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).
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 $1kW\le P\le 2kW$ and $1kVAR\le Q\le 2kVAR$. 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 D_{ab} = D_{bc} = D_{ca} = 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.
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 I =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?
Base load power plants are
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:
${C}_{1}\left({P}_{1}\right)=0.01{P}_{1}^{2}+30{P}_{1}+10;100\mathrm{MW}\le {P}_{1}\le 150\mathrm{MW}$
${C}_{2}\left({P}_{2}\right)=0.05{P}_{2}^{2}+10{P}_{2}+10;100\mathrm{MW}\le {P}_{2}\le 180\mathrm{MW}$
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 t_{1} 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 F_{1} and F_{2} in the system shown in the figure
If the fault takes place at location F_{1}, then the voltage and the current at bus A are V_{F1} and I_{F1} respectively. If the fault takes place at location F_{2}, then the voltage and the current at bus A are V_{F2} and I_{F2} respectively. The correct statement about voltages and currents during faults at F_{1} and F_{2} is
A 2-bus system and corresponding zero sequence network are shown in the figure.
The transformers T_{1} and T_{2} are connected as
In an unbalanced three phase system, phase current I_{a} =1∠(-90^{o}) pu, negative sequence current I_{b2}= 4∠(150^{o}) pu, zero sequence current I_{c0 }3∠90^{o} pu. The magnitude of phase current I_{b} 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 S_{1} and S_{2} are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.
The contributions of S_{1} and S_{2} 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 V_{1} in p.u. and δ_{2} 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, P_{g1} and P_{g2} 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 P_{1} and P_{2} 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 (P_{1}+jQ_{1}), where, 1 kW≤P_{1}≤1.5 kW and 0.5 kVAR≤Q_{1}≤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 30^{o}. 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 P_{max} sinδ. If the values of δ and $\raisebox{1ex}{$d\delta $}\!\left/ \!\raisebox{-1ex}{$dt$}\right.$ at the instant of fault clearing are 45^{o} and 3.762 radian/s respectively, then P_{max} (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 $10\angle -150\xb0$ A and if the voltage at the load terminals is $100\angle 60\xb0$ V, then the
For a power system network with n nodes, Z_{33} 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
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 P_{D} = 40 MW, connected at bus 2.
The fuel cost of generators G1 and G2 are :
C_{1}(P_{G}_{1})=10,000 Rs/MWh and C_{2}(P_{G2})=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: I_{positive} = j1.5 pu, I_{negative} = –j0.5 pu, I_{zero} = –j1 pu. The type of fault in the system is
For the system shown below, S_{D1} and S_{D2} are complex power demands at bus 1 and bus 2 respectively. If $\left|{V}_{2}\right|$=1 pu , the VAR rating of the capacitor (Q_{G2}) 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
G_{2} = 100MVA, 15 kV, positive sequence reactance X=10% on its own base L_{1} and L_{2} = 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
In the above system, the three-phase fault MVA at the bus 3 is
Consider a step voltage wave of magnitude 1pu travelling along a lossless transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is
Consider two buses connected by an impedance of (0+j5) Ω. The bus 1 voltage is $100\angle 30\xb0$V, and bus 2 voltage is 100∠ 0^{o}$100\angle 0\xb0$V.The real and reactive power supplied by bus 1, respectively, are