Editing Electric power transmission (section)

===Long line===
The long line model is used when a higher degree of accuracy is needed or when the line under consideration is more than {{cvt|250|km}} long. Series resistance and shunt conductance are considered to be distributed parameters, such that each differential length of the line has a corresponding differential series impedance and shunt admittance. The following result can be applied at any point along the transmission line, where <math>\gamma</math> is the [[propagation constant]].
:<math>
\begin{align}
A &= D = \cosh(\gamma x) \text{ per unit}\\[3mm]
B &= Z_c \sinh(\gamma x) \Omega\\[2mm]
C &= \frac{1}{Z_c} \sinh(\gamma x) S
\end{align}
</math>

To find the voltage and current at the end of the long line, <math>x</math> should be replaced with <math>l</math> (the line length) in all parameters of the transmission matrix. This model applies the [[Telegrapher's equations]].