# Power Systems

 Question 1
Bus 1 with voltage magnitude $V_1 = 1.1 p.u.$ is sending reactive power $Q_{12}$ towards bus 2 with voltage magnitude $V_2 = 1 p.u.$ through a lossless transmission line of reactance X. Keeping the voltage at bus 2 fixed at 1 p.u., magnitude of voltage at bus 1 is changed, so that the reactive power $Q_{12}$ sent from bus 1 is increased by 20%. Real power flow through the line under both the conditions is zero. The new value of the voltage magnitude, $V_1$, in p.u. (rounded off to 2 decimal places) at bus 1 is _______ .
 A 0.118 B 1.12 C 1 D 0.82
GATE EE 2020      Load Flow Studies
Question 1 Explanation:
With real power zero, load angle $\delta =0$
with initial values, $V_{1}=1.1, \; \; \; V_{2}=1$
$Q_{12}=\frac{V_{1}^{2}}{X}-\frac{V_{1}V_{2}}{X}\sin \delta$
$\, \, =\frac{(1.1)^{2}}{X}-\frac{1.1\times 1}{X}\sin 0=\frac{0.11}{x}$

With increased value of voltage,
new value of $\; Q_{12}=1.2Q_{12},\; \; V_{2}=1$
$1.2\, Q_{12}=\frac{V_{1}^{2}}{X}-\frac{V_{1}\times 1}{X}=1.2\times \frac{0.11}{X}$
$V_{1}^{2}-V_{1}-0.132=0$
$V_{1}=1.12,\; \; -0.118$
Hence the practical value in per unit,$V_{1}=1.12$ p.u.
 Question 2
Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:
 A $\begin{bmatrix} -t_it_jY & t_j^2 Y\\ t_i^2 Y & -t_it_jY \end{bmatrix}$ B $\begin{bmatrix} t_it_jY & -t_j^2 Y\\ -t_i^2 Y & t_it_jY \end{bmatrix}$ C $\begin{bmatrix} t_i^2 Y & -t_it_jY\\ -t_it_jY & t_j^2 Y \end{bmatrix}$ D $\begin{bmatrix} t_it_jY & -(t_i-t_j)^2Y\\ -(t_i-t_j)^2Y & t_it_jY \end{bmatrix}$
GATE EE 2020      Performance of Transmission Lines, Line Parameters and Corona
Question 2 Explanation:

\begin{aligned} I&=Y(t_{i}V_{i}-V_{j}t_{j}) \\ I_{i}&=t_{i}I \\ &=t_{i}^{2}YV_{i}-t_{i}t_{j}YV_{j} \\ I_{j}&=-t_{j}I \\ &=-I_{i}t_{j}YV_{i}+t_{i}^{2}YV_{j} \\ \begin{bmatrix} I_{i}\\ I_{j} \end{bmatrix}&=\begin{bmatrix} t_{i}^{2}Y &-t_{i}t_{j}Y \\ -t_{i}t_{j}Y &t_{j}^{2}Y \end{bmatrix}\begin{bmatrix} V_{i}\\ v_{j} \end{bmatrix} \end{aligned}
 Question 3
Out of the following options, the most relevant information needed to specify the real power (P) at the PV buses in a load flow analysis is
 A solution of economic load dispatch B rated power output of the generator C rated voltage of the generator D base power of the generator
GATE EE 2020      Load Flow Studies
Question 3 Explanation:
Most relevant information needed to specify P at PV buses is solution of economic load dispatch.
 Question 4
A lossless transmission line with 0.2 pu reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to 80% of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:
 A 1 B 3.61 C 5 D 6.25
GATE EE 2020      Performance of Transmission Lines, Line Parameters and Corona
Question 4 Explanation:
$I_{f}=\frac{1}{Z_{Th}}=\frac{1}{0.2}$
=5 pu for 100% of line
Relay is operated for 80%
$Z_{f}=0.8\, Z_{t}\Rightarrow 0.8\times 0.2=0.16\, p.u.$
For 80% of line,
$I_{f}=\frac{1}{0.16}=6.25\: p.u.$
 Question 5
In a 132 kV system, the series inductance up to the point of circuit breaker locationis 50 mH. The shunt capacitanceat the circuit breaker terminal is 0.05 $\mu F$. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is_____
 A 100 B 250 C 500 D 1000
GATE EE 2019      Switch Gear and Protection
Question 5 Explanation:
\begin{aligned} L&=50mH\\ C&=0.05\mu F\\ R_{cr}&=\frac{1}{2}\sqrt{\frac{L}{C}}\\ &=\frac{1}{2}\sqrt{\frac{50 \times 10^{-3}}{0.05 \times 10^{-6}}}\\ &=500\Omega \end{aligned}
 Question 6
In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________
 A 12.8 B 28.4 C 20.5 D 32.6
GATE EE 2019      Power System Stability
Question 6 Explanation:
\begin{aligned} X &=0.25+0.2+0.4||0.4 \\ &=0.45+0.2=0.65pu \\ P&=V_{pu} \times I_{pu} \cos \phi \\ 0.8 &=1 \times I_{pu} \times 0.8 \\ I_{pu} &= 1pu\\ E &= V+jI_aX_s\\ &=1+1\angle -36.86^{\circ} \times j0.65 \\ &= 1.484 \angle 20.51^{\circ}pu\\ \delta &= 20.51^{\circ} \end{aligned}
 Question 7
A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactancesof 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a reactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ______
 A 2.2 B 1.8 C 3.6 D 4.2
GATE EE 2019      Fault Analysis
Question 7 Explanation:
\begin{aligned} X_1&=0.25 \; p.u.\\ X_2&=0.15 \; p.u.\\ X_0&=0.05 \; p.u.\\ I_{f(LG)}&=I_{f(3-\phi )}\\ \frac{3V_{pu}}{(X_1+X_2+X_0+3X_n)}&=\frac{V_{pu}}{X_1}\\ \frac{3 \times 1}{(0.25+0.15+0.05+3X_n)}&=\frac{1}{0.25}\\ \frac{3}{0.46+3X_n}&=\frac{1}{0.25}\\ \Rightarrow \;\; X_n&=0.1\; p.u.\\ X_n&=0.1 \times Z_B\\ &=0.1 \times \frac{30^2}{50}\\ &=1.8\Omega \end{aligned}
 Question 8
A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 $\mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be ___________.
 A 418.85 B 256.25 C 458.45 D 369.28
GATE EE 2019      Performance of Transmission Lines, Line Parameters and Corona
Question 8 Explanation:
\begin{aligned} V_s&= 400kV\\ l&=300km\\ L_1&=1mH/km/phase\\ C_1&=0.01 \mu F/km/phase\\ v&=\frac{1}{\sqrt{L_1C_1}}\\ &=\frac{1}{\sqrt{1 \times 10^{-3} \times 0.01 \times 10^{-6}}}\\ &=3.16 \times 10^5 km/sec\\ \beta '&=\frac{2 \pi f l}{v}\\ &=\frac{2 \pi \times 50 \times 300}{3.16 \times 10^5}=0.29\\ A&=1-\frac{\beta ^2}{2}\\ &=1-\frac{(0.29)^2}{2}=0.955\\ V_R&=\frac{V_S}{A}=\frac{400}{0.955}=418.85kV \end{aligned}
 Question 9
The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 $\Omega$. If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is ________
 A 50 B 100 C 150 D 200
GATE EE 2019      Switch Gear and Protection
Question 9 Explanation:
\begin{aligned} I_{sec}&=5 \times 20=100A \\ V &=I_{sec}R =100 \times 0.01\\ &=1V \\ \text{VA } &\text{output of the CT} \\ &= VI_{sec}=100 \times 1\\ &= 100VA \end{aligned}
 Question 10
Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is_________
 A 50 B 75 C 100 D 150
GATE EE 2019      Fault Analysis
Question 10 Explanation:
Net reactance of parallel connection,
\begin{aligned} X&=\frac{0.25}{5}=0.05\;p.u.\\ I_{SC}&=\frac{1}{X}=\frac{1}{0.05}=20\; p.u.\\ \text{SC MVA}&=20 \times 5\\ &=100 \text{ MVA} \end{aligned}

There are 10 questions to complete.