Surge impedance loading or the natural loading of the line is defined as the load that can be delivered by a line having no resistance (loss-less line). Where the loading is driven at unity power factor.
Where V_{RL} is receiving end line to line voltage in kV
Z_{0} is the surge impedance of the line.
Hence SIL or surge impedance loading is the power delivered by the line when the line is terminated by the surge impedance (Z_{0}) or characteristics impedance (Z_{C}) of the line.
The expression of SIL gives the maximum power that can be delivered by a line. This expression is useful in designing transmission lines.
Table of Contents
Surge Impedance (Z_{0})
Surge impedance of the line is the square root of the ratio of line impedance (Z) and shunt admittance (Y).
Where, Z = R + jX and Y= G + jB
[R= resistance, X= reactance, G= conductance, B= susceptance]Surge impedance is the characteristics impedance of the loss-free or loss-less line.
A lossless line is a line that has no or negligible resistance (R) and conductance (C).
For a heavy copper conductor which has negligible R and C, the surge impedance is given by
Z_{0} is a pure resistance. Its value varies between 400 Ω and 600 Ω for overhead transmission lines. For underground cables, its value lies between 40 Ω and 60 Ω.
Surge Impedance Loading of Transmission Line
For a long transmission line, the performance parameters can be written in terms of ABCD constants as
Where V_{S} and I_{S} are sending end voltage and current respectively. V_{R} and I_{R} are receiving end voltage and current respectively.
γ is the propagation constant. The propagation constant determines the behavior of an electromagnetic wave in the transmission line.
α is the attenuation constant. α causes signal amplitude to decrease along the line.
β is phase constant. β determines sinusoidal amplitude per phase of the signal along the line.
For loss-less line α=0 i.e. no attenuation of the signal takes place.
Consider a transmission line of length ‘ l’ terminated with surge or characteristics impedance (Z_{0}). ‘x’ is the distance from the receiving end side of the line i.e. for receiving end x=0 and for sending end x=l.
From relation (i)
I(x) is current at x distance away from receiving end.
V_{R} and I_{R} are the voltage and current at the receiving ends respectively.
Here for the line terminated by Z_{0}. Receiving end current is
So,
Hence, when a line is terminated by Z_{0} voltage along the line is constant.
The expression of current is
Complex power flowing at any point in the line is given by
The above expression is the expression of surge impedance loading (SIL). This shows that real power flow in the line terminated by surge impedance is constant and reactive power flow is zero.
Is reactive power flow actually zero during surge impedance loading?
During surge impedance loading of the line whatever reactive power losses take place in the series reactance of the line. This reactive power is compensated or produced by the shunt capacitance of the line and net reactive power flow in the line is zero.
The table below shows surge impedance and SIL for various voltage levels.
Vrated (kV) |
Z0 (Ω) |
SIL = (Vrated)^{2} / Z_{0 (MW) } |
230 |
380 |
140 |
345 |
285 |
420 |
500 |
250 |
1000 |
765 | 257 |
2280 |
The voltage versus length curve shows the voltage profile for loading the line in different conditions.
- If the line loading is equal to SIL. The voltage profile of the line is flat.
- If the line loading is greater than SIL. The line has inductive nature.
- If the line loading is less than SIL. The line has capacitive nature.
Reducing Surge Impedance of Line
The maximum power transfer capacity of the line or SIL can be increased by decreasing the surge impedance of the line. The surge impedance of the line cannot be reduced as much by varying the spacing of the conductors. As the spacing between the conductors is mainly governed by the system voltage. But there are some other methods to reduce the surge impedance (Z_{0}) of the line as stated below.
Using Series Capacitor
For a lossless line propagation, the constant is
The use of a series capacitor reduces the inductance (L) of the line thereby reducing the phase constant (β). The use of a series capacitor increases the system stability limit. But during short circuit conditions, it causes difficulties. The capacitor also helps in reducing line voltage drops and voltage variations.
Using Shunt Capacitor
The surge impedance of the line is
By using a shunt capacitor the surge impedance Z_{0} is reduced furthermore as the value of C increases the phase constants β also increase. The use of synchronous machines causes the load stability to worsen (get bad). Hence, on long transmission lines where stability limits are present, this method cannot be used.
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