GATE EE 2024 | Load Flow Studies Question 5 | Power System Analysis

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?

GATE EE 2024 Power System Analysis - Load Flow Studies Question 6 English

$\gamma = m\beta$

$\beta = m\gamma$

$\alpha = m\gamma$

$\alpha = m\beta$

GATE EE 2021

MCQ (Single Correct Answer)

-0.67

A 3-bus network is shown. Consider generators as ideal voltage sources. If rows 1,2 and 3 of the $Y_{h s}$ matrix correspond to bus 1,2 and 3 respectively, then $Y_{h s}$ of the network is

GATE EE 2021 Power System Analysis - Load Flow Studies Question 3 English

$\left[\begin{array}{ccc}-4 j & j & j \\ j & -4 j & j \\ j & j & -4 j\end{array}\right]$

$\left[\begin{array}{ccc}-4 j & 2 j & 2 j \\ 2 j & -4 j & 2 j \\ 2 j & 2 j & -4 j\end{array}\right]$

$\left[\begin{array}{ccc}-\frac{3}{4} j & \frac{1}{4} j & \frac{1}{4} j \\ \frac{1}{4} j & -\frac{3}{4} j & \frac{1}{4} j \\ \frac{1}{4} j & \frac{1}{4} j & \frac{-3}{4} j\end{array}\right]$

$\left[\begin{array}{ccc}\frac{-1}{2} j & \frac{1}{4} j & \frac{1}{4} j \\ \frac{1}{4} j & -\frac{1}{2} j & \frac{1}{4} j \\ \frac{1}{4} j & \frac{1}{4} j & \frac{-1}{2} j\end{array}\right]$

GATE EE 2018

MCQ (Single Correct Answer)

-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

$$15^\circ $$

$$28.48^\circ $$

$$31.20^\circ $$

$$28.74^\circ $$

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

-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. GATE EE 2017 Set 1 Power System Analysis - Load Flow Studies Question 12 English

GATE EE 2017 Set 1 Power System Analysis - Load Flow Studies Question 12 English

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

$$\left[ {\matrix{ { - j19.9} & {j20} & 0 \cr {j20} & { - j39.9} & {j20} \cr 0 & {j20} & { - j19.9} \cr } } \right]\,pu$$

$$\left[ {\matrix{ { - j39.95} & {j20} & 0 \cr {j20} & { - j39.9} & {j20} \cr 0 & {j20} & { - j39.95} \cr } } \right]\,pu$$

$$\left[ {\matrix{ { - j19.95} & {j20} & 0 \cr {j20} & { - j39.9} & {j20} \cr 0 & {j20} & { - j29.95} \cr } } \right]\,pu$$

$$\left[ {\matrix{ { - j19.95} & {j20} & {j20} \cr {j20} & { - j39.9} & {j20} \cr {j20} & {j20} & { - j19.95} \cr } } \right]\,pu$$

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