You are about to calculate a power factor correction, which allows you to measure real, apparent, reactive and phase angle power. If you consider the equation of the right triangle, to calculate the angle you need to know the formulas of the cosine, the sine and the tangent. You will also need to know the Pythagorean theorem (c² = √ (a² + b²)) to calculate the length of the sides. You will then need to know the power units. The apparent one is measured in volts - amperes (VA). True power is measured in watts (W) and reactive power in reactive volt-amps (VAR). There are several equations for these calculations and will be discussed in the article. Now you have the basics to start calculating all powers.
Steps
Step 1. Calculate the impedance
Pretend that the impedance is in the same position as the apparent power in the previous photo. Hence, to find the impedance, it is necessary to use the Pythagorean theorem c² = √ (a² + b²).
Step 2. So, the total impedance (represented as "Z") is equal to the sum of the squares of the real power and the reactive power squared
Then consider the square root of the result.
(Z = √ (60² + 60²)). Entering the digits into a scientific calculator will result in 84.85Ω. (Z = 84, 85Ω)
Step 3. Find the phase angle
So now you have the hypotenuse which is the impedance. You also have the adjacent side which is the real power, and you have the opposite side which is the reactive power. Thus, to find the angle it is possible to use any law among those stated above. For example, we use the rule that the tangent is found by dividing the opposite side by the adjacent one (reactive / real).
You should have a similar equation: (60/60 = 1)
Step 4. Take the inverse of the tangent and calculate the phase angle
The arctangent corresponds to a button on your calculator. Thus, by calculating the inverse of the tangent of the equation in the previous step, you will have the phase angle. The equation should look like this: tan ‾ ¹ (1) = phase angle. So the result should be 45 °.
Step 5. Calculate the total current (amps)
The current is in amperes, represented with an A. The formula used to calculate the current is voltage divided by the impedance: 120V / 84, 85Ω, which is approximately 1, 141A. (120V / 84, 84Ω = 1, 141A).
Step 6. It is necessary to calculate the apparent power, which is represented by an S
To calculate the apparent power, it is not necessary to use the Pythagorean theorem, because the hypotenuse is the impedance. Recalling that apparent power is in the volt-ampere units, we can calculate the apparent power using the formula: voltage squared divided by the total impedance. The equation should look like this: 120V² / 84.85Ω. You should get 169.71 VA. (120² / 84.85 = 169.71)
Step 7. Now you need to calculate the real power, represented by P, after finding the current in step 4
The real power, in watts, is calculated by multiplying the square of the current (1.11²) by the resistance (60Ω) of the circuit. You should find 78.11 watts. The equation should be: 1, 141² x 60 = 78, 11.
Step 8. Calculate the power factor
To calculate the power factor, the following information is needed: watts and volt-amperes. You calculated this information in the previous steps. The watts are 78, 11 and the volt-amperes are 169, 71. The formula for the power factor, also represented as Pf, is the number of watts divided by the number of volt-amperes. You should have an equation similar to the following: 78, 11/169, 71 = 0, 460.
This value can also be expressed as a percentage, by multiplying 0, 460 by 100, which gives a power factor of 46%
Warnings
- When calculating impedance, the inverse tangent function must be used on the calculator and not the normal tangent function. The latter would give an incorrect phase angle.
- This is just a very simple example of how to calculate a phase angle and power factor. There are much more complicated circuits with higher capacitive power, resistances and reactance.
