Classification of lines by length and model validity

Transmission lines are classified by length because the effect of shunt capacitance (charging current) grows with length. The usual limits for 50 Hz lines are:

Why every line can use the long-line model

• The long-line model solves the line's differential equations exactly with distributed $r$, $L$, $C$ ($A = \cosh\gamma l$, $B = Z_c\sinh\gamma l$, $C = \sinh\gamma l/Z_c$). It makes no approximation, so it is valid for any length.
• For a short line, $\gamma l$ is small, so $\cosh\gamma l \approx 1$, $Z_c\sinh\gamma l \approx Z$ and $\sinh\gamma l/Z_c \approx 0$. The model reduces to the short-line result. For a medium line, $A \approx 1 + ZY/2$ and $B \approx Z$, which are the nominal-model values.
• So the result is always correct; only the calculation is longer.

Why the short-line model cannot be used for all lines

• It assumes $C = 0$, so the charging current and the reactive power generated by the line are ignored, and $I_S = I_R$.
• For medium and long lines the charging current is a large part of the line current. Ignoring it gives wrong sending-end voltage, current, power factor, regulation and efficiency.
• It cannot show the Ferranti effect (no-load $V_R > V_S$) or the variation of voltage and current along the line.
• So it is valid only where the charging current is negligible, that is, for short lines.