The oneline diagram of the system is shown in Fig.E5-1. The data for the components in the system are given in per unit in Tables E6-1,2 and 3. The base values are Shase-100 MVA, Vbase-15 kV at bus 1. The ratings of the devices are: Generator Gl: Generator G2: Transformer T1: Transformer T2: 400 MVA, 15 kV 800 MVA, 15 kV 400 MVA, 15 A/345 Y kV 800 MVA, 345 Y/15 A kV T2 Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi. Gl T1 + ◎ L2 L3 Ll 나 口口 800 MW 280 Mvar FIGURE E5-1 © m TABLE E5-1 Bus input data ㅁ 80 MW V δ Po QG PL QL QCmax QCimin Bus Туре p.u degrees p.u. p.u. p.u. p.u. p.u. p.u. 1 Swing 1.0 0 - - 0 0 - 2 Load - - 0 0 8.0 2.8 Voltage- 3 1.05 - 5.2 0.8 0.4 4.0 -2.4 controlled 4 Load 0 0 0 0 0 5 Load 0 0 0 0 0 TABLE E5-2 Line input data R x G B Bus-to-bus Maximum MVA p.u. p.u. p.u. p.u. p.u. 2-4 0.009 0.1 0 1.72 12.0 2-5 0.0045 0.050 0 0.88 12.0 4-5 0.00225 0.025 0 0.44 12.0 TABLE E5-3 Transformer input data R X Ge B Maximum MVA Bus-to-bus p.u. p.u. p.u. p.u. p.u. 1-5 0.0015 0.02 0 1.72 6.0 2-5 0.00075 0.01 0 0.88 10.0 (a) Calculate Ybus for the system using the data in the tables. (b) Using the initial values given in Table 1, perform one Gauss-Seidel iteration for bus 2 and 3 voltages V2(1) and 3(1). Note that bus 3 is a voltage-controlled bus. Therefore, correction must be applied to the magnitude of V3(1) to force it to have the specified value (||=1.05). (c) In the Newton-Raphson method, calculate the initial power mismatches at all the buses 2-5. Also, calculate the Jacobian matrix elements of the partition J11. (NOTE: a power mismatch at a bus "k" is defined as AP(n)-Pack-Pac (n), where P is the scheduled real power and P(n) is the power calculated from the power flow equation after iteration n.
The oneline diagram of the system is shown in Fig.E5-1. The data for the components in the system are given in per unit in Tables E6-1,2 and 3. The base values are Shase-100 MVA, Vbase-15 kV at bus 1. The ratings of the devices are: Generator Gl: Generator G2: Transformer T1: Transformer T2: 400 MVA, 15 kV 800 MVA, 15 kV 400 MVA, 15 A/345 Y kV 800 MVA, 345 Y/15 A kV T2 Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi. Gl T1 + ◎ L2 L3 Ll 나 口口 800 MW 280 Mvar FIGURE E5-1 © m TABLE E5-1 Bus input data ㅁ 80 MW V δ Po QG PL QL QCmax QCimin Bus Туре p.u degrees p.u. p.u. p.u. p.u. p.u. p.u. 1 Swing 1.0 0 - - 0 0 - 2 Load - - 0 0 8.0 2.8 Voltage- 3 1.05 - 5.2 0.8 0.4 4.0 -2.4 controlled 4 Load 0 0 0 0 0 5 Load 0 0 0 0 0 TABLE E5-2 Line input data R x G B Bus-to-bus Maximum MVA p.u. p.u. p.u. p.u. p.u. 2-4 0.009 0.1 0 1.72 12.0 2-5 0.0045 0.050 0 0.88 12.0 4-5 0.00225 0.025 0 0.44 12.0 TABLE E5-3 Transformer input data R X Ge B Maximum MVA Bus-to-bus p.u. p.u. p.u. p.u. p.u. 1-5 0.0015 0.02 0 1.72 6.0 2-5 0.00075 0.01 0 0.88 10.0 (a) Calculate Ybus for the system using the data in the tables. (b) Using the initial values given in Table 1, perform one Gauss-Seidel iteration for bus 2 and 3 voltages V2(1) and 3(1). Note that bus 3 is a voltage-controlled bus. Therefore, correction must be applied to the magnitude of V3(1) to force it to have the specified value (||=1.05). (c) In the Newton-Raphson method, calculate the initial power mismatches at all the buses 2-5. Also, calculate the Jacobian matrix elements of the partition J11. (NOTE: a power mismatch at a bus "k" is defined as AP(n)-Pack-Pac (n), where P is the scheduled real power and P(n) is the power calculated from the power flow equation after iteration n.
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter3: Power Transformers
Section: Chapter Questions
Problem 3.33P: Consider the three single-phase two-winding transformers shown in Figure 3.37. The high-voltage...
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Transcribed Image Text:The oneline diagram of the system is shown in Fig.E5-1. The data for the components in
the system are given in per unit in Tables E6-1,2 and 3. The base values are Shase-100
MVA, Vbase-15 kV at bus 1. The ratings of the devices are:
Generator Gl:
Generator G2:
Transformer T1:
Transformer T2:
400 MVA, 15 kV
800 MVA, 15 kV
400 MVA, 15 A/345 Y kV
800 MVA, 345 Y/15 A kV
T2
Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi.
Gl
T1
+
◎
L2
L3
Ll
나
口口
800 MW
280 Mvar
FIGURE E5-1
©
m
TABLE E5-1 Bus input data
ㅁ
80 MW
V
δ
Po
QG
PL
QL
QCmax
QCimin
Bus
Туре
p.u
degrees
p.u.
p.u.
p.u.
p.u.
p.u.
p.u.
1
Swing
1.0
0
-
-
0
0
-
2
Load
-
-
0
0
8.0
2.8
Voltage-
3
1.05
-
5.2
0.8
0.4
4.0
-2.4
controlled
4
Load
0
0
0
0
0
5
Load
0
0
0
0
0
Transcribed Image Text:TABLE E5-2 Line input data
R
x
G
B
Bus-to-bus
Maximum MVA
p.u.
p.u.
p.u.
p.u.
p.u.
2-4
0.009
0.1
0
1.72
12.0
2-5
0.0045
0.050
0
0.88
12.0
4-5
0.00225
0.025
0
0.44
12.0
TABLE E5-3 Transformer input data
R
X
Ge
B
Maximum MVA
Bus-to-bus
p.u.
p.u.
p.u.
p.u.
p.u.
1-5
0.0015
0.02
0
1.72
6.0
2-5
0.00075
0.01
0
0.88
10.0
(a) Calculate Ybus for the system using the data in the tables.
(b) Using the initial values given in Table 1, perform one Gauss-Seidel iteration
for bus 2 and 3 voltages V2(1) and 3(1). Note that bus 3 is a voltage-controlled
bus. Therefore, correction must be applied to the magnitude of V3(1) to force it
to have the specified value (||=1.05).
(c) In the Newton-Raphson method, calculate the initial power mismatches at all
the buses 2-5. Also, calculate the Jacobian matrix elements of the partition J11.
(NOTE: a power mismatch at a bus "k" is defined as AP(n)-Pack-Pac (n),
where P is the scheduled real power and P(n) is the power calculated
from the power flow equation after iteration n.
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