Transmission Line Parameter Calculation

Transmission line length formula:

$Length=\frac{\sqrt{XB}}{2\Pi f }\times$ the velocity of light in km/s

Now suppose a transmission line parameter data is as follows

R= 0.010 pu, X= 0.085 pu, B=0.176 pu.

The base value of power and voltage is given as

V_{b} = 230 k V, S_{b} = 100 M V A

Then the length is

$Length=\frac{\sqrt{0.085\times0.176}}{2\times3.1416 \times 60} \times(3\times 10^5 km/s)$

Length = 97.33 km

Now we will calculate the resistance value:

$\mathbf{R_{actual}= R_{base}\times R_{pu}}$

$R_{base}= X_{base}= \frac{V_{b}^{2}}{S_{b}} = \frac{(230\times 10^3)^{2}}{100\times 10^6} = 529$

$R_{actual}= 529\times 0.01 = 5.29 \Omega$

$R_{\Omega /km} = R_{actual}/Line Length = 5.29/97.33= 0.0543 \Omega /km$

$Zero Sequence Resistance R_{0}= 0.0543 \times 3 = 0.0163 \Omega / km$

Inductance Value Calculation:

X= 0.085 pu

X_{b a s e} = R_{b a s e} X_{b a s e} = 529 X_{a c t u a l} = 529 \times 0.085 = 44.965 L_{a c t u a l} = \frac{X_{a c t u a l}}{2 πf} = \frac{44.965}{2 \times 3.1416 \times 60} = 0.1192

$X_{base}= R_{base} = 529$

$X_{actual}= 529\times 0.085 = 44.965$

So L actual is 0.1192 Henry

Want to get the value in per kilometer, so we will divide this value by the total length of the transmission line(97.33 km)

L_{H / k m} = \frac{0.1192}{97.33} = 1.225 \times 10^{- 3} H / k m

Zero sequence Inductance will be

L_{0} = 1.225 \times 10^{- 3} \times 3 = 3.676 \times 10^{- 3} H / k m

Capacitor Value Calculation:

In order to find the value of capacitance, first, we have to calculate the value of susceptance which is the reciprocal of