1. What is the 3-Phase To 1-Phase Calculator?

Definition: This calculator computes the missing electrical parameter in a balanced system by converting values between three-phase and single-phase circuits using the formula \( \sqrt{3} \times I_3 \times V_3 = I_1 \times V_1 \).

Purpose: It is used in electrical engineering to relate currents and voltages between three-phase and single-phase systems, assuming a balanced three-phase setup.

2. How Does the Calculator Work?

The calculator uses the following formula:

Formula: \[ \sqrt{3} \times I_3 \times V_3 = I_1 \times V_1 \] Rearranged forms: \[ I_3 = \frac{I_1 \times V_1}{\sqrt{3} \times V_3}, \quad V_3 = \frac{I_1 \times V_1}{\sqrt{3} \times I_3}, \quad V_1 = \frac{\sqrt{3} \times I_3 \times V_3}{I_1}, \quad I_1 = \frac{\sqrt{3} \times I_3 \times V_3}{V_1} \] where:

• \( I_3 \): 3-phase current (A)
• \( V_3 \): 3-phase voltage (V)
• \( V_1 \): 1-phase voltage (V)
• \( I_1 \): 1-phase current (A)

Steps:

• Enter three of the four values: 3-phase current (A), 3-phase voltage (V), 1-phase voltage (V), 1-phase current (A). Leave the unknown field blank (step size 0.01).
• The calculator identifies the missing value and computes it using the appropriate formula.
• Results are displayed rounded to 4 decimal places, with validation for positive values and exactly three inputs.

3. Importance of 3-Phase To 1-Phase Calculation

Calculating these conversions is crucial for:

• Power System Design: Helps in designing and analyzing electrical systems that involve both three-phase and single-phase components.
• Load Balancing: Ensures proper distribution in balanced systems to prevent inefficiencies or damage.
• Engineering Applications: Used in transformers, motors, and other equipment interfacing between phase types.

4. Using the Calculator

Examples:

• Example 1: Calculate 1-phase current with 3-phase current 10 A, 3-phase voltage 400 V, 1-phase voltage 230 V:
  • Leave 1-Phase Current blank.
  • \( I_1 = \frac{\sqrt{3} \times 10 \times 400}{230} \approx 30.1300 \) A
  • Result: 1-Phase Current (\( I_1 \)) = 30.1300 A
• Example 2: Calculate 3-phase voltage with 3-phase current 10 A, 1-phase voltage 230 V, 1-phase current 30 A:
  • Leave 3-Phase Voltage blank.
  • \( V_3 = \frac{30 \times 230}{\sqrt{3} \times 10} \approx 398.3697 \) V
  • Result: 3-Phase Voltage (\( V_3 \)) = 398.3697 V

5. Frequently Asked Questions (FAQ)

Q: What assumptions does this calculator make?
A: It assumes a balanced three-phase system with equal voltages and currents across phases.

Q: Why is √3 used in the formula?
A: √3 accounts for the 120-degree phase difference in three-phase systems.

Q: Can this be used for unbalanced systems?
A: No, for unbalanced systems, more detailed analysis is required.

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