## Surge Impedance

surge Impedance or characteristics impedance is the ratio of the amplitudes of voltage and current of a single wave propagating along the line i.e a wave travelling in one direction in the absence of reflections in other direction.surge impedance is the characteristics impedance of a loss-free line.The square root of the ratio of line impedance(Z) and shunt admittance(Y) is called the surge impedance(Z0) of the line. where Z=R+jX and y=G+jB

For a heavy copper and well insulated line the resistance(R) and leakage conductance(G) can be taken as Zero and thus which is a pure resistance.Its value varies between 400Ω and 600Ω in case of overhead transmission lines and 40Ω and 60Ω in case of underground cables.

The surge impedance can be calculated by measuring the line impedance at the sending end when

1.line at the receiving end is open circuited.

2.line at the receiving end is short circuited.

when the line is open circuited(IR) is zero and the sending end voltage (VS) and sending end current(IS) are given by:  similarly when the line is short circuited at the receiving end,the receiving end voltage(VR) reduces to zero and the sending end voltage(VS) and sending-end current(IS) are given by:  Now, substituting in equation (i) we get,  The loading when the receiving end of the transmission line is terminated by a resistive load equal to the surge impedance of the line is known as surge impedance loading(SIL).It is also defined as the load(of unity power factor) that can be delivered by the line of negligible resistance. ;it is also the natural power of the line.

where ,

VL-L=line to line voltage

Z0=characteristics impedance

This gives the limit of the maximum power that can be delivered by a line and is useful in the design of the transmission lines.the power transmitted through a long transmission line can be increased either by increasing the value of receiving end line voltage(V L-L ) or by reducing surge impedance(Zo).surge impedance loading is the most common method adopted for increasing the power limit of heavily loaded long transmission lines.But it becomes non practicable and no economical to increase the value of receiving-end line voltage beyond its limit.

The loading of the line is defined on the basis of SIL and increases with the increase in voltage. where

z=line impedance

r=resistance per unit length

l=inductance per unit length

g=conductance per unit length

c=capacitance per unit length

If the line is loss-less then,  For 132KV line,

single circuit,Zo=400Ω

Double circuit,Zo=200Ω

1. If the line loading is equal to SIL,line has flat voltage profile.
2. If the line loading is greater than SIL,line acts as inductor.
3. If the line loading is less than SIL ,line acts as capacitor. fig:voltage profile of a transmission line based on the values of SIL

The value of surge impedance(Z0) cannot be varied because the spacing between the conductors depends upon the line voltage which cannot be reduced much.But there are some other method to reduces surge impedance(Z0) by using a series capacitor with the transmission lines or shunt capacitors with the transmission lines.

series capacitor

By use of series capacitors surge impedance(Z0) and the phase shift(β) gets reduced due to decrease of the line inductance(L) .It improves the system stability limit.These capacitors are also helpful in reducing line drops and voltage variations.

shunt capacitors

By use of shunt capacitors surge impedance(Z0) is reduced  and the phase shift(β) is increased due to increase in the value of C.When synchronous machines are used ,loads stability conditions becomes worse.This method is used in case of long transmission lines where stability limits are present.