more understandable. Apparently it's only when in "discontinuous" mode (pulses too slow to keep things backed up) that the "effect" takes place. One might say:

"Oh yes, I do like it when my Buck Converter goes discontinuous."

...but then people will think you are being pretentious. :wink:

 

[safe]

"Brain Storming" a little here for fun...

The "Buck Converter" uses a capacitor to hold a charge before it switches that charge into a pulse... right?

So let's imagine a combination regenerative braking / PWM controller that has ultra capacitors built right into it. All you would need to do is have a "rack" of ultra capacitors that are constantly either getting charged by the battery or the regen and then the controller just rotates through them for release. Rather than cycling the energy back to the battery you just store up your energy in the controller and it releases when the throttle is next used. I think the controllers do this "a little" already, but you could seriously increase the capacitance and basically solve the "regen issue" to some degree in the controller itself. (no need for external ultra capacitors because they would be built in already)

 

[fechter]

nlc did a similar test here, except the motor was held immobile.
This were his results for battery volts/amps & amps in the phase cables:

36V 20A 45A
48v 20A 52A
72V 20a 65A


What voltage were you running at, fechter?

Geez... my French is really bad. I really couldn't follow that.


Anyway, I was testing at 48v. I suspect the winding resistance of my BMC motor is lower than a Xlyte motor, but the measurements they made are pretty close to what I got.

It would be nice to test it on a dynamometer.

 

[fechter]

This chart from Wikipedia does a good job of making the "Buck Converter" (PWM) more understandable. Apparently it's only when in "discontinuous" mode (pulses too slow to keep things backed up) that the "effect" takes place. One might say:

"Oh yes, I do like it when my Buck Converter goes discontinuous."

...but then people will think you are being pretentious. :wink:

When it goes discontinuous the output voltage can go way up. This would only happen at exteremely light load. I don't think I run my controller in the discontinuous mode very often. This would be like backing off the throttle almost all the way when coasting down a slight hill. I'm more of an on/off kind of guy with the throttle.

 

[safe]

This page http://www.4qdtec.com/pwm-01.html on the 4qd website explains the basics well.

"A popular 'old wife's tale' is that PWM causes the motor to heat more than pure d.c. Like most old wives' tales, this springs from a partial truth nurtured by misunderstanding. The 'myth' comes about because, if the frequency is too low, the current is discontinuous (or at least variable over the pwm waveform) because the motor's inductance cannot maintain the current properly during the off period of the waveform. So the motor current will be pulsed - not continuous.

So consider an oversimplified case where the current is either on or off. If the current flows for, say, 1/3 of the time and you require a torque from the motor equivalent to that given by 1 amp continuous, them you clearly need an average current of 1 amp. To do this with a 33% duty cycle you must have 3 amps (the current flows for for 1/3 of the time).

Now a current of 3 amps will give 9 times (I squared) the heating effect of 1 amp continuous.

But if 3 amps is flowing for only 1/3 the total time - so the heating in the motor is 9 times for 1/3 the time - or a factor of 3 greater than the steady 1 amp!"

Okay, now let's see if I have understood this paragraph. While the "naive" person like myself might "assume" that the 1 amp torque @ 33% throttle would create:

1 amp @ 33% means 3 amps "in action" so maybe 9 times heating?

Which is WRONG. But what is RIGHT is that:

9 times heating divided by "heat time" (33%) still creates 3 times the heat.

So if I'm "understanding" this correctly the HEAT IS REAL, but it's only a factor of three not nine for this example. So if you were to have gears and could achieve the 1 amp torque using just a regular old 1 amp current then you would only get a "heat factor" of one.

So it's a valid statement to say that the PWM "effect" increases the heating because it increases the current, but rather than:

Direct Current Heat Increase = Current Squared

PWM Current Heat Increase - Current Squared times Duty Cycle (0% - 100%)

Correct?

So we would expect for torque values of 1 amp:

10% Duty Cycle - 1 amp @ 10% = 10 Amps (squared) = 100 * Duty Cycle of 10% = Heat increase of 10 times.

