1
GATE EE 2024
+1
-0.33

The figure shows the single line diagram of a 4-bus power network. Branches $b_1$, $b_2$, $b_3$, and $b_4$ have impedances $4z$, $z$, $2z$, and $4z$ per-unit (pu), respectively, where $z = r + jx$, with $r > 0$ and $x > 0$. The current drawn from each load bus (marked as arrows) is equal to $I$ pu, where $I \neq 0$. If the network is to operate with minimum loss, the branch that should be opened is

A

$b_1$

B

$b_2$

C

$b_3$

D

$b_4$

2
GATE EE 2018
Numerical
+1
-0.33
A 1000 $$\times$$ 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).
3
GATE EE 2017 Set 2
+1
-0.3
The figure show the per-phase representation of a phase-shifting transformer connected between buses $$1$$ and $$2,$$ where $$\alpha$$ is a complex number with non-zero real and imaginary parts.
For the given circuit, $${Y_{bus}}$$ and $${Z_{bus}}$$ are bus admittance matrix and bus impedance matrix, respectively, each of size $$2\, \times \,2$$. Which one of the following statements is true?
A
Both $${Y_{bus}}$$ and $${Z_{bus}}$$ are symmetric
B
$${Y_{bus}}$$ is symmetric and $${Z_{bus}}$$ is unsymmetric
C
$${Y_{bus}}$$ is unsymmetric and $${Z_{bus}}$$ is symmetric
D
Both $${Y_{bus}}$$ and $${Z_{bus}}$$ are unsymmetric
4
GATE EE 2017 Set 2
Numerical
+1
-0
In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $$\,100\,\, \times \,\,100.$$ If there are $$20$$ PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.