Upload
truongbao
View
222
Download
3
Embed Size (px)
Citation preview
Exercises of course ELEC0029
Power flow computation and sensitivity analysisin a simple system
T. Van Cutsem
February 2018
1 / 27
System data
Lines data
UN (kV) X (Ω/km) X/R ωC/2 (µS/km) SN (MVA) km
380 0.3 10 1.5 1350 50150 0.4 5 1.2 300 50
Transformers data
orig extr R (pu) X (pu) B (pu) SN (MVA) n (“extr” side)
A B 0 0.14 0 500 1.08F B 0 0.14 0 250 1.08D B 0 0.14 0 300 1.00E C 0 0.14 0 600 1.00
2 / 27
Operating point data
I generators:I voltage at bus A: 15 kVI voltage at bus F: 15 kVI production of F: 150 MW
I loads:I at bus E: 400 MW / 120 MvarI at bus D: 100 MW / 30 Mvar
3 / 27
I Specify the data at all buses and run a power flow computation todetermine the electrical state of the system. In this computationassume that transformers D-B and E-C are of Yd11 type, and takeinto account the phase angle of their transformer ratios.
The data are available in the file 6bus.dat, while the results can bedisplayed on the one-line diagram by using the file 6bus.svg
I Detail the active and reactive power balances of the system.
I Check that line D-E and transformer C-E operate below theirthermal ratings.
4 / 27
Transformers D-B et E-C of type Yd11; complex ratios
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
0.9912
1.0000
−106
−14
−53
14
54
352
163
348
128−347
−137
154
56
1.0363
1.0134
1.0194
−347
−5.9 −7.8
20.2
0.0
100
30
1.0000
150
79
−0.9
400
120
17.6
5 / 27
I Simulate the misuse of a transformer E-C of type Yy0, whiletransformer D-B is of type Yd11. Show that the resulting electricalstate is unacceptable.
6 / 27
Transformer D-B of type Yd11 and E-C of type Yy0
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
0.9205
1.0000
−207
87
−310
20
332
372
296
90
206−90
−221
432
147
0.9967
0.9495
0.9732
−90
−6.5 −6.9
11.2
0.0
100
30
1.0000
150
145
−1.3
400
120
−8.3
7 / 27
I Getting back to the correct configuration of the transformers,perform a new power flow computation in which the phase angles ofthe transformer ratios are set to zero. Comment on the resultsobtained.
Unless otherwise specified, the phase angles are neglected in thesequel.
8 / 27
Phase angles of transformer ratios neglected
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−12.4
0.9912
1.0000
−106
−14
−53
14
54
352
163
348
128−347
−137
154
56
1.0363
1.0134
1.0194
−347
−5.9 −7.8
−9.8
0.0
100
30
1.0000
150
79
−0.9
400
120
9 / 27
I Assuming that transformer D-B is equipped with a phase shiftingdevice allowing to vary progressively the phase angle of itstransformer ratio, study the impact of this phase angle on branchpower flows and bus voltage magnitudes.
10 / 27
Varying the phase angle of the ratio of transformer D-B
1∠0 for E-C and 1∠φ for D-B. Example for φ = −10.
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−10.6
0.9815
1.0000
−132
12
−153
7
157
355
179
248
136−247
−151
257
68
1.0315
1.0073
1.0145
−247
−6.0 −7.3
−2.6
0.0
100
30
1.0000
150
87
−0.9
400
120
11 / 27
Variation of φ
-100
0
100
200
300
400
500
600
-15 -10 -5 0 5 10 15
phi (deg)
P B-C (MW)P D-E (MW)P B-D (MW)
0
20
40
60
80
100
120
140
160
-15 -10 -5 0 5 10 15
phi (deg)
Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
1.01
1.015
1.02
-15 -10 -5 0 5 10 15
phi (deg)
V C (pu)V D (pu)V E (pu)
12 / 27
I Assuming that transformer D-B is equipped with a tap changerallowing to vary progressively (the magnitude of) its transformerratio, study the impact of this ratio on branch power flows and busvoltage magnitudes.
I Same question for an identical variation of the ratios of bothtransformers D-B an E-C.
13 / 27
Varying the (magnitude) of the ratio of transformer D-B
1∠0 for E-C and n∠0 for D-B. Example for n = 0.95.
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−12.2
1.0029
1.0000
−74
−46
−61
48
62
352
162
340
91−339
−102
162
91
1.0364
1.0541
1.0232
−339
−5.9 −7.8
−9.7
0.0
100
30
1.0000
150
79
−0.9
400
120
14 / 27
Variation of n
0
50
100
150
200
250
300
350
400
90 95 100 105 110
n (pu)
P B-C (MW)P D-E (MW)P B-D (MW)
-50
0
50
100
150
200
90 95 100 105 110
n (pu)
Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
90 95 100 105 110
n (pu)
V C (pu)V D (pu)V E (pu)
15 / 27
Same variation of the ratios of transformers D-B et E-C
n∠0 for both transformers. Example for n = 0.95.
