Power System Reliability Monitoring and Control for Transient ......Power System Reliability...
Transcript of Power System Reliability Monitoring and Control for Transient ......Power System Reliability...
Power System Reliability Monitoring and Control
for Transient Stability
May 15, 2017
Naoto Yorino Yutaka SasakiHiroshima University
The 14h International Workshops on Electric Power Control Centers (EPCC 14) May 14-17 2017, Wiesloch, Germany
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Security Issues for Future Power Systems
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Backgraund Transient Stability (TS) is a critical factor in West Japan System.
Cf. Real time generator shedding system is in service. (EPCC 2013*) Increase in renewable energy (RE) generations and uncertainties. Possibility of critical power flows due to RE requires Investigation for Monitoring
and Control Method.
ContentsWe propose the following methods. 1. Real time TS Monitoring in terms of Critical Clearing Time (CCT)2. CCT-Distribution Factor (CCT-DF)3. System Control Method based on CCT-DF
(*) Bulk Power System Stabilizing Controller utilizing the Reduced External Equivalents of Adjacent Areashttp://www.epcc-workshop.net/archive/2013/assets/downloads/mochizuki-presentation-bulk-power-system.pdf
PV in Japan: 32GW in 2016.3, 64GW in 2030 (Peak load:170GW)
What is CCT
CCT exists between S‐CT and U‐CT
S‐CTU‐CTFault
Unstable (U)
Stable (S)
Gen
Ang
le δ
Time (s)
Fault Clearing
CCT is a critical value of fault clearing time (CT) for system stability- Stable when CCT > Rely Operation Time (ROT)- Unstable when CCT < ROT
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CCT can be an effective TS index
Characteristics of CCT
The reasons for using CCT as a TS index.• CCT directly indicates the degree of TS.• Possible use for system control • Several options for the computation of CCT.
Methods for the computation of CCT• Bisection method using Conventional TS simulation tool.
(Accurate but time consuming computation)• Energy Function Methods (Fast but inaccurate)• Critical Trajectory (CTrj) Method*
(Acceptable accuracy and computation time, Proposed method)
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(*) CTrj Method is presently upgraded.• N. Yorino, A. Priyadi, H. Kakui, M.Takeshita “A New Method for Obtaining Critical Clearing Time for Transient
Stability,” IEEE Transactions on Power Systems Vol. 25, No. 3. pp. 1620-1626 · September 2010.• N.Yorino, E. Popov, Y. Zoka, Y. Sasaki, H. Sugihara, ”An Application of Critical Trajectory Method to BCU
Problem for Transient Stability Studies,” IEEE Transactions on Power Systems, Vol. 28, No. 4, pp. 4237-4244, November 2013.
Critical Trajectory Method (CTrj Method)
CTrj Method computes simultaneously CCT and the critical trajectory (#3) by solving a set of critical conditions.
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Internal Angle of G1 (Fault D)WEST Japan 10-machine Model
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
t [s]
delta
in C
OA
[ra
d]
G1②
③
①
② Critically Unstable Trajectoryobtained by Simulation
① Critically Stable Trajectoryobtained by Simulation
③ Critical Trajectoryobtained by CTrj method
Example of Obtained Critical Trajectory
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WEST Japan 10-machine Model, G1-G4(Fault D)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
t [s]
delta in C
OA
[ra
d]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
t [s]
delta in C
OA
[ra
d]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
t [s]
delta in C
OA
[ra
d]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
t [s]
delta in C
OA
[ra
d]
① Stable Trajectory
② Unstable Trajectory
③ Critical Trajectory
G1 G2
G3
