predictive wide-area modeling of large power system ... · power system networks using synchronized...

Predictive Wide-Area Modeling of Large Power System Networks Using

Synchronized Phasor Measurements

Aranya Chakrabortty

North Carolina State University, Raleigh, NC

ISGT 2014, Washington DC

1

NYC before blackout

NYC after blackout

2 Main Lessons Learnt from the 2003 Blackout:

Main trigger: 2003 Northeast Blackout

1. Need significantly higher resolution measurements

2. Local monitoring & control can lead to disastrous results

From traditional SCADA (System Control and Data

Acquisition) to PMUs (Phasor Measurement Units)

Coordinated control instead of selfish control

Applications so far

1. Oscillation Monitoring Algorithms1.1 Mode meter – PNNL

1.2 Real-time monitor – WSU, BPA

1.3 Ringdown & ambient – UW, MTU

1.4 Predictive models – RPI, NCSU, Imperial

1.5 Mode shapes – WSU, KTH, SCE

1.6 Voltage stability –ABB, SCE, Quanta

2. Phasor State Estimator2.1 Three-phase PSE – VA Tech, Dominion

2.2 PMU placement algorithms – NEU, RPI

2.3 Bad data detectors – NEU, RPI, ISO-NE

2.4 Dynamic PSE – VA Tech, PNNL

2.5 PSE installations - CURENT

ElectricPowerSystem

ControlCenterLevel

Applications and DecisionLevel

Low BandwidthCommunications

(ICCP)

ControlActions

Stability AssessmentContingency Analysis

InterareaControl

Real-Time Dispatch

Conventional State Estimator

High BandwidthComunications(Internet)

Dispatch

Situation Awareness

DisturbancesStochastic Load Variations Unintentional MisoperationEventLevel

Real-Time Decision and Optimization

Decisions

Phasor State Estimator

PMU

PMUPMU

PMU

Wide-Area Modeling

0 50 100 150 200 250 300

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

Time (sec)

Bu

s V

olta

ge

(p

u)

Bus 1

Bus 2

Midpoint

Massive volumes of PMU data from

various locations

Dynamic models of the grid at

various resolutions

• Periodic updates of the grid models is imperative for reliable

monitoring & control

Grid Dynamic Models

• Synchronous Generator Models

• Power Flow Equations

Control input

Excitation voltage

Bus voltage and phase angle

Algebraic variables

Measured by PMU

iiE iiV

kkV ikik jxr

dijx'

kL

kL jQP

LkI~

nkI~

To rest of

network

iGI

~ ikI~

Grid Dynamic Models

• Transmission Line Model

Pi-model

• Load Models

iiE

iG Bus i

Bus k

iiV kkV

kL

1

~LI1G

Bus 1 11 V

2G

iG1nG

nGBus 2

22 V

Bus iiiV

Bus n-111 nnV

nnV

Bus n

2

~LI

LiI~

1,

~nLI

nLI ,

~

11 E

22 E

iiE 11 nnE

nnE

• Total Network Model

L(G) = fully connected

network graph Controllable inputs

mP

FE

• low bandwidth

• used mostly for AGC

• mechanical system wear and tear

• much higher bandwidth

• used for oscillation damping

• electrical input

Output Equation

…(1)

…(2)

Canada

Washington

Oregon

Malin

Pacific AC

Intertie

Table Mountain

Pacific AC

Intertie

Vincent

Montana

Wyoming

Utah

Arizona

New Mexico

Pacific

HVDC

Intertie

Lugo

Los Angeles

Baja CA

(Mexico)

