wide-area control of power systems · wide-area control of power systems aranya chakrabortty north...

Wide-Area Control of Power Systems

Aranya Chakrabortty

North Carolina State University

Pre-Conference Workshop, American Control Conference

July 5, 2016, Boston, MA

Designs, Experiments & Open Problems

What is Wide-Area Control ?

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW

Approximate Generation CapacitiesUS West Coast


21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW



No Control at all

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW



Decentralized local PSS

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW


System-wide data feedback over 1200 miles


A Mathematical Perspective

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW


𝑦 𝑡 = 𝐴0 +

𝐴1𝑒λ1𝑡 + … + 𝐴𝑚𝑒

λ𝑚𝑡 +

𝐴𝑚+1𝑒λ1𝑡 + … +𝐴𝑛𝑒

λ𝑛𝑡

DC mode

Inter-area modes (due to slow eigenvalues)

Intra-area modes (due to fast eigenvalues)

Impulse response of power flow after a small-signal

disturbance

A Mathematical Perspective

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW


𝑦 𝑡 = 𝐴0 +

𝐴1𝑒λ1𝑡 + … + 𝐴𝑚𝑒

λ𝑚𝑡 +

𝐴𝑚+1𝑒λ1𝑡 + … +𝐴𝑛𝑒

λ𝑛𝑡

DC mode

Inter-area modes (due to slow eigenvalues)

Intra-area modes (due to fast eigenvalues)

Can be

easily placed

by local PSS

Difficult to

place by local

PSS only,

easier by

wide-area

feedback

Lead to 1996 blackout

on the west coast

Impulse response of power flow after a small-signal

disturbance

However, Balancing Regions are Sensitive to Data Privacy!

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW


21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW

Approximate Generation Capacities

Third-Party Private Cloud

+ Controllable Network

One option: Move all computations to the cloud

However, Balancing Regions are Sensitive to Data Privacy!

ASG3

V3∠θ3

V4∠θ4

jx12

V5∠θ5

V1∠θ1

r12

jx3 P3

E2∠δ2

E3∠δ3

E1∠δ1

E4∠δ4

E5∠δ5

VM

VM

VM VM

VM

US West Coast

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW


ASG3

V3∠θ3

V4∠θ4

jx12

V5∠θ5

V1∠θ1

r12

jx3 P3

E2∠δ2

E3∠δ3

E1∠δ1

E4∠δ4

E5∠δ5

VM

VM

VM VM

VM



Virtual Machines (VMs) communicate to compute

control signal privately

Balancing Regions are Sensitive to Data Privacy!

US West Coast

21000 MW

6000 MW

8400 MW

9000 MW

2000 MW

Area 1

Area 2

Area 3

Area 4

Area 5

Up to 3000 MW

Up to 6000 MW

Up to 9000 MW

Above 12000 MW


ASG3

V3∠θ3

V4∠θ4

jx12

V5∠θ5

V1∠θ1

r12

jx3 P3

E2∠δ2

E3∠δ3

E1∠δ1

E4∠δ4

E5∠δ5

VM

VM

VM VM

VM

Close the loop from cloud to grid

Balancing Regions are Sensitive to Data Privacy!



US West Coast

VM

VM

VM VM

VM

Interesting Things Going on in the Communication Plane

Imagine a VM to be a mirror image of a generator

5000 Generators in the west coast = 5000 VMs in the cloud

Network Flooding!

Too much bandwidth to buy!

= 5000C2 or 12,497,500 links

ASG3

V3∠θ3

V4∠θ4

jx12

V5∠θ5

V1∠θ1

r12

jx3 P3

E2∠δ2

E3∠δ3

E1∠δ1

E4∠δ4

E5∠δ5

VM

VM

VM VM

VM

Shared

Resources

Cloud Platform (Google, Amazon, AT&T, GENI, DETER)

Controllable

Network (eg. SDN)

Tutorial tomorrow at

WeC21

VM

VM

VM VM

VM


Controllable

Network (eg. SDN)


• Question # 1: How to make wide-area control designs simpler and

scalable, a.k.a how to reduce the number of links?

