The most crucial factor in calculating the maximum loading capacity (MW loading) of transmission lines is surge impedance loading (SIL). We must first comprehend the idea of surge and surge impedance (Zs) and its physical relevance before we can fully comprehend.

## Surge Impedance

Surge Impedance or characteristics impedance is the ratio of the voltage and current amplitudes of a single wave propagating along the line, i.e., a wave traveling in one direction in the absence of reflections in another direction. Surge impedance is the 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(Z_{0}) 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 pure resistance. Its value varies between **400Ω and 600Ω** in the case of overhead transmission lines and 40Ω and 60Ω in the case of underground cables.

**Calculation of Surge Impedance**

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

**line at the receiving end is open-circuited.**- l
**ine 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,

**Surge Impedance Loading**

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 by increasing the value of receiving end line voltage (V L-L ) or reducing surge impedance(Zo). SIL is the most common method adopted for increasing the power limit of heavily loaded long transmission lines. But increasing the value of receiving-end line voltage beyond its limit becomes non-practicable and not economical.

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

*where*

*z=line impedance*

*y=line admittance*

*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**

- If the line loading is equal to SIL,line has flat voltage profile.
- If the line loading is greater than SIL,line acts as inductor.
- If the line loading is less than SIL ,line acts as capacitor.

Read Also: short-transmission-lines

**How to improve surge impedance loading?**

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 methods to reduce surge impedance (Z_{0}) by using a series capacitor with the transmission lines or shunt capacitors with the transmission lines.

**Series capacitor**

By use of series capacitors (Z_{0}) and the phase shift (β) gets reduced due to the 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 (Z_{0}) 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/

**References**

- https://www.electrical-technology.com/2019/10/surge-impedance-loading.html
- https://www.electricalvolt.com/2022/04/what-is-surge-impedance-loading-definition-meaning/
- http://abhinavbhattarai.com.np/2020/09/02/what-is-loading-on-electric-circuit/
- https://www.notesforengineering.com/sequence-impedance-and-network-of-power-system-elements/