calculating power loss from wire resistance

[auraslip]

I found this spread sheet meant for pro audio


Assuming full power, the 14 gauge wiring on stock kits, and that the battery and phase cables all total 20 feet.

It should be easy to re-purpose this spreadsheet for ebikes. I'm just curious about doing the calculations for the phase cables. Would it be completely inaccurate to use the current from the battery and just count all the phase cables as one?

 

[Ricky_nz]

I found this spread sheet meant for pro audio


Assuming full power, the 14 gauge wiring on stock kits, and that the battery and phase cables all total 20 feet.

It should be easy to re-purpose this spreadsheet for ebikes. I'm just curious about doing the calculations for the phase cables. Would it be completely inaccurate to use the current from the battery and just count all the phase cables as one?

It would be inaccurate.
The power loss is dependant on current in the conductor and the current in the phases is not directly proportional to battery current.
You can have a controller drawing 10A off the battery but providing say 100A to the motor under some conditions which due to I2R would cause significantly more loss.

You would need to know the phase current limits of the particular controller to work it out.
The loses are worked out over one wire so you need to work out the current in one phase.

You could use some assumptions like phase current maxing out at 1.5*battery current but any errors in the approximation could give large errors due to the squaring of current in the power calculation.

 

[auraslip]

Ok, so I made a rough draft. Basically the same thing as the first spreadsheet, but it's got a ways to go. Feel free to add stuff to it.

In the future I'd like to add a list of kits and the gauge and length of wire that comes with them. Also the resistance of connectors won't be over looked. I found a short list here of some R/C connects and their resistance. I'll try to find the resistance of anderson connects as well as the connects that come on stock kits.

You could use some assumptions like phase current maxing out at 1.5*battery current but any errors in the approximation could give large errors due to the squaring of current in the power calculation.

Alright.....so here is what I'm thinking. This will be useful to two types of people; those interested in efficiency and range, and those interested in power and fun. So what I can do is use WOT full speed cruising current through the phase wire, which IIRC is equal to battery current, to calculate loss in range and efficiency.

For people interested in tearing around town or bike trails at lower speeds and with more starts and stops we can use a phase current multiplier that is higher..... I'm not sure how we go about doing that though.

 

[Ricky_nz]

Ok, so I made a rough draft. Basically the same thing as the first spreadsheet, but it's got a ways to go. Feel free to add stuff to it.

In the future I'd like to add a list of kits and the gauge and length of wire that comes with them. Also the resistance of connectors won't be over looked. I found a short list here of some R/C connects and their resistance. I'll try to find the resistance of anderson connects as well as the connects that come on stock kits.

You could use some assumptions like phase current maxing out at 1.5*battery current but any errors in the approximation could give large errors due to the squaring of current in the power calculation.

Alright.....so here is what I'm thinking. This will be useful to two types of people; those interested in efficiency and range, and those interested in power and fun. So what I can do is use WOT full speed cruising current through the phase wire, which IIRC is equal to battery current, to calculate loss in range and efficiency.

For people interested in tearing around town or bike trails at lower speeds and with more starts and stops we can use a phase current multiplier that is higher..... I'm not sure how we go about doing that though.

Good to state the assumptions, trying to model everything would be overkill but a couple of assumptions helps. I would list any assumptions used on the first page of the spreadsheet to aid users and help avoid misinterpretation of the results.
Another assumption at this point is that the controller is a typical ebike controller using squarewave drive as the phase currents are different on the sinewave one I'm working on.

I think you will still have a bit of trouble defining the usage patterns. Are you looking for worst case or average power loss?
Worst case being easy to calculate but trying to decide on typical usage may be difficult. % of time in worst case conditions based on user type?

It might be good to include the battery impedance. Maybe with a table that can be defined of typical values per cell like the wire table you already have. eg selection for turnigy nano, normal turnigy, 3 C lifepo4 and lead and highlight the losses in the battery too. Should be able to give a pretty good idea of expected voltage sag under full load.
I like where you are going with connectors, I can see pointing out that someone will see their anderson connector dissipating 20W of heat or more would be useful to indicate that they have made the wrong choice of connector etc.

 

[northernmike]

Just use the biggest wire that isn't ridiculous.

Have a look at the connectors on your motor, controller, batteries, and think about the voltages and currents you're expecting.

Since the battery / controller connections are going to remain at battery potential for the entire discharge, consider power at battery voltage and size accordingly.

And since the controller / motor connections are going to have to withstand voltages from zero to battery voltage, and varying amounts of current, (more at lower voltages on take-off) size these accordingly.

You know approx. resistance of copper from tables found all over the place, such as:

4 .000292
6 .000465
8 .000739
10 .00118
12 .00187
14 .00297
16 .00473
18 .00751
20 .0119
22 .0190
24 .0302
26 .0480
28 .0764

(AWG - ohms / foot)

So it's pretty easy to ballpark.

Why worry so hard about the math? Are you building a 20 foot long stretch limo bike and want to save weight?

Just use the biggest conductor that will fit, and if you're noticing heat, do the impossible and go bigger.

There's some great threads around about replacing phase wires in hub motors for this exact kind of thing.

I know the math is sexy.

Just consider your options:

a) Do the math, and know that you need as big a conductor as you can get for minimum loss...

or

b) Use as big a conductor as you can get, and spend the time you would have spent doing math riding your bike



Sorry dude there just comes a point, you know!

