Event Detection and Localization in Distribution Grids with Phasor …oardakan/files/PESGM... ·...
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Event Detection and Localization in Distribution Grids with Phasor Measurement Units Omid Ardakanian * , Ye Yuan † , Roel Dobbe ‡ , Alexandra von Meier ‡ , Steven Low § , and Claire Tomlin ‡ * University of Alberta, † Huazhong University of Science and Technology, ‡ University of California, Berkeley, § California Institute of Technology Introduction Identification Algorithm Synchrophasor data provide unprecedented insights into the operating state of the system which can be used to uniquely determine the system model (i.e. the admittance matrix) and quickly identify the critical events, e.g. switching operations, tap changes, and faults Goal: given time-synchronized voltage and current phasor measurements in a polyphase distribution network, recover the admittance matrix Y and detect any changes due to events (faults, reconfiguration, etc) ➔ Y must be sparse and symmetric Central operator reactive, conservative w/ ad-hoc interventions Real-time monitoring & automatic control proactive, distributed and participative Event Localization Algorithm (requires a small no. of samples) Experimental Setup Identification result |ΔY| for a switching event Modified IEEE 13 bus test feeder 1. Compute real and reactive powers consumed at each node in every time slot 2. Simulate events at the specified times and update the admittance matrix 3. Perform power flow analysis for every time slot in OpenDSS 4. Add Gaussian white noise to the results to simulate phasor measurements 5. Solve the convex problems using the CVX toolbox to update the admittance matrix Y. Yuan, O. Ardakanian, S. Low, and C. Tomlin, “On the inverse power flow problem,” https://arxiv.org/abs/1610.06631, Tech. Rep., Oct. 2016. -> For correspondence, [email protected]. • Performed extensive simulations on IEEE 13, 34, 37, and 123 test feeders • Identified various events and pinpointed them to a small geographical area • Studied sensitivity of the proposed techniques to the synchrophasor measurement error Paper No: 17PESGM510 2 6 6 6 4 I 1 (1) ... I 1 (K ) I 2 (1) ... I 2 (K ) . . . . . . . . . I N (1) ... I N (K ) 3 7 7 7 5 | {z } I K bus = Y bus 2 6 6 6 4 V 1 (1) ... V 1 (K ) V 2 (1) ... V 2 (K ) . . . . . . . . . V N (1) ... V N (K ) 3 7 7 7 5 | {z } V K bus . Ohm’s Law for successive time slots 1…K: Challenges: 1. is low rank => standard least square does not work, it has infinite number of solutions; 2. Measurement error; 3. Limited deployment of sensors. V K bus I 1 I 2 = Y 11 Y 12 Y > 12 Y 22 | {z } Y X V 2 V 2 = Y 11 X + Y 12 Y > 12 X + Y 22 | {z } Y X V 2 Step 1: Use similarity transformation to re-arrange data matrices: Step 3: Rewrite Ohm’s law as Compute Y X = arg min Y 2C D⇥R I 1 I 2 - Y V 2 2 . I 1 =(Y 11 X + Y 12 ) V 2 I 2 = ( Y > 12 X + Y 22 ) V 2 Step 4: Obtain Y 12 = arg min Y 2C (D-R)⇥R k(Y 11 X + Y ) V 2 - I 1 k 2 Y 12 Step 2: Compute T V K bus = V 1 V 2 , T I K bus = I 1 I 2 . X = V 1 V † 2 . C , I 2 V † 2 - (V † 2 ) > I > 1 X = -X > ⇤ Y 11 ⇤ X + Y 22 min vec(Y 11 ) vec(Y 22 ) 0 s.t.: ⇥ -X > ⌦ X > I ⇤ vec(Y 11 ) vec(Y 22 ) = vec(C ), Y 11 2 S (D-R)⇥(D-R) , Y 22 2 S R⇥R . min vec(Y 11 ) vec(Y 22 ) 1 s.t.: ⇥ -X > ⌦ X > I ⇤ vec(Y 11 ) vec(Y 22 ) = vec(C ), Y 11 2 S (D-R)⇥(D-R) , Y 22 2 S R⇥R . Convex relaxation Y 11 , Y 22 I t!t+K bus = ⇥ I bus (t),I bus (t + 1),...,I bus (t + K ) ⇤ V t!t+K bus = ⇥ V bus (t),V bus (t + 1),...,V bus (t + K ) ⇤ ΔY , Y 1 bus - Y 0 bus Detection Algorithm e(k )= I bus (k ) - ˆ I bus (k ) = I bus (k ) - Y 0 bus V bus (k ) Check if e(k) is white noise if yes, continue; otherwise, detect the event. Formulation Event Detection and Localization Algorithm Step 5: Obtain Example Results Further Information
Transcript of Event Detection and Localization in Distribution Grids with Phasor …oardakan/files/PESGM... ·...
