phasor-only state estimation

8/10/2019 Phasor-Only State Estimation

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Phasor-Only State Estimation

Ali Abur

Department of Electrical and Computer Engineering

Northeastern University, Boston

[email protected]

PSERC Webinar

October 7, 2014


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Talk Outline

Background and terminology

State estimation

Phasor measurements

Phasor-only state estimationWLS: exact cancellations

LAV: improved robustness

Extension to 3-phase networks

Observability and error identificationClosing remarks

2


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(Static) state estimation

Measurement type: SCADA / Synchrophasor

Formulation: Nonlinear / Linear

Network model: + sequence / 3-phase

Dynamic state estimation

Wide-area, using gen/load/network variables

Local, using gen variables, boundary measurementsor estimates

3


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Modeling

Gen

1

Gen

2

Gen

NG

Load 1 Load 2

Load NLTransmission Network[Lines + Transformers]

Measurements4


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Modeling [ SSE ]

Gen

1

Gen

2

Gen

NG

Load 1 Load 2

Load NL

Transmission Network

[Lines + Transformers]

Estimated Measurements

SSE: Estimation of the snap-shot

at time t

Linear or NL

Pos Seq or 3-Phase

SCADA or Phasor or

Mixed SCADA/Phasor

5


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Modeling [ DSE ]

Gen

1

Gen

2

Gen

NG

Load 1 Load 2

Load NL

Transmission Network

[Lines + Transformers]

Estimated Measurements

DSE: Single machine / zonal / wide-area

Detailed Gen and Load modelsFrequency and power angle estimation

Zone-2

Zone-1

Zone NZ

Tracking the network and

dynamic gen/load state

variables in real-time

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Timeline

[z(t)]

()

()

+ + 2 + 3 + 4

DSE /

Local

SSE /

Wide-area

DSE /

Wide-area

SSE

DSE

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Timeline

[z(t)]

()

()

+ + 2 + 3 + 4

DSE /

Local

SSE /

Wide-area

DSE /

Wide-area

DSE

8


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Talk Outline


State estimation

Phasor measurements





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Static state estimation:

Objective and measurements

Objective: To obtain the best estimate of the state of the system

based on a set of measurements.

State variables: voltage phasors at all buses in the system

Measurements:

Power injection measurements

Power flow measurements

Voltage/Current magnitude measurements

Synchronized phasor measurements

SCADA

Measurem

ents

Introduced by Schweppe and his co-workers in 1969.

Schweppe, F.C., Wildes, J., and Rom, D., Power system static state estimation: Parts I, II, III,Power Industry Computer Applications (PICA), Denver, CO, June 1969.

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State estimation: data/info flow diagram

Topology Processor

Network Observability Analysis WLS State Estimator

Bad Data Processor

Parameter and Topology Error Processor

Analog MeasurementsPi, Qi, Pf, Qf, V, I

TopologyProcessor

StateEstimator

NetworkObservability Check

V,Bad DataProcessor

Network Parameters, Branch Status,

Substation Configuration

Parameter and Topology Errors

Detection, Identification,

Correction

Load Forecasts

Generation Schedules

PM +

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Topology Processor

Network Observability Analysis Robust LAV State Estimator

Bad Data Processor

Parameter and Topology Error Processor

Analog MeasurementsPi, Qi, Pf, Qf, V, I

TopologyProcessor

StateEstimator

NetworkObservability Check

V,Bad DataProcessor

Network Parameters, Branch Status,

Substation Configuration

Parameter and Topology Errors

Detection, Identification,

Correction

Load Forecasts

Generation Schedules

State estimation: data/info flow diagram

PM +

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Talk Outline


State estimation

Phasor measurements





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Phasor measurement units (PMU)

Synchronized Phasor Measurements and TheirApplications by A.G. Phadke and J.S. Thorp

Invented by Professors Phadke and Thorp in 1988.

They calculate the real-time phasor measurements

synchronized to an absolute time reference provided by

the Global Positioning System.

