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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
