Power Systems

Q. A 50 Hz, four pole turbo generator rated 100 MVA, 11 kV has an inertia constant of 8.0 MJ/MVA. Mechanical input is suddenly raised to 80 MW for an electrical load of 50 MW. If the acceleration is maintained for 10 cycles, the rotor speed at the end of this period is

1. 1404.526 rpm
2. 1608.635 rpm
3. 1515.625 rpm
4. 1505.625 rpm

Q. A 25 MVA, 13.2 kV alternator with solidly grounded netural has a substransient reactance of 0.25 p.u. The negative and zero sequence reactance are 0.35 and 0.1 p.u. respectively. A single line to ground fault occurs at the terminals of an unloaded alternator, then the fault current is

1. 3530 A
2. 5025 A
3. 4685 A
4. 8025 A

Q. For the Y-bus matrix of a 4-bus system given in per unit , the buses having shunt elements are
$Y_{BUS}=j\left[\begin{array}{cccc}-5& 2& 2.5& 0\\ 2& -10& 2.5& 4\\ 2.5& 2.5& -9& 4\\ 0& 4& 4& -8\end{array}\right]$

1. 3 adn 4
2. 2 and 3
3. 1 and 2
4. 1, 2 and 4

Q. A power system consists of 300 buses out of which 20 buses are generator bus, 25 buses are ones with reactive power support and 15 buses are the ones with fixed shunt capacitors. All the other buses are load buses.It is proposed to perform a load flow analysis in the system using Newton- Raphson method. The size of the Newton Raphson Jacobian matrix is

1. $553\times 553$
2. $540\times 540$
3. $555\times 555$
   
4. $554\times 554$

Q.

Write about the cement bridge.

Q. Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are

$I{C}_1=20+0.3P_1$,
$I{C}_2=30+0.4P_2$,
$I{C}_3=30$

where P${}_i$ is the power in MW generated by units for i = 1, 2 and 3.

Assume that all the three units are operating all the time. Minimum and maximum loads on each units are 50 MW and 300 MW respecitvely. If the plant is operating on economic load dispatch to supply the total power demand of 700 MW, the power generated by each unit is

1. P${}_1$ = 242.86 MW; P${}_2$ = 157.14 MW; and P${}_3$ = 300 MW
2. P${}_1$ = 157.14 MW; P${}_2$ = 242.86 MW; and P${}_3$ = 300 MW
3. P${}_1$ = 300.0 MW; P${}_2$ = 300.0 MW; and P${}_3$ = 100 MW
4. P${}_1$ = 233.3 MW; P${}_2$ = 233.3 MW; and P${}_3$ = 233.4 MW

Q. A synchronous generator of reactance 1.20 p.u. is connected to an infinite bus bar through transformers and a line of total reactance of 0.6 p.u. The generator no load voltage is 1.20 p.u. and its inertia constant is H = 4 MWs/MVA. The resistance and machine damping may be assumed negligible. The system frequency is 50 Hz. If the generator is loaded to 50% of the maximum power limit, then the frequency of natural oscillations is

1. 4.76 Hz
2. 0.764 Hz
3. 3.52 Hz
4. 0.467 Hz

Q. A 100 MVA synchronous generator operates at full load at a frequency of 50 Hz. The load is suddenly reduced to 50 MW. Due to time lag in governor system, the steam valve begins to close after 0.4 sec. The frequency at t = 0.4 sec is ______ Hz (Given H = 4 MJ/MVA)

1. 51.23

Q. A 50 Hz synchronous generator is connected to an infinite bus through a line. The per unit reactances of the generator and the line are j0.3 p.u. and j0.2 p.u. respectively. The generator no load voltage is 1.1 p.u. and that the infinite bus is 1.0 p.u. The inertia constant of the generator is 3 MW-sec/MVA. If the generator is loaded to its maximum power transfer capacity and a small perturbation is given, then the resulting natural frequency of oscillations is _____Hz.

1. 1.53

Q. A synchronous generator is rated 25 MVA, 11 kV. It is star connected with neutral point solidly grounded. The generator is operating at no-load rated voltage. Positive, negative and zero sequence reactance are 0.2 p.u., 0.2 p.u. and 0.08 p.u. respectively. A line to line fault occurs on b and c phase of generator. Then the magnitude of fault current will be

1. 1.312 kA
2. 5.68 kA
3. 2.2724 kA
4. 0.7578 KA

Q. A 10 MVA, 13.8 kV alternator has positive, negative and zero sequence reactances of 30%, 40% and 5% respectively. The value of resistance that must be placed in the generator neutral so that the fault current for a LG fault of zero fault impedance will not exceed the rated line current is ________$\Omega$.

1. 18.43

Q. A 50 Hz, 4-pole turbo generator rated 100 MVA, 11 kV has an inertia constant of 10 MJ/MVA. If the mechanical input is suddenly raised to 90 MW for an electrical load of 60 MW. Neglect mechanical and electrical losses. Then the rotor acceleration is ______electrical degrees /sec${}^2$.

