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Is it possible to calculate what input power (watts) is needed to run a given PWM at a certain line frequency (hertz)?

I have all the motor parameters, I know:

  • P-nom, nominal power, kW
  • U-nom, nominal voltage, V
  • f-nom, nominal (line) frequency, Hz
  • N-nom, nominal speed, RPM
  • I-nom, nominal current, A
  • cosPhi, power factor
  • pole count

I need to make a function that takes in a line frequency and outputs power used by the motor at that frequency.

EDIT Will give some more information on what i'm actually trying to achieve.

I work at a company that makes inverters that has true sinusoidal line frequencies. PWM chops up the volt into pulses with different widths that makes it so the flow resembles a sinus wave. When doing this energy is lost into uninteresting forms of energy for the system (sound, heat, etc) that we can disregard. Especially at lower frequencies. At 50Hz our inverter is not that much more energy saving than a PWM, our big strength is that at lower hertz (like 10-30Hz) there is a big waste in PWM motors.

My boss asked me to make a program that can show 2 line graphs, one for our inverter and one for a standard/average PWM inverter. Where the Y-axis of the graph is power consumed (watts) and the X-axis is the line frequency from the inverter to the motor (hertz).

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    \$\begingroup\$ If your PWM works properly, its frequency should not influence the motor power. Only the duty cycle is supposed to control the power. Do you mean variable-frequency drive instead of PWM, maybe? \$\endgroup\$
    – Jonathan S.
    Commented Nov 10, 2022 at 13:36
  • \$\begingroup\$ But i thought PWM motors were less effiecient at lower speeds? Thats the reason im tasked with making this function. To calculate the waste of energy at different hertz. \$\endgroup\$
    – CantFindGoverningFrameWork
    Commented Nov 10, 2022 at 13:38
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    \$\begingroup\$ PWM = pulse width modulation. The frequency doesn't change. PWM controlled motors might be less efficient at low speed (I don't know,) but it won't have to do with the frequency. You might be trying to figure out the power for a particular pulse width (duty cycle.) That would be a reasonable thing to think about. \$\endgroup\$
    – JRE
    Commented Nov 10, 2022 at 13:55
  • \$\begingroup\$ Depends on the motor type. Which is yours? \$\endgroup\$
    – winny
    Commented Nov 10, 2022 at 13:57
  • \$\begingroup\$ This question requires many questions to answer. different motors give different torque vs speed profiles. The motor controller will have different losses based on the frequency. You will have to do bench testing to achieve what you want, or if you can find the data from the motor supplier and the motor controller. \$\endgroup\$
    – glasshouse1991
    Commented Nov 10, 2022 at 14:05

1 Answer 1

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I assume there is an inverter driving the motor because you mentioned PWM (pulse width modulation). First let's be clear on what is meant by "frequency". There is line frequency, the output frequency of the inverter which determines the rotational speed of the motor. Then there is PWM frequency, which is the switching frequency of the transistors in the inverter. This frequency is independent of the motor speed. So the wording of your question is a bit confusing, but I assume you mean the line frequency, the output of the inverter to the motor, affecting its speed.

Based on the mention of HVAC, this motor is driving a fan, perhaps? In this case, yes, the input power does decrease with decreasing line frequency. But the exact input power drawn at any particular frequency depends on the load at that frequency (the operating point), and to a lesser amount on the motor losses at that operating point. The load is determined by system characteristics, for example, fan characteristics, air flow, and back pressure, all of which vary with speed. Without all this information, it is impossible to calculate how much power the motor will draw.

The motor parameter you have listed are of little use. These appear to be motor ratings, characterizing the motor at a single operating point (rated load). It tells you what the motor can do, not how it will perform in your system. The easiest way to obtain a power vs frequency function (if you have the complete system available) is to run it and measure the input power at different frequencies.

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  • \$\begingroup\$ Thanks. that clears some things up a little bit for me. I still have this task from my boss though, and when i asked a co-worker for help he told me that we can kinda make the algorithm as simple as possible. Disregard air flow, and all things that only have a minor effect. If the result is within a few percentage points of the real answear i think its fine. We are only going to use this to demonstrate that PWM motors waste energy compared to true sinusoidal frequencies. (we make inverters, the algorhitm im supposed to do is only for selling purposes and wont be used in actual tech) \$\endgroup\$
    – CantFindGoverningFrameWork
    Commented Nov 11, 2022 at 10:51
  • \$\begingroup\$ And yes, a fan. I guess we can assume some values for the fan (that are roughly average from the market). If i know the load at when at nominal frequency, cant i then calculate the load at frequencies offset from the nominal one? Or is the load at 40Hz totally "disconnected" to the load at 50Hz? So two fans that both have load X on 50Hz might not have the same load at 40Hz? \$\endgroup\$
    – CantFindGoverningFrameWork
    Commented Nov 11, 2022 at 10:56
  • \$\begingroup\$ What might be helpful is if you did a little reading on the Affinity Laws. In particular, the one that says that shaft power is proportional to the cube of the shaft speed. The shaft speed is proportional to line frequency, so reducing frequency by 20% (from 50Hz to 40Hz) likewise reduces shaft speed; the output shaft power is reduced by nearly 50% Maybe that's close enough for your purpose \$\endgroup\$
    – user28910
    Commented Nov 11, 2022 at 14:37
  • \$\begingroup\$ I cannot find any source/page about Affinity Laws that mentions "line frequency". I found one that that talks about frequency, but i suspect they are talking about the frequency of rotations and not line frequency (which is the confusion that happened with my post, i was talking about line, everyone thought i talked about rotational). Are you sure "shaft speed" is proportional to line frequency? I would like to confirm with with a source telling me this is so before i use this in anyway. \$\endgroup\$
    – CantFindGoverningFrameWork
    Commented Nov 15, 2022 at 10:45
  • \$\begingroup\$ Shaft speed is approx. proportional to line frequency. Assuming you have an induction motor, shaft rotational frequency is line frequency minus slip frequency, divided by the number of pole pairs. Slip varies with load, typically around 1% at rated load. For example, 50Hz line, 4 pole motor, 1% slip: shaft speed is 24.75 Hz, 1485 rpm \$\endgroup\$
    – user28910
    Commented Nov 15, 2022 at 15:50

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