Length Using Area Of X-Section (1-Phase 2-Wire Mid-Point Earthed) 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 The Length Using Area Of X-Section (1-Phase 2-Wire Mid-Point Earthed) Formula?

The Length Using Area Of X-Section formula calculates the maximum length of an underground AC wire for a 1-phase 2-wire mid-point earthed system, considering cross-sectional area, power losses, 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: This formula determines the maximum wire length that can be used while maintaining acceptable power loss levels, considering the electrical properties of the system.

3. Importance Of Length Calculation

Details: Accurate length calculation is crucial for designing efficient underground AC power distribution systems, minimizing energy losses, ensuring voltage stability, and optimizing material usage.

4. Using The Calculator

Tips: Enter all values in appropriate units. Area in square meters, losses in watts, voltage in volts, phase difference in radians, power in watts, and resistivity in ohm-meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is phase difference important in this calculation?
A: Phase difference affects the power factor, which significantly impacts the actual power delivered and the resulting voltage drop along the wire length.

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

Q3: How does wire area affect the maximum length?
A: Larger cross-sectional areas reduce resistance, allowing for longer wire lengths while maintaining acceptable power loss levels.

Q4: What are common line loss percentages in power systems?
A: Typical distribution systems aim for 3-5% total line losses, though this varies based on system design and regulatory requirements.

Q5: Does this formula account for temperature effects?
A: The basic formula uses resistivity at a specific temperature. For precise calculations, temperature-corrected resistivity values should be used.