# GATE Questions & Answers of Power Systems Electrical Engineering

#### Power Systems 115 Question(s) | Weightage 13 (Marks)

Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively $Z$ and $X$. are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be

The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix}Z_s&Z_m&Z_m\\Z_m&Z_s&Z_m\\Z_m&Z_m&Z_s\end{bmatrix}$ . If the positive sequence impedance is $\left(1+\;j\;10\right)\;\Omega$ , and the zero sequence is $\left(4+\;j\;31\right)\;\Omega$ , then the imaginary part of $Z_m\;(in\;\Omega)$ is ______(up to 2 decimal places).

The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are j0.1 pu, j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

A 1000 × 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).

The positive, negative and zero sequence impedances of a three phase generator are $Z_1Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$ the fault current $I_{f1}=kI_f$ , where $I_f$ is the fault current with zero fault impedance. The relation between $Z_{f\;}and\;k$ is

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1},$ and $Q_{G2},$ and line reactive power loss $(Q_{loss})$ respectively are

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°, then its value (in degree) at the end of the first iteration is

$A\;3$-bus power system is shown in the figure below, where the diagonal elements of $Y$-bus matrix are: $Y_{11}=-j12\;pu,\;Y_{22}=-j15\;pu$ and $Y_{33}=-j7\;pu.$

The per unit values of the lines reactances $p,q$ and $r$ shown in the figure are

A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L2, L2, L3, L4, L5, L6. The generator-bus G1 is connected as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in popular form is________.

A load is supplied by a 230 V, 50 Hz. The active power P and the reactive power Q consumed by the load such that and . A capacitor connected across the load for power factor correction generates 1 kVAR reactive power. The worst case power factor after power correction is

The bus admittance matrix for a power system network is

$\begin{bmatrix}j39.9&j20&j20\\j20&-j39.9&j20\\j20&j20&j39.9\end{bmatrix}pu$

There is a transmission line, connected between buses 1 and 3, which is represent by the circuit shown in figure.

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

The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the faults current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is ___________ (assume fault impedance to be zero).(Give the answer up to one decimal place.)

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sin $\delta$, where $\delta$ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuit is removed, the maximum value of $\delta$ , as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is $P_{max}\;\sin\;\delta$, the values of  $P_{max}$, in pu is ________ . (Give the answer up to three decimal places.)

The nominal$-\mathrm\pi$ circuit of a transmission line is shown in the figure.

Impedance $Z=100\angle\;80^\circ\;\Omega$ and reactance $X=3300\;\Omega$. The magnitude of the characteristic impedance of the transmission line, in $\Omega$, is_______________. (Give the answer up to one decimal place.)

In a load flow problem solved by newton-Raphson method with polar coordinates, the size of the Jactobian is 100 × 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__________.

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab = Dbc = Dca = 1m as shown in figure below. The resistances of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01 m. Neglecting the effect of ground, the magnitude of positive sequence reactance $\Omega/km$ (rounded off three decimal places) is________

A 3-phase, 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25$\Omega$ and 3.925$\Omega$ respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is___________.

Two generate units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger units is______ MW.

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous aped and delivering 60 MW power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is_____________ electrical degrees.

In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this iteration,

The magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is 1.0 pu. The voltage magnitude at bus B during a three-phase fault at bus A is 0.8 pu. The voltage magnitude at bus A during a three-phase fault at bus B, in pu, is ________.

A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz, the capacitance per phase of the bank, expressed in microfarads, is ________.

A 30 MVA, 3-phase, 50 Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactances, 15%, 15% and 5% respectively. A reactance (Xn) is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phases ‘b’ and ‘c’, with a fault impedance of j0.1 p.u. The value of Xn (in p.u.) that will limit the positive sequence generator current to 4270 A is _________.

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three-phase system is to be 5% more than that of the inductance per conductor of the single-phase system. The distance D, in meters, is _______.

A power system with two generators is shown in the figure below. The system (generators, buses and transmission lines) is protected by six overcurrent relays R1 to R6. Assuming a mix of directional and nondirectional relays at appropriate locations, the remote backup relays for R4 are

A power system has 100 buses including 10 generator buses. For the load flow analysis using Newton-Raphson method in polar coordinates, the size of the Jacobian is

The inductance and capacitance of a 400 kV, three-phase, 50 Hz lossless transmission line are 1.6 mH/km/phase and 10 nF/km/phase respectively. The sending end voltage is maintained at 400 kV.To maintain a voltage of 400 kV at the receiving end, when the line is delivering 300 MW load, the shunt compensation required is

A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a synchronousreactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to the generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is ________.

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and 1.0 p.u. The p.u. reactances of different components in the system are also shown in the figure. The infinite bus voltage magnitude is 1.0 p.u. A three phase fault occurs at the middle of line 2.

The ratio of the maximum real power that can be transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is _________.

At no load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is ____________.

Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedances of j0.4 p.u., j0.3 p.u. and j0.15 p.u., respectively. If the pre-fault voltage is 1 p.u., for a line-to-ground (L-G) fault at the terminals of the generators, the fault current, in p.u., is ___________.

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and the current, are given by: ${V}_{1}$ =500 kV, ${V}_{2}$ =485 kV and =1.5 kA. If the direction of power flow is to be reversed (that is, from System 2 to System 1) without changing the electrical connections, then which one of the following combinations id feasible?

P: wind farms.
Q: run-of-river plants.
R: nuclear power plants.
S: diesel power plants.

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below:

The incremental cost (in Rs/MWh) of the power plant when it supplies 200 MW is _____.

Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

Assertion: Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions.

Reason: Accuracy depends on the power mismatch vector tolerance.

A 50 Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle δ is 5º, when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of δ in degrees, 0.02 second after the fault is ________.

A sustained three-phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?

The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t1 by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle $\delta$ shows the transient correctly?

A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is
$\left[\begin{array}{ccc}-j6& j3& j4\\ j3& -j7& j5\\ j4& j5& -j8\end{array}\right]\mathrm{pu}.$
If the shunt capacitance of all transmission line is 50% compensated, the imaginary part of the ${3}^{\mathrm{rd}}$row${3}^{\mathrm{rd}}$column element (in pu) of the bus admittance matrix after compensation is

The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers ${P}_{1}$ and ${P}_{2}$ in MW, and are given by

$\frac{d{C}_{1}}{d{P}_{1}}=0.2{P}_{1}+50$
$\frac{d{C}_{2}}{d{P}_{2}}=0.24{P}_{2}+40$

Where

20MW$\le {P}_{1}\le$150 MW
20MW$\le {P}_{2}\le$150MW.

For a certain load demand, ${P}_{1}$ and ${P}_{2}$ have been chosen such that $d{C}_{1}/d{P}_{1}$ = 76 Rs/MWh and $d{C}_{2}/d{P}_{2}$ = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then ${P}_{2}$ is _____________.

A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is ___________.

A 3-phase transformer rated for 33 kV/11 kV is connected in delta/star as shown in figure. The current transformers (CTs) on low and high voltage sides have a ratio of 500/5. Find the currents ${i}_{1}$ and ${i}_{2}$,if the fault current is 300 A as shown in figure.

The undesirable property of an electrical insulating material is

Three-phase to ground fault takes place at locations F1 and F2 in the system shown in the figure

If the fault takes place at location F1, then the voltage and the current at bus A are VF1 and IF1 respectively. If the fault takes place at location F2, then the voltage and the current at bus A are VF2 and IF2 respectively. The correct statement about voltages and currents during faults at F1 and F2 is

A 2-bus system and corresponding zero sequence network are shown in the figure.

The transformers T1 and T2 are connected as

In an unbalanced three phase system, phase current Ia =1(-90o) pu, negative sequence current Ib2= 4(150o) pu, zero sequence current Ic0 390o pu. The magnitude of phase current Ib in pu is

A distribution feeder of 1 km length having resistance, but negligible reactance, is fed from both the ends by 400V, 50 Hz balanced sources. Both voltage sources S1 and S2 are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.

The contributions of S1 and S2 in 100 A current supplied at location P respectively, are

A two bus power system shown in the figure supplies load of 1.0+j0.5 p.u.

The values of V1 in p.u. and δ2 respectively are

The fuel cost functions of two power plants are

Plant ${P}_{1}:{C}_{1}=0.05P{g}_{1}^{2}+AP{g}_{1}+B$

Plant ${P}_{2}:{C}_{2}=0.10P{g}_{2}^{2}+3AP{g}_{2}+2B$

where, Pg1 and Pg2 are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 1000 MW load at incremental fuel cost of 100 Rs/MWh, the ratio of load shared by plants P1 and P2 is

A single phase induction motor draws 12 MW power at 0.6 lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to 0.8 lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is __________.

A three phase star-connected load is drawing power at a voltage of 0.9 pu and 0.8 power factor lagging. The three phase base power and base current are 100 MVA and 437.38 A respectively. The line-to-line load voltage in kV is ________.

Shunt reactors are sometimes used in high voltage transmission systems to

The horizontally placed conductors of a single phase line operating at 50 Hz are having outside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10-12 F/m. The capacitance to ground per kilometer of each line is

A three phase, 100 MVA, 25 kV generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are 0.2 pu, 0.2 pu, and 0.05 pu, respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is _______

In a long transmission line with r,l,g and c are the resistance, inductance, shunt conductance and capacitance per unit length, respectively, the condition for distortionless transmission is

For a fully transposed transmission line

A 183-bus power system has 150 PQ buses and 32 PV buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimum number of simultaneous equations to be solved is ___________.

