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. The following brief article
will explain the concept of SIL.

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. 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 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 concept of a surge impedance is more readily applied to
telecommunication systems than to power systems. However,
we can extend the concept to the power transferred across a
transmission line. The surge impedance loading or SIL (in
MW) is equal to the voltage squared (in kV) divided by the
surge impedance (in ohms). In equation form:

Note in this formula that the SIL is dependent only on the
kV the line is energized at and the line's surge impedance.
The line length is not a factor in the SIL or surge
impedance calculations. Therefore the SIL is not a measure
of a transmission line's power transfer capability as it
does not take into account the line's length nor does it
consider the strength of the local power system.

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.

Figure 1 is a graphic illustration of the concept of SIL.
This particular line has a SIL of 450 MW. Therefore is the
line is loaded to 450 MW (with no Mvar) flow, the Mvar
produced by the line will exactly balance the Mvar used by
the line.

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