Power Factor Calculator

True Power (P):

Reactive Power (Q):

Apparent Power (S, VA): Phase Angle (φ, deg): Power Factor (PF):

1. What is a Power Factor Calculator?

Definition: This calculator computes the apparent power (\( S \)), phase angle (\( \phi \)), and power factor (PF) of an AC electrical system, using true power (\( P \)) and reactive power (\( Q \)).

Purpose: It is used in electrical engineering to analyze power efficiency, calculate total power, and determine the phase relationship between voltage and current.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\( S^2 = P^2 + Q^2 \)
\( \phi = \arctan\left(\frac{Q}{P}\right) \)
\( \text{PF} = \frac{P}{S} \)

Where:

\( S \) is the apparent power (Volt-Amperes, VA)
\( P \) is the true power (Watts, W)
\( Q \) is the reactive power (Volt-Amperes Reactive, VAR)
\( \phi \) is the phase angle (degrees, deg)
\( \text{PF} \) is the power factor (unitless, between 0 and 1)

Steps:

Enter the true power (\( P \)) and select a unit (mW, W, kW, MW, GW, BTU/hr)
Enter the reactive power (\( Q \)) and select a unit (mVAR, VAR, kVAR, MVAR, GVAR)
Convert true power to Watts and reactive power to VAR
Calculate the apparent power using \( S = \sqrt{P^2 + Q^2} \)
Calculate the phase angle using \( \phi = \arctan\left(\frac{Q}{P}\right) \), converted to degrees
Calculate the power factor using \( \text{PF} = \frac{P}{S} \)

Display format:

If a value is > 10000 or < 0.0001 (and not zero), use scientific notation (e.g., \( 1.23456e-3 \))
Otherwise, display with 5 decimal places

3. Importance of Power Factor Calculation

Details: Understanding power factor, apparent power, and phase angle helps optimize electrical systems, reduce energy losses, and improve efficiency. A low power factor indicates inefficient power usage, which can increase electricity costs.

4. Using the Calculator

Tips: Input a non-negative value for true power. Reactive power can be positive or negative, depending on whether the load is inductive or capacitive. The power factor will always be between 0 and 1.

Examples:

Example from Image: \( P = 100 \, \text{W} \), \( Q = 100 \, \text{VAR} \):
- \( S = \sqrt{100^2 + 100^2} = 141.42136 \, \text{VA} \)
- \( \phi = \arctan\left(\frac{100}{100}\right) \times \frac{180}{\pi} = 45.00000 \, \text{deg} \)
- \( \text{PF} = \frac{100}{141.42136} = 0.70711 \)
Industrial Load: \( P = 50 \, \text{kW} \), \( Q = 30 \, \text{kVAR} \):
- Convert: \( 50 \, \text{kW} = 50 \times 10^3 \, \text{W} \), \( 30 \, \text{kVAR} = 30 \times 10^3 \, \text{VAR} \)
- \( S = \sqrt{(50 \times 10^3)^2 + (30 \times 10^3)^2} = 58309.51845 \, \text{VA} \)
- \( \phi = \arctan\left(\frac{30 \times 10^3}{50 \times 10^3}\right) \times \frac{180}{\pi} = 30.96376 \, \text{deg} \)
- \( \text{PF} = \frac{50 \times 10^3}{58309.51845} = 0.85749 \)
Small Device: \( P = 500 \, \text{mW} \), \( Q = 300 \, \text{mVAR} \):
- Convert: \( 500 \, \text{mW} = 0.5 \, \text{W} \), \( 300 \, \text{mVAR} = 0.3 \, \text{VAR} \)
- \( S = \sqrt{0.5^2 + 0.3^2} = 0.58310 \, \text{VA} \)
- \( \phi = \arctan\left(\frac{0.3}{0.5}\right) \times \frac{180}{\pi} = 30.96376 \, \text{deg} \)
- \( \text{PF} = \frac{0.5}{0.58310} = 0.85749 \)

5. Frequently Asked Questions (FAQ)

Q: What is power factor?
A: Power factor is the ratio of true power to apparent power in an AC circuit, indicating how efficiently electrical power is converted into useful work.

Q: What does the phase angle represent?
A: The phase angle (\( \phi \)) is the angle between the voltage and current in an AC circuit, indicating the presence of reactive power.

Q: How can I improve power factor?
A: Power factor can be improved by adding capacitors (for inductive loads) or inductors (for capacitive loads) to reduce reactive power.

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