Karkirina Bîrakîna Zêdetin an SIL

Surge Impedance Loading dikeçarên nîşanên elektrîk serbest bûyê yên hewce bike ştandîn ku li ser kêmûn û kapasîtayê de dibe. Lekin pêşî SIL bikin têne, yekem êdibina xwe ya Surge Impedance (Zs) bixebitînin. Di navbera du rêzikane de din bide.
Rêzik 1
Yek dikareya bilind e ku hêzên derxistinê zor (> 250 km) inductance û kapasîtayê ji alîkar biyînin. Kema hêza bîne, kapasîtayê reaktiv powerê bihêvîne û inductance reaktiv powerê jê bikerde. Eger hevgirtina du reaktiv poweran bikin, ew heqeqa berdest bûyê:

Lê,
V = Tensiona faseyê
I = Currenta hêzê
Xc = Capacitive reactance per phase
XL = Inductive reactance per phase
Bikin hesabkirin

Lê,
f = Frekanca sistemê
L = Inductance per unit length of the line
l = Length of the line
Nîsanîna ku hewce bûyê,

Vê qadere bi dimensiona resistance e Surge Impedance e. Dibe te dîtin ku loada resistance ya pir hemî reaktiv powerê ya kapasîtayê ji inductanceyê ve digire. Hewce bûyê Zc ya lossless line e.

Rêzik 2
Ji bo hilêvekirina rigorî ya hêzên derxistinê zor, ew heqeqa bûyê ji bo voltage û current da ku heta her dema x ji alîkar bûyê

Lê,
Vx and Ix = Voltage and Current at point x
VR and IR = Voltage and Current at receiving end
Zc = Characteristic Impedance
δ = Propagation Constant

Z = Series impedance per unit length per phase
Y = Shunt admittance per unit length per phase
Value of δ in above equation of voltage we get

Lê,

We observe that the instantaneous voltage consists of two terms each of which is a function of time and distance. Thus they represent two travelling waves. The first one is the positive exponential part representing a wave travelling towards receiving end and is hence called the incident wave. While the other part with negative exponential represents the reflected wave. At any point along the line, the voltage is the sum of both the waves. The same is true for current waves also.
Now, if suppose the load impedance (ZL) is chosen such that ZL = Zc, and we know

Thus

and hence the reflected wave vanishes. Such a line is termed as infinite line. It appears to the source that the line has no end because it receives no reflected wave.
Hence, such an impedance which renders the line as infinite line is known as surge impedance.It has a value of about 400 ohms and phase angle varying from 0 to –15 degree for overhead lines and around 40 ohms for underground cables.

The term surge impedance is however used in connection with surges on the transmission line which may be due to lightning or switching, where the line losses can be neglected such that

Now that we have understood Surge Impedance, we can easily define Surge Impedance Loading.
SIL is defined as the power delivered by a line to a purely resistive load equal in value to the surge impedance of that line. Hence we can write

The unit of SIL is Watt or MW.
When the line is terminated by surge impedance the receiving end voltage is equal to the sending end voltage and this case is called flat voltage profile. The following figure shows the voltage profile for different loading cases.

It should also be noted that surge impedance and hence SIL is independent of the length of the line. The value of surge impedance will be the same at all the points on the line and hence the voltage.
In case of a Compensated Line, the value of surge impedance will be modified accordingly as

Where, Kse = % of series capacitive compensation by Cse

KCsh = % of Shunt capacitive compensation by Csh

Klsh = % of shunt inductive compensation by Lsh

The equation for SIL will now use the modified Zs.

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