1
GATE EE 2024
+2
-1.33

For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit (pu), and the differences of the voltage phase angles are very small. The line reactances are marked in the figure, where $\alpha$, $\beta$, $\gamma$, and $x$ are strictly positive. The bus injections $P_1$ and $P_2$ are in pu. If $P_1 = mP_2$, where $m > 0$, and the real power flow from bus 1 to bus 2 is 0 pu, then which one of the following options is correct?

A

$\gamma = m\beta$

B

$\beta = m\gamma$

C

$\alpha = m\gamma$

D

$\alpha = m\beta$

2
GATE EE 2018
+2
-0.67
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4 sin $$\delta$$ + 0.15 sin 2$$\delta$$, where $$\delta$$ is the load angle. Newton-Raphson method is used to calculate the value of $$\delta$$ for P = 0.8 pu. If the initial guess is $$30^\circ$$, then its value (in degree) at the end of the first iteration is
A
$$15^\circ$$
B
$$28.48^\circ$$
C
$$31.20^\circ$$
D
$$28.74^\circ$$
3
GATE EE 2017 Set 1
+2
-0.6
The bus admittance matrix for a power system network is $$\left[ {\matrix{ { - j39.9} & {j20} & {j20} \cr {j20} & { - j39.9} & {j20} \cr {j20} & {j20} & { - j39.9} \cr } } \right]\,pu.$$\$
There is a transmission line connected between buses $$1$$ and $$3,$$ which is represented by the circuit shown in figure.

If this transmission line is removed from service what is the modified bus admittance matrix?

A
$$\left[ {\matrix{ { - j19.9} & {j20} & 0 \cr {j20} & { - j39.9} & {j20} \cr 0 & {j20} & { - j19.9} \cr } } \right]\,pu$$
B
$$\left[ {\matrix{ { - j39.95} & {j20} & 0 \cr {j20} & { - j39.9} & {j20} \cr 0 & {j20} & { - j39.95} \cr } } \right]\,pu$$
C
$$\left[ {\matrix{ { - j19.95} & {j20} & 0 \cr {j20} & { - j39.9} & {j20} \cr 0 & {j20} & { - j29.95} \cr } } \right]\,pu$$
D
$$\left[ {\matrix{ { - j19.95} & {j20} & {j20} \cr {j20} & { - j39.9} & {j20} \cr {j20} & {j20} & { - j19.95} \cr } } \right]\,pu$$
4
GATE EE 2015 Set 1
+2
-0.6
Determine the correctness or otherwise of the following Assertion (a) and the Reason (R).
Assertion (A): Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions.
Reason (R): Accuracy depends on the power mismatch vector tolerance.
A
Both (A) and (R) are true and (R) is the correct reason for (A)
B
Both (A) and (R) are true but (R) is not the correct reason for (A)
C
Both (A) and (R) are false
D
(A) is false and (R) is true
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