## How to Calculate motor KW given actual RPM , Voltage and Frequency

## How to Calculate motor KW given actual RPM , Voltage and Frequency

(OP)

Hi Guys,

I have set up a test rig in which I use a power supply to vary the Voltage and Frequency to a 3.73KW AC motor. I am also able to measure the shaft RPM using a tachometer. I just need to know of a way to calculate the power based on this info.

Background:

I just needed to get the response of my load over a wide range of speeds so I kept the input frequency constant at 30Hz (for no good reason really) and varied the voltage. Now I have a bunch of voltage, frequency and RPM readings and am having trouble finding motor power.

I tried to find motor torque and find power that way, based on this old eng-tips post i found but not very realistic answers :

"

Derive the torque from rated speed and rated HP.

Actually I believe the slip formula is a little oversimplified.

Rated slip is synchronous speed minus rated speed.

Example: 1800 RPM - 1750 RPM = 50 RPM slip.

(1800 RPM - Measured RPM)/Slip RPM = % HP loading.

Caveat. This depends on the nameplate value for motor speed being accurate. I have not used this method in the field and have no idea of the precision of the nameplate speed as reported by the manufacturer. A small error in reported speed will result in a large error in calculated HP."

I have set up a test rig in which I use a power supply to vary the Voltage and Frequency to a 3.73KW AC motor. I am also able to measure the shaft RPM using a tachometer. I just need to know of a way to calculate the power based on this info.

Background:

I just needed to get the response of my load over a wide range of speeds so I kept the input frequency constant at 30Hz (for no good reason really) and varied the voltage. Now I have a bunch of voltage, frequency and RPM readings and am having trouble finding motor power.

I tried to find motor torque and find power that way, based on this old eng-tips post i found but not very realistic answers :

"

Derive the torque from rated speed and rated HP.

Actually I believe the slip formula is a little oversimplified.

Rated slip is synchronous speed minus rated speed.

Example: 1800 RPM - 1750 RPM = 50 RPM slip.

(1800 RPM - Measured RPM)/Slip RPM = % HP loading.

Caveat. This depends on the nameplate value for motor speed being accurate. I have not used this method in the field and have no idea of the precision of the nameplate speed as reported by the manufacturer. A small error in reported speed will result in a large error in calculated HP."

## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

Power consumption really has nothing to do with RPM or frequency directly, Power is A * V * PF (* 1.732 for 3 phase). So if you just get a good meter that can read the PF, you're golden. A kW meter does that.

Now if you want to know the power delivered by motor, that's a slightly different situation. You will also need to know the efficiency of the motor, in fact the efficiency of the entire circuit (depending on how you are varying the frequency and where you measure the values). Motor delivered power then would be A * V * PF * eff (* 1.732 for 3 phase). Shaft power would also have to account for mechanical losses as well.

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## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

http://

If that link doesn't work, go to www.selinc.com and search for a paper titled Induction Motors Part 1 - Analysis.

You can get a rough approximation of motor kW input using the Steinmetz model if you compute the slip.

But if you need something closer than 10% or so, you'd be better off with a kW meter as Jeff suggested already.

David Castor

www.cvoes.com

## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

Sounds like you were varying voltage in attempt to vary speed? I imagine you didn't get a very wide speed range.

Regarding the slip method, on a rough basis slip is proportional to output power with full-load slip (determined by nameplate) corresdponding to full load output power (also from nameplate) and output power proportional to slip in between.

There are some caveats as you have mentioned and the calc will inevitably be rough in most real-world situations. As a rough approximation in the linear region of torque speed curve for small slips:

P ~ s*V^2 / Rrotor

We see there is voltage squared dependence which must be taken into account if V deviates from nameplate.

We can also see Rrotor plays a role, which suggests temperature plays a role. Exactly what temperature was assumed in nameplate conditions I don't know... was a source of previous discussion here:

http://www

Also nameplate RPM is not exact to begin with... NEMA has some spec about 5rpm... either accurate to within 5 rpm or rounded to nearest 5 rpm (I don't remember which... there is a factor of 2 difference in those two tolerances of course)

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## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

@electricpete, i was having trouble with the slip method , maybe because I just plugged in the formula. But now that I look at it- you say slip is proportional to power , but isn't it inversely proportional ? because maximum torque/power is developed at rated RPM and this is where we have minimum slip so aren't they inversely proportional ? I was going off their being proportional and was getting lower power for higher speeds. Shouldn't we have high slip at low speed and lower slip at higher speed .check the image i attached. And you're right about varying frequency giving finer resolution of speeds :) guess that's why they have VFDs not VVDs.

## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

http://f

## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

we have three variables: Slip, Power (output), and speed. Slip and power are proportional to each other. Speed varies in opposite direction of the first two (although I wouldn't say "inversely proportional").

We can have:

low output power , low slip, high speed

or

hi output power, high slip, low speed

"High" slip is high relative to other slips in the range of normal operation which would all be lower. These points would all be far to the right of the curve with s<0.1, speed > 90%.

I have attached graph which may help.

"because maximum torque/power is developed at rated RPM and this is where we have minimum slip"

This is the part that seemed tripping you up...I'm not sure why you say minimum slip corresponds to max torque/power.

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## RE: How to Calculate motor KW given actual RPM , Voltage and Frequency

Thank you electricpete.