1. What is a Three-Phase Power Calculator?

Definition: This calculator computes the apparent power (kVA), active power (kW), and reactive power (kvar) for a balanced three-phase AC system based on line-to-line voltage, current, and power factor.

Purpose: It is used in electrical engineering to analyze power consumption, size equipment, and optimize energy efficiency in industrial and commercial applications.

2. How Does the Calculator Work?

The calculator uses the following formulas for a balanced three-phase system:

Where:

• \( S \) is the apparent power (kVA)
• \( P \) is the active power (kW)
• \( Q \) is the reactive power (kvar)
• \( V \) is the line-to-line voltage (volts)
• \( I \) is the line current (amps)
• \( \cos \phi \) is the power factor (0 to 1)
• \( \sin \phi \) is the sine of the phase angle

Steps:

• Enter the line-to-line voltage (\( V \)) and select a unit (V, kV, MV)
• Enter the current (\( I \)) and select a unit (mA, A, kA)
• Enter the power factor (\( \cos \phi \), between 0 and 1)
• Convert voltage and current to base units (volts and amps)
• Calculate apparent, active, and reactive power using the formulas

Display format:

• If the result 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 Three-Phase Power Calculation

Details: Accurate power calculations ensure proper sizing of transformers, generators, and cables, prevent overloads, and optimize energy efficiency in three-phase systems, which are common in industrial and commercial settings.

4. Using the Calculator

Tips: Input positive values for voltage and current. Use realistic power factor values (e.g., 0.8–0.95 for motors, 1 for resistive loads). Select appropriate units for voltage and current based on your system (e.g., kV for high-voltage systems, mA for small currents).

Example: Calculate power for \( V = 400 \, \text{V} \), \( I = 20 \, \text{A} \), \( \cos \phi = 0.85 \).

• Apparent Power: \( S = \sqrt{3} \cdot 400 \cdot 20 \cdot 10^{-3} = 13.85641 \, \text{kVA} \)
• Active Power: \( P = \sqrt{3} \cdot 400 \cdot 20 \cdot 0.85 \cdot 10^{-3} = 11.77875 \, \text{kW} \)
• Reactive Power: \( \sin \phi = \sqrt{1 - 0.85^2} = 0.52678 \), \( Q = \sqrt{3} \cdot 400 \cdot 20 \cdot 0.52678 \cdot 10^{-3} = 7.30104 \, \text{kvar} \)

5. Common Conversion Table

The following table provides quick reference power calculations for common voltage and current values (\( \cos \phi = 0.85 \)):

Voltage (V)	Current (A)	Apparent Power (kVA)	Active Power (kW)	Reactive Power (kvar)
400	10	6.92820	5.88897	3.65052
400	20	13.85641	11.77875	7.30104
480	15	12.47044	10.59988	6.57194
11,000	50	952.62794	809.73375	502.07476

Use this table for quick lookups or to verify calculator results.

6. Frequently Asked Questions (FAQ)

Q: What is the difference between apparent, active, and reactive power?
A: Apparent power (kVA) is the total power in the circuit, active power (kW) is the power consumed by the load, and reactive power (kvar) is the power stored and returned due to inductive or capacitive elements.

Q: Why is the power factor important?
A: The power factor indicates the efficiency of power usage. A lower power factor means more reactive power, increasing losses and requiring larger equipment.

Q: What voltage and current units should I use?
A: Use units appropriate for your system (e.g., kV for high-voltage grids, mA for small currents). The calculator converts them automatically to volts and amps.

Q: Does this calculator work for unbalanced systems?
A: No, this calculator assumes a balanced three-phase system where all phases have equal voltage, current, and power factor.

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