Surge impedance and Surge impedance loading (SIL) of Transmission line


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.

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.

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:

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.

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.

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:

  1. 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.

  1. 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.

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