Power
Factor Correction Capacitors
In this article we are going to develop an algorithm or method to find
out capacitors for power factor correction. This is the simplified
example that
we propose for this matter...

An inductive load (motor)
is connected in series to a 60 Hz
 220 VAC source and dissipates 5.4 kW with a power factor of 0.82. We
have to
calculate the capacitor that we have to connect in parallel to improve
the
factor to 0.96. 
This is a graphical
concept of what we’re trying to do for
this correction:
where
Vrms = 220 VAC
f = 60 Hz
PF = 0.82
P = 5.4 kW
Our task is to find the
capacitor C to get a corrected PF =
0.92.
We know that AC power
flow has three components: real or
active power P, measured in watts (W); apparent power S, measured in
voltamperes
(VA); and reactive power Q, measured in reactive voltamperes (var).
The
following righttriangle describes the relationship for those three
components.
If we add a capacitor in
parallel, the reactive power of the
system will change (decrease). The difference between the original
reactive
power Q_{1} and the resulting reactive power Q_{2}
(after placing the
capacitor) is called Qc. The final capacitor is a value depending on
the
reactive power Qc (in var), the frequency (in Hz) and the voltage at
the load
(Vrms). This diagram shows the idea and we present the formulas.
We can
develop a very simple code to find out how to correct the power factor
in the
system above. We only need a little bit of knowledge of basic
trigonometry...
clear all, clc
%
Known data: voltage source, frequency, starting power factor
%
and corrected (final) power factor
Vrms =
220
f = 60
P =
5.4e3
fp1 =
0.82
fp2 =
0.96
%
We calculate the initial angle, apparent and reactive powers
th1 =
acosd(fp1)
S1 =
P/fp1
Q1 = S1
* sind(th1)
%
We calculate the final angle, apparent and reactive powers
th2 =
acosd(fp2)
S2 =
P/fp2
Q2 = S2
* sind(th2)
%
We calculate the difference in reactive powers
Qc = Q1
 Q2
%
We express the capacitor in microfarads
C =
[num2str(Qc / (2*pi*f * Vrms^2)*1e6, 4) ' uF']
The results shown in the
command window are:
Vrms = 220
f = 60
P = 5400
fp1 = 0.8200
fp2 = 0.9600
th1 = 34.9152
S1 = 6.5854e+003
Q1 = 3.7692e+003
th2 = 16.2602
S2 = 5625
Q2 = 1.5750e+003
Qc = 2.1942e+003
C = 120.3 uF
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