Surge
Impedance Loading (SIL) is the most important parameter for determining the maximum loading capacity (MW loading) of transmission lines. Before understanding
SIL in detail, at first we have to understand the concept of Surge and Surge impedance (Zs) and its physical
significance. So let’s discuss the topic in detail.
What is Surge Impedance (Zs)?
Surge impedance is nothing but the characteristic impedance (Zc) of the lossless transmission line. It is also known as the Natural impedance of the line.
As we all know that a long transmission line (length > 250 km) is represented by a distributed parameter model. In Distributed parameter model of the long transmission line, resistance (R), inductance (L), capacitance (C), and conductance (G) are uniformly
distributed over the whole length of the line (As shown in the below figure).
Let us assume that the line has shunt admittance (y) per unit length series impedance (z) per
unit length. Then the Characteristic impedance (Zc) of any lossless transmission line is defined as the square root of (z/y).
Where, z = R + jwL and y = G + jwC.
If we put the value of z and y in the definition of (Zc), then we found that Characteristic Impedance is a complex quantity. However, for lossless transmission line (R=0 and G= 0)
z = jwL and y = jwC.
Hence
according to the definition, Characteristic Impedance (Zc) is calculated as:
Characteristic Impedance (Zc) = square root
of (jwL/jwC).
On
simplifying it we got a result as:
Zs= Zc = square root of (L/C).
The above quantity has a dimension of resistance is known as the Surge impedance of the line. When a purely resistive load of value equal to surge impedance is connected at the
receiving end of the line, then the reactive power generated by the shunt capacitor will be completely absorbed by the series inductor of the
transmission line.
The value of Surge
impedance for overhead transmission line is around 400 ohm, whereas surge
impedance value for underground cable is around 40 ohm.
Significance of Surge impedance
The significance of surge impedance is that if a pure resistance load that is equal to the surge impedance is connected to the end of the line with no resistance, a voltage surge introduced by the shunt capacitor to the sending end of the line would be completely absorbed by the series inductance at the receiving end of the transmission line.
In this case, the voltage at receiving end would have the same magnitude as the sending end voltage and also have a phase angle lagging with respect to sending end by an amount equal to the time required to travel across the line from sending end to receiving end.
Surge impedance (Zs) is a technical term that is used mostly in
electrical science in connection with the Surges
on transmission lines which may appear due to switching or lightning operation in our Electrical power system.
What happens if the line terminates in surge impedance?
If a
lossless transmission line terminates in its surge impedance (i.e. if the load is a pure resistance of value equal to the characteristic impedance of the line), then that transmission line is known as the infinite line or flat
line.
So, in that case, many interesting phenomena
happen in such a line:
- There will not be any
reflection of forwarding traveling waves and hence there will be no
standing wave in the line. Therefore, the voltage will be the same
throughout the line. Hence in this case, receiving end and sending end voltage
will be the same.
- The line will compensate
itself. That is, the reactive power demanded by the series inductance of the
line will be supplied by the shunt capacitance. That's why there will be no
voltage drop (due to series inductance) and also no voltage boost (due to shunt
capacitance).
- The load, as seen by the
generator, is a pure resistance that will be equal to characteristic impedance.
Hence the line is observed as equivalent to a pair of wires with zero
resistance.
Now
coming to our main topic Surge impedance loading (SIL) and its significance.
What is Surge impedance loading (SIL)?
In our
power system there are some limitations of loading on the transmission line
network. Generally, loading of any transmission line depends on some factors
like:
- Thermal
limitation (I2R Limitation)
- Voltage regulation
- Stability limitation
So in context to these limitations Surge impedance loading (SIL) is an important parameter in electrical science to predict the maximum
loading capacity of any transmission line. It is the maximum MW loading of the transmission line at which reactive power balance occurs. [ ##eye## Fundamentals of LVDT]
SIL is defined as the maximum load (at unity power factor) that can be delivered by the transmission line when the loads terminate with a value
equal to surge impedance (Zs) of the line. Simply if any line terminates with surge
impedance then the corresponding loading in MW is known as Surge Impedance
Loading (SIL). In other words we can define surge impedance loading (SIL) as: SIL is the maximum load connected in transmission line for which total reactive power generated (Capacitive VAR) is equal to total reactive power consumed (Inductive VAR). So that to maintain an exact balance of reactive power consumption (by series inductance of line) and generation (by shunt capacitance of line). That's why the net flow of reactive power in transmission line will be zero and hence transmission line is assumed to be loaded as purely resistive load.
SI unit of surge impedance loading (SIL) is Mega-Watt (MW).
Mathematically SIL is expressed as:
SIL (in
MW) = (Square of line voltage in kV)/(Surge impedance in ohm)
Hence the formula for SIL will be:
The
above expression gives the maximum power limit that can be delivered by any
transmission line which is very useful in designing the transmission line. SIL
can be used for the comparison of loads that can be transmitted through the overhead
transmission lines at different line voltages.