Intermountain

HVDC

Line

PMU

PMU PMU

PMU

PMU

NE Cluster

N ClusterW ClusterS Cluster

E Cluster

PMU Locations

Pleasant Garden

ErnstRural Hall

AntiochPisgahAndersonBush

River

Oakboro

1. Western cluster – Mitchel River, Antioch, Marshall, Pisgah,

Tucksagee, Shiloh, North Greenville

2. Eastern cluster – Harrisburg, Peacock, Allen, Lincoln, Oakboro

3. Northern cluster – Ernst, Sadler, Rural Hall, North Greensboro

4. North-eastern cluster – Pleasant Garden, East Durham,

5. Southern cluster – Shady Grove, Anderson, Hodges, Bush River

Use PMU data to Construct Inter-area Clustered Models

WECC (500 KV) Duke Energy (500 & 235 KV)

PMU

PMU

PMU

6-machine, 19-bus, 3-area power system

Wide-Area Model Reduction

Area 1

Area 2 Area 3

Aggregate

Transmission

Network

PMU

PMU

PMU

6-machine, 19-bus, 3-area power system

• How to approach this model-reduction

problem solely using PMU measurements now?

• Operators may be more interested in this

model to study inter-area oscillations

Wide-Area Model Reduction

PMU

measurements

After Kron Reduction Full-order System Looks Like:

Full order

Network

Reduced order

“Equivalent”

NetworkCast it as a

Nonlinear Least

Squares parameter

estimation problem

60 65 70 75 80 85 90

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time (sec)

Fa

st O

scill

atio

ns (

pu

)

Bus 1

Bus 2

Midpoint

0 50 100 150 200 250 3000.9

0.95

1

1.05

1.1

1.15

Time (sec)

Slo

w V

olta

ge

(p

u)

0 50 100 150 200 250 300

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

Time (sec)

Bu

s V

olta

ge

(p

u)

Bus 1

Bus 2

Midpoint

+

Band-passFilter

Oscillations Quasi-steady State

Pre-Filtering of PMU data – Examples from WECC disturbances

Choose pass-band

covering typical

swing mode range

14

Pre-Filtering + Mode Separation in PMU data

0 5 10 15 20-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time (sec)

Inte

rare

a O

scill

atio

ns (

pu

)

Bus 1

Bus 2

Midpoint

60 65 70 75 80 85 90

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time (sec)

Fa

st O

scill

atio

ns (

pu

)

Bus 1

Bus 2

Midpoint

Oscillations Interarea Oscillations

• Can use modal identification methods such as: ERA, Prony, Steiglitz-McBride

ERA

15

Model Identification via L1-L2 minimization

Convexify the problem as

L2-L1 opt.

IEEE 39-Bus System

Linear LS Nonlinear LS

Decentralized Topology ID by each RTO

Area 1 Area 2 Area3 Area 4

j

ij

Em

d

m

d

m

iBA LuBXAXiidd

||||||2

1min

2

2

1

,

Extract slow oscillatory components of PMU data y(t) using modal decomposition methods,

Then cast as a sparse optimization problem:

Structured Model Identification from PMU data

Joint work with

Southern

California Edison

Intra-tie Impedance: June 18 Line Trip Event

Intra-tie Impedance Estimation from PMU data

• It was observed that each area has a different pre- and post-fault reactancevalue. Values for June 18th 2010 and Jun 23rd 2010 events are listed:

AreaPre-fault Impedance

ohms

Post-fault Impedance

ohms

Colstrip 24.8888 30.0108

Grand Coulee 9.3117 6.6197

Malin -3.2501 5.8459

Vincent 19.8367 21.8125

Palo Verde 34.4677 32.7578

Area Pre-fault Impedance

ohms

Post-fault Impedance

ohms

Colstrip 26.5861 27.5240

Grand Coulee 4.1314 3.1600

Malin 0.9872 -1.7481

Vincent 17.0301 17.4487

SVC at

Malin

Inertia & Damping Estimation

mP

D

D

D

D

YEEYEEYEE

YEEYEEYEE

YEEYEEYEE

YEEYEEYEE

M

M

M

M

4

3

2

1

4

3

2

1

4343442241441

3443332231331

4224322321221

1441133112211

4

3

2

1

4

3

2

1

000

000

000

000

000

000

000

000

Recall Swing Equations:

Known from previous steps of

estimation

• Parameters appear in nonlinear form

• The input is not known (modeled as impulse for convenience)

Wide-Area Models are Essential for Wide-Area Monitoring

n

j

j

jnn

j

z

j

MdkkSSS

j

ij1

22/)1(

1 *

21

2 )(

Kinetic EnergyPotential Energy

)])(sin()cos)[cos(21

opopop

e

(δx

EE 2 H

~1 1V

ejx

Gen1 2 2V

~Gen2

Load

P

• There are commonly used metrics that operators like to keep an eye on

• Use wide-area models + PMU data to assess transient stability margins – Energy functions/

Lyapunov functions

Can be the

reduced-order

model

PMU PMU

Recall storage functions for passive systems,

Total Energy = Kinetic Energy + Potential Energy

50 100 150 200 250 3000

0.5

1

1.5

2

2.5

3

3.5

Time (sec)

Sw

ing

Co

mp

on

en

t o

f P

ote

nti

al E

ne

rgy

( V

A-s

)

50 100 150 200 250 3000

0.5

1

1.5

2

2.5

3

3.5

Time(sec)

Kin

eti

c E

ne

rgy

( M

W-s

)

50 100 150 200 250 3000

0.5

1

1.5

2

2.5

3

3.5

Time (sec)

Sw

ing

En

erg

y F

un

cti

on

VE (

MW

-s )

• Total energy decays exponentially – damping stability

• Total energy does not oscillate – Out - of - phase osc.

Kinetic Energy

August 4, 2000 event in WECC

Potential Energy

Wide-Area Models area Useful for Wide-Area Control

• Inter-area oscillation damping – output-feedback based MIMO control design for the

full-order power system to shape the closed-loop phase angle responses of the reduced-

order model

• System-wide voltage control – PMU-measurement based MIMO control design for

coordinated setpoint control of voltages across large inter-ties

- FACTS controllers (SVC, CSC, STATCOM)

L R

Area 1

PMU

PMU

PMU1

2

4 5 6

7

8

910

121314

15

16

Area 2

1

2

3

4

14e 12e

34e32e

31e

21

circcirc PP

1

2

3

4

14e 12e

Smart Islanding – max flow min-cut

2 critical problems

Wide-Area Power Flow Control using PMUs and FACTS

Wide-Area

UPFC/CSC

Damping

Controller

Adaptation

Loop

Time-

varying

Models Kalman Filtering &

Phasor State

Estimator

Reconfiguring

Boundary

Control

PDC for

Area 1

Network

Boundary

PMU PMU PMU PMU

PMU

PMU PMU

From Power Flow

Controllers in each areaTo control center dispatch

decisioning

To damping

actuators in Area 1

Communication links

Local Control System for

Area 1IEEE 118-bus power

system

Semi-Supervisory Power Flow Dispatch Control

WAMS-ExoGENI Lab

1. Real PMU Data from WECC (NASPI data)

2. RTDS-PMU Data (Schweitzer PhasorLab)

3. FACTS-TNA with NI CRIO PMUs

We can provide all three data via our new

PMU and RTDS facilities at the FREEDM

center

We have just completed setting up an

intra-campus local PMU

communication network

with UNC Chapel Hill and Duke University.

Real-time Digital Simulators

Conclusions

1. WAMS is a tremendously promising technology for control + signal processing researchers

2. Control + Communications + Computing must merge

3. Plenty of new research problems – EE, Applied Math, Computer Science

4. Plenty of new system identification + big data analytics problems

5. Right time to think mathematically – Network theory is imperative

6. Right time to pay attention to the bigger picture of the electric grid

7. Needs participation of young researchers!

8. Promises to create jobs and provide impetus to power engineering

Thank You

Email: achakra2@ncsu.edu

Webpage: http://people.engr.ncsu.edu/achakra2