②
③
①①
①
②
②
③
③
G4
①
②
③
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Example of Obtained Critical Trajectory
CCT Computation Performance of CTrj Method
FaultPoints
Exact Computation CTrj Method (E) Error[%]CCT[s] CPU[s] CCT[s] CPU[s] Iter.A 0.084 1.002 0.083 0.223 27 -1.19%B 0.127 0.989 0.124 0.125 21 -2.36%C 0.113 0.979 0.113 0.130 22 0.00%D 0.151 0.985 0.150 0.102 19 -0.66%E 0.177 1.091 0.179 0.095 17 1.13%F 0.203 1.205 0.204 0.170 30 0.49%G 0.228 1.097 0.229 0.085 15 0.44%H 0.263 0.987 0.261 0.096 18 -0.76%I 0.347 1.320 0.346 0.074 13 -0.29%J 0.093 1.102 0.091 0.169 30 -2.15%K 0.128 1.108 0.125 0.127 22 -2.34%L 0.157 1.256 0.154 0.174 27 -1.91%
West Japan 10-Generator System (at Night)
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IEEJ West Japan Model
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PV
λ1
PV
λ2
Main Power Flow: λ1Distributed Flow: λ2
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TS Assessment in terms of CCT
Increase in Distributed flow λ2
when λ1 =1.5 [GW]CCTs with changing λ2 when λ1 =0 [GW]
λλ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
G6[GW] 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
G8[GW] 2.28 2.08 1.88 1.68 1.48 1.28 1.08 0.88 -λ
λ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A 0.212 0.210 0.208 0.205 0.202 0.198 0.193 0.187
B 0.397 0.402 0.405 0.405 0.403 0.398 0.389 0.377
C 0.279 0.279 0.279 0.279 0.279 0.279 0.279 0.279
D 0.317 0.317 0.317 0.317 0.317 0.317 0.317 0.317
E 0.504 0.525 0.539 0.539 0.549 0.546 0.536 0.519
F 0.289 0.289 0.289 0.289 0.289 0.289 0.289 0.289
G 0.469 0.501 0.519 0.519 0.522 0.510 0.448 0.409
H 0.313 0.313 0.313 0.313 0.313 0.313 0.313 0.313
I 0.282 0.282 0.282 0.282 0.282 0.282 0.282 0.282
J 0.299 0.299 0.299 0.299 0.299 0.299 0.299 0.299
K 0.349 0.349 0.349 0.349 0.349 0.349 0.349 0.350
L 0.493 0.493 0.456 0.417 0.378 0.340 0.275 0.246
M 0.366 0.366 0.365 0.364 0.362 0.359 0.348 0.340
N 0.301 0.301 0.298 0.294 0.289 0.283 0.268 0.259
O 0.501 0.501 0.504 0.501 0.493 0.480 0.439 0.410
P 0.168 0.168 0.168 0.168 0.168 0.168 0.168 0.168
Q 0.487 0.487 0.464 0.439 0.413 0.385 0.328 0.299
R 0.485 0.485 0.487 0.487 0.484 0.479 0.461 0.447
S 0.180 0.180 0.178 0.176 0.174 0.170 0.163 0.158
T 0.300 0.300 0.300 0.300 0.300 0.300 0.300 0.300
λ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A 0.087 0.084 0.080 0.076 0.069 0.061 0.047 0.027
B 0.135 0.130 0.123 0.112 0.099 0.081 0.057 0.024
C 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273
D 0.316 0.316 0.316 0.316 0.316 0.316 0.316 0.296
E 0.284 0.283 0.279 0.269 0.269 0.232 0.202 0.164
F 0.652 0.652 0.652 0.652 0.652 0.652 0.652 0.620
G 0.287 0.281 0.281 0.249 0.249 0.200 0.169 0.134
H 0.314 0.314 0.314 0.315 0.315 0.313 0.310 0.303
I 0.278 0.278 0.278 0.279 0.279 0.279 0.279 0.279
J 0.299 0.299 0.299 0.299 0.299 0.299 0.299 0.299
K 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350
L 0.221 0.221 0.207 0.192 0.174 0.131 0.104 0.072
M 0.254 0.254 0.249 0.241 0.230 0.195 0.170 0.139
N 0.158 0.158 0.154 0.148 0.141 0.122 0.109 0.092
O 0.294 0.294 0.283 0.267 0.248 0.199 0.168 0.134
P 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.164
Q 0.214 0.214 0.201 0.186 0.169 0.128 0.101 0.068
R 0.290 0.290 0.286 0.278 0.266 0.228 0.199 0.164
S 0.086 0.086 0.084 0.081 0.077 0.066 0.058 0.046
T 0.301 0.301 0.301 0.301 0.301 0.301 0.300 0.298
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0.0
0.1
0.2
0.3
0.4
0.5
0.0 1.5
0.0
0.1
0.2
0.0 0.4 0.8 1.2
0.07
CCT[sec]
Main flow λ1
0.07
OQ
BA
P
OQ
BA
P
Local flow λ2
TS Assessment in terms of CCT
- Main flow λ1 is increased until 1.5 at which distributed flow λ2 is increased.- λ2 is caused by PV generation.- CCT < 0.07 implies instability. (0.07s is Relay operation time.)
