GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 64 of 65

Marks: +1, -0

In the figure shown, self-impedances of the two transmission lines are

1.5 {j}

p.u. each, and

Z_{ {m}}=0.5 {j}

p.u. is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that

δ>0

, the maximum steady-state real power that can be transferred in p.u from Bus- 1 to Bus- 2 is:

Solution:

P_{\max }=\;{|E||V|}/{X_{\;\text "Th "\;}}

A=1/2{[\table 1 , -1 ; 1 , -1]}

{y}_{\;\text "prim "\;}= {Z}_{\;\text "prim "\;}^{-1}

Z_{ {prim}}=[\table 1.5 , 0.5 ; 0.5 , 1.5]

1.5 × 1.5-0.25

2.25-0.25=2

y_{\;\text "prim "\;}=\;{1}/{2}[\table 1.5 , -0.5 ; -0.5 , 1.5]

{y}_{\;\text "Bus "\;}= {A}^{⊤}[ {y}_{\;\text "prim "\;}] {A}=\;{1}/{2}[\table 1 , 1 ; -1 , -1][\table 1.5 , -0.5 ; -0.5 , 1.5]=[\table 1 , -1 ; -1 , 1]

Z_{\;\text "Bus "\;}=y_{\;\text "Bus "\;}^{-1}=[\table 1 , 1 ; 1 , 1]

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