Phase lag, power factor and efficiency in a Bafang G310 / Baserunner system.

[zacksc]

I have been trying to develop a practical, empirical understanding of power flow and phase current in an e-bike system and I'm thinking that maybe understanding two particular scenarios could be a good start. For specificity, let’s say we have a Bafang G310 motor (standard winding) controlled by a Baserunner (powered by a 36 volt battery), and let’s consider two particular riding situations:
1) bike is moving on level terrain at a constant speed of 10 miles per hour. Battery current is about 7 to 10 amps. (throttle voltage roughly 1.9 volts.)
or,
2) bike is going up a steep hill at very low speed (3 mph). Battery current is 20 amps. (Throttle voltage is maybe about 2.4 volts.)

So here is what I would guess, and please tell me if this is all wrong: I think that in case 1, where the bike is moving freely, the current might lag the voltage significantly; the power factor might be as low as maybe 0.5 perhaps? Is that accurate at all?

In case 2, on the other hand, going up a steep hill, I am wondering if the load becomes more resistive and the current lag becomes less, bringing the power factor closer to 1 in this high load situation? Again, I am not really sure if this is correct at all and would love feedback.

I would also like to understand a bit about power loss, i. e., heat generated in the controller and in the motor. I am thinking that in the low-speed, high torque situation, the motor is not very efficient. If, for example, the motor efficiency is 0.8 in that torque-speed situation, then the heat generation rate would be about 140 Watts. (0.2*I*V, where I and V are the dc battery current and voltage to the controller, respectively.) Is that in the right ballpark at all?

I am thinking that the heat loss in the controller is mostly I2R loss associated with the resistance of the MOSFETs (about 4 milliOhms) and therefore tends to be relatively higher in low power factor situations where the phase current is high relative to the motor wattage? Would love to get expert feedback here and improve (or begin) my understanding. Thanks.

 

[zacksc]

Just focussing on power, heat and efficiency, in that first scenario
(1) bike is moving on level terrain at a constant speed of 10 miles per hour. Battery current is about 10 amps. (throttle voltage roughly 1.9 volts.) )
I am thinking that the total power coming from the battery is about 360 Watts (just using the dc IV product) and I wondering:
how much of that 360 Watts tends to end up as heat in the motor, and
how much ends up as heat in the controller?
Any thoughts, ideas, guesses?

And, in the second scenario, walking up a ramp at low speed drawing 20 dc amps, how much of the 700 watts the battery is putting out end up as heat in the motor? Could it be as much as 40% or so (i.e., 280 Watts)? Is that plausible?

 

[HrKlev]

Have you been on ebikes.ca website and played with the simulator there? The g310 motor is included in the presets, so you can simulate all kinds of scenarios. It is also a really great recording of a live session about motor efficiency in the news section over there that answers a lot. I am pretty much in the same boat as you, and has been staring at the simulator and how to use it for some hours now....

 

[zacksc]

Have you been on ebikes.ca website and played with the simulator there? The g310 motor is included in the presets, so you can simulate all kinds of scenarios. It is also a really great recording of a live session about motor efficiency in the news section over there that answers a lot. I am pretty much in the same boat as you, and has been staring at the simulator and how to use it for some hours now....

Cool! Thanks a lot. I will work with that and hopefully post again later. I think I can infer the power factor from that, and the phase lag, if I assume the the motor voltage is the same as the battery voltage? (I am trying to think about how the controller works and what role the MOSFET plays in that. Thinking it could be that the battery voltage is applied between source and drain and maybe a sinusoidal voltage applied to the gate? Not really sure how one would get from positive to negative voltage for the MOSFET output though? I think you need that in a controller...?
Anyway, I would like to assume the the peak voltage in the phase current sine wave is generally the same as the d.c. battery voltage. I wonder if that is correct?

 

[district9prawn]

Your understanding seems to be correct. For our EVs we don't tend to look at it in terms of power factor, but in terms of motor back emf.

In case 2, on the other hand, going up a steep hill, I am wondering if the load becomes more resistive and the current lag becomes less, bringing the power factor closer to 1 in this high load situation? Again, I am not really sure if this is correct at all and would love feedback.

Yes at low enough speed the winding resistance is the dominant part of the motor impedance. At high speed you could almost ignore the winding resistive.

I am thinking that the heat loss in the controller is mostly I2R loss associated with the resistance of the MOSFETs (about 4 milliOhms) and therefore tends to be relatively higher in low power factor situations where the phase current is high relative to the motor wattage?

At high current resistive losses will be where most of the mosfet losses are. At low currents, switching loss will be higher.

 

[goku]

1) bike is moving on level terrain at a constant speed of 10 miles per hour. Battery current is about 7 to 10 amps. (throttle voltage roughly 1.9 volts.)
or,
2) bike is going up a steep hill at very low speed (3 mph). Battery current is 20 amps. (Throttle voltage is maybe about 2.4 volts.)

So here is what I would guess, and please tell me if this is all wrong: I think that in case 1, where the bike is moving freely, the current might lag the voltage significantly; the power factor might be as low as maybe 0.5 perhaps? Is that accurate at all?

In case 2, on the other hand, going up a steep hill, I am wondering if the load becomes more resistive and the current lag becomes less, bringing the power factor closer to 1 in this high load situation? Again, I am not really sure if this is correct at all and would love feedback.

hmm... I think the inverter in the motor drive makes it tricky to approximate the power factor. The motor drive produces a square wave and corrects the frequency of this wave by feedback. And the displacement power factor (leading and lagging pf) is calculated from the first harmonic of this square wave. So it is true that the impedance of the load changes based on the motor speed (because the inverter produces a square wave at a corresponding higher frequency), but I think the inverter corrects for this.

But in general, If I'm not mistaken, the power factors of inverters for bldc motors are pretty high.

 

[zacksc]

I thought the base runner was what is called a sine wave controller. So I kind of assume the MOSFets were producing sine wave voltages for the motor coil's.?

 

[zacksc]

Thanks Goku. I am thinking my previous reply to you is all wrong and very much oversimplified. I need to think more about what you said and try to understand

 

[goku]

Thanks Goku. I am thinking my previous reply to you is all wrong and very much oversimplified. I need to think more about what you said and try to understand

I'm not an expert and I may have got it wrong too lol.

I think the wiki page on pulse width modulation has some good resource to get started. Or really any article on pulse width modulation should help.

I thought the base runner was what is called a sine wave controller. So I kind of assume the MOSFets were producing sine wave voltages for the motor coil's.?

That's a good observation actually. You're right that a sine wave is produced for the motor coils. But the MOSFETS can only produce a square wave. Fortunately, this square wave is a sum of many (infinitely many) sine waves. And this square wave is produced such that the motor can only "see" and respond to a particular sine wave.

So in that sense, a sine wave controller means that the inverter knows exactly how to accomplish this. Not all controllers do this. For instance, a much simpler algorithm is the 6-step commutation where the controller does not explicitly try to generate a sine wave. It produces a specific constant voltage in phase A,B,C for every 60 degree segment (and there are 6 of these segments, hence the name).