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Waveforms of Generator Swings (Fault A)
G12
G13,11
Chugoku & Kyushu
Kansai & Chubu
λ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A 0.087 0.084 0.080 0.076 0.069 0.061 0.047 0.027
B 0.135 0.130 0.123 0.112 0.099 0.081 0.057 0.024
C 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273
D 0.316 0.316 0.316 0.316 0.316 0.316 0.316 0.296
E 0.284 0.283 0.279 0.269 0.269 0.232 0.202 0.164
F 0.652 0.652 0.652 0.652 0.652 0.652 0.652 0.620
G 0.287 0.281 0.281 0.249 0.249 0.200 0.169 0.134
H 0.314 0.314 0.314 0.315 0.315 0.313 0.310 0.303
I 0.278 0.278 0.278 0.279 0.279 0.279 0.279 0.279
J 0.299 0.299 0.299 0.299 0.299 0.299 0.299 0.299
K 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350
L 0.221 0.221 0.207 0.192 0.174 0.131 0.104 0.072
M 0.254 0.254 0.249 0.241 0.230 0.195 0.170 0.139
N 0.158 0.158 0.154 0.148 0.141 0.122 0.109 0.092
O 0.294 0.294 0.283 0.267 0.248 0.199 0.168 0.134
P 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.164
Q 0.214 0.214 0.201 0.186 0.169 0.128 0.101 0.068
R 0.290 0.290 0.286 0.278 0.266 0.228 0.199 0.164
S 0.086 0.086 0.084 0.081 0.077 0.066 0.058 0.046
T 0.301 0.301 0.301 0.301 0.301 0.301 0.300 0.298
λλ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
G6[GW] 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
G8[GW] 2.28 2.08 1.88 1.68 1.48 1.28 1.08 0.88
-λ
λ1= 1.5 [GW]Increase in Distributed flow λ2
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G12
λ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A 0.087 0.084 0.080 0.076 0.069 0.061 0.047 0.027
B 0.135 0.130 0.123 0.112 0.099 0.081 0.057 0.024
C 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273
D 0.316 0.316 0.316 0.316 0.316 0.316 0.316 0.296
E 0.284 0.283 0.279 0.269 0.269 0.232 0.202 0.164
F 0.652 0.652 0.652 0.652 0.652 0.652 0.652 0.620
G 0.287 0.281 0.281 0.249 0.249 0.200 0.169 0.134
H 0.314 0.314 0.314 0.315 0.315 0.313 0.310 0.303
I 0.278 0.278 0.278 0.279 0.279 0.279 0.279 0.279
J 0.299 0.299 0.299 0.299 0.299 0.299 0.299 0.299
K 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350
L 0.221 0.221 0.207 0.192 0.174 0.131 0.104 0.072
M 0.254 0.254 0.249 0.241 0.230 0.195 0.170 0.139
N 0.158 0.158 0.154 0.148 0.141 0.122 0.109 0.092
O 0.294 0.294 0.283 0.267 0.248 0.199 0.168 0.134
P 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.164
Q 0.214 0.214 0.201 0.186 0.169 0.128 0.101 0.068
R 0.290 0.290 0.286 0.278 0.266 0.228 0.199 0.164
S 0.086 0.086 0.084 0.081 0.077 0.066 0.058 0.046
T 0.301 0.301 0.301 0.301 0.301 0.301 0.300 0.298
λλ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
G6[GW] 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
G8[GW] 2.28 2.08 1.88 1.68 1.48 1.28 1.08 0.88
-λ
λ1: 1.5 [GW]
Waveforms of Generator Swings (Fault B)
Increase in Distributed flow λ2
13
Chugoku & Kyushu
Kansai & Chubu
G12,13,11
G8
λ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A 0.087 0.084 0.080 0.076 0.069 0.061 0.047 0.027
B 0.135 0.130 0.123 0.112 0.099 0.081 0.057 0.024
C 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273
D 0.316 0.316 0.316 0.316 0.316 0.316 0.316 0.296
E 0.284 0.283 0.279 0.269 0.269 0.232 0.202 0.164
F 0.652 0.652 0.652 0.652 0.652 0.652 0.652 0.620
G 0.287 0.281 0.281 0.249 0.249 0.200 0.169 0.134
H 0.314 0.314 0.314 0.315 0.315 0.313 0.310 0.303
I 0.278 0.278 0.278 0.279 0.279 0.279 0.279 0.279
J 0.299 0.299 0.299 0.299 0.299 0.299 0.299 0.299
K 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350
L 0.221 0.221 0.207 0.192 0.174 0.131 0.104 0.072
M 0.254 0.254 0.249 0.241 0.230 0.195 0.170 0.139
N 0.158 0.158 0.154 0.148 0.141 0.122 0.109 0.092
O 0.294 0.294 0.283 0.267 0.248 0.199 0.168 0.134
P 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.164
Q 0.214 0.214 0.201 0.186 0.169 0.128 0.101 0.068
R 0.290 0.290 0.286 0.278 0.266 0.228 0.199 0.164
S 0.086 0.086 0.084 0.081 0.077 0.066 0.058 0.046
T 0.301 0.301 0.301 0.301 0.301 0.301 0.300 0.298
λλ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
