Assignment # 02
Power System Analysis & Design
Due date: 17 – 12 – 2018 (1 pm)
Total Marks: 3 x 10 = 30
Solve all Questions in sequence. Each question has 3 mark.
Solve following end problems of text book “Power System Analysis” by John J. Granger, W. D.
Stevenson. (No Need to submit)
Problems
10.2
11.2
10.3
11.3
10.4
11.4
10.5
11.5
10.6
11.6
10.7
11.7
10.1
11.8
10.14
11.9
10.15
11.11
11.1
11.16
Solve following end problems of text book “Power System Analysis” by John J. Granger, W. D.
Stevenson. (Submit following questions)
Question 1: With bus 1 in figure as slack bus, use Fast decoupled load flow to obtain load flow solutions
(Two iterations). Use data not given by suitable assumptions
Impedance of sample network of figure
Bus code p-q
Imp. Z pq
Line charging Y'pq /2
1-2
2-3
3-4
1-3
1-4
0.12 + j0.05
j0.025
0.05 + j0.02
j0.015
0.25 + j0.075
j0.02
0.45 + j0.045
j0.015
0.05 +j0.015
j0.01
Scheduled generation and loads
Bus code Generation
" Load
MW
MVARS
MW
MVARS
P
1
0
0
0
0
2
0
0
50
25
3
100
0
0
0
4
0
0
125
30
Question 2: For the system in Figure the ratings of the various components are:
Generator:
25 MVA, 12.4 kV, 10% subtransient reactance
Motor:
20 MVA, 3.8 kV, 15% subtransient reactance
25 MVA, 11/33 kV, 8% reactance
Transformer T1:
Transformer T2:
20 MVA, 33/3.3 kV, 10% reactance
Line:
20 ohms reactance
The system is loaded so that the motor is drawing 15 MW at 0.9 loading power factor, the motor terminal
voltage being 3.1 kV. Find the subtransient current in generator and motor for a fault at generator bus. [Hint:
Assume a suitable voltage base for the generator. The voltage base for transformers, line and motor would then be
given by the transformation ratios. For example, if we choose generator voltage base as 11 kV. the line voltage
base is 33 kV and motor voltage base is 3.3 kV. Per unit reactances are calculated accordingly.]
Question 3: Two synchronous motors are connected to the bus of a large system through a short transmission
line as shown in Figure The ratings of various components are:
Motors (each):
1 MVA, 440 V, 0.1 pu transient reactance
Line:
0.05-ohm reactance
Large system:
Short circuit MVA at its bus at 440 V is 8.
When the motors are operating at 440 V, calculate the short circuit current (symmetrical) fed into a threephase fault at motor bus.
Question 4: A synchronous generator rated 500 kVA, 440 V, 0.1 pu subtransient reactance is supplying a passive
load of 400 kW at 0.8 lagging power factor. Calculate the initial symmetrical rms current for a three-phase fault at
generator terminals.
Question 5: A generator-transformer unit is connected to a line through a circuit breaker. The unit ratings are:
Generator:
10 MVA, 6.6 kV; X"d= 0.1 pu, X’d = 0.20 pu and
Xd = 0.80 pu
Transformer: 10 MVA, 6.9/33 kV, reactance 0.08 pu
The system is operating no load at a line voltage of 30 kV, when a three-phase fault occurs on the line just beyond the
circuit breaker. Find
(a) the initial symmetrical rms current in the breaker,
(b) the maximum possible DC off-set current in the breaker,
(c) the momentary current rating of the breaker,
(d) the current to be interrupted by the breaker and the interrupting kVA, and
(e) the sustained short circuit current in the breaker.
Question 6: Consider the 3-bus system of Figure. The generators are 100 MVA, with transient reactance 10% each.
Both the transformers are 100 MVA with a leakage reactance of 5%. The reactance of each of the lines to a base of 100
MVA, 110 KV is 10%. Obtain the short circuit solution for a three-phase solid short circuit on bus 3. Assume prefault
voltages to be 1 pu and prefault currents to be zero.
Question 7: A 625-kVA, 2.4 kV generator with " = .
is
connected to a bus through a circuit breaker as shown in the figure.
Connected though circuit breakers to the same bus are three synchronous
motors rated 250 hp (1 hp = 746 watts), 2.4 kV, unity power factor, 85%
.
efficiency, having " = .
(a) Find the symmetrical subtransient short-circuit current in
amperes which must be interru pted by breakers A and B for three-phase faults at points P and Q
neglecting the pre-fault current. Choose a base of 625 kVA and 2.4 kV.
(b)
Specify the current interrupting capability and closing and latching current (RMS and Peak) of the
bus circuit-breakers, by using E/X method. For this system X/R is unknown. Further, assume that
the voltage range factor for the circuit-breaker is, K = 1.21.
(c)
Draw the standard ANSI/IEEE operating time diagram for the Circuit-Breakers, also label different
instances and periods on the diagram.
Question 8: A three-phase Y-connected unbalanced source is connected to a Y-connected load consisting
of three resistors. The neutral of load is connected to the neutral of the source through 5 Ω resistance. The
resistance in phase ‘a’ is 10 Ω, in phase ‘b’ is 30 Ω, and in phase ‘c’ is 20 Ω. The line-to-neutral source
voltage in phase ‘a’ is ∠ , in phase ‘b’ is ∠−
, and in phase ‘c’ is ∠
. Select the line to
neutral voltage of phase ‘a’ as reference and by using method of symmetrical components, determine (i)
current in all three phases, (ii) voltage across each load resistance, and (iii) voltage across the resistance
connected between the neutrals. Neglect the generator synchronous impedance.
Question 9:
(a)
For the given network, find the sub-transient fault current in per-unit for a symmetrical fault on bus
2. Also, find the fault current contribution from generator 1, and voltage at bus 1 and 3. Assume
that no current is flowing prior to the fault and that the pre-fault voltage at bus 2 is . ∠
per unit.
Use Thevenin’s Theorem in the calculations.
(b)
Draw the zero-sequence network of the system shown in figure below. All generators are solidly
grounded.
Y grounded-∆
∆-Y
TL1
TL2
∆-Y
grounded
∆
TL3
Y
Y
∆
∆
Y-∆
Question 10: In the three-bus network shown in the following figure, a line-end symmetrical short-circuit
fault occurs on line ①-②, on the line side of the breaker at bus ②. Neglecting prefault currents and assuming
rated system voltage at the fault point, calculate the subtransient current into the fault when only the near-end
breaker at bus ② opens. Also find the after-fault voltage at bus ②.
=
0.0857
0.0532
0.0432
0.0532
0.0992
0.0498
0.0432
0.0498$
0.1026