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Power Systems Problems / Weedy & Grainger
Selected from Books:
 J.A. Harrison, The essence of electric power systems (H)
 B.M. Weedy, Electric power systems (W)
 J.J. Grainger, W.D. Stevenson, Power system analysis (G)
1.
H3.5
A star-connected load consisting of a resistor of 80 and and inductor of 0.191H
in each phase is connected to a 415V, three-phase, 50Hz supply. Calculate: (a) the
line current I; (b) the real power P consumed by the load; and (c) the reactive
power Q consumed by the load. From P and Q calculate the load phase angle ,
and show that P  3VI cos and Q  3VI sin  .
2.
H3.8
A star-connected load of (75+j48) per phase is supplied from a 50Hz alternator
through a transmission line of (5+j12) per coductor. Three capacitors, each 5F,
are connected in delta across the alternator terminals. If the alternator terminal
voltage is 440V, calculate: (a) the real power; (b) the reactive power, generated by
the alternator, and hence find the alternator power factor.
3.
H4.8
A 50Hz, 50MVA transformer with a 132kV primary and a 33kV secondary has a
reactance of 0.1pu per phase. What is the reactance in ohms per star phase: (a)
referred to the primary; (b) referred to the secondary.
4.
H4.11
The figure below represents a one-line diagram of part of a three-phase power
system. Calculate the voltage of the grid busbar V g , when the load busbar is at
11kV and the load current is 1kA at unity power factor.
5.
W6.12
Determine the voltage at bus (2) and the reactive power at bus (3) in the figure
below after the first iteration of a Gauss-Seidel load flow method. Assume the
initial voltage to be 10 pu. All the quantities are in per unit on a common base.
6.
W1.5
The variation of load (P) with time (t) in a power supply system is given by the
expression,
P kW   4000  8t  0.00091t 2
where t is in hours over a total period of one year.
This load is supplied by three 10MW generators and it is advantageous to fully
load a machine before connecting the others. Determine:
(a) the load factor on the system as a whole;
(b) the total magnitude of installed load if the diversity factor is equal to 3;
(c) the minimum number of hours each machine is in operation;
(d) the approximate peak magnitude of installed load capacity to be cut off to
enable only two generators to be used.
7.
G16.6
A power system is identical to that of Example 16.3, except that the impedance of
each of the parallel transmission lines is j0.5 and the delivered power is 0.8 per
unit when both the terminal voltage of the machine and the voltage of the infinite
bus are 1.0 per unit. Determine the power-angle equation for the system during the
specified operating conditions.
8.
G16.9
A generator having H = 6.0MJ/MVA is delivering power of 1.0 per unit to an
infinite bus through a purely reactive network when the occurence of a fault
reduces the generator output to zero. The maximum power that could be delivered
is 2.5 per unit. When the fault is cleared, the original network conditions again
exist. Determine the critical angle and critical clearing time.
9.
G16.10
A 60Hz generator is supplying 60% of Pmax to an infinite bus through a reactive
network. A fault occurs which increases the reactance of the network between the
generator internal voltage and the infinite bus by 400%. When the fault is cleared,
the maximum power that can be delivered is 80% of the original maximum value.
Determine tha critical clearing angle for the condition described.
10. H6.2
A symmetrical three-phase short circuit occurs on the 22kV busbars of the circuit
shown as a one-line diagram in the figure below. Calculate the fault current and
the fault apparent power.
11. H6.3
A symmetrical three-phase fault occurs on the 11kV busbars of the circuit below.
Calculate the fault apparent power and the fault current.
12. W7.2
Two 100MVA, 20kV turbo-generators (each of transient reactance 0.2 pu) are
connected, each through its own 100MVA, 0.1 pu reactance transformer, to a
common 132kV busbar. From this busbar, a 132kV feeder, 40km in length,
supplies an 11kV load through a 132/11kV transformer of 200MVA rating and
reactance 0.1 pu. If a balanced three-phase short circuit occurs on the low voltage
terminals of the load transformer, determine, using a 100MVA base, the fault
current in the feeder and the rating of a suitable circuit breaker at the load end of
the feeder. The feeder impedance per phase is (0.035+j+.14)/km.
13. W7.8
A single line-to-earth fault occurs in a radial transmission system. The following
sequences exist between the source of supply (an infinite busbar) of voltage 1 pu to
the point of the fault: Z1 = (0.3+j0.6)pu, Z2 = (0.3+j0.55)pu, Z0 = (1+j0.78)pu. The
fault path to earth has a resistance of 0.66 pu. Determine the fault current and the
voltage at the point of the fault.
14. W7.12
A 33kV, 60Hz overhead line has a capacitance to ground per phase of
approximately 0.7F. Calculate the reactance of a suitable arc-suppression coil.
15. H5.1
A turbine generator is delivering 20MW at 50Hz to a local load; it is not connected
to the grid. The load suddenly drops to 15MW; and the turbine governor starts to
close the steam valve after a delay of 0.5s. The stored energy in the rotating parts is
80MJ at 3000rev/min. What is the generated frequency at the end of the 0.5s
delay?
16. H5.2
A 10km length of 400kV, three-phase overhead line can be represented by an
inductive reactance of 2.7 per phase. The receiving-end busbars are at 400kV
when supplying a load of 1GW at a power factor of 0.8 lagging. What is the
sending-end voltage?
17. H5.3
A 50Hz, 132kV line is 5km long. At the receiving end there is a load of 100MVA.