Event Detection and Localization in Distribution Grids with Phasor Measurement Units
Omid Ardakanian*, Ye Yuan†, Roel Dobbe‡, Alexandra von Meier‡, Steven Low§, and Claire Tomlin‡
*University of Alberta, †Huazhong University of Science and Technology, ‡University of California, Berkeley, §California Institute of Technology
Introduction Identification Algorithm
Synchrophasor data provide unprecedented insights into the operating state of the system which can be used to uniquely determine the system model (i.e. the admittance matrix) and quickly identify the critical events, e.g. switching operations, tap changes, and faults
Goal: given time-synchronized voltage and current phasor measurements in a polyphase distribution network, recover the admittance matrix Y and detect any changes due to events (faults, reconfiguration, etc)
➔ Y must be sparse and symmetric
Central operatorreactive, conservative w/ ad-hoc interventions
Real-time monitoring & automatic control proactive, distributed and participative
Event Localization Algorithm(requires a small no. of samples)
Experimental Setup
Identification result |ΔY| for a switching eventModified IEEE 13 bus test feeder
1. Compute real and reactive powers consumed at each node in every time slot
2. Simulate events at the specified times and update the admittance matrix
3. Perform power flow analysis for every time slot in OpenDSS
4. Add Gaussian white noise to the results to simulate phasor measurements
5. Solve the convex problems using the CVX toolbox to update the admittance matrix
Y. Yuan, O. Ardakanian, S. Low, and C. Tomlin, “On the inverse power flow problem,” https://arxiv.org/abs/1610.06631, Tech. Rep., Oct. 2016. -> For correspondence, [email protected].
• Performed extensive simulations on IEEE 13, 34, 37, and 123 test feeders• Identified various events and pinpointed them to a small geographical area• Studied sensitivity of the proposed techniques to the synchrophasor
measurement error
Paper No: 17PESGM510
2
6664
I1(1) . . . I1(K)I2(1) . . . I2(K)...
. . ....
IN (1) . . . IN (K)
3
7775
| {z }IKbus
= Ybus
2
6664
V1(1) . . . V1(K)V2(1) . . . V2(K)
.... . .
...VN (1) . . . VN (K)
3
7775
| {z }V Kbus
.
Ohm’s Law for successive time slots 1…K:
Challenges: 1. is low rank => standard least square does not work, it has
infinite number of solutions; 2. Measurement error;3. Limited deployment of sensors.
V Kbus
I1I2
�=
Y11 Y12
Y>12 Y22
�
| {z }Y
XV2
V2
�=
Y11X + Y12
Y>12X + Y22
�
| {z }YX
V2
Step 1: Use similarity transformation to re-arrange data matrices:
Step 3: Rewrite Ohm’s law as
Compute YX = arg minY2CD⇥R
����
I1I2
�� YV2
����2
.
I1 = (Y11X + Y12)V2
I2 =�Y>
12X + Y22
�V2
Step 4: Obtain
Y12 = arg minY2C(D�R)⇥R
k(Y11X + Y)V2 � I1k2Y12
Step 2: Compute T V K
bus =
V1
V2
�, T IKbus =
I1I2
�.
X = V1V†2.
C , I2V†2 � (V†
2)>I>1 X
= �X> ⇤ Y11 ⇤X + Y22
min
����
vec(Y11)vec(Y22)
�����0
s.t.:⇥�X> ⌦X> I
⇤ vec(Y11)vec(Y22)
�= vec(C),
Y11 2 S(D�R)⇥(D�R),Y22 2 SR⇥R.
min
����
vec(Y11)vec(Y22)
�����1
s.t.:⇥�X> ⌦X> I
⇤ vec(Y11)vec(Y22)
�= vec(C),
Y11 2 S(D�R)⇥(D�R),Y22 2 SR⇥R.
Convex relaxation
Y11, Y22
It!t+Kbus =
⇥Ibus(t), Ibus(t+ 1), . . . , Ibus(t+K)
⇤
V t!t+Kbus =
⇥Vbus(t), Vbus(t+ 1), . . . , Vbus(t+K)
⇤
�Y , Y 1bus � Y 0
bus
Detection Algorithme(k) = Ibus(k)� Ibus(k)
= Ibus(k)� Y 0busVbus(k)
Check if e(k) is white noiseif yes, continue;otherwise, detect the event.
Formulation Event Detection and Localization Algorithm
Step 5: Obtain
Example Results
Further Information