Calculation of Surge impedance loading
(SIL)
As we
know that long transmission lines (length > 250 km) are represented by the distributed parameter model. In this model, the capacitance and inductance are
distributed uniformly along the line. When the line is charged then the shunt
capacitance generates reactive power and feeds to the line while the series
inductance absorbed the reactive power. Hence voltage drop occurs in line due
to series, inductance is compensated by the shunt capacitance of the line.
If we
take a balance of reactive powers due to inductance and capacitance then we got
an expression as:
On
simplifying we got as:
Here
the quantity having a dimension of resistance is surge impedance denoted by the
symbol Zs. It is considered as a purely resistive load which when connected at
the receiving end of the transmission line, then the reactive power generated by
shunt capacitance will be completely absorbed by the series inductance of the line.
Now the exact value of SIL can be calculated by putting the surge impedance (Zs) value in
the above mathematical formula of SIL is expressed as:
SIL (in MW) = (Square of line voltage in
kV)/(Surge impedance in ohm)
Effect of
Surge impedance loading (SIL)
From the above expression of SIL we observed that SIL
depends on the line voltage at the receiving end.
Normally a line is loaded above SIL
for better utilization of the conductor. In other words, we can say that SIL should always be less than the maximum loading capacity of the line.
Have a Look: [ ##eye## Electrical Bonding]
When the line is loaded less than its SIL, then it acts
like a shunt capacitor which means it will supply MVAR to the system. In this
case, receiving end voltage will be greater than sending end voltage. In such a case line has to be compensated with an inductor to bring down the voltage at a normal level.
However when the line is loaded above its SIL, then it acts like a shunt reactor that will absorb MVAR from the system. In such a case
a voltage drop occurs in the line, due to this receiving end voltage will be
smaller than sending end voltage. Hence a compensator is required to maintain
voltage level.
The below figure contains a graphic of the effect of SIL. For a particular line of
SIL value 450 MW. So if the line is loaded to 450 MW, then MVAR produced by the line will exactly balance the MVAR absorbed by the line. Hence
there will no flow of reactive power in the line.
Also when we observed line voltage vs length curve of transmission line ( as shown in below figure), we concluded different voltage profile for loading the line in different conditions.
- If the loading is equal to SIL, then voltage profile of the line is Flat.
- If the loading is greater than SIL, then the line has inductive nature.
- If the loading is less than SIL, then the line has capacitive nature.
How to
improve surge impedance loading?
From
the above expression of SIL, we observe that the transmitted Electrical power
through a transmission line can be either increased by increasing the value of
the receiving end line voltage (VLL) or by reducing the value of
surge impedance (Zs). Since Voltage transmission capability is
increasing day by day. So the most commonly adopted method for increasing the
power limit of the heavily loaded transmission line is by increasing the
voltage level. But there is a limit beyond which it is neither economical nor
practical to increase the receiving end line voltage of the power network.
Other option
is by reducing the value of surge impedance (Zs) or charestristics impedance of transmission line, we can easily improve its surge impedance loading (SIL).
Since surge impedance is directly
proportional to inductance and inversely proportional to the capacitance. Hence the
value of surge impedance can be reduced either by increasing capacitor (C) of
line or by decreasing inductance (L) of line. But the inductance of the line cannot reduce
easily.
[ ##eye## Construction and Working of RVDT]
Further the capacitance value can be increased in two ways either by using series capacitor or by using shunt capacitor. Hence there are two methods to improve surge impedance loading of transmission line:
- Using series capacitor: By the
use of series capacitor surge impedance and also phase shift gets reduced due
to a decrease in inductance value (L). It also improves system stability. This
capacitor also helps in reducing the line voltage drop. But the main problem in
this method is It causes difficulty under the short circuit condition as a series
capacitor will get damaged.
- Using shunt capacitor: Also by the use of a shunt capacitor surge
impedance is reduced but the phase shift of the system increases. This affects the
poor stability of the system especially when the synchronous machines are
present in the load. So this method is not feasible where the stability limit
is the main concern in the power system.
Hence surge impedance loading of line is increased by using either series capacitor or shunt capacitor in transmission line. But practically series capacitor is more feasible and effective method for improving SIL of line.
I hope you understand the concept in simple and easy way. Still If you have any doubt then please ask it in a comment.
Thanks....
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Very good ...
ReplyDelete😄😄
ReplyDeleteBest Explaination so far
ReplyDeletea thyrister lA has a characterise R1 0.72 =7200 what is ratio of voltage appearing at the end of the line having a surge impedance of 500 ohm due to a 500 kv surge when 1) the line is open circuited 2) the line is terminated by arrester 3) the value of R omh
ReplyDeleteNicely explained...
ReplyDeleteWhat is surge impedance value for transmission line
ReplyDeleteWhat is surge impedance value for cable
ReplyDeleteSurge impedance value for cable is around 40-50 ohm
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