 

[Doctorbass]

Here is another here.. more complete

I used it alot when i was in car audio

Go down to that page:


Basic car Audio Electronic
http://www.bcae1.com/wire.htm

The main site: http://www.bcae1.com/
Doc

 

[grindz145]

If you measured the resistance experimentally, it would work well. However, what would kill you is the delta T. It's really not linear, so if it's accurate at 20C it might not even be close to accurate at 40C. Worth trying just for fun though...

 

[Doctorbass]

If you measured the resistance experimentally, it would work well. However, what would kill you is the delta T. It's really not linear, so if it's accurate at 20C it might not even be close to accurate at 40C. Worth trying just for fun though...

Yes.. and that's why our controller are damping the output power after few minutes of overload when we overpower them without upgrading their shunt. The shunt resistance increase, making the microcontroller chip to see higher current than actually is.

Doc

 

[auraslip]

I like where you are going with connectors, I can see pointing out that someone will see their anderson connector dissipating 20W of heat or more would be useful to indicate that they have made the wrong choice of connector etc.

Pretty much exactly the point. I just repaired a guys chinese electric scooter, and I was trying to explain to him why the tiny 14 gauge wires were wasteful and why the tiny automotive bullet connects were scorched!

Even in a mid power bike a harness upgrade is a pretty decent upgrade. At the least it might shame hub makers into making motors with decent wiring.

I like the idea of best case scenario and worse. That seems like an easy way to do it. Can someone explain when the phase multiplier will come into play? It's when your not at WOT and when you're accelerating right?

The shunt resistance increase, making the microcontroller chip to see higher current than actually is.

aren't shunts made of a metal that doesn't change resistance with heat?

 

[texaspyro]

And if you are buying your cables from car audio suppliers/China BEWARE!. Most are not pure copper (even if they say that they are). And big well known names are not above pulling this scam. I typically see over three times the resistance of a genuine copper cable... i.e. 10 gauge wire is effectively 16 gauge. And you wondered where the smoking goo came from...

 

[auraslip]

Speaking of which - are there any decent sources of wire in the north america?
after shipping hobbyking wire comes out to like $1 a foot for 8 gauge

 

[auraslip]

Did a little bit more work. This one makes two assumptions for worst/best case scenarios. No phase multiplication and 2x phase multiplication. Trying to integrate closses from connectors, but all I have are bullet 8mm bullet connects laying around - no andersons for me


Here is the link to the current version. If someone wants to do some range calculations, it'd save me some time

 

[neptronix]

YIKES.

My "500w" MAC hub motor has 16 gauge phase wires. Seems very small!!
I am running 30 amps / 80amp phase which in reality is more like 38amps from the battery..
I checked the resistance calculator here

on this site:
http://www.bcae1.com/wire.htm

should i use battery current to check my voltage loss, or use phase current to see what my power loss is.

Because my battery current number.. i lose 0.7v

 

[bjosta]

How much do we lose in the connectors?
I have "11.5" AWG phase wires wires, should I terminate these a few cm from the axle into say a 4mm bullet and then go to 8AWG? Would there be any point? Assuming I need 1.5m to reach the controller.

 

[auraslip]

should i use battery current to check my voltage loss, or use phase current to see what my power loss is.

You'd use both. From battery to controller the current is the same as a watt meter or cycle analyst would say. From the controller to the hub motor the phase current (and voltage) varies from 1x battery current all the way up to 2.5x battery current. This is why we need two measurements of cable length.
Of course this is only in some conditions, and my understanding is that you'd spend much more time closer to the "best case scenario".

How much do we lose in the connectors?
I have "11.5" AWG phase wires wires, should I terminate these a few cm from the axle into say a 4mm bullet and then go to 8AWG? Would there be any point? Assuming I need 1.5m to reach the controller.

If you are up to the task, it could certainly be a decent upgrade. You might not perceive a difference at 500w, but it'll be there. IIRC people had some problems with melting phase cables at higher power ratings on these geared motors.

I'm not sure about the resistance of connectors. You could measure the resistance of yours, and I'll start making a list!

 

[phyllis]

When I was testing the throttle circuit, I was mostly doing full throttle accelerations from a dead stop. I did notice the thing heats up quick, but I'm glad to hear it runs cooler at speed.
When you are pulling high loads at low rpm, the current going to the motor (and therefore flowing through the FETs) may be several times the battery current due to the buck converter effect. I measured somewhere between 3-4 times higher under worst conditions with a Crystalyte analog controller and my BMC motor. When the motor is at or near full speed, the PWM is at 100%, so the motor current equals the battery current.

from "use extra caps!"

I also just read around here somewhere that phase current is (1/pwm duty cycle) * battery current. However with the induction in the motor I am not sure if it's accurate for calculating wire loss.

 

[auraslip]

I also just read around here somewhere that phase current is (1/pwm duty cycle) * battery current.

yup, that's how it's done. I assumed worst case as %50pwm / 2X phase current multiplier.

induction in the motor I am not sure if it's accurate for calculating wire loss.

how would induction effect the current in flowing through the wires?

 

[phyllis]

I don't know exactly. But I think maybe the formula above assumes infinite induction in the motor and infinite voltage stiffness in the supply to the FETs (caps and battery). I picture induction as a sort of flywheel, that resists change in velocity (current).
If there is *no* induction in the motor, then the current will rise instantly to batt V / motor R when FETs are turned on. If R is 10mOhm and V is 100, then it's 10 000 A. Since heat loss in the wire is proportional to I^2, in this case the loss at 50% duty cycle is higher than the infinite induction case.
Somewhere in between would be a real motor, having some current ripple at the pwm frequency. I don't know if it's a sizeable amount, generally.