Power transfer limit vs SIL ratio and length

Surge impedance loading (SIL) is the power delivered when a lossless line is terminated in its surge impedance $Z_c = \sqrt{L/C}$:

$$SIL = \frac{V_L^2}{Z_c}\ \text{MW}$$

At SIL the reactive power generated by line capacitance equals that absorbed by inductance, so the voltage is flat along the line.

Dependency on surge impedance

• SIL $\propto 1/Z_c$. Lowering $Z_c$ (bundled conductors, compact phase spacing, shunt capacitance increase, series compensation) raises SIL and hence the power limit.
• Typical $Z_c$: about 400 Ω for single-conductor lines, 250–300 Ω for bundled EHV lines.

Dependency on length

• Max power $P = \frac{V_sV_r}{Z_c\sin\beta l}$ (lossless line). As length $l$ increases, $\sin\beta l$ increases, so power in multiples of SIL falls.
• Short lines (< 80 km) are limited by thermal rating (about 2.5–3 × SIL); medium lines (80–320 km) by voltage drop (about 1.5–2.5 × SIL); long lines (> 320 km) by stability (about 1 × SIL or less).

So power transfer limit $= \text{m.f.}(L) \times V^2/Z_c$: it increases with $V^2$, decreases with $Z_c$, and decreases with line length.