Length Of Wire Using Area Of X-Section(3-Phase 3-Wire OS) Calculator

Formula Used:

\[ L = \frac{3 \times A \times (V_m)^2 \times P_{loss} \times (\cos(\Phi))^2}{2 \times \rho \times (P)^2} \]

Area Of Overhead AC Wire (A):

m²

Maximum Voltage Overhead AC (V_m):

Line Losses (P_loss):

Phase Difference (Φ):

rad

Resistivity (ρ):

Ω·m

Power Transmitted (P):

Length Of Overhead AC Wire (L):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Length Of Wire Using Area Of X-Section(3-Phase 3-Wire OS) Formula?

The Length Of Wire Using Area Of X-Section(3-Phase 3-Wire OS) formula calculates the total length of an overhead AC wire in a three-phase three-wire system based on its cross-sectional area, maximum voltage, line losses, phase difference, resistivity, and transmitted power.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ L = \frac{3 \times A \times (V_m)^2 \times P_{loss} \times (\cos(\Phi))^2}{2 \times \rho \times (P)^2} \]

Where:

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

Explanation: This formula accounts for the relationship between wire length and various electrical parameters in a three-phase three-wire overhead AC system.

3. Importance Of Length Calculation

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

4. Using The Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all parameters except phase difference which should be non-negative. Use consistent units throughout.

5. Frequently Asked Questions (FAQ)

Q1: Why is the cosine of phase difference squared in the formula?
A: The squared cosine term accounts for the power factor's effect on both real power transmission and line losses in the AC system.

Q2: What is the typical resistivity value for copper wires?
A: Copper has a resistivity of approximately 1.68×10⁻⁸ Ω·m at 20°C. Aluminum is about 2.82×10⁻⁸ Ω·m.

Q3: How does wire length affect system performance?
A: Longer wires generally result in higher resistance, increased voltage drop, and greater power losses for the same cross-sectional area.

Q4: Can this formula be used for DC systems?
A: No, this specific formula is designed for three-phase AC systems. DC systems use different formulas that don't include power factor considerations.

Q5: What are practical limitations of this calculation?
A: The calculation assumes uniform wire properties, constant temperature, and ideal conditions. Real-world factors like temperature variations, skin effect, and proximity effect may affect accuracy.