Two main questions for this talk:

Shared

Resources

Controllable

Network (eg. SDN)


WeC21

VM

VM

VM VM

VM


Controllable

Network (eg. SDN)


• Question # 1: How to make wide-area control designs simpler and

scalable, a.k.a how to reduce the number of links?


Shared

Resources

Controllable

Network (eg. SDN)


WeC21

• Question # 2: How to control VM-to-VM delays?

Several Papers So Far

Q1: How to Reduce the Number of Comm. Links

Network clustering: Power grids often exhibit physical clustering

Construct a reduced-order network by node/state aggregation.

1

23

45

6 7

89

10

Example:

𝒮1 = 1,2 , 𝒮2 = 3,4,5 , 𝒮3 = 6,7,8,9,10

Details of this method – Please see FrC06.5 – Network Control Systems III




1

23

45

6 7

89

10

Example:

𝒮1 = 1,2 , 𝒮2 = 3,4,5 , 𝒮3 = 6,7,8,9,10


𝑃 =

1

2

1

20 0 0 0 0 0 0 0

0 01

3

1

3

1

30 0 0 0 0

0 0 0 0 01

5

1

5

1

5

1

5

1

5

Projection Matrix




1

23

45

6 7

89

10

Example:

𝒮1 = 1,2 , 𝒮2 = 3,4,5 , 𝒮3 = 6,7,8,9,10


𝒮1, … , 𝒮3

Aggregate

nodes/

Super-nodes

P

𝑥 = −ℒ𝑥 + 𝐼𝑛𝑢 + 𝑏𝑑 𝑡

Full-order system:

𝑢 = −𝐾𝑥

min𝐾

0

∞

𝑥𝑇𝑄𝑥 + 𝑢𝑇𝑅𝑢 𝑑𝑡

Full-order LQR:

w.r.t.

Reduced-order system:

𝑥 = −𝑃ℒ𝑃𝑇 𝑥 + 𝐼𝑟 𝑢 + 𝑃𝑏𝑑 𝑡

Model reduction:

𝑥 = 𝑃𝑥

𝑄 = 𝑃𝑄𝑃𝑇

𝑅−1 = 𝑃𝑅−1𝑃𝑇

Design reduction:

Reduced-order LQR:

w.r.t.

min 𝐾

0

∞

𝑥𝑇 𝑄 𝑥 + 𝑢𝑇 𝑅 𝑢 𝑑𝑡

𝑢 = − 𝐾 𝑥


1

23

45

6 7

89

10

𝒮1, … , 𝒮3

P

𝑥 = −ℒ𝑥 + 𝐼𝑛𝑢 + 𝑏𝑑 𝑡

Full-order system:

𝑢 = −𝐾𝑥

min𝐾

0

∞

𝑥𝑇𝑄𝑥 + 𝑢𝑇𝑅𝑢 𝑑𝑡

Full-order LQR:

w.r.t.

Reduced-order system:

𝑥 = −𝑃ℒ𝑃𝑇 𝑥 + 𝐼𝑟 𝑢 + 𝑃𝑏𝑑 𝑡

Model reduction:

𝑥 = 𝑃𝑥

𝑄 = 𝑃𝑄𝑃𝑇

𝑅−1 = 𝑃𝑅−1𝑃𝑇

Design reduction:

Reduced-order LQR:

w.r.t.

min 𝐾

0

∞

𝑥𝑇 𝑄 𝑥 + 𝑢𝑇 𝑅 𝑢 𝑑𝑡

𝑢 = − 𝐾 𝑥


Objective:

Consider the transfer matrices of the closed-loop systems from disturbance input:

𝑔 𝑠 = 𝑠𝐼 − −ℒ − 𝐾 −1𝑏 and 𝑔 𝑠 = 𝑠𝐼 − −ℒ − 𝑃𝑇 𝐾𝑃−1𝑏,

find clustering sets 𝒮1, … , 𝒮𝑟 such that

𝑃 = argmin𝑃

𝑔 𝑠 − 𝑔 𝑠 ℋ2

with the projected controller 𝑢 = 𝑃𝑇 𝐾𝑃𝑥.