Heat index for PWM:

10% - 10 times
20% - 5 times
33% - 3 times
50% - 2 times

 

[xyster]

Heat index for PWM:

10% - 10 times
20% - 5 times
33% - 3 times
50% - 2 times

If this is true, as it looks from the 4qd explanation to be, then most of a motor's inefficiency, as measured by heat production, seems to be caused by this effect. But if we instead vary the speed with a variable resistor, then wouldn't that resistor dissipate this heat instead of the motor? Whereas, couldn't we avoid this inefficiency all together by using a one-speed motor, altering the vehicle's velocity by gears only? I'm surprised Safe hasn't thought of this. Darn, I'm smart. I should patent something like that! :wink:

 

[Toorbough ULL-Zeveigh]

HEAT IS REAL

No, steel is real.

The extra heat is imaginary because the current thru an inductor has a real component & an imaginary component. This is a common rookie mistake. Read up on the difference between real power vs apparant power.

Many a would-be inventor has fallen into this trap thinking they have discovered a new source of energy from a generator or efficiency out of a motor.

 

[safe]

The extra heat is imaginary because the current thru an inductor has a real component & an imaginary component.

So the heat is imaginary? :wink:

When the motor begins to smoke would that also be imaginary? :wink:

The article http://www.4qdtec.com/pwm-01.html begins by saying that the "rookie mistake" is to think that PWM causes heating which it does not do of it's own accord. The article then goes on to explain how you DON'T get the "full heating effect" of increased amps which would be:

Heat = Current Squared

...but instead you get that result and divide by the "Duty Cycle" which only gives you a small fraction of the heating you would normally expect. So you end up with:

Heat = ( Current Squared ) ( Times the "Duty Cycle" Percentage )

So the "rookie mistake" is to assume that at a 10% "Duty Cycle" you get an "imaginary" current of 10 times the original amount which then gets squared to get 100 and so the "rookie" says:

"At 10% 'Duty Cycle' the heat is 100 times worse! Oh my gosh! "

...but the wise veterans "know" that you don't actually get 100 times the heating because the current isn't constant so you have to take only the portion that applies to the "Duty Cycle". So in the end you get:

"Rookie Expectation times the 'Duty Cycle' to get the REAL HEAT."

So in the end the 100 times factor is reduced to ONLY 10 times.

The "rookie" is WRONG... heat does not follow the squared rule, but it still is increased.

(either that or the article is wrong because I'm just repeating what the article wrote)

 

[fechter]

If you look at the current waveform on a typical controller, the switching is happening so fast that the peak current is barely above the average current. It doesn't get ugly until you go discontinuous. I think 4QD explains this somewhere. Therefore, the motor heating with a PWM controller is nearly the same as it would be for pure DC.

As I mentioned before, a discontinuous state would be a very low percentage of the time during typical vehicle operation.

If the switching frequency is too low, then all bets are off, as the peak/average ratio will go way up, especially if it's so low that the inductor current reaches steady state.

 

[safe]

It doesn't get ugly until you go discontinuous. I think 4QD explains this somewhere. Therefore, the motor heating with a PWM controller is nearly the same as it would be for pure DC.

And the "discontinuous" state occurs differently (I would presume) depending on the Inductance of the motor. They talked in that article about a motor with charactoristics such that the "discontinuous" state was never likely reached. If I'm "on the right track" then the point at which the "discontinuous" state kicks in depends on the motor. (on the chart they are claiming it is not a factor until about 15% current)

I think I found that "point" on my motor when I let it drop below a certain very low rpm. I'd have to say when you get down to the "bottom quarter" (or less) of the powerband that you run the risk of dipping into the "discontinuous" area and that seems to be when things radically heat up. It would not surprise me to see three to five times the heat being built up in that region. (which is a small part of the powerband)

As Xyster so cynically pointed out... it might be a good idea to have "gears" to avoid these "discontinuous" zones...

