Pole count/PWM freq of stock motor

[Attila_iii]

Okay, lets see if I can write a quick something that will make sense about this carrier frequency issue. There are a few things to keep in mind. If you think of electricity in terms of water flowing through a pipe it will make more sense. So, Voltage would be the pressure, and water flowing would be the Current. These are two very important distinctions to understand. Big difference between voltage and current.
Now lets talk about MOSFETS. These are nothing more than a switch. They are either on or off. So, when they switch on, full battery voltage is seen at the output. When they switch off, the output voltage goes to zero. This happens very fast, in the order of micro or nano seconds depending on the MOSFET. If we looked at the voltage on an O-Scope, for a single switch cycle Off-On-Off The rise would look like a vertical line, from 0 to full battery voltage. Great, we made a square wave, but how does that make a motor turn?
Simple answer, it doesn't not by itself. Remember the Voltage and Current analogy in the beginning of this post. Voltage is pressure that allows current to flow. But it's the current that produces torque in the motor. Current flowing through a conductor creates a magnetic field. Wrap that conductor around an iron core multiple times and it amplifies that magnetic field and makes it stronger. So the motor does not care what the voltage signal looks like, it only cares about what the Current looks like.
If we look at the output current on an O-Scope it will look like a sinewave. Each leg of the output will be 120 degress out of phase with the others. This makes a rotating magnetic field. This interacts with the permanent magnets in the motor and produces torque.
Ok Great!! but what does this have to do with the carrier frequency??
This is where the explanation gets a little tricky. Remember the voltage output of an ESC looks like a square wave. What matters is how long the MOSFET is gated on to create those voltage "pulses". This is what is known as Pulse Width Modulation, or PWM. Again if we looked at the VOLTAGE with an O-Scope, we would see a square wave, but they are not all symmetrical. Look at the image below. This is a representation of of both voltage and current in a single phase. The purple is voltage, This is the PWM voltage output seen at the motor. The green wave is the current seen at the motor. Notice how the current wave form is a little "fuzzy" looking? This is because of the carrier frequency. The lower the carrier frequency, the fuzzier the current waveform will look. The higher we go, the smoother it looks. The only noticeable difference increasing the carrier frequency will have is audible noise, and more heat in the ESC due to switching losses.

[DoubleCH]

Digging out this old thread because I did some tests with different PWM again with my Protos yesterday...

The above post is just basic 3-phase motor general knowledge some of us already know. What I expected were some specifics to reply to earlier posts.

Originally Posted by helidude71

For starters, can you tell if the "KV x Volts x Poles / 20" formula makes any sense?
Also would be great to read some more on the subject.
Go ahead please!

Oh, I run the Parkfly P2632 on "3800 x 11.1 x 6 / 20" = 12.6 => 12 KHz PWM. (YEP30A ESC.)
Works fine, only slightly above ambient, even if you use a bit more timing advance.
I can't run the Parkfly hot as some seem to claim.

BTW, helidude, even no-load P2632 runs warmer than Hyperion/LYnx motors on the bench or in-flight any PWM any timing. That's just the nature of the EDF motor.

Originally Posted by DoubleCH

I think the purpose of PWM formula is to prevent running PWM too low into the range of motor running frequency which may result in a step when changing throttle. Any other time, a lower PWM will result in finer throttle change and less power loss. So my goal is to fly the lowest PWM frequency unless I notice any glitch in response to some particular throttle value change. The fastest brushless I've run is the hp08s at 8000kV 2S (equivalent to 5333kV 3S) and I've never experienced any glitch running 8kHz with BLHeli so I don't bother running higher PWM.

This popular formula has been floating around for brushless motors for RC heli. There's 1 characteristics these small brushless motors have that may not apply to other 3-phase motors in general. We're talking tiny powerful motors that run 60k+ rpm such that it may be fast enough to run into PWM frequency. That's why I believe the well-known formula comes in. IMO, since we run governor which means in operation the motor is never going to run at full speed, we can get away running lower PWM than the formula suggests in fear of running fast enough into PWM territory. Well, big industrial 3-phase motor could be running many more poles so even though running slower it may also be running close to PWM frequency? Could you comment on the formula thing?

