Surge impedance loading and significance

Surge impedance loading (SIL) is the power delivered by a transmission line to a purely resistive load equal to its surge impedance $Z_c$ (for a lossless line, $Z_c = \sqrt{L/C}$).

$$\text{SIL} = \frac{V_L^2}{Z_c}\ \text{(MW, with } V_L \text{ in kV line-to-line)}$$

Example: a 400 kV line with $Z_c \approx 400\ \Omega$ has SIL $= 400^2/400 = 400$ MW.

Physical meaning

At SIL, the reactive power produced by the line's shunt capacitance equals the reactive power absorbed by its series inductance:

$$\omega C V^2 = \omega L I^2 \;\Rightarrow\; \frac{V}{I} = \sqrt{\frac{L}{C}} = Z_c$$

So the line neither needs nor supplies reactive power. For a lossless line the voltage magnitude is the same all along the line (flat voltage profile) and only the phase angle changes.

Significance in power systems

1. Benchmark of loading: a line loaded at SIL has a flat voltage profile and unity power factor all along it.
2. Below SIL (light load): the line generates net reactive power, so the receiving-end voltage rises (Ferranti effect). Shunt reactors are needed.
3. Above SIL (heavy load): the line absorbs reactive power, so voltage falls along the line. Shunt capacitors or series compensation are needed.
4. Loadability: the practical loading of a line is expressed in multiples of SIL. Short lines can carry several times SIL (thermal limit), but long EHV lines are limited by voltage drop and stability to roughly 1–1.5 × SIL (about 1.3 × SIL for a 300 km line).
5. Raising transmission capacity: SIL increases with $V^2$ and with lower $Z_c$. This is why higher voltages, bundled conductors (which lower $L$ and raise $C$) and series capacitors are used.
6. Planning and compensation: comparing actual load with SIL tells engineers how much reactive compensation the line needs.