 

[safe]

It would be interesting to see a dyno run with some of the motors we typically use (like the Unite, Transmagnetics or one of the Hub Motors) and place a temperature guage in the motor and actually find out where the heating "boundry" occurs. I would not be surprised if different motors yield radically different results so that on some motors there is almost no "discontinuous" related effect.

 

[safe]

Formulas?

How the heck am I going to model this chart in my spreadsheet?

Rgiht now I have what amounts to a straight line trying to imitate the PWM "effect" when it's obvious that the "actual" is much different. I'm thinking of a simplified concept along the lines of the chart below.

Anyone ever successfully modeled these formulas in a spreadsheet? Know any good links about that?

It would be great to be as realistic as possible so that I can get accurate numbers on the hub torque. If I'm reading this correctly the "perceived" voltage actually goes way up at low rpms and that is what actually allows the higher current. At least that seems to be the way the chart looks. Am I correct with this?

Maybe my formulas should address the voltage side alone and allow the current to simply fall into place?

 

[Matt Gruber]

those 4qd articles persuaded me to bypass it. If it is so finnicky why depend on it? Truth is, they just want to scare you away from their competition, and a bypass is NOT their competition.

anyway i spend a lot of time at LOW, like 1-2 mph, and my mbike draws 1 to 2 amps 36v and nothing gets hot.

 

[safe]

...anyway i spend a lot of time at LOW, like 1-2 mph, and my mbike draws 1 to 2 amps 36v and nothing gets hot.

Fully loaded on a hill where the motor is failing to pull the weight or coasting along on flat ground with no load?

Without load you don't get heat. Heat is only when the rpms are low, the load is full (so that your motor can't get itself out of the low rpms) and your motors inductance / controller configuration creates a "discontinuous" state with the current.

You might say:

"Well that never happens for me."

...and it might be true for your case, but on my bike which weighs 140 lbs and I weigh 185 lbs and for my little Unite motor that is only 750 Watts and in my taller gear I can literally burn up my motor if I get on too steep of a hill. And from my experience the "worst" of the "effect" is at the very lowest edge of the powerband. It's down below 1/4 and more like 1/8 of the powerband that a motor that can take me for 20 miles (like yesterday) without heating, can all of sudden exhibit heating behavior that is disproportional to that when the motor is running at peak power and high rpm.

So it varies...

 

[xyster]

my little Unite motor that is only 750 Watts and in my taller gear I can literally burn up my motor if I get on too steep of a hill.

Strange -- my little motor is also rated for only 750 Watts, but never gets hot climbing even the steepest hills. Guess this goes to show how much more efficient a hubmotor is over gears :lol:

http://www.poweridestore.com/X-5-750W-Rear-Hub-Motor-Kit

The Motor Kit comes with the following:

X-5 750W Single Speed Hub Motor

:wink:

 

[Matt Gruber]

U climb steep hills at 10%? LOL
IMPOSSIBLE w/750w at 10%

U R just LUGGING it.
i thought u had low gearsfor that?

u smoked it and ruined it. buy a new one.

 

[safe]

U climb steep hills at 10%? LOL
IMPOSSIBLE w/750w at 10%.

At about 13.3 mph I'm "okay". Once the hill gets steep enough that I'm forced to drop below 13.3 mph it starts to fall into a sort of heat related "death spiral". Fortunately for me I can climb most any hill around here with this gear. With my "tall gearset" my lowest gear starts at 20.9 mph so I fall into the "death spiral" on hills that are 10% or less. (notice how 20.8 mph corresponds to my FOURTH GEAR in the low gearset) If the hill is short I can survive, but if the hill is long then it eventually starts to smoke.

So if you are going to have a lot of weight and a micro sized motor you need lot's of gears to handle your full range of speeds... Below are my gearing for the "low gearset" of the 14 tooth sprocket.