Originally Posted by DoubleCH

Another data point, high PWM doesn't always create problem only on the ESC side it seems. I tried my Proto's stock Scorpion motor at anything higher than the lowest 8kHz with the stock YGE (not cheap YEP) and the motor ran hotter. I have to run that motor at 8kHz.

I just tried my Protos motor yesterday again. Switching to 8kHz from 10kHz with the same flight pack I instantly and consistently get 1% more HS (measured with RPM sensor on the motor wires) on the bench without blades. In flight, if any power and temperature difference it favors 8kHz. I'm not talking cheap motor/ESC. This is very reliable and great performing Scorpion motor and YGE ESC. Why does the motor run hotter at higher PWM? Someone says running higher PWM means more inductive load and less resistive load. I haven't come across any application from my personal experience that favors higher than 8kHz PWM.

[Attila_iii]

Originally Posted by helidude71

For starters, can you tell if the "KV x Volts x Poles / 20" formula makes any sense?
Also would be great to read some more on the subject.
Go ahead please!

Okay, yes the previous information I posted might be common knowledge for some, but I wanted to make sure everyone was on board before I continued on. I believe that formula is an incorrect version of a standard motor formula for the "synchronous" or no load speed of an electric motor.

So, lets discuss Kv first off. This is the motors velocity constant. This is kind of misleading for these types of motors. Because it's the frequency of the AC current that we talked about above, that determines the speed of the motor. However, as we all probably know, the stator in these motors is nothing more than coils of wire. Put a meter across any of the phases, and the winding resistance is really low. Apply ohms law to this, and calculate for the current, I=E/R and it looks like the current should be beyond control. As an example, the Scorpion HKII -2221 I have in my 450X has a winding resistance of 0.016 ohms. So, 11.1V/0.016 = 693.75A (Note, this is simplified for an example, the formula is a little different for a three phase system) But you get the point.
Some of you may already know, that as a motor begins to spin, it creates Counter Electro Motive Force, or Counter EMF, Back EMF, all the same thing. This is essentially a voltage opposite in polarity to what is being applied from the ESC. So, what the motor KV actually tells is the equilibrium point for a specified voltage. So, again the motor in my 450X is a 4400Kv motor. That means, the Counter EMF will limit the speed to 4400RPM/V applied with NO load. This is why we can use this to determine the no load speed of the motor.

Okay, so now the messed up formula that you see all over the place on these forums.
The formula to determine the speed of a three phase motor is:

RPM = 120 * f / P

Where:
RPM is the speed of the motor
f is the frequency of the current going to the motor in Hz (Not the carrier frequency)
P is the number of Pole pairs in the motor

If we rearrange the formula to solve for frequency we get:

f = RPM * P / 120

We know the no load speed of our motors using the Kv * Battery voltage so we can substitute that in for RPM.

f = Kv * V * P / 120

Look familiar? That 20 should be a 120. That constant is the phase angle relationship in a three phase system. Each phase of a three phase system is 120 degrees out of phase with each other. Just for visual reference, look at the zero point on the y axis. The black sine wave starts here. Move Horizontally along that zero point to the red sine wave. It's at 120 degrees, the blue one at 240 degrees, and then we start over at 360 with the black one. This is where the 120 comes from. Someone missed the 1 in front of that I think.




So, using my motor as an example again:

4400Kv * 11.1V * 6 / 120 = 2442 Hz

So the output frequency of the current wave form from the ESC is 2442. The carrier frequency is 8Khz, (This is the default setting for CC Phoenix Edge 50) So we are not even close to approaching the carrier frequency of the ESC.

I will see about getting my scope from the office and taking some snap shots of voltage and current with the scope to prove it out. I'm out of the office all this week, so I will see about throwing something up there next week.

I hope this helps you guys. Keep the feedback and questions coming. I'm happy to share my knowledge.

[DoubleCH]

Originally Posted by Attila_iii

This is where the 120 comes from. Someone missed the 1 in front of that I think.

