Power Formula For 3 Phase System

Three-phase AC Power Formula:

\[ P = \sqrt{3} \times V \times I \times \cos \phi \]

Power (P):

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1. What is the Three-Phase Power Formula?

The three-phase power formula calculates the real power in a balanced three-phase AC system. It is widely used in industrial and commercial electrical systems for accurate power measurement and system design.

2. How Does the Calculator Work?

The calculator uses the three-phase power formula:

\[ P = \sqrt{3} \times V \times I \times \cos \phi \]

Where:

\( P \) — Real power in watts (W)
\( V \) — Line-to-line voltage in volts (V)
\( I \) — Line current in amperes (A)
\( \cos \phi \) — Power factor (dimensionless, 0 to 1)
\( \sqrt{3} \) — Mathematical constant (approximately 1.732)

Explanation: The formula calculates the actual power consumed in a three-phase system, accounting for the phase relationship between voltage and current through the power factor.

3. Importance of Three-Phase Power Calculation

Details: Accurate three-phase power calculation is essential for electrical system design, load balancing, equipment sizing, energy management, and cost estimation in industrial and commercial applications.

4. Using the Calculator

Tips: Enter line-to-line voltage in volts, line current in amperes, and power factor (between 0 and 1). All values must be positive, with power factor between 0 and 1 inclusive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between line and phase voltage?
A: In three-phase systems, line voltage is measured between any two lines, while phase voltage is measured between a line and neutral. The formula uses line voltage.

Q2: Why is power factor important?
A: Power factor represents the efficiency of power usage. A lower power factor means more apparent power is required to deliver the same real power, leading to higher energy costs.

Q3: When should I use this formula?
A: Use this formula for balanced three-phase systems with sinusoidal waveforms. It's commonly used for motor loads, transformers, and industrial power distribution.

Q4: What are typical power factor values?
A: Power factor typically ranges from 0.7 to 1.0. Induction motors have 0.8-0.9 PF, while resistive loads have 1.0 PF. Poor power factor (below 0.9) may require correction.

Q5: Can this formula be used for unbalanced systems?
A: No, this formula is for balanced three-phase systems. For unbalanced systems, calculate power for each phase separately and sum the results.