PMUs facilitate direct measurement of phase angle

differences between remote bus voltages in a power grid.

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Phasor Measurement Units (PMU)Phasor Data Concentrators (PDC)[*]

GPS CLOCK

AntennaPMU 1

PT

CT

PDC

[*] IEEE PSRC Working Group C37 Report

CORPORATE

PDC

REGIONAL

PDC

DATA STORAGE

& APPLICATIONS

DATA STORAGE

& APPLICATIONS

PMU 2

PMU 3

PMU 4PMU K

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Taken verbatim from: IEEE C37.244-2013 PDC Guide

PDC Definition:

A function that collects phasor data, and discrete event

data from PMUs and possibly from other PDCs, andtransmits data to other applications.

PDCs may buffer data for a short time period, but do not

store the data. This guide defines a PDC as a function

that may exist within any given device.

Phasor Data Concentrator (PDC)

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Phasor voltage measurements

Reference

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Reference phasor

+1

--2

--3 +1

--2

--3

Reference

Reference

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US Energy Information Administration: http://www.eia.gov/todayinenergy/detail.cfm?id=5630

Under the Recovery Act SGIG and SGDP programs, their numbers rapidly increased : 166 1126

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Measurements provided by PMUs

PMU

V phasor

I phasors

ALL 3-PHASES ARE TYPICALLY MEASURED

BUT

ONLY POSITIVE SEQUENCE COMPONENTS ARE REPORTED

= []0+

+ =

[+ +

]

=

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Talk Outline


State estimation

Phasor measurements





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Measurement equations

onlyparametersnetworkofFunctionH

ModelLinearXHZ

tsMeasuremenPhasor

XhH

ModellinearNonXhZtsMeasuremenSCADA

x

:

)(:

)(

+=

+=

A.G. Phadke, J.S. Thorp, and K.J. Karimi, State Estimation with Phasor Measurements,

IEEE Transactions on Power Systems, vol. 1, no.1, pp. 233-241, February 1986.

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Talk Outline


State estimation

Phasor measurements





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Phasor-only WLS state estimation

varianceerroriiR

ERHRHG

solutionDirectZRHGX

sidualrXHZrtoSubject

rMinimize

problemestimationstateWLS

ModelLinearXHZ

i

TT

T

m

i i

i

),(:

)cov(}{;

e

:

2

1

11

2

2

===

=

=

+=

24


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[ ]

matrixincidencebus-branch:

matrixadmittancebranch:

matrixidentity:

A

Y

U

VAY

U

currentsBranch

voltagesBus

I

VZ

b

b

m

m

m

+

=

=

Consider a fully measured system:

Note: Shunt branches are neglected initially, they will be introduced later. 25


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[ ]

[ ] [ ]

++=

++

+=

+

+=

jfeH

jfeAjbg

U

jdc

jfe

I

VLet

F

mm

mm

m

m

)(

26

Ph l WLS i i


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Phasor-only WLS state estimation:

Complex to real transformation

[ ]

+

=

+

=

feHZ

f

e

gAbA

bAgA

U

U

d

c

f

e

m

m

m

m

][

27


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Ph l WLS t t ti ti


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Phasor-only WLS state estimation:

Correction for shunt terms

XHRHGX

XHZRHGX

ZRHGXXE

XEHuE

XHuuXHXHHZ

shT

sh

Tcorr

T

sh

sh

sh

)(

}{

}{}{

)(][

11

11

11

=

=

==

=

+=+=++=

Very sparse

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System Case

MSE

WLSDecoupled

WLS

A1 0.59 0.592 0.59 0.59

3 0.62 0.62

B

1 0.61 0.61

2 0.61 0.603 0.62 0.63

C

1 0.59 0.59

2 0.58 0.59

3 0.58 0.59

Average MSE Values ( for 100 Simulations)

Fast Decoupled WLS Implementation Results

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MEAN CPU TIMES OF 100 SIMULATIONS

System Case

CPU Times (ms)