Xue & Chakrabortty, 2016

Boker, Nudell, Chakrabortty, 2015

Benefits of Clustered Design

Major Simplification in Implementation

Example:

𝑢 = 𝑃𝑇 𝐾𝑃𝑥 allows for a two-layer strategy

1

23

45

6

7

89

10

1. State aggregation 𝑥 = 𝑃𝑥,


2. Design 𝐾

Example:


1

23

45

6

7

89

10

𝑥1

𝑥2𝑥3

𝑥4 𝑥5𝑥6

𝑥7

𝑥8𝑥9

𝑥10

𝑥1 + 𝑥2

2

𝑥3 + 𝑥4 + 𝑥5

3

𝑥6 + 𝑥7 + 𝑥8 + 𝑥9 + 𝑥10

5




Example:


3. Reduced-order feedback

𝑢 = 𝐾 𝑥 =

∎△†

,

1

23

45

6

7

89

10

∎△

†


2. Design 𝐾



Example:


4. Control inversion 𝑢 = 𝑃𝑇 𝑢 =

∎

2

∎

2

△

3

△

3

△

3

†

5

†

5

†

5

†

5

†

5

𝑇

1

23

45

6

7

89

10

∎

2 †

5

△

3


3. Reduced-order feedback

𝑢 = 𝐾 𝑥 =

∎△†

,

2. Design 𝐾



Example:


12

3

4

56

7

8

9

10

Regular LQR controller: Clustered LQR controller:

45 communication links in total 13 communication links in total

12

3

4

56

7

8

9

10

Can be better than L1 sparsity promotion

(Dorfler, Jovanovic, Chetkov, Bullo, 2014)


IEEE 68-bus,16-machine power system

Beware: Clusters Can Move with Wind Penetration

Mukherjee and Chakrabortty, 2016

Chandra, Gayme, Chakrabortty, 2015

16 generators spread across 5 coherent areas

No wind plant, only sync gens

Gens 1 and 8 are in Area 1

IEEE 68-bus,16-machine power system

Beware: Clusters Can Move with Wind Penetration

With 1050 MW (7% of total connected load) at

Bus 57, coherency structure changes, and

Gens 1 and 8 slip to Area 2

16 generators spread across 5 coherent areas

No wind plant, only sync gens

Gens 1 and 8 are in Area 1

Mukherjee and Chakrabortty, 2016

Chandra, Gayme, Chakrabortty, 2015

VM

VM

VM VM

VM


Shared

Resources

Controllable

Network (eg. SDN)



• Question # 1: How to reduce the number of links?

• Question # 2: How to control VM-to-VM delays?

Q2: How to Control VM-to-VM Delays?

Make the control design “aware” of the delays, not just tolerant to the worst-case

upper bound of the delays

(Soudbaksh, Chakrabortty, Annaswamy, CDC 2014)

𝑥(𝑡) = 𝐴𝑥(𝑡) + 𝐵𝑢(𝑡 − 𝜏)

Continuous-time plant with delays

Traditional approach for robustness: Consider worst-case delay τmax to be known, and design

robust controller that is tolerant to this upper bound

Often leads to very conservative designs as the actual delay may be way less than τmax

Local or self delay (usually negligible)

Intra-area delay (20-50 ms)

Inter-area delay (50 – 200 ms)





𝑥(𝑡) = 𝐴𝑥(𝑡) + 𝐵𝑢(𝑡 − 𝜏)


𝑥 𝑘 + 1 = 𝐴𝑑𝑥[𝑘] +

𝑖=1

𝑛

𝑗=1

𝑔(𝑖)

𝐵𝑗1𝑖 𝑢𝑖𝑗[𝑘] +

𝑖=1

𝑛

𝐵𝑖2𝑖 𝑢𝑖𝑔(𝑖)[𝑘 − 1]

Discrete-time plant with delays





𝑥(𝑡) = 𝐴𝑥(𝑡) + 𝐵𝑢(𝑡 − 𝜏)


𝑥 𝑘 + 1 = 𝐴𝑑𝑥[𝑘] +

𝑖=1

𝑛

𝑗=1

𝑔(𝑖)

𝐵𝑗1𝑖 𝑢𝑖𝑗[𝑘] +

𝑖=1

𝑛

𝐵𝑖2𝑖 𝑢𝑖𝑔(𝑖)[𝑘 − 1]

