GATE Electrical Engineering

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a NewtonRaphson lo...

The bus impedance matrix of a 3-bus system (in pu) is $$ Z_{\text {bus }}=\left[\begin{array}{lll} j 0.059 & j 0.061 & j 0.038 \\ j 0.061 & j 0.093 & j 0.066 \\ j 0.038 & j 0.066 &...

Consider a distribution feeder, with $R / X$ ratio of 5 . At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receivi...

Two units, rated at 100 MW and 150 MW , are enabled for economic load dispatch. When the overall incremental cost is $10,000 \mathrm{Rs}$./MWh, the units are dispatched to 50 MW an...

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 $$\matrix{ {{F_1}({P_{G1}})...

The bus admittance ($$Y_{bus}$$) matrix of a 3-bus power system is given below. $$\quad\quad$$$$\matrix{ 1 & \quad\quad\quad2\quad\quad & 3 \cr } $$ $$\matrix{ 1 \cr 2 \cr 3 \cr }...

A 50 Hz, 275 kV line of length 400 km has the following parameters: Resistance, R = 0.035 $$\Omega$$/km; Inductance, L = 1 mH/km; Capacitance, C = 0.01 $$\mu$$F/km; The line is rep...

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

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

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ______. (round off to nearest integer).

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by Plant 1 : C 1 = 350 + 6P 1 + 0.004P$$_1^2$$ Plant 2 : C 2 = 450 + aP 2 + 0.003P$$_2^2$$ wher...

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...

A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular ac...

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are $$ \frac{d F_1}{d P_1}=40+0.2 P_1 \text { and } \frac{d F_2}{d P_2}=32+0.4 P_2 $$ The...

Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus. $P V$ buses and $P Q$ buses for load flow study. The number of...

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 $I_{B 0}=0.1 \angle 0^0$ p.u. If phase-A current $I_...

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 $$\d...

The positive, negative and zero sequence impedances of a three phase generator are Z 1 , Z 2 and Z 0 respectively. For a line-to-line fault with fault impedance Z f , the fault cur...

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 machi...

The series impedance matrix of a short three-phase transmission line in phase coordinates is $$\left[ {\matrix{ {{Z_s}} & {{Z_m}} & {{Z_m}} \cr {{Z_m}} & {{Z_s}} & {{Z_m}} \cr {{Z_...

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, respectivel...

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...

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 s...

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...

A 3-phase 50 Hz generator supplies power of 3 MW 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 $$\...

A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack b...

A load is supplied by a $$230$$ $$V,$$ $$50$$ $$Hz$$ source. The active power $$P$$ and the reactive power $$Q$$ consumed by the load are such that $$1$$ $$kW$$ $$ \le P \le 2\,kW\...

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 t...

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...

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 th...

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 sy...

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 withou...

A 30 MVA, 3-phase, 50Hz, 13.8 kV, star-connected synchronous generator has positive, negative and zero sequence reactances, 15%, 15% and 5% respectively. A reactance (X n ) is conn...

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 belo...

A $$3$$-bus power system network consists of $$3$$ transmission lines. The bus admittance matrix of the uncompensated system is $$\left[ {\matrix{ { - j6} & {j3} & {j4} \cr {j3} &...

Determine the correctness or otherwise of the following Assertion (a) and the Reason (R). Assertion (A): Fast decoupled load flow method gives approximate load flow solution becaus...

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 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 $$${{d{C_1}...

Base load power plants are $$P.$$ wind farms $$Q.$$ run-of-river plants $$R.$$ nuclear power plants $$S.$$ diesel power plants

For a $$400$$ $$km$$ long transmission line, the series impedance is $$(0.0 + j0.5)$$ $$\Omega /km$$ and the shunt admittance is $$(0.0 + j5.0)$$ $$\mu \,mho/km.$$ The magnitude of...

A single phase induction motor draws $$12MW$$ power at $$0.6$$ lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of mo...

The fuel cost functions of two power plants are Plant $${P_1}:\,{C_1} = 0.05\,Pg_1^2 + AP{g_1} + B$$ Plant $${P_2}:\,{C_2} = 0.10\,Pg_2^2 + 3AP{g_2} + 2B$$ Where, $$P{g_1}$$ and $$...

For a fully transposed transmission line

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...

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 distortion...

A three phase, $$100$$ $$MVA,$$ $$25$$ $$kV$$ generator has solidly grounded neutral. The positive, negative, and the zero sequence reactance's of the generator are $$0.2$$ $$pu$$,...