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−11.8
1.0487
1.0000
−105
−15
−55
15
56
352
159
346
123−345
−133
156
55
1.0374
1.0705
1.0210
−345
−5.9 −7.8
−9.5
0.0
100
30
1.0000
150
77
−0.9
400
120
16 / 27
Same variation of n in both transformers
50
100
150
200
250
300
350
400
90 95 100 105 110
n (pu)
P B-C (MW)P D-E (MW)P B-D (MW)
0
20
40
60
80
100
120
140
90 95 100 105 110
n (pu)
Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)
0.85
0.9
0.95
1
1.05
1.1
1.15
90 95 100 105 110
n (pu)
V C (pu)V D (pu)V E (pu)
17 / 27
I Let ARTERE (the power flow computation software) adjustautomatically the ratios of both transformers D-B and E-C so as tobring the voltages at buses D and E in the dead-band [1.02 1.04] pu
18 / 27
Automatic adjustment of the ratios of both transformersto bring the voltages at buses D and E in [1.02 1.04] pu
iter max mismatches : MW Mvar phi(MVA)
1 395.2 407.1 605.1
2 27.4 62.4 78.0
3 1.0 1.2 2.0
4 0.1 0.1 0.1
in-phase trfo taps : 2 down 0 up
4 4.4 58.8 90.6
5 0.2 0.8 1.0
6 0.0 0.1 0.1
in-phase trfo taps : 1 down 0 up
6 4.5 61.1 83.7
7 0.1 0.7 0.7
8 0.0 0.0 0.0
in-phase trfo taps : 1 down 0 up
8 4.5 63.5 86.9
9 0.1 0.7 0.7
10 0.0 0.0 0.0
transfo ctld bus volt set-pt tol ratio tap max
E-C E 1.0275 1.0300 0.0100 0.963 14 25
D-B D 1.0350 1.0300 0.0100 0.988 16 2519 / 27
Situation after the transformers have been adjusted
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−12.1
1.0275
1.0000
−121
1
−51
−2
51
352
161
351
143−349
−151
151
38
1.0368
1.0350
1.0184
−349
−5.9 −7.8
−9.6
0.0
100
30
1.0000
150
78
−0.9
400
120
20 / 27
I Study the effect of varying the voltage of generator F on thereactive power productions of both generators, on the branch powerflows and on the bus voltage magnitudes.
I Same question for an identical variation of the voltages of bothgenerators A and F.
21 / 27
Varying the voltage of generator F
Example: VF = 0.98 pu
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−12.5
0.9828
1.0000
−106
−14
−53
14
54
352
189
348
129−347
−137
154
56
1.0283
1.0052
1.0112
−347
−5.9 −7.9
−9.9
0.0
100
30
0.9800
150
55
−0.8
400
120
22 / 27
Variation of VF
0
50
100
150
200
250
0.96 0.98 1 1.02 1.04
V F (pu)
Q Gen A (MVar)Q Gen F (MVar)
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
0.96 0.98 1 1.02 1.04
V F (pu)
V C (pu)V D (pu)V E (pu)
23 / 27
Variation of VF
50
100
150
200
250
300
350
0.96 0.98 1 1.02 1.04
V F (pu)
P B-C (MW)P D-E (MW)P B-D (MW)
0
20
40
60
80
100
120
140
0.96 0.98 1 1.02 1.04
V F (pu)
Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)
24 / 27
Same variation of voltages of generators A and F
Example: VF = VA = 0.98 pu
150 kV
380 kVpuissances réactives (Mvar)
puissances actives (MW)
D E
A
B
C
modules tensions (pu)15 kV phases tensions (deg)
F
−13.0
0.9658
0.9800
−106
−14
−53
15
54
352
168
348
131−347
−139
154
57
1.0124
0.9888
0.9949
−347
−6.2 −8.1
−10.3
0.0
100
30
0.9800
150
81
−0.9
400
120
25 / 27
Variation of VF = VA
60
80
100
120
140
160
180
0.96 0.98 1 1.02 1.04
V Gen (pu)
Q Gen A (MVar)Q Gen F (MVar)
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
0.96 0.98 1 1.02 1.04
V Gen (pu)
V C (pu)V D (pu)V E (pu)V B (pu)
26 / 27
Variation of VF = VA
50
100
150
200
250
300
350
0.96 0.98 1 1.02 1.04
V Gen (pu)
P B-C (MW)P D-E (MW)P B-D (MW)
0
20
40
60
80
100
120
140
0.96 0.98 1 1.02 1.04
V Gen (pu)
Q B-C (MVar)Q D-E (MVar)Q B-D (MVar)
27 / 27