Power Factor Correction, and its possible application to the hobby
> Power dissipated by a load is referred to as true power. True power is symbolized by the letter P and is measured in the unit of Watts (W).
> Power merely absorbed and returned in load due to its reactive properties is referred to as reactive power. Reactive power is symbolized by the letter Q and is measured in the unit of Volt-Amps-Reactive (VAR).
> Total power in an AC circuit, both dissipated and absorbed/returned is referred to as apparent power. Apparent power is symbolized by the letter S and is measured in the unit of Volt-Amps (VA).
> These three types of power are trigonometrically related to one another. In a right triangle, P = adjacent length, Q = opposite length, and S = hypotenuse length. The opposite angle is equal to the circuit's impedance (Z) phase angle.
http://searchcio-midmarket.techtarget.c ... 19,00.html
http://www.pcguide.com/ref/power/ext/basicsPower-c.html
http://en.wikipedia.org/wiki/Electric_power
S = I * E
where S is Apparent Power, I is Load current, and E is Load voltage
To determine the reactive power triangle quantity, we use the Pythagorean Theorem “backwards,” given the length of the hypotenuse (apparent power) and the length of the adjacent side (true power):
Q = sqr_root(S^2 - P^2)
The ratio between real power and apparent power in a circuit is called the power factor. Where the waveforms are purely sinusoidal, the power factor is the cosine of the phase angle (φ) between the current and voltage sinusoid waveforms. Equipment data sheets and nameplates often will abbreviate power factor as "cosφ" for this reason.
Power factor equals 1 when the voltage and current are in phase, and is zero when the current leads or lags the voltage by 90 degrees. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle, where leading indicates a negative sign.
http://en.wikipedia.org/wiki/Power_factor
Power Factor = P/S
where P is the true power, and S is the apparent power
Since P=V*I, and I=V/R, then P=V^2/R
P = V^2/R
... solving for the value R...
R = V^2/P
Given the Formula... w/x = y/z
then wz = xy and/or w = xy/z
To substitute real numbers... 1/2 = 2/4
then 1*4=2*2 and/or 1 = (2*2)/4
In Ohm's Law, R = V/I
then V(1) = IR
Note: In any real number/integer multiplied by 1 is the same as the number/integer given.
Capacitive Reactance Xc
http://en.wikipedia.org/wiki/Reactance
where f is the Line voltage frequency (in our case, it's 60Hz)
... Xc is the capacitive reactance in ohms,
... C is the capacitive value in Farads
I will replace the symbol in the formula with pie
Xc = 1/(2piefC)
... solving for the value C...
C = 1/(2piefXc)
Now, enough with the formula mumbo jumbo and proceed with an example. Shall we...
Here's a pic of the power meter output on my tank's return/transfer pump RIO2500 courtesy of the good gentleman Mr.
Obet Carlos (much appreciated brudah for stopping by at my place ).
From the reading, we can enumerate some variables for our mathematical formulas...
Power = 27.8 watts
Ampere Load = 0.251A
Input Voltage = 236.3V
Frequency = 60Hz
Total Power = volts * ampere
True Power = volts * ampere * power factor
By getting the Total Power value, the result would be 59.3VA
Power factor is True Power/Total Power, and the value is 0.469. Rounding off, the power factor of my tank's RIO2500
is 0.47. Not good, but it's typical.
Using the formula of the capacitive reactance Xc, to perform power factor correction, I would need a power/starting
capacitor with a value of 2.49 uF.
Here are the other reading we got...
Sunsun 6W
Sunsun 12W
RO Skimmer pump rated at 18w
2 x Osram 72w powering a single tube of 4ft T5-HO
2 x Osram 72w powering a pair of 2ft T5-ho tubes
Generic 55w powering a single 4ft T5HO
Ikhea 32w powering a single 2ft T5HO
Ikhea 22w powering a single 2ft T5HO
Cheers!