Discrete-time plant with delays

𝐵𝑖2𝑖 =

𝑇−𝜏𝑖𝑖

𝑇

𝑒𝐴𝑧𝐵𝑖𝑑𝑧

𝐵𝑗1𝑖 = 𝑇−𝜏𝑖(𝑗+1)

𝑇−𝜏𝑖𝑗 𝑒𝐴𝑧𝐵𝑖𝑑𝑧 if j=g(i)

= 0𝑇−𝜏𝑖𝑗 𝑒𝐴𝑧𝐵𝑖𝑑𝑧 otherwise

50 bus power system model, 14 generators, 4 coherent areas

each generator has 15 state variables

Intra-area delay = 30 ms, Inter-area delay = 60 ms

Phase angle response Excitation voltage response


Implementation of Distributed Control Algorithm

RTDS152.14.125.32/33/232

Lab Computers152.14.125.109/

10.0.0.X

PMU110.0.0.3

PMU210.0.0.4

PMU310.0.0.5

PMU410.0.0.6

PMU510.0.0.7

PMU610.0.0.8

GTAO

Rib

bo

n c

able

s

NetgearSwitch

Eth

ern

et c

able

s BEN port

BEN

VLAN904

GTNET10.0.0.9

VM1 VM2

VM3 VM4

VM6

Control Signals

Internal Fibre Optic Cable

VM5

ExoGENIOakland, CA Rack Site

Co

ntro

l Signals

PM

U d

ata

PMU basedWAMS at NCSU

Implementation of Distributed Control Algorithm

0 1 2 3 4 5 6

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

un

its

P5

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

un

its

P4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

un

its

P3

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

un

its

P2

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

un

its

P1

Control Signals from ExoGENI Control Signals from RSCAD

0 1 2 3 4 5 6

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

G5Input

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

G4Input

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

G3Input

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

G2Input

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

G1Input

t1 t2

1sec

t1-t2 = 0.2 sec = 200 ms!

Depending on network

traffic and distance

wide-area delays can

be almost 200-300 ms

DESIGN the delays – by arrival/departure rate control, capacity control, abort

VM i

VM j

Internet(does not do multi-casting)

n copies of xi[k]

Capacity of each link = c

Rate of sending or receiving data = r bits/s (sampling rate)


τij = Total M/M/1 average delay from i j = 1

𝑐−𝑛𝑖𝑟+ 0 +

1

𝑐−𝑚𝑗𝑟

ni = # of VMs that VM i

is sending data to

mj = # of VMs that VM j

is receiving data from

Internet





1

𝑐−𝑚𝑗𝑟


is sending data to



Internet

Two things to control (in real-time as the event is running)





1

𝑐−𝑚𝑗𝑟


is sending data to



Internet


Who talks to who at any iteration?

VM 1

VM 3

VM 2

Note: directed graph





1

𝑐−𝑚𝑗𝑟


is sending data to



Internet


Who talks to who at any iteration? Down-sample PMU measurements or not?

VM 1

VM 3

VM 2

Skip samples

Use r as a design variable – rate controlNote: directed graph

1

3

46

5

7

89

10

2

𝑥1 + 𝑥2

2

𝑥3 + 𝑥4 + 𝑥5

3

𝑥6 + 𝑥7 + 𝑥8 + 𝑥9 + 𝑥10

5

𝑥1

𝑥2 𝑥3

𝑥4 𝑥5𝑥6

𝑥7

𝑥8𝑥9

𝑥10

Design SDN controller for updating delay

bounds in the shared network

Wide-area network

Model

Predictive

Control

Model

Predictive

Control

τ

𝑔 𝑠 − 𝑔 𝑠 ℋ2

Network co-design problem

(protocols, security+privacy, cost-optimality)

Back-to-Back Co-Design of Controllers at Cyber and Physical Layers


Architecture of ExoGENI-WAMS CPS Testbed

PMU based WAMS at NC State

US-wide ExoGENI with access point through

RENCI/UNC Chapel Hill

Middleware provided by Green

Energy Corporation and RTI

THANK YOU

Email: [email protected]

Website: http://people.engr.ncsu.edu/achakra2
mailto:[email protected]

wide-area control of power systems · wide-area control of power systems aranya chakrabortty north...

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