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

2

Security Issues for Future Power Systems

2

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

33

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)

4

(*) 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.

5

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

6

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

7

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)

8

IEEJ West Japan Model

5

PV

λ1

PV

λ2

Main Power Flow: λ1Distributed Flow: λ2

9

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

10

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.)

11

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

12

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)

14

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)

15

Chugoku & Kyushu

Kansai & Chubu

CCT-Distribution Factor (CCT-DF)

16

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

17

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

18

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

19

-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

20

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

22

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

24

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

25

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.

26

Thank you !

The 14h International Workshops on Electric Power Control Centers (EPCC 14) May 14-17 2017, Wiesloch, Germany

By Naoto Yorino, Yutaka Sasaki