Length Using Load Current (Single-Phase Three-Wire OS) Calculator

Formula Used:

\[ Length\ of\ Overhead\ AC\ Wire = \frac{Line\ Losses \times Area\ of\ Overhead\ AC\ Wire}{2 \times (Current\ Overhead\ AC)^2 \times Resistivity} \] \[ L = \frac{P_{loss} \times A}{2 \times I^2 \times \rho} \]

Line Losses (P_loss):

Watt

Area of Overhead AC Wire (A):

m²

Current Overhead AC (I):

Ampere

Resistivity (ρ):

Ω·m

Length of Overhead AC Wire:

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1. What is the Length Calculation Formula?

The Length Using Load Current formula calculates the length of overhead AC wire based on line losses, wire area, current, and material resistivity. This calculation is essential for power transmission system design and efficiency optimization.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{P_{loss} \times A}{2 \times I^2 \times \rho} \]

Where:

\( L \) — Length of Overhead AC Wire (meters)
\( P_{loss} \) — Line Losses (Watts)
\( A \) — Area of Overhead AC Wire (m²)
\( I \) — Current Overhead AC (Amperes)
\( \rho \) — Resistivity (Ω·m)

Explanation: The formula calculates wire length by considering the relationship between power losses, current flow, wire cross-sectional area, and material resistance properties.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for determining voltage drop, power loss estimation, and ensuring efficient power transmission in overhead AC systems.

4. Using the Calculator

Tips: Enter line losses in watts, wire area in square meters, current in amperes, and resistivity in ohm-meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is the factor 2 included in the denominator?
A: The factor 2 accounts for the two conductors in a single-phase three-wire system where both carry current and contribute to power losses.

Q2: What is typical resistivity for copper conductors?
A: Copper has a resistivity of approximately 1.68 × 10⁻⁸ Ω·m at 20°C, while aluminum is about 2.82 × 10⁻⁸ Ω·m.

Q3: How does temperature affect the calculation?
A: Resistivity increases with temperature, so calculations should use resistivity values at the expected operating temperature.

Q4: Can this formula be used for DC systems?
A: While similar principles apply, DC systems have different loss characteristics and may require modified formulas.

Q5: What are practical limitations of this calculation?
A: This calculation assumes uniform conductor properties and doesn't account for environmental factors, skin effect, or proximity effect in AC systems.