Power Transmitted using Area of X-Section (DC Three-Wire US) Calculator

Formula Used:

\[ P = \sqrt{\frac{A \times P_{line} \times V_m^2}{2 \times \rho \times l}} \]

Area of Underground DC Wire (A):

m²

Line Losses (P_line):

Maximum Voltage (V_m):

Resistivity (ρ):

Ω·m

Length of Wire DC (l):

Power Transmitted (P):

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1. What is the Power Transmitted Calculation?

The Power Transmitted calculation determines the amount of electrical power that can be efficiently transferred through an underground DC three-wire system, taking into account various physical and electrical parameters of the transmission line.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = \sqrt{\frac{A \times P_{line} \times V_m^2}{2 \times \rho \times l}} \]

Where:

\( P \) — Power Transmitted (W)
\( A \) — Area of underground DC wire (m²)
\( P_{line} \) — Line Losses (W)
\( V_m \) — Maximum Voltage (V)
\( \rho \) — Resistivity (Ω·m)
\( l \) — Length of Wire DC (m)

Explanation: This formula calculates the maximum power that can be transmitted through a DC three-wire underground system while accounting for line losses, wire characteristics, and system voltage.

3. Importance of Power Transmission Calculation

Details: Accurate power transmission calculation is crucial for designing efficient electrical distribution systems, minimizing energy losses, ensuring proper equipment sizing, and maintaining system reliability in underground DC three-wire installations.

4. Using the Calculator

Tips: Enter all values in appropriate units (area in m², line losses in W, maximum voltage in V, resistivity in Ω·m, and length in m). All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is this specific to DC three-wire systems?
A: This formula is specifically designed for underground DC three-wire systems, which have different characteristics and requirements compared to AC systems or overhead DC transmission.

Q2: What factors affect power transmission capacity?
A: Wire area, resistivity, system voltage, line length, and acceptable line losses all significantly impact the maximum power that can be transmitted.

Q3: How does wire area affect power transmission?
A: Larger wire areas reduce resistance, allowing for higher power transmission with lower line losses for the same voltage level.

Q4: What are typical resistivity values for underground cables?
A: Resistivity varies by material - copper is approximately 1.68×10⁻⁸ Ω·m, while aluminum is about 2.82×10⁻⁸ Ω·m at 20°C.

Q5: How do line losses affect system efficiency?
A: Higher line losses reduce overall system efficiency and generate heat, which must be managed in underground installations to prevent cable damage.