The surge impedance loading or SIL of a transmission line is the
MW loading of a transmission line at which a natural reactive power balance
occurs.
Transmission lines produce reactive power (Mvar) due to their
natural capacitance. The amount of Mvar produced is dependent on the
transmission line's capacitive reactance (XC) and the voltage (kV) at which the
line is energized. In equation form the Mvar produced is:
Transmission lines also utilize reactive power to support their
magnetic fields (inductive). The magnetic field strength is dependent on
the magnitude of the current flow in the line and the line's natural inductive
reactance (XL). It follows then that the amount of Mvar used by a
transmission line is a function of the current flow and inductive reactance.
In equation form the Mvar used by a transmission line is:
A transmission line's surge impedance loading or SIL is simply
the MW loading (at a unity power factor) at which the line's Mvar usage is
equal to the line's Mvar production. In equation form we can state that
the SIL occurs when:
If we take the square root of both sides of the above equation
and then substitute in the formulas for XL (=2pfL) and XC (=1/2pfC) we arrive
at:
The term 
in
the above equation is by definition the "surge impedance. The
theoretical
in
the above equation is by definition the "surge impedance. The
theoretical
significance of the surge impedance is that if a purely resistive
load that is equal to the surge impedance were connected to the end of a
transmission line with no resistance, a voltage surge introduced to the sending
end of the line would be absorbed completely at the receiving end. The
voltage at the receiving end would have the same magnitude as the sending end
voltage and would have a phase angle that is lagging with respect to the
sending end by an amount equal to the time required to travel across the line
from sending to receiving end.
The value of the SIL to a system operator is realizing that when
a line is loaded above its SIL it acts like a shunt reactor - absorbing Mvar
from the system - and when a line is loaded below its SIL it acts like a shunt
capacitor - supplying Mvar to the system.