A 183-bus power system has 150PQ 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 o...

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 respect...

In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ negative sequence current $$\,{{\rm I}_{b2}} = 4\angle \left( {...

The complex power consumed by a constant-voltage load is given by $$\left( {{P_1} + {J_{q1}}} \right).\,\,$$ Where, $$\,1\,\,kW \le \,\,{P_1} \le \,\,\,1.5\,\,kW\,\,\,$$ and $$\,\,...

The undesirable property of an electrical insulating material is

Shunt reactors are sometimes used in high voltage transmission systems to

A single load is supplied by a single voltage source. If the current flowing from the load to the source is $$10\angle - {150^0}$$ A and if the voltage at the load terminals is $$1...

The angle $$\delta $$ in the swing equation of a synchronous generator is the

For a power system network with $$n$$ nodes, $${Z_{33}}$$ of its bus impedance matrix is $$j0.5$$ per unit. The voltage at mode $$3$$ is $$1.3\angle - {10^0}\,\,$$ per unit. If a c...

The sequence components of the fault current are as follows: $${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$ $${{\rm I}_{zero}} = - j1\,\,pu.$$ The typ...

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...

The bus admittance matrix of a three-bus three-line system is $$y = j\left[ {\matrix{ { - 13} & {10} & 5 \cr {10} & { - 18} & {10} \cr 5 & {10} & { - 13} \cr } } \right]$$ If each...

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

A lossy capacitor $${C_x}$$, rated for operation at $$5$$ $$kV,$$ $$50$$ $$Hz$$ is represented by an equivalent circuit with an ideal capacitor $${C_p}$$ in parallel with a resisto...

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...

A negative sequence relay is commonly used to protect

A $$50$$ $$Hz$$ synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant...

A three-phase, $$33$$ kV oil circuit breaker is rated $$1200$$ A, $$2000$$ MVA, $$3$$s. The symmetrical breaking current is

Consider two buses connected by an impedance of $$\left( {0 + j5} \right)\Omega .$$ The bus $$1$$ voltage is $$100$$$$\angle {30^ \circ }\,\,\,V,$$ and bus $$2$$ voltage is $$100\a...

Match the items in List-$$I$$ (Type of transmission line) with the items in List-$$II$$ (Type of distance relay preferred) and select the correct answer using the codes below the l...

Match the items List-$${\rm I}$$ (To) with the items in List-$${\rm II}$$ (Use) and select the correct answer using the codes given below the lists. List-$${\rm I}$$ $$A.$$ improve...

For the $${Y_{bus}}$$ matrix of a $$4$$-bus system given in per unit, the buses having shunt elements are $$${Y_{BUS}} = j\left[ {\matrix{ { - 5} & 2 & {2.5} & 0 \cr 2 & { - 10} &...

Out of the following plant categories (i) Nuclear , (ii) Run-of-river, (iii) Pump Storage, (iv) Diesel The base load power plants are

A $$500$$ $$MW,$$ $$21$$ $$kV,$$ $$50$$ $$Hz,$$ $$3$$-phase, $$2$$-pole synchronous generator having a rated $$p.f.=$$$$0.9,$$ has a moment of inertia $$\,\,27.5\,\, \times \,\,{10...

For a fixed value of complex power flow in a transmission line having a sending end voltage $$V$$, the real power loss will be proportional to

Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...

Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...

An extra high voltage transmission line of length $$300$$ km can be approximate by a lossless line having propagation constant $$\beta = 0.00127$$ radians per km. then the percenta...

A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the system with cost curves $${C_1}$$ and $${C_2}$$ respectively defi...

Voltage phasors at the two terminals of a transmission line of length $$70$$ km have a magnitude of $$1.0$$ per unit but are $$180$$ degrees out of phase. Assuming that the maximum...

A lossless transmission line having Surge Impedance Loading $$(SIL)$$ of $$2280$$ $$MW.$$ A Series capacitive compensation of $$30$$% is emplaced. Then $$SIL$$ of the compensated t...

Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...

Suppose we define a sequence transformation between ''a-b-c'' and ''p-n-0''' variables as follows: $$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\ma...

The total reactance and total susceptance of a lossless overhead $$EHV$$ line, operating at $$50$$ $$Hz,$$ are given by $$0.045$$ pu and $$1.2$$ pu respectively. If the velocity of...