I don't believe someone just missed the 1 in the 120. That formula is not finding each motor winding frequency. It's supposed to find the optimal PWM drive for the motor. IOW, we can simplify the formula to find the PWM drive for the the motor to PWM = f * 6 where f is the frequency of the current going thru' each winding. Where does this 6 comes from is the key? I don't believe that's the pole count because the formula seems to apply to 10-pole, 12-pole or 14-pole motors, and number of stator arms doesn't come into play. Maybe this magic number 6 doesn't have to equate to anything but a factor that's been tested for optimal operation. Let's think about it. If we cut the full sine wave cycle in half and look at just the positive half, running PWM 6 times the winding frequency means there're only 3 PWM pulses within this positive half. It may mean something or it may mean nothing at all (as in my case since I always run 8kHz in all my applications).

[Attila_iii]

Originally Posted by DoubleCH

I don't believe someone just missed the 1 in the 120. That formula is not finding each motor winding frequency. It's supposed to find the optimal PWM drive for the motor. IOW, we can simplify the formula to find the PWM drive for the the motor to PWM = f * 6 where f is the frequency of the current going thru' each winding. Where does this 6 comes from is the key? I don't believe that's the pole count because the formula seems to apply to 10-pole, 12-pole or 14-pole motors, and number of stator arms doesn't come into play. Maybe this magic number 6 doesn't have to equate to anything but a factor that's been tested for optimal operation. Let's think about it. If we cut the full sine wave cycle in half and look at just the positive half, running PWM 6 times the winding frequency means there're only 3 PWM pulses within this positive half. It may mean something or it may mean nothing at all (as in my case since I always run 8kHz in all my applications).

That formula I posted is an actual motor formula, it's taught in school. Do a search on "Motor Synchronous Speed Formula" . If I had to make a guess, someone took that with some limited knowledge and bastardized it. The "6" in your simplified version is not the pole count in this case. Take a closer look. The "20" in the formula flying around the forums, is one sixth of the 120 in the published formula for synchronous speed. Someone seems to think that if you take the PWM frequency 6 times higher than the synchronous speed, you will get the optimum PWM frequency. That is where the 6 is coming from in your simplified formula. Trust me, it's not that simple. If it were, do you not think the ESC manufactures would work this into software to automatically adjust the PWM frequency for you based on the motor info you put into it?

Todays VFD's typically run at a PWM frequency of 4KHz. Larger ones run at a default of 2KHz, but can be run at 4KHz without derating. Above 4KHz, the drive has to be derated to prevent overheating and blowing out the IGBT's. The drives are engineered this way. Could they be designed to run at a higher frequency? Sure they can, but the physical size of the drive would increase and so would the price, with no visible increase in performance.
The same is going to be true of the ESC's used in in RC applications. The higher you take the PWM frequency, the more heat you are going to generate in the ESC. The more heat, the lower the efficiency. I seriously doubt you are going to get any noticeable payback in performance by cranking up the PWM frequency in your ESC. But to prove the point, I will run an experiment on it and publish the data. Give me a couple of weeks to get it done. .

[DoubleCH]

Originally Posted by Attila_iii

Someone seems to think that if you take the PWM frequency 6 times higher than the synchronous speed, you will get the optimum PWM frequency. That is where the 6 is coming from in your simplified formula.

That's exactly what I'm saying about the forumla (not MY formula) floating around HF. I know the motor speed formula and not 1 second has I ever doubted that (I'm an EE BTW).

Trust me, it's not that simple. If it were, do you not think the ESC manufactures would work this into software to automatically adjust the PWM frequency for you based on the motor info you put into it?

While I'm not saying the formula floating around HF is great, I don't think someone just pull the number 6 out of a hat. Why is it impossible that say, just say, someone may have worked out maybe from massive experience data from lots of people with lots of various applications for RC heli motors over long period of time that a rule of thumb may suggest around 6 is a good number to use? Don't get stuck up with textbook knowledge we already know. There may also be real-world optimal usage from past experience. Again, I'm not saying it's that simple, but it's easier for ESC to ask for PWM drive frequency than to ask for motor kV and drive voltage and number of poles.

The same is going to be true of the ESC's used in in RC applications. The higher you take the PWM frequency, the more heat you are going to generate in the ESC. The more heat, the lower the efficiency. I seriously doubt you are going to get any noticeable payback in performance by cranking up the PWM frequency in your ESC. But to prove the point, I will run an experiment on it and publish the data. Give me a couple of weeks to get it done. .