WLSDecoupled

WLS

A1 5 2.42 5.7 2.7

3 9.3 3.9

B

1 7.5 3.5

2 8.7 3.9

3 14.8 5.8

C

1 137.4 75.9

2 169.5 95.7

3 284.7 165.6

Fast Decoupled WLS Implementation Results

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Talk Outline


State estimation

Phasor measurements





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L1 (LAV) Estimator

]1,,1,1[

||1

=

+=

=

T

m

i

T

c

rXHZtoSubject

rcMinimize

Robust but with known deficiency:

Vulnerable to leverage measurements

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No leverage points

L1 estimator successfully rejects bad data

Motivating example: simple regression

Wrong data

x

yy

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Leverage point exists and contains gross error:

L1 estimator fails to reject bad measurement

Wrong data

(leverage point)

Motivating example: simple regression

y

x

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Leverage points in measurement model

Flow measurements on the lines with impedances, which arevery different from the rest of the lines.

Using a very large weight for a specific measurement.

Mili L., Cheniae M.G., and Rousseeuw P.J., Robust State Estimation of Electric Power

Systems IEEE Transactions on Circuits and Systems, Vol. 41, No. 5, May 1994, pp.349-358.

1

=

xxx

YYY

xxx

xxx

xxx

xxx

HR

LEVERAGE

MEASUREMENT

zexH =+

Scaling both the measured value and the measurement jacobian row will

eliminate leveraging effect of the measurement.

Leave zero injections since they are error free by design.

Incorporate equality constraints in the formulation.37


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Properties of L1 estimator

Efficient Linear Programming (LP) code existsto solve it for large scale systems.

Use of simple scaling eliminates leverage

points. This is possible due to the type ofphasor measurements (either voltages orbranch currents).

L1 estimator automatically rejects bad datagiven sufficient local redundancy, hence baddata processing is built-in.

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Conversion to Equivalent LP Problem

zrHxts

rT

=+..

||cmin

0

..cmin

=

y

zMyts

yT

][][

]00[c

IIHHMVUXXy

cc

TTTT

b

T

a

mmnn

T

==

=

VUrXXx ba

== -

39

d d


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Bad data processing

LP problem is solved once. Choice of initial basis impactssolution time/iterations.

Update the

estimates

Normalized Residuals Test (NRT):

NRT is repeated as many times as the number of bad data.

WLS: Post estimation bad data processing / re-estimation

L1: Linear Programming Solution

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Small system example

IEEE 30-bus system Line 1-2 parameter is

changed to transform 1into a leverage measurement

Case 1: Base case true solution

Case 2: Bad leverage

measurement without scaling

Case 3: Same as Case 2, but using

scaling

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Small system example


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Case-1 Case-2 Case-3

V (pu)

(deg) V (pu)

(deg) V (pu)

(deg)

1 1 5.2 1.0118 -3.5462 1 5.2

2 1 -3.74 0.9999 -3.74 1 -3.74

3 0.9952 0.13 1.004 -3.8964 0.9952 0.13

4 0.9992 -4.81 0.9992 -4.81 0.9992 -4.81

5 1 -9.02 0.9999 -9.02 1 -9.02

6 0.9851 -7.41 0.9851 -7.41 0.9851 -7.41

7 0.9869 -8.88 0.9869 -8.88 0.9869 -8.88

Small system exampleBase case

True Solution Leverage Measurements

Bad data

No scalingLeverage Measurements

Bad data

With scaling

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Large test case:


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Large test case:3625 bus + 4836 branch utility system

Case a: No bad measurement.

Case b: Single bad measurement.

Case c: Five bad measurements.

Case a Case b Case c

LAV 3.33 s. 3.36 s. 3.57 s.

WLS 2.32 s. 9.38 s. 50.2 s.

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Phasor only state estimation:


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Phasor-only state estimation:

WLS versus L1 (LAV)

WLS : Linear solution

Requires bad-data analysis

Normalized residuals test

Re-