For a 400 km long transmission line, the series impedance is (0.0 + j0.5) Ω/km and the shunt admittance is (0.0 + j5.0) μmho/km. The magnitude of the series impedance (in Ω) of the equivalent π circuit of the transmission line is ________.

The complex power consumed by a constant-voltage load is given by (P1+jQ1), where, 1 kW≤P1≤1.5 kW and 0.5 kVAR≤Q1≤1 kVAR. A compensating shunt capacitor is chosen such that |Q|≤0.25 kVAR, where Q is the net reactive power consumed by the capacitor-load combination. The reactive power (in kVAR) supplied by the capacitor is _________.

The figure shows the single line diagram of a single machine infinite bus system.

The inertia constant of the synchronous generator H=5 MW-s/MVA. Frequency is 50 Hz. Mechanical power is 1 pu. The system is operating at the stable equilibrium point with rotor angle δ equal to 30o. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in pu is Pmax sinδ. If the values of δ and $d\delta }{dt}$ at the instant of fault clearing are 45o and 3.762 radian/s respectively, then Pmax (in pu) is _______.

A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is $10\angle -150°$ A and if the voltage at the load terminals is $100\angle 60°$ V, then the

For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The voltage at node 3 is 1.3 $\angle$10° per unit. If a capacitor having reactance of –j3.5 per unit is now added to the network between node 3 and the reference node, the current drawn by the capacitor per unit is

In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1 $\Omega$.

The voltage phase angles in rad at buses 2 and 3 are

In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1 $\Omega$.

If the base impedance and the line-to-line base voltage are 100 $\Omega$ and 100 kV, respectively, then the real power in MW delivered by the generator connected at the slack bus is

The bus admittance matrix of a three-bus three-line system is

$Y=j\left[\begin{array}{ccc}-13& 10& 5\\ 10& -18& 10\\ 5& 10& -13\end{array}\right]$

If each transmission line between the two buses is represented by an equivalent $\mathrm{\pi }$-network, the magnitude of the shunt susceptance of the line connecting bus 1 and 2 is

The figure shows a two-generator system supplying a load of PD = 40 MW, connected at bus 2.

The fuel cost of generators G1 and G2 are :

C1(PG1)=10,000 Rs/MWh and C2(PG2)=12,500 Rs/MWh

and the loss in the line is ${P}_{loss\left(pu\right)}=0.5{P}_{G1\left(pu\right)}^{2}$,where the loss coefficient is specified in pu on a 100 MVA base. The most economic power generation schedule in MW is

The sequence components of the fault current are as follows: Ipositive = j1.5 pu, Inegative = –j0.5 pu, Izero = –j1 pu. The type of fault in the system is

For the system shown below, SD1 and SD2 are complex power demands at bus 1 and bus 2 respectively. If $\left|{V}_{2}\right|$=1 pu , the VAR rating of the capacitor (QG2) connected at bus 2 is

A cylindrical rotor generator delivers 0.5 pu power in the steady-state to an infinite bus through a transmission line of reactance 0.5 pu. The generator no-load voltage is 1.5 pu and the infinite bus voltage is 1 pu. The inertia constant of the generator is 5 MW-s/MVA and the generator reactance is 1 pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is

A nuclear power station of 500 MW capacity is located at 300 km away from a load center. Select the most suitable power evacuation transmission configuration among the following options

A negative sequence relay is commonly used to protect

For enhancing the power transmission in along EHV transmission line, the most preferred method is to connect a

A load center of 120 MW derives power from two power stations connected by 220 kV transmission lines of 25 km and 75 km as shown in the figure below. The three generators G1,G2 and G3 are of 100 MW capacity each and have identical fuel cost characteristics. The minimum loss generation schedule for supplying the 120 MW load is

A three – bus network is shown in the figure below indicating the p.u. impedance of each element

The bus admittance matrix, Y -bus, of the network is

Two generator units G1 and G2 are connected by 15 kV line with a bus at the midpoint as shown below

G1 = 250MVA, 15 kV, positive sequence reactance X=25%  on its own base

G2 = 100MVA, 15 kV, positive sequence reactance X=10%  on its own base L1 and L2 = 10 km, positive sequence reactance X = 0.225 Ω/km

For the above system,positive sequence diagram with p.u values on the 100 MVA common base is

Two generator units G1 and G2 are connected by 15 kV line with a bus at the midpoint as shown below

G1 = 250MVA, 15 kV, positive sequence reactance X=25%  on its own base

G2 = 100MVA, 15 kV, positive sequence reactance X=10%  on its own base L1 and L2 = 10 km, positive sequence reactance X = 0.225 Ω/km

In the above system, the three-phase fault MVA at the bus 3 is

Consider two buses connected by an impedance of (0+j5) Ω. The bus 1 voltage is $100\angle 30°$V, and bus 2 voltage is 100∠ 0o$100\angle 0°$V.The real and reactive power supplied by bus 1, respectively, are