how to solve for value of power-factor correction capacitor?

Question

how can i solve the correct value of the power-factor correction capacitor placed across an AC line that has a total load of 16.5|_83degrees ohms and a line voltage of 220V 60Hz.

thanks in advance..

Answer 1

*Can you please go through the following links?
# http://www.ambercaps.com/lighting/power_factor_correction_concepts.htm
http://www.electrocube.com/support/bullet5.asp
http://ecmweb.com/mag/electric_primer_power_factor/
http://www.classictesla.com/download/pf_cap.pdf
Example:
A 3/4 HP electric motor has a power factor of .85. The nameplate current is 10 Amps at 115 Volts, or 1150 Volt Amps.

Apparent power = 1150 Volt Amps
Active power (P) = .85 * 1150 = 977.5 Watts
Reactive Power (Q) = sqrt(1150^2 - 977.5^2) = 605 VAR
So, we need about 600 var of power factor correction. I'm rounding to a couple digits, because, in reality, it's unlikely that the power factor is known to more accuracy, nor will any of the PFC components be that precise. (10% accuracy would be quite good for a capacitor). Now, assume we want to put the capacitor in parallel with the motor: Calculating the required impedance from Q = E^2/X, where Q is the reactive power needed:

600 = 115^2/X => X = 115^2/600 = 22 ohms (rounding to 2digits)
C = 1 /( 2 * pi * f *X) = 1/ (377 * 22) = 120 uF (again, rounding to 2 digits)
which is a fairly large capacitor in a constant duty environment (i.e. motor run, as opposed to motor start, where the capacitor is only in the circuit for a short time). You can calculate the RMS current through the capacitor either by dividing the VARs by the line voltage (600/115) or by dividing line voltage by reactance (115/22); both come out at around 5 1/4 Amps, so you'd want a capacitor rated at somewhat more current (e.g. 7-10 A). The capacitor's series resistance should be pretty low, or it will dissipate a fair amount of energy. If the dissipation factor were 1%, you'd be dissipating about 6 Watts in the capacitor.

One can also put the PFC capacitor in series with the load. In this case the capacitor would carry the entire load current of 10A, but, the required value is different. For a series compensation, you'd determine the series equivalent of the load (we used a parallel model, above). For the series model, you use currents, instead of voltages:

600 VAR = I^2 * X => 600 = 10*10 * X => X = 6 ohms


And converting an impedance to a capacitance: C=1/(377*6) = 440 uF.

So, not only would the capacitor be larger, but it would need to carry the entire load current. For this example, at least, parallel PFC seems to be a better approach. Only if the power factor were very poor, so the reactive impedance was quite large (and the corresponding capacitance low) would series compensation seem to be useful.

If the line voltage were higher, the correction impedance would be increased as the square of the line voltage. The capacitance would be reduced as the square of the line voltage. That is, if the same motor were run off 230 Volts, the capacitor would only need to be about 30 uF. And if we were to do power factor compensation at the distribution voltage of 4160 volts (for example), you would only need about .1 uF. This is why power factor correction is usually done in the distribution network at MV or HV, and not at the end voltage.

Answer 2

Power Factor Correction Capacitor Calculator

Answer 3

follow these simple steps to calculate the proper size of capacitor for power factor correction

How to Calculate the Suitable Capacitor Size in Farads & kVAR for Power factor Improvement (Easiest way ever)

http://www.electricaltechnology.org/2013/11/How-to-Calculate-Suitable-Capacitor-Size-for-Power-factor-Improvement.html

Answer 4

The current is 220/16.5< 83º lagging (suppose)=13.33<83 amp
To bring the power factor to 1 you have to add a current of
13.33*sin 83=13.23 amp leading 90º
so
C*2pi*60*220 =13.23
so C=159.5 micro farad in parallel with your load.

Answer 5

wait a few more hrs. I have to get my TI calculator to do the complex numbers. but wat u can do mean time is this if u have ur TI-89 or any other TI can do complex-phasor transformation.