Modelling 500 km as medium, 50 km as long

500 km line modelled as a medium line (nominal-Π or T)

• A 500 km line is a long line. Its parameters are distributed, and $\gamma l$ is large (about 0.5 rad at 50 Hz), so $\cosh\gamma l$ and $\sinh\gamma l$ are no longer close to $1 + ZY/2$ and $\gamma l$.
• The nominal model lumps all capacitance at one or two points. This gives errors in $A$, $B$, $C$ and hence in the sending-end voltage, current, power factor, regulation and losses. The error grows rapidly with length.
• The Ferranti rise at light load and the reactive power generated by the line are wrongly estimated, so the size of shunt reactors and the insulation level may be chosen wrongly.
• The results are therefore inaccurate and unsafe for design. The exact long-line model (or its equivalent-Π) must be used.

50 km line modelled by the long-line model

• The long-line equations are exact for any length, so the results will be correct.
• For 50 km, $\gamma l$ is very small, so $\cosh\gamma l \approx 1$, $Z_c\sinh\gamma l \approx Z$, $\sinh\gamma l/Z_c \approx Y \approx 0$. The answers become almost the same as the short-line model ($A = 1$, $B = Z$, $C = 0$).
• The only cost is unnecessary calculation with complex hyperbolic functions, for no practical gain.