Overhead lines
Surge impedance loading (SIL)
- where
- surge impedance loading (MW)
- rated line-to-line voltage (kV)
- surge impedance (Ω)
- line current at SIL (A)
Explain this equation
Gives the surge impedance loading: the real power a lossless line carries when terminated in its own surge impedance. At that load the line’s reactive generation in its capacitance exactly matches the reactive loss in its inductance.
V is the line-to-line voltage, so V²/Z_c is the three-phase power directly in MW when V is in kV and Z_c in ohms. The current at SIL is the phase voltage V/√3 divided by Z_c; the ×1000 converts kA to A.
At SIL the voltage and current along the line are in phase everywhere and the voltage profile is flat. Lighter loads leave surplus charging vars and voltage rises; heavier loads cause the line to absorb vars and voltage sags.
Sense check: 132 kV lines have SIL near 40–50 MW, 400 kV single-conductor lines about 400–550 MW. SIL rises with V², so doubling voltage gives four times the SIL.
Watch out: SIL is not a rating. Short lines are thermally limited far above SIL; long lines may be stability-limited below a small multiple of it.
Natural load at which a lossless line’s reactive generation and absorption balance, so the voltage profile is flat.
Enter your values to see the result.
Good to know
Below SIL a line generates reactive power (voltage tends to rise); above SIL it absorbs it. Typical SILs: 132 kV about 40–50 MW, 275 kV about 180–200 MW, 400 kV single conductor about 400 MW, quad-bundle up to about 600–700 MW. Long lines are often loaded to a multiple of SIL set by stability limits (St Clair curve).
Common mistake
Treating SIL as a thermal rating. It is a reactive-balance point; short lines routinely carry several times SIL.
Limits
Lossless line, balanced three-phase, voltage at rated value. Real lines have resistance, so the flat profile is only approximate.
Sources
- Glover, J.D., Overbye, T.J. & Sarma, M.S. Power System Analysis and Design (Cengage), chapters 4–5: transmission line parameters and steady-state operation
- Grainger, J.J. & Stevenson, W.D. Power System Analysis (McGraw-Hill), chapters 4–6: inductance, capacitance and current-voltage relations of a transmission line
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.