Line Transmission - Very simple

[danilorj]

Homework Statement

Consider a transmission circuit of 1600 km, 500 kV unitary parameters z1=j0.2 ohms/km and y1=j10 microsiemens/km. Evaluate the series reactor and the derivation capacitor necessaries to take the electric length of the circuit to 1.05*pi rad. Suppose the compensation is focused in the receiving and sending ends of line. Also suppose that the derivation compensation is 80%.

Homework Equations

teta = sqrt(Z*Y).

The Attempt at a Solution

 

[Valkarie]

Let's first calculate the electric length of the line. Z1 = j0.2 ohms/km Y1 = j10 microsiemens/kmteta_1 = sqrt(Z1*Y1) = sqrt(j0.2*j10) = sqrt(-2) = 1.414 rad Electric length is teta_1*L = 1.414 * 1600 = 2272.8 rad Now we need to take the electric length to 1.05*pi rad Let's calculate the extra length needed extra_length = 1.05*pi - 2272.8 = 0.14 rad Now we can calculate the reactor X_r that should be added in series with the line X_r = teta_1*extra_length/L = 1.414 * 0.14/1600 = 0.00022 ohms Now let's calculate the derivation capacitor C_d. For 80% compensation, the derivation capacitor should be equal to 0.8*X_r/teta_1 C_d = 0.8*0.00022/1.414 = 0.00015 microfarads