Maximum Voltage using Area of X-section (1 Phase 3 Wire US) Calculator

Maximum Voltage Underground AC Formula:

\[ V_m = \frac{2 \cdot P}{\cos(\Phi)} \cdot \sqrt{\frac{\rho \cdot L}{P_{loss} \cdot A}} \]

Power Transmitted (P):

Watt

Phase Difference (Φ):

rad

Resistivity (ρ):

Ω·m

Length of Underground AC Wire (L):

Line Losses (P_loss):

Watt

Area of Underground AC Wire (A):

m²

Maximum Voltage Underground AC (V_m):

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1. What is Maximum Voltage using Area of X-section?

Maximum Voltage Underground AC is defined as the peak amplitude of the AC voltage supplied to the line or wire in a 1-phase 3-wire underground system, calculated based on the cross-sectional area of the wire and other electrical parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_m = \frac{2 \cdot P}{\cos(\Phi)} \cdot \sqrt{\frac{\rho \cdot L}{P_{loss} \cdot A}} \]

Where:

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

Explanation: This formula calculates the maximum voltage in an underground AC system by considering power transmission, phase difference, material resistivity, wire length, power losses, and cross-sectional area.

3. Importance of Maximum Voltage Calculation

Details: Accurate maximum voltage calculation is crucial for proper system design, ensuring electrical safety, optimizing power transmission efficiency, and selecting appropriate insulation materials for underground cables.

4. Using the Calculator

Tips: Enter all values in appropriate units (power in watts, phase difference in radians, resistivity in Ω·m, length in meters, line losses in watts, and area in square meters). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is phase difference important in this calculation?
A: Phase difference affects the power factor, which influences the actual power delivered and the voltage requirements in AC systems.

Q2: How does wire area affect maximum voltage?
A: Larger wire area reduces resistance, which decreases power losses and allows for lower maximum voltage requirements for the same power transmission.

Q3: What is typical resistivity for copper vs aluminum wires?
A: Copper has resistivity of about 1.68×10⁻⁸ Ω·m, while aluminum has about 2.82×10⁻⁸ Ω·m at 20°C.

Q4: How do line losses affect system design?
A: Higher line losses require higher voltage to maintain the same power delivery, increasing system costs and complexity.

Q5: When should this calculation be used?
A: This calculation is essential when designing underground AC power distribution systems, particularly for 1-phase 3-wire configurations commonly used in residential and commercial applications.