High-voltage transmission line parameter engine. Computes per-phase inductance (L), capacitance (C), inductive reactance (XL), capacitive susceptance (Bc), distributed surge impedance (Zc), Surge Impedance Loading (SIL in MW), Ferranti effect no-load voltage rise, and transmission transfer efficiency.
Governing Formulas & Standards
Standards Basis: IEEE Std 738 / IEC 60909 / CIGRE Green Book on Overhead Lines
L = 2 \times 10^{-7} \ln\left(\frac{GMD}{GMR}\right) \quad ; \quad C = \frac{2\pi \epsilon_0}{\ln(GMD/r_{eq})} \quad ; \quad SIL = \frac{V_{LL}^2}{Z_c}
Calculates series inductance L (H/m) and shunt capacitance C (F/m) from conductor geometric configuration, yielding characteristic surge impedance Z_c = √(L/C) (typically 350–400 Ω for unbundled and 250–300 Ω for bundled lines).
Worked Engineering Example: 400 kV 200 km Twin-Bundle Overhead Transmission Line
- Series Inductance & Reactance: L = 2×10⁻⁷ × ln(10.5 / 0.088) = 0.956 mH/km | X_L = 2π × 50 × 0.956×10⁻³ × 200 → X_L = 60.07 Ω (0.300 Ω/km)
- Shunt Capacitance & Susceptance: C = (2π × 8.854×10⁻¹²) / ln(10.5 / 0.095) = 11.82 nF/km | B_c = 2π × 50 × 11.82×10⁻⁹ × 200 → B_c = 7.427 × 10⁻⁴ S (3.71 μS/km)
- Surge Impedance (Zc): Z_c = √(L / C) = √(0.956×10⁻³ / 11.82×10⁻⁹) → 284.4 Ω
- Surge Impedance Loading (SIL): SIL = 400² / 284.4 → 562.6 MW
- No-Load Ferranti Voltage Rise: ΔV = 400 × (ω² L C l²) / 2 = 400 × (314.16² × 0.956×10⁻⁶ × 11.82×10⁻⁹ × 200²) / 2 → +8.9 kV (2.23% voltage rise at open-circuit)
Final Solution: Surge Impedance: 284.4 Ω | SIL: 562.6 MW | Charging Current: 171.5 A (118.8 MVAr total 3-phase)
Frequently Asked Questions
- What is the physical meaning of Surge Impedance Loading (SIL)?
- SIL is the load level at which the reactive power generated by line capacitance (V²ωC) exactly equals the reactive power absorbed by line inductance (I²ωL). At SIL, the voltage profile along the line is flat without requiring shunt reactors or capacitors.
- Why do long EHV lines experience the Ferranti effect at light load?
- At no-load or light load, line charging current travels through the line series inductance, creating a voltage boost that causes the receiving end voltage to exceed the sending end voltage.
Interactive calculation engine and real-time CAD solver available online at https://amithvijayan.in/tools/transmission-line-parameters.