#### The Sugar Engineers

# Electric Motor Absorbed Power Estimation - Fitting Curves

## Power Factor

The power factor data shown below:

fits a curve of the form:

pf = a - b · e^{c·log(1-x/100)}

where

- a, b, and c are constants
- and x is the percentage of rated power absorbed
- a = pf (when x=100%)
- a-b = pf (when x=0%)
- and c is found by trial and error

## Efficiency

The efficiency data shown below:

can be transformed to a straight line graph by plotting percentage load over efficiency against percentage load, a follows

It can be seen from the above graph that the value of the function at no load is missing; but can be calculated from

x/η = √3·V·I_{NL}·cosφ

Because this curve is a straight line it can be parametised by a simple linear regression routine.

So we now have functions for power factor and efficiency in terms of percentage motor load and we can use these in

P = η·√3·V·I·cosφ

to estimeate the absorbed power.

## Online Calculations

you can do the above calculations online web