Length of Line using Area of X-Section(Two-Wire One Conductor Earthed) Calculator

Formula Used:

\[ Length of Wire DC = \frac{Area of Overhead DC Wire \times (Maximum Voltage Overhead DC^2) \times Line Losses}{Resistivity \times (Power Transmitted^2) \times 2} \]

Area of Overhead DC Wire:

m²

Maximum Voltage Overhead DC:

Line Losses:

Resistivity:

Ω·m

Power Transmitted:

Length of Wire DC:

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1. What is the Length Calculation Formula?

The formula calculates the length of DC wire based on area, maximum voltage, line losses, resistivity, and transmitted power. It's specifically designed for two-wire one conductor earthed systems in overhead DC transmission.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ Length of Wire DC = \frac{Area of Overhead DC Wire \times (Maximum Voltage Overhead DC^2) \times Line Losses}{Resistivity \times (Power Transmitted^2) \times 2} \]

Where:

Area of Overhead DC Wire — Cross-sectional area of the wire (m²)
Maximum Voltage Overhead DC — Peak voltage of the DC supply (V)
Line Losses — Total power losses in the line (W)
Resistivity — Material's resistance property (Ω·m)
Power Transmitted — Power delivered at receiving end (W)

Explanation: This formula accounts for the relationship between wire dimensions, electrical properties, and power transmission characteristics to determine optimal wire length.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for efficient power transmission system design, minimizing losses, ensuring voltage stability, and optimizing material usage in overhead DC lines.

4. Using the Calculator

Tips: Enter all values in appropriate units (area in m², voltage in V, losses in W, resistivity in Ω·m, power in W). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is the formula specific to two-wire one conductor earthed systems?
A: This configuration has specific electrical characteristics that differ from other wiring systems, requiring specialized calculation methods.

Q2: What is the significance of the factor 2 in the denominator?
A: The factor 2 accounts for the return path in the two-wire system, where current flows through both conductors.

Q3: How does resistivity affect the wire length calculation?
A: Higher resistivity materials require shorter lengths to maintain the same power transmission efficiency, as they offer more resistance to current flow.

Q4: What are typical resistivity values for common conductor materials?
A: Copper: 1.68×10⁻⁸ Ω·m, Aluminum: 2.82×10⁻⁸ Ω·m, Silver: 1.59×10⁻⁸ Ω·m at 20°C.

Q5: How do line losses impact the maximum achievable length?
A: Higher acceptable line losses allow for longer wire lengths, but efficiency decreases. There's always a trade-off between length and transmission efficiency.