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 Sbase=100 MVA, Vbase-15 kV at bus 1. The ratings of the devices are: Generator Gl: Generator G2: 400 MVA, 15 kV 800 MVA, 15 kV Transformer T1: 400 MVA, 15 A/345 Y kV Transformer T2: 800 MVA, 345 Y/15 A kV ©. T2 Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi. G1 ΤΙ m= Θ m ค 白白 L3 L2 13 LI 800 MW 280 Mver FIGURE E5-1 ☐ TABLE E5-1 Bus input data 80 MW 40MVar V $ Po Qo PL QL QCmax QGmin Bus Type 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 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 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 Jii. (NOTE: a power mismatch at a bus "K" is defined as AP (n) =P - Pacale(n), where 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 Sbase=100 MVA, Vbase-15 kV at bus 1. The ratings of the devices are: Generator Gl: Generator G2: 400 MVA, 15 kV 800 MVA, 15 kV Transformer T1: 400 MVA, 15 A/345 Y kV Transformer T2: 800 MVA, 345 Y/15 A kV ©. T2 Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi. G1 ΤΙ m= Θ m ค 白白 L3 L2 13 LI 800 MW 280 Mver FIGURE E5-1 ☐ TABLE E5-1 Bus input data 80 MW 40MVar V $ Po Qo PL QL QCmax QGmin Bus Type 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 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 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 Jii. (NOTE: a power mismatch at a bus "K" is defined as AP (n) =P - Pacale(n), where 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
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.61P
Related questions
Question
Please solve section a,b and c step by step in detail handwritten and no ai/chatgpt answers they are wrong thanks.
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 Sbase=100
MVA, Vbase-15 kV at bus 1. The ratings of the devices are:
Generator Gl:
Generator G2:
400 MVA, 15 kV
800 MVA, 15 kV
Transformer T1:
400 MVA, 15 A/345 Y kV
Transformer T2:
800 MVA, 345 Y/15 A kV
©.
T2
Lengths of transmission lines: L1=200 mi, L2=100 mi, L3-50 mi.
G1
ΤΙ
m=
Θ
m
ค
白白
L3
L2
13
LI
800 MW
280 Mver
FIGURE E5-1
☐
TABLE E5-1 Bus input data
80 MW
40MVar
V
$
Po
Qo
PL
QL
QCmax
QGmin
Bus
Type
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
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 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 Jii.
(NOTE: a power mismatch at a bus "K" is defined as AP (n) =P - Pacale(n),
where is the scheduled real power and P(n) is the power calculated
from the power flow equation after iteration n.
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