Question

An overhead line is equipped with shunt inductive reactor at receiving end to maintain sending end voltage equal to the receiving end voltage. If the ABCD parameters of line are A = D = 0.9 ∠0, B = 200 ∠90 Ω and C = 0.95 × 10^-3 ∠90 s, what should be the ohmic value of the reactor to maintain same voltage on both sides?   

1. 1055 Ω 
2. 105.26 Ω 
3. 2000 Ω
4. 1052.6 Ω

Answer 1

Correct Answer - Option 3 : 2000 Ω

Concept:

For the transmission line ABCD parameters,

Sending end voltage becomes

V_s = A V_R + B I_R

For, V_s = V_R

V_R = AV_R + BI_R

⇒ V­_R (1 - A) = B I_R

\( \Rightarrow \frac{{{V_R}}}{{{I_R}}} = \frac{B}{{1 - A}}\)

Calculation:

ABCD parameters of the line

A = D = 0.9 ∠0°, B = 200 ∠90° Ω, C = 0.95 × 10^-3 ∠90° S

Since a ohmic reactor is connected at the receiving end to maintain V_S = V_R

Let the reactor is X_L

\(\Rightarrow {X_L} = \frac{{{V_R}}}{{{I_R}}}\)

Where V_R = Receiving end voltage

I_R = receiving end current

\( \Rightarrow \frac{{{V_R}}}{{{I_R}}} = \frac{B}{{1 - A}} = \frac{{200\angle 90^\circ }}{{1 - 0.9\angle 0^\circ }} = 2000\angle 90^\circ \) 

\( \Rightarrow {X_L} = \frac{{{V_R}}}{{{I_R}}} = 2000\angle 90^\circ {\rm{\Omega }}\)