Transmission Line Models

L and C depend on conductor spacing and height, so geometry is a design variable. Bundled conductors exist mostly to reduce L and to control the surface field.

The boundaries are conventions. What changes is how wrong the simpler model is, and what drives it is the charging current — which at 400 kV is substantial even with nothing connected at the far end.

Under load the receiving-end voltage falls, and because X ≫ R on a transmission line the drop is mostly I·X. That is why reactive power controls voltage while real power controls frequency — the two are almost decoupled.

On a lightly loaded long line the opposite happens. The charging current is capacitive, so it leads, and its drop across the line's inductance adds to the sending voltage. A 400 km line can arrive 10% high with nothing connected — the Ferranti effect — which is why shunt reactors are switched in at light load.

At SIL, reactive power absorbed by the series inductance exactly equals that generated by the shunt capacitance, so the voltage profile is flat end to end. SIL = V²/Z_s with Z_s = √(L/C) ≈ 400 Ω for an overhead line.

Below SIL the line is a net source of reactive power; above it, a net sink. It is the natural operating point, and how far a line sits from it determines what reactive compensation it needs.

When the field at a conductor's surface exceeds roughly 30 kV/cm the air ionises — corona — wasting power, generating radio interference and audible hiss, and worsening in rain. Since surface gradient falls with radius, EHV conductors are made far larger than the current requires, or bundled.

An insulator string has the analogous problem. Stray capacitance to the earthed tower makes the disc nearest the conductor carry the largest share of voltage, so it fails first and string efficiency falls as discs are added. A grading ring adds capacitance to the line conductor and equalises the distribution.

A long line is almost never thermally limited — it runs out of stability margin first. Since P ≈ (V₁V₂/X)·sin δ, series capacitors that cancel part of X raise the transfer limit without new conductors.