The line can be represented by a resistance of 0.16 per phase per km and an
inductance of 1.3mH per phase per km. Calculate the voltage drop along the line if
the voltage 132 kV is at the sending end of the line and if the load power factor is:
(a) 0.8 lagging; (b) 0.95 lagging, and (c) 0.93 leading.
18. W5.3
The load at the receiving end of a three-phase, overload line is 25MW, power
factor 0.8 lagging, at a line voltage of 33kV. A synchronous compensator is
situated at the receiving end and the voltage at both ends of the line is maintained
at 33kV. Calculate the MVAr of the compensator. The line has resistance 5 per
phase and inductance reactance (line-to-neutral) 20 per phase.
19. W10.2
A highly capacitive circuit of capacitance per phase 100F is disconnected by a
circuit breaker, the source inductance being 1mH. The breaker gap breaks down
when the voltage across it reaches twice the system peak line-to-neutral voltage of
38kV. Calculate the current flowing with the breakdown and its frequency and
compare it with the normal charging current of the circuit.
20. W10.4
The effective inductance and capacitance of a faulted system as viewed by the
contacts of a circuit breaker are 2mH and 500F, respectively. The circuit
breaker chops the fault current when it has an intantaneous value of 100A.
Calculate the restriking voltage set up across the circuit breaker. Neglect
resistance.
21. W10.9
A long overhead line has a surge impedance of 500 and an effective resistance at
the frequency of the surge of 7/km. If a surge of magnitude 500kV enters the line
at a certain point, calculate the magnitude of this surge after it has traversed 100km
and calculate the resistive power loss of the wave over this distance. The wave
velocity is 3x105km/s.
22. H4.7
A circuit breaker for the 400kV grid can break a 50.5kA symmetrical three-phase
fault current. What is the rating of the circuit breaker?
23. G10.14
A 625kV generator with X”d = 0.20 per unit is connected to a bus through a circuit
breaker, as shown in the figure below. Connected through circuit breakers to the
same bus are three synchronous motors rated 250hp, 2.4kV, 1.0 power factor, 90%
efficiency, with X”d = 0.20 per unit. The motors are operating at full load, unity
power factor, and rated voltage, with the load equally divided among the machines.
(a) Draw the impedance diagram with the impedances marked in per unit on a
base of 625kVA, 2.4kV.
(b) Find the symmetrical short-circuit in amperes, which must be interrupted by
breakers A and B for a three-phase fault at point P. Simplify the calculations
by neglecting the prefault current.
(c) Repeat part (b) for a three-phase fault at point Q.
(d) Repeat part (b) for a three-phase fault at point R.
24. G10.15
A circuit breaker having a nominal rating of 34.5kV and a continuous current
rating of 1500A has a voltage range factor K of 1.65. Rated maximum voltage is
38kV and the rated short-circuit current at that voltage is 22kA. Find (a) the
voltage below which rated short-circuit current does not increase as operating
voltage decreases and the value of that current and (b) rated short-circuit current at
34.5kV.
25. W3.13
Two identical transformers each have a nominal or no-load ratio of 33/11kV and a
reactance of 2 referred to the 11kV side; resistance may be neglected. The
transformers operate in parallel and supply a load of 9MVA, 0.8 p.f. lagging.
Calculate the current taken by each transformer when they operate five tap steps
apart (each step is 1.25 per cent of the nominal voltage).
26. H4.4
A three-phase power line consists of three parallel conductors in the same
horizontal plane. The two outer conductors are each 1m from the centre conductor.
If the conductor diameter is 6mm, calculate the average inductance per phase of a
1km length of the line. Assume the expression for the inductance per metre length.
27. W3.10
In a three-core cable, the capacitance between the three cores short-circuited
together and the sheath is 0.87F/km, and that between two cores connected
together and the third core is 0.84F/km. Determine the kVA required to keep
16km of this cable charged when the supply is 33kV, three phase, 50Hz.
28. G4.3
An AAC is composed of 37 strands, each having a diameter of 0.333cm. Compute
the dc resistance in ohms per kilometer at 75C. Assume that the increase in
resistance due to spiraling is 2%.
29. G5.6
A three-phase 60Hz line has flat horizontal spacing. The conductors have an
outside diameter of 3.28cm with 12 m between conductors. Determine the
capacitive reactance to neutral in ohm-meters and the capacitive reactance of the
line in ohms if its length is 125 mi.
30. H6.1
Three 11kV, 100MVA generators are connected to common busbars. Each is
connected via a 100MVA inductor and an identical circuit breaker. The inductors
have reactances of 0.15pu, 0.20pu and 0.30pu. If the generators each have a
transient reactance of 0.25pu, what is the minimum circuit-breaker rating to protect
the generators against a fault on the common busbars?
31. H6.4
The figure below represents a one-line diagram of a power system. A symmetrical
three-phase fault occurs on the 33kV busbars as shown. Calculate the fault level,
the fault current and the line voltage at the point P, under the fault condition, but
neglect the resistance of each of the line impedances Z1 and Z2.
32. H6.5
Referring to the previous question, is it possible to limit the fault current to 3.1kA
by increasing the reactance of the 100MVA inductor? If so, to what value must it
be raised?
33. H6.6
Reffering again to the circuit in guestion H6.4, calculate the fault level and fault
current, taking the resistances of the lines into account. Does the inclusion of these
resistances make a significant difference to the answers?
34. H6.7
Suppose the system in question H6.4 was modified by the addition of a grid feed
of 500MVA short-circuit rating onto the 132kV busbars at the point P. A
symmetrical short circuit occurs on the 33kV busbars as shown. Calculate the fault
apparent power and the fault current.