Calculate the power factor correction

Content

To step
Warnings
Necessities

With the power factor correction you can calculate the apparent power, power, reactive power and the phase angle. Consider the equation of a right triangle. To calculate an angle you need to know the cosine, sine and tangent. You must also use the Pythagorean theorem (c² = a² + b²) to calculate the dimensions of the sides of the triangle. You also need to know which units each type of ability has. Apparent power is measured in Volt-Amps. Power is measured in Watts and reactive power is expressed in units of Volt-Amp Reactive (VAR). There are several equations to calculate these and all will be covered in this article. You now have the basis for what you are trying to calculate.

To step

Calculate the impedance. (Pretend impedance is in the same place as the apparent power in the image above). To determine the impedance, use the Pythagorean theorem, c² = √ (a² + b²).
Thus, the total impedance (shown as "Z") is equal to the power squared, plus the reactive power squared, after which you take the square root of the answer.
- (Z = √ (60² + 60²)). So if you enter that into your scientific calculator, you will get 84.85Ω as the answer. (Z = 84.85Ω).
Determine the phase angle. So now you have the hypotenuse, which is impedance. You also have an adjacent side, the ability, and you have the opposite side, the reactive ability. So to find the angle you can use one of the aforementioned formulas. For example, we use the tangent formula, or the opposite side divided by the adjacent (reactive / power).
- You then have an equation like: (60/60 = 1)
Take the inverse of the tangent for the phase angle. The inverse tangent is a button on your calculator. So now take the inverse tangent of the equation in the previous step and you get the phase angle. Your equation should look something like this: tan ‾ ¹ (1) = phase angle. your answer will then be 45 °.
Calculate the total current (Amps). The current is also shown as an "A" in the unit Ampere. The formula used to calculate the current is the voltage divided by the impedance, so this is: 120V / 84.85Ω. You now have an answer of about 1.141A. (120V / 84.84Ω = 1.141A).
You must now calculate the apparent power displayed as "S". You don't need to use the Pythagorean theorem to calculate apparent power, because your hypotenuse is considered your impedance. Remember that apparent power uses the unit Volt-Ampere: we can calculate apparent power using the formula: Voltage squared divided by total impedance. Your equation should look like this: 120V² / 84.85Ω. Now you should get an answer like: 169.71VA. (120² / 84.85 = 169.71).
You must now calculate the power displayed as "P". To calculate the power, you need the current as you did in step four. Power is in Watts and is calculated by multiplying the current squared (1,141²) by the resistance (60Ω) in your circuit. You should get an answer of 78.11 watts. The equation should look like this: 1.141² x 60 = 78.11.
Calculate the power or power factor! To calculate the power factor you need the following information: Watt and Volt-Ampere. You calculated this information in the previous steps. The power is equal to 78.11W and Volt-Ampere is 169.71VA. The power factor formula, also represented as Pf, is Watts divided by Volt-Amp. Your equation now looks like this: 78.11 / 169.71 = 0.460.
- This can also be expressed as a percentage, so multiply 0.460 by 100, which gives a power factor of 46%.

Warnings

When calculating impedance, you use the inverse tangent function and not just the regular tangent function on your calculator. Otherwise you will get an incorrect phase angle.
This was just a very simple example of calculating a phase angle and power factor. There are much more complicated circuits, including capacitance and higher resistances and apparent resistor.