List of top Power Systems Questions asked in GATE EE

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is an infinite bus having a voltage of magnitude $|V_3| = 1.0 \, \text{p.u.}$ and angle of $-15^\circ$. A variable current source, $|I|\angle \phi$ is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, $\phi = \theta \pm \tfrac{\pi}{2}$, where $\theta$ is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as: \begin{center} \includegraphics[width=0.65\textwidth]{19.jpeg} \end{center}

A 50 Hz, 275 kV line of length 400 km has the following parameters: Resistance, $R = 0.035 \,\Omega/\text{km}$
Inductance, $L = 1 \,\text{mH}/\text{km}$
Capacitance, $C = 0.01 \,\mu\text{F}/\text{km}$
The line is represented by the nominal-$\pi$ model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by $V_S$ and $V_R$, respectively) maintained at 275 kV, the phase angle difference $(\theta)$ between $V_S$ and $V_R$ required for maximum possible active power to be delivered to the receiving end, in degree is \underline{\hspace{2cm}} (Round off to 2 decimal places).

The bus admittance ($Y_{\text{bus}}$) matrix of a 3-bus power system is given below. \[ Y_{\text{bus}} = \begin{bmatrix} -j15 & j10 & j5 \\ j10 & -j13.5 & j4 \\ j5 & j4 & -j8 \end{bmatrix} \] Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

The expressions of fuel cost of two thermal generating units as a function of the respective power generation $P_{G1$ and $P_{G2}$ are given as} \[ F_{1}(P_{G1}) = 0.1aP_{G1}^2 + 40P_{G1} + 120 \; \text{Rs/hour}, 0 \leq P_{G1} \leq 350 \, MW \] \[ F_{2}(P_{G2}) = 0.2P_{G2}^2 + 30P_{G2} + 100 \; \text{Rs/hour}, 0 \leq P_{G2} \leq 300 \, MW \] where $a$ is a constant. For a given value of $a$, optimal dispatch requires the total load of $290 \, MW$ to be shared as $P_{G1} = 175 \, MW$ and $P_{G2} = 115 \, MW$. With the load remaining unchanged, the value of $a$ is increased by $10%$ and optimal dispatch is carried out. The changes in $P_{G1}$ and in the total cost of generation, $F = F_{1} + F_{2}$, will be as follows:

For the three-bus power system shown in the figure, the trip signals to the circuit breakers $B_{1$ to $B_{9}$ are provided by overcurrent relays $R_{1}$ to $R_{9}$, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R--L loads with isolation of minimum portion of the network using minimum number of directional relays is:} \begin{center} \includegraphics[width=0.5\textwidth]{06.jpeg} \end{center}

Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in parallel to share a load of 500 MW. Assuming free governor action, the load shared in MW, by the 250 MW generating unit is _________. (round off to nearest integer)

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by \[ \text{Plant 1: } C_1 = 350 + 6P_1 + 0.004P_1^2 \] \[ \text{Plant 2: } C_2 = 450 + aP_2 + 0.003P_2^2 \] where $ P_1 $ and $ P_2 $ are the power generated by plant 1 and plant 2, respectively, in MW and $ a $ is constant. The incremental cost of power ($ \lambda $) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are

Two balanced three-phase loads, as shown in the figure, are connected to a 100$\sqrt{3}$ V three-phase, 50 Hz main supply. Given $ Z_1 = (18 + j24) \, \Omega $ and $ Z_2 = (6 + j8) \, \Omega $, the ammeter reading, in amperes, is ________. (round off to nearest integer)

In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of 100$\sqrt{3}$ V with phase sequence ABC. The star connected load has $ Z_A = 10 \, \Omega $ and $ Z_B = 20 \angle 60^\circ \, \Omega $. The value of $ Z_C $ in $ \Omega $, for which the voltage difference across the nodes $ n $ and $ n' $ is zero, is

The most commonly used relay, for the protection of an alternator against loss of excitation, is

The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘r’, as shown in the figure below, is

The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are

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

In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and $Z_m = 0.5j$ p.u is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that $\delta > 0$, the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is

Two generators have cost functions with incremental-cost characteristics:
\[ \frac{dF_1}{dP_1} = 40 + 0.2 P_1, \frac{dF_2}{dP_2} = 32 + 0.4 P_2 \] They must supply a total load of 260 MW. Find the optimal generation (economic dispatch) ignoring losses.

Suppose $I_A, I_B$ and $I_C$ are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current is $I_{B0} = 0.1\angle 0^\circ$ p.u. If the phase-A current $I_A = 1.1\angle 0^\circ$ p.u and phase-C current $I_C = (1\angle 120^\circ + 0.1)$ p.u, then $I_B$ in p.u is

The dimension of the sub-matrix $M$ in the Newton-Raphson Jacobian is $\underline{\hspace{2cm}}$.