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 Lengths of transmission lines: L1-200 mi, L2=100 mi, L3-50 mi. TI Gl 다 @ L3 T2 G2 80 MW 40 Mvar Ll L2 800 MW 280 Mvar FIGURE E5-1 TABLE E5-1 Bus input data V $ Po QG P1. QL Bus Туре Qomas Qamin 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 Maximum MVA Bus-to-bus 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 2-5 0.0015 0.02 0 1.72 6.0 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 V3(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 - Pa(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 Lengths of transmission lines: L1-200 mi, L2=100 mi, L3-50 mi. TI Gl 다 @ L3 T2 G2 80 MW 40 Mvar Ll L2 800 MW 280 Mvar FIGURE E5-1 TABLE E5-1 Bus input data V $ Po QG P1. QL Bus Туре Qomas Qamin 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 Maximum MVA Bus-to-bus 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 2-5 0.0015 0.02 0 1.72 6.0 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 V3(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 - Pa(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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Please solve section a) step by step in detail and also please no ai or chat gpt answers they are wrong thank you.
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
Lengths of transmission lines: L1-200 mi, L2=100 mi, L3-50 mi.
TI
Gl
다
@
L3
T2
G2
80 MW
40 Mvar
Ll
L2
800 MW
280 Mvar
FIGURE E5-1
TABLE E5-1 Bus input data
V
$
Po
QG
P1.
QL
Bus
Туре
Qomas
Qamin
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
Maximum MVA
Bus-to-bus
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
2-5
0.0015
0.02
0
1.72
6.0
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 V3(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 - Pa(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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