Length using Area of X-Section (1-Phase 2-Wire US) Calculator

Formula Used:

\[ Length of Underground AC Wire = \frac{Area of Underground AC Wire \times Line Losses \times (Maximum Voltage Underground AC \times \cos(Phase Difference))^2}{4 \times (Power Transmitted^2) \times Resistivity} \] \[ L = \frac{A \times P_{loss} \times (V_m \times \cos(\Phi))^2}{4 \times (P^2) \times \rho} \]

Area of Underground AC Wire:

m²

Line Losses:

Maximum Voltage Underground AC:

Phase Difference:

rad

Power Transmitted:

Resistivity:

Ω·m

Length of Underground AC Wire:

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1. What is Length using Area of X-Section (1-Phase 2-Wire US)?

This calculation determines the length of an underground AC wire in a 1-phase 2-wire US system based on the wire's cross-sectional area, line losses, maximum voltage, phase difference, transmitted power, and material resistivity.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{A \times P_{loss} \times (V_m \times \cos(\Phi))^2}{4 \times (P^2) \times \rho} \]

Where:

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

Explanation: The formula calculates wire length by considering the relationship between power transmission, voltage, losses, and material properties.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for proper cable installation, voltage drop estimation, and ensuring efficient power transmission in underground AC systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all parameters except phase difference which can be zero or positive. Use consistent units throughout.

5. Frequently Asked Questions (FAQ)

Q1: Why is phase difference important in this calculation?
A: Phase difference affects the power factor, which influences the actual power being transmitted and thus impacts the length calculation.

Q2: What are typical resistivity values for common conductor materials?
A: Copper: ~1.68×10⁻⁸ Ω·m, Aluminum: ~2.82×10⁻⁸ Ω·m. Values may vary based on material purity and temperature.

Q3: How does wire area affect the calculated length?
A: Larger cross-sectional areas generally allow for longer wire lengths while maintaining acceptable voltage drop and power loss levels.

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

Q5: Can this formula be used for overhead lines?
A: While the basic principles are similar, overhead lines have different considerations (temperature, sag, etc.) that may require adjustments to the formula.