Length Using Line Losses (2-Phase 3-Wire US) Calculator

Formula Used:

\[ Length of Underground AC Wire = \frac{Line Losses \times Area of Underground AC Wire \times (Maximum Voltage Underground AC \times \cos(Phase Difference))^2}{(2+\sqrt{2}) \times (Power Transmitted^2) \times Resistivity} \]

Line Losses:

Watt

Area of Underground AC Wire:

m²

Maximum Voltage Underground AC:

Volt

Phase Difference:

Radian

Power Transmitted:

Watt

Resistivity:

Ω·m

Length of Underground AC Wire:

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1. What is the Length Using Line Losses Formula?

The Length Using Line Losses formula calculates the length of underground AC wire in a 2-Phase 3-Wire US system based on line losses, wire area, maximum voltage, phase difference, power transmitted, and resistivity. This calculation helps in designing efficient electrical distribution systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{P_{loss} \times A \times (V_m \times \cos(\Phi))^2}{(2+\sqrt{2}) \times (P^2) \times \rho} \]

Where:

\( L \) — Length of Underground AC Wire (m)
\( P_{loss} \) — Line Losses (W)
\( A \) — Area of Underground AC Wire (m²)
\( V_m \) — Maximum Voltage Underground AC (V)
\( \Phi \) — Phase Difference (rad)
\( P \) — Power Transmitted (W)
\( \rho \) — Resistivity (Ω·m)

Explanation: The formula accounts for electrical properties and losses to determine the optimal wire length for efficient power transmission.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for minimizing power losses, ensuring voltage stability, and designing cost-effective electrical distribution systems with proper wire sizing.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all parameters. Phase difference should be in radians (0 to 2π).

5. Frequently Asked Questions (FAQ)

Q1: Why is the (2+√2) factor used in the denominator?
A: This factor accounts for the specific configuration of a 2-Phase 3-Wire US system in the power loss calculation.

Q2: What is typical resistivity for copper wires?
A: Copper has resistivity of approximately 1.68×10⁻⁸ Ω·m at 20°C, though this varies with temperature and purity.

Q3: How does phase difference affect the calculation?
A: Phase difference affects the power factor (cosΦ), which influences the effective power transmission and consequently the length calculation.

Q4: What are acceptable line losses for electrical systems?
A: Typically, line losses should be kept below 5% of total power transmitted for efficient systems, though this varies by application.

Q5: Can this formula be used for overhead lines?
A: This specific formula is designed for underground AC wire systems. Overhead lines may require different calculations due to varying environmental factors.