RMS Voltage using Line Losses (2-Phase 3-Wire US) Calculator

Formula Used:

\[ V_{rms} = \frac{P \times \sqrt{(2+\sqrt{2}) \times \rho \times L / (A \times P_{loss})}}{\cos(\Phi)} \]

Power Transmitted (P):

Resistivity (ρ):

Ω·m

Length of Underground AC Wire (L):

Area of Underground AC Wire (A):

m²

Line Losses (P_loss):

Phase Difference (Φ):

rad

Root Mean Square Voltage (V_rms):

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1. What is RMS Voltage using Line Losses (2-Phase 3-Wire US)?

The RMS Voltage using Line Losses calculation determines the root mean square voltage in a 2-phase 3-wire underground AC system by accounting for power transmitted, line losses, and various electrical properties of the transmission system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_{rms} = \frac{P \times \sqrt{(2+\sqrt{2}) \times \rho \times L / (A \times P_{loss})}}{\cos(\Phi)} \]

Where:

\( V_{rms} \) — Root Mean Square Voltage (V)
\( P \) — Power Transmitted (W)
\( \rho \) — Resistivity (Ω·m)
\( L \) — Length of Underground AC Wire (m)
\( A \) — Area of Underground AC Wire (m²)
\( P_{loss} \) — Line Losses (W)
\( \Phi \) — Phase Difference (rad)

Explanation: This formula calculates the RMS voltage by considering the power transmission efficiency, material properties, and phase characteristics of the electrical system.

3. Importance of RMS Voltage Calculation

Details: Accurate RMS voltage calculation is crucial for designing efficient power transmission systems, minimizing energy losses, and ensuring proper equipment operation in underground AC networks.

4. Using the Calculator

Tips: Enter all values in appropriate units. Power, resistivity, length, area, and losses must be positive values. Phase difference should be in radians between 0 and π/2 for typical applications.

5. Frequently Asked Questions (FAQ)

Q1: Why is RMS voltage important in power systems?
A: RMS voltage represents the equivalent DC voltage that would deliver the same power to a load, making it essential for power calculations and equipment ratings.

Q2: What factors affect line losses in underground systems?
A: Line losses are influenced by conductor material, cross-sectional area, length, current magnitude, and operating temperature.

Q3: How does phase difference affect voltage calculation?
A: Phase difference affects the power factor, which impacts the relationship between apparent power and real power in the system.

Q4: When is this calculation most applicable?
A: This calculation is specifically designed for 2-phase 3-wire underground AC power transmission systems.

Q5: What are typical resistivity values for common conductors?
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.