I'm planning to weld a coaster brake hub fitting onto my transaxle so that I can experiment with alternative gears. My 14 and 22 tooth options are too far apart. The "ideal" for around town seems to be about a 16 tooth or an 18 tooth, somewhere around there... so I'll try that out later...

 

[Matt Gruber]

here is my 1 speed w/voltage shift
17 mph 36v 500w
20 mph 43v ~600w
25 mph 53v ~736 watts!.
about like your 1st to almost 4th spread.
Note how my motor power goes up just when i need it.
a constant voltage(like always 36v) system
can not do this. cv tends to more easly overload and overheat when shifting up or not being able to shift down.

The cool thing about PWM is that it kind of rearranges the pack electricly so, say at half throttle it's like the pack is now double amps, just like if the pack was rewired for half volts.

 

[safe]

Now we are wandering outside the PWM "effect" and into the engine size debate. Given roughly a 3 to 1 ratio of motor size to gearing you can cover all the same territory. The fixed gear does just fine if the controller has a low current limit and a high voltage and overall has a surplus of power. The geared solution expands greatly the abilities of motors with limited power.

But back to the actual PWM "effect" as an "issue". At low enough rpms the "discontinuous" current flow causes an increase in apparent voltage and therefore an increase in current. From this there are two things to remember:

1. The increased current creates an additional amount of torque that can assist at the very low end of the powerband. (or it might destroy an internally geared hub if you are not careful)

2. The increased current does not all produce heat. Rather than a squared relationship that one normally expects for heat you get the squared times the duty cycle percentage to arrive at an "increased", but only "moderately increased" heating effect. This only occurs in the "discontinuous" rpm zone, so if you can avoid it with either gears or brute force (power) then the problem goes away.

 

[Matt Gruber]

on a "death spiral" steep hill
have u cut back throttle to keep it cool?

 

[xyster]

on a "death spiral" steep hill
have u cut back throttle to keep it cool?

An excellent question.

At the same throttle setting,

Amps In X Volts In = Amps Out X Volts Out

But this is not a constant, it changes with throttle setting. So Amps Out at low throttles settings will be less than Amps Out at high throttle settings (even though it's higher than Amps In at the same settings). Hence, heat will be less with lower throttle settings.

As far as I understand all this anyway...

 

[Matt Gruber]

the driver feeds the motor.
bad skills= overheat
good driving= happy motor
it it climbs at 13mph but gets hot
try 9 or 10 mph or ~60% of level speed. U have to try it, it may not work like mine. Learn what the motor likes. That's good driving.

mine drops to 16a @ 9mph on overpass where full throttle= ~32a at 12-13mph at 36v

 

[xyster]

the driver feeds the motor.
bad skills= overheat
good driving= happy motor
it it climbs at 13mph but gets hot
try 9 or 10 mph or ~60% of level speed.
mine drops to 16a @ 9mph on overpass

Mine sucks 10-15a @ 20mph on overpass-grade grades. You must be a really bad driver! Just kidding, voltage probably has more to do with it.... :wink:

 

[fechter]

That's an interesting point.

I'm not sure of the answer, but my intuition tells me that if I did two runs on the same hill, one at full throttle, and one going very slow, like 5mph, that the motor would be hotter after the fast run.

For sure, the slow run would be drawing less current from the batteries, so Peukert losses or battery resistance losses, would be much less, which would consume less available energy from the battery.

On the slow run, the motor would have more time to dissipate the wasted heat, so it could dissipate more energy without getting too hot. I'm not sure if that compensates for the additional inefficiency.

If you take the example to the extreme, imagine going up a hill at like 1/2 mph. The torque needed to climb the hill, and therefore the motor current, will be nearly the same at 1/2 mph as it is at, say, 10mph (assuming the difference in wind and rolling resistance is negligible up to that speed).

To complete climbing the hill, the same total energy is needed in both cases. The amps going through the motor is the same in both cases. It takes 20 times longer in the slow case, so it would seem like it should create 20 times more wasted energy.

I'm not sure how you would test this. A thermometer in the windings might do it.