1. 270

Q. A 75 MVA, 10 kV synchronous generator has $X_d=0.4p.u$. The $X_d$ value (in p.u) to base of 100 MVA 11 kV is

1. 0.578
2. 0.279
3. 0.412
4. 0.44

Q. The Gauss Seidel load flow method has following disadvantages. Tick the incorrect statement.

1. Unreliable convergence
2. Slow convergence
3. Choice of slack bus affects convergence
4. A good initial guess for voltages is essential for convergence

Q. A generator delivers power of 1.0 p.u. to an infinite bus through a purely reactive network. The maximum power that could be delivered by the generator is 2.0 p.u. A three-phase fault occurs at the terminals of the generator which reduces the generator output to zero. The fault is cleared after $t_c$ second. The original network is then restored. The maximum swing of the rotor angle is found to be ${\delta }_{max}=110$ electrical degree. Then the rotor angle in electrical degrees at $t=t_c$ is

1. 55
2. 70
3. 69.14
4. 72.4

Q. Two generating 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 unit is

1. 400

Q. A three-phase short-circuit fault occurs at point F. in the system shown in figure below. The fault current is _____________A.

1. 878.5

Q.

Which service design process makes the most use of data supplied by demand management?

Q. The main objectives of load frequency control in a power system are:
1. To bring the steady state error to zero after load change.
2. To maintain the net tie-line
3. To maintain voltage on all buses.
4. To economize the cost of generation

1. 1 and 2.
2. 2 and 3
3. 3 and 4
4. 1, 2, 3 and 4.

Q. A constant load of 300 MW is supplied by two 200 MW generators, for which incremental fuel costs are:
$\frac{d{C}_1}{d{P}_{G1}}=0.10P_{G1}+20.0;\frac{d{C}_2}{d{P}_{G2}}=0.12P_{G2}+15$
[Where $P_G$ is in MW and C in Rs/hr]
If the most economic division of load between the generators is X and Y MW, then saving in Rs/day obtained compared to equal load sharing is Rs, _____ per day.

1. 218.16

Q. 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 PQ buses and a slack bus, the total number of buses in the system is

1. 61

Q. The network shown in the given figure has impedances in p.u. as indicated. The diagonal element $Y_{22}$ of the bus admittance matrix $Y_{BUS}$ of the network is

1. -j 19
2. +j 20
3. + j 0.2
4. -j 19.95

Q. A power system consists of 61 buses. If there are 20 PV buses in addition to PQ buses and a slack bus then the size of the Jacobian matrix is

1. $100\times 100$
2. $102\times 102$
3. $99\times 99$
4. $122\times 122$

Q. Two 11 kV, 20 MVA, three-phase, star connected generators operate in parallel as shown in figure. The positive, negative and zero sequence reactance of each being respectively j0.18, j0.15, j0.10 p.u. The star point of one of the generator is isolated and that of the other is earthed through a 2 $\Omega$ resistor. A single line to ground fault occurs at the terminals of one of the generators. Value of the current flowing in the grounding resistor is

1. 14.72 kA
2. 3.07 kA
3. 11.52 kA
4. 8.35 kA

Q. Steady state stability of power system is the ability of the power system to

1. maintain voltage at the rated voltage level
2. maintain frequeny exactly at 50 Hz
3. 
   maintain a spinning reserve mrgin at all times
4. maintain synchronism

Q. A generator with constant 1.0 p.u. terminal voltage supplies power through step-up transformer of 0.12 p.u. reactance and a double- circuit line to an infinite bus bar as shown in the figure. The infinite bus voltage is maintained at 1.0 p.u. Neglecting the resistances and susceptances of the system, the steady state stability power limit of the system is 6.25 p.u. If one of the double-circuit is tripped, then resulting steady stability power limit in p.u. will be

1. 12.5 p.u.
2. 3.125 p.u.
3. 10.0 p.u.
4. 5.0 p.u

Q. In a system, there are two generators operating in parallel. One generator, of rating 250 MVA, has an inertia constant of 6 MJ/MVA while the other generator of 150 MVA has an inertia constant of 4 MJ/MVA. The inertia constant for the combined system on 100 MVA common base is MJ/MVA.

1. 21

Q. A generator is connected through a 20 MVA, 13.8/138 kV step down transformer, to a transmission line. At the receiving end of the line a load is supplied through a step down transformer of 10 MVA. 138/69 kV rating. A 0.72 p.u. load, evaluated on load side transformer ratings as base values, is supplied from the above system. For system base values of 10 MVA and 69 kV in load circuit, the value of the load (in per unit) in generator circuit will be.

1. 36
2. 1.44
3. 0.72
4. 0.18

Q. A two bus system is shown below,



If 150 MW is transmitted from plant 2 to the load, a transmission loss of 15 MW is incurred. The incremental fuel costs of the two plants are:

$\frac{d{C}_1}{d{P}_{G1}}=0.04P_{G1}+20Rs/MWh$

$\frac{d{C}_2}{d{P}_{G2}}=0.02P_{G2}+16Rs/MWh$

The power received by load is ____ MW. (Assume system $\lambda$ = Rs. 25/MWh)

1. 274.75

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

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

1. $j\left[\begin{array}{ccc}0.3& -0.2& 0\\ -0.2& 0.12& 0.08\\ 0& 0.08& 0.02\end{array}\right]$
2. $j\left[\begin{array}{ccc}-15& 5& 0\\ 5& 7.5& -12.5\\ 0& -12.5& 2.5\end{array}\right]$
3. $j\left[\begin{array}{ccc}0.1& 0.2& 0\\ 0.2& 0.12& -0.08\\ 0& -0.08& 0.10\end{array}\right]$
4. $j\left[\begin{array}{ccc}-10& 5& 0\\ 5& 7.5& 12.5\\ 0& 12.5& 10\end{array}\right]$