G6[GW] 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
G8[GW] 2.28 2.08 1.88 1.68 1.48 1.28 1.08 0.88
-λ
λ1: 1.5 [GW]Increase in Distributed flow λ2
Waveforms of Generator Swings (Fault Q)
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Chugoku & Kyushu
Kansai & Chubu
G12G13
G11
λ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
A 0.087 0.084 0.080 0.076 0.069 0.061 0.047 0.027
B 0.135 0.130 0.123 0.112 0.099 0.081 0.057 0.024
C 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273
D 0.316 0.316 0.316 0.316 0.316 0.316 0.316 0.296
E 0.284 0.283 0.279 0.269 0.269 0.232 0.202 0.164
F 0.652 0.652 0.652 0.652 0.652 0.652 0.652 0.620
G 0.287 0.281 0.281 0.249 0.249 0.200 0.169 0.134
H 0.314 0.314 0.314 0.315 0.315 0.313 0.310 0.303
I 0.278 0.278 0.278 0.279 0.279 0.279 0.279 0.279
J 0.299 0.299 0.299 0.299 0.299 0.299 0.299 0.299
K 0.350 0.350 0.350 0.350 0.350 0.350 0.350 0.350
L 0.221 0.221 0.207 0.192 0.174 0.131 0.104 0.072
M 0.254 0.254 0.249 0.241 0.230 0.195 0.170 0.139
N 0.158 0.158 0.154 0.148 0.141 0.122 0.109 0.092
O 0.294 0.294 0.283 0.267 0.248 0.199 0.168 0.134
P 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.164
Q 0.214 0.214 0.201 0.186 0.169 0.128 0.101 0.068
R 0.290 0.290 0.286 0.278 0.266 0.228 0.199 0.164
S 0.086 0.086 0.084 0.081 0.077 0.066 0.058 0.046
T 0.301 0.301 0.301 0.301 0.301 0.301 0.300 0.298
λλ2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
G6[GW] 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
G8[GW] 2.28 2.08 1.88 1.68 1.48 1.28 1.08 0.88
-λ
λ1: 1.5 [GW]Increase in Distributed flow λ2
Waveforms of Generator Swings (Fault S)
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Chugoku & Kyushu
Kansai & Chubu
CCT-Distribution Factor (CCT-DF)
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We propose CCT-Distribution Factor for contingency k, defined as: ( )
( )k
kj
j
CCTDFP
( ) :
:
k
j
CCTP
CCT for contingency kOutput of generator j before fault
Numerical Test
1) is absorbed by slack generator .
2) Compute CCT by CTrj method and evaluate Repeat j=1,..n
0 0.1: 0.1j j jP P P 15P
jDF
CCT-DF in West J System
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Gen # 21 22 23 24 25 26 27 28 29 30
DF 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.001 0.001 0.001
Gen # 1 2 3 4 5 6 7 8 9 10
DF ‐0.011 ‐0.010 ‐0.010 ‐0.010 ‐0.007 ‐0.006 ‐0.005 ‐0.002 ‐0.002 ‐0.002
Gen # 11 12 13 14 15 Slack 16 17 18 19 20
DF 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000
-0.080-0.060-0.040-0.0200.0000.0200.0400.0600.080
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G1
-0.080-0.060-0.040-0.0200.0000.0200.0400.0600.080
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G7
-0.080
-0.030
0.020
0.070
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G17
CCT CCT CCT
1GP 7GP 17GP
• Actual simulated value of CCT deviation, -------- Estimation by CCT-DF
CCT-DF for critical fault A obtained at 1.5, 0.4
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Preventive Control between Two Generators
Estimated Control Effect between Gens i and j,
( ) ( ) ( ),
( )7, 1
( )17, 1
( )28, 1
( )17, 7
[ ]
0.006
0.011
0.012
0.005
k k kGi Gj Gi Gj
kG G
kG G
kG G
kG G
CCT DF DF P
CCT P
CCT P
CCT P
CCT P
Relative Control between Generators i and j
(G17 -> G1)
(G7 -> G1)
(Gi -> Gj)
(G28 -> G1)
(G17 -> G7)
• Gi increases and Gj decreases: ,:Gi Gj Gi GjP P P
Comparison of Estimated and Actual Control Effects
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-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G7-G1
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G17-G1
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G28-G1
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
G17-G7
7 , 1G GP 17 , 1G GP
28 , 1G GP 17 , 7G GP
CCT CCT
CCTCCT
Proposed Real-time Monitoring & Control for TS
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Repeat on-line:
・Step 1: Load and RE forecast・Step 2: State Estimation・Step 3: Computation of CCT (CTrj method)・Step 4: Monitoring of TS constraint: .