I know higher PWM taxes the ESC more. What I have doubt is the claim that higher PWM makes motor run cooler with size, pole-count, and speed of RC heli motors. If any detectable lower motor temp by running higher PWM, it's probably coming from the ESC FETs switching loss (i.e. outputs are staying too long in the transition states than at full on and full off states, resulting in averaging out the resulting voltage, like using the FETs as resistors to drop voltage).

[Attila_iii]

Originally Posted by DoubleCH

That's exactly what I'm saying about the forumla (not MY formula) floating around HF. I know the motor speed formula and not 1 second has I ever doubted that (I'm an EE BTW).

While I'm not saying the formula floating around HF is great, I don't think someone just pull the number 6 out of a hat. Why is it impossible that say, just say, someone may have worked out maybe from massive experience data from lots of people with lots of various applications for RC heli motors over long period of time that a rule of thumb may suggest around 6 is a good number to use? Don't get stuck up with textbook knowledge we already know. There may also be real-world optimal usage from past experience. Again, I'm not saying it's that simple, but it's easier for ESC to ask for PWM drive frequency than to ask for motor kV and drive voltage and number of poles.

I don't know about you, but unless I know the person and their experience, I'm not just going to take something at face value and run with it. I have been working with motor controllers for 20 years, and motor and Generator Theory for 25+. Cranking up the PWM is going to cause more heat in the ESC. I seriously doubt it's going to have an effect on the motor temperature. The noise level should drop. If you're an EE, then you know the law of diminishing returns. Just because a little is good does not mean a lot is better. There is going to be a tipping point at which any perceived gain in performance, temperature benefit or whatever, is going to be minimal. I'm sorry but I just don't believe the magic factor of 6 is going to work for all instances. I'll run some tests on my set up and check the temperature of the ESC, Motor, Noise levels, Battery temperature, and run times. I'll throw in head speed as well. We'll see if this magic factor of 6 works with my set up. Based on this formula, I should have my PWM up around 14-15K, almost double to where I have it set now. I can tell you my motor is just warm at 8KHz after running a battery through it. I'm betting my ESC is going to be pretty toasty at 14KHz after a battery. But, I'll test it just to see, and I will post my results, pictures of the setup, and a full explanation. The only way to get to the bottom of it and put this to rest. I'll let the data speak for itself.

I know higher PWM taxes the ESC more. What I have doubt is the claim that higher PWM makes motor run cooler with size, pole-count, and speed of RC heli motors. If any detectable lower motor temp by running higher PWM, it's probably coming from the ESC FETs switching loss (i.e. outputs are staying too long in the transition states than at full on and full off states, resulting in averaging out the resulting voltage, like using the FETs as resistors to drop voltage).

Sounds like we are on the same page then. I don't believe there is going to be any benefit to jacking up the PWM. If anything, it will be a detriment to the ESC. Older VFD's used to have a much lower switching frequency. In the hundreds of Hz range. The newer VFD's with IGBT's, switch at 2-4KHz. There were never any problems with the motors at lower carrier frequencies. With the advent of the IGBT, and the higher carrier frequencies, we started seeing problems with the motors. First turn failures in the motor winding, bearing pitting etc. There are energy advantages to the higher carrier frequency, but there are also problems with it, and the motors had to be made "VFD" ready. There is an upper limit to this energy savings. I think 8KHz is probably going to be optimal for most ESC's and motor combos. But I'll wait for the results of the test just to see the data displayed in one place.

[DoubleCH]

I thought I've mentioned enough times that I don't believe in the PWM-to-choose formula and I always use 8kHz. I'm just playing devil's advocate with the formula.
https://www.helifreak.com/showpost.p...6&postcount=17
https://www.helifreak.com/showpost.p...5&postcount=16

[thruster]

Soon will be programming a couple of rc helicopter esc's for the first time. What PWM frequency should I use? Ha ha.......actually by now I'm somewhat convinced to use 8Khz.

[Attila_iii]

Originally Posted by thruster

Soon will be programming a couple of rc helicopter esc's for the first time. What PWM frequency should I use? Ha ha.......actually by now I'm somewhat convinced to use 8Khz.

Stick with 8KHz. I haven't had a chance to run the tests yet. The weather here has been nice, so I have been trying to get my deck built. I haven't forgotten, just have been extremely busy with work, house, kids etc. I'll run the tests and put this to bed... eventually.