・If TS Constraint is violated,Step 5: Compute CCT-DF (CTrj method)Step 6: Determine ΔP using CCT-DF to satisfy TS constraint:
Step 7: Perform preventive control of ΔP.
“ΔP” may be optimally determined among possible controls.
CCT Thresh
CCT DF P Thresh
Monitoring of System Operation Reliability under Uncertainty
21
Implementation of CCT-DF into the formulation in [4] will make more reliable TS monitoring including:(1) the worst case optimal operation under uncertainty(2) the size of the feasible region, d ( d>0: feasibility, d<0: infeasibility)(3) the worst case of uncertainty
t0
t1
t2
u(t0)
RSSRDF
dd
[4] N. Yorino, M. Abdillah, Y, Sasaki, Y. Zoka, “Robust Power System Security Assessmentunder Uncertainties Using Bi‐Level Optimization”, IEEE Transactions on Power Systems, toappear, 2017.
Security assessment against uncertainty
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Power Flow , =0 Constraints (+ CCT-DF) , 0, 0,1,⋯ ,
Control Variables Uncertainties
Upper bound,
Lower bound,
, d= -
Objective function
Constraints
Cost directiond
The worst minimumThe worst maximum
TS assessment against uncertainty is possible using the following formulation.
23
Example of Operation Reliability Monitoring under Uncertainty
Feasible region(Positive d)
Infeasible region(Negative d)
Lower bound: the worst case optimal operation under uncertainty
Size of the feasible region, d ( d>0: feasibility, d<0: infeasibility)
Cost
Conclusions
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PV generations may cause various power flows where transientstability (TS) is critical in West Japan System.
We propose a monitoring and control method for TS using criticalclearing time (CCT) based on the critical trajectory method.
We also suggest the use of the sensitivity of CCT to generatoroutputs for a preventive control of TS, which is referred to as CCT-Distribution Factor in this presentation.
Effective treatment of uncertainty is required in the future.
References
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1. T. Suizu, K. Mochizuki, N. Yorino, “Bulk Power System Stabilizing Controller utilizing theReduced External Equivalents of Adjacent Areas,” http://www.epcc‐workshop.net/archive/2013/assets/downloads/mochizuki‐presentation‐bulk‐power‐system.pdf
2. N. Yorino, A. Priyadi, H. Kakui, M.Takeshita “A New Method for Obtaining Critical Clearing Timefor Transient Stability,” IEEE Transactions on Power Systems Vol. 25, No. 3. pp. 1620‐1626 ∙September 2010.
3. N. Yorino, E. Popov, Y. Zoka, Y. Sasaki, H. Sugihara, ”An Application of Critical TrajectoryMethod to BCU Problem for Transient Stability Studies,” IEEE Transactions on Power Systems,Vol. 28, No. 4, pp. 4237‐4244, November 2013.
4. N. Yorino, M. Abdillah, Y, Sasaki, Y. Zoka, “Robust Power System Security Assessment underUncertainties Using Bi‐Level Optimization”, IEEE Transactions on Power Systems, to appear,2017.
5. E Y. Sasaki, N. Yorino, Y. Zoka, F. I. Wahyudi, “Robust Stochastic Dynamic Load Dispatch againstUncertainties,” IEEE Transactions on Smart Grid, to appear, 2017.
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Thank you !
The 14h International Workshops on Electric Power Control Centers (EPCC 14) May 14-17 2017, Wiesloch, Germany
By Naoto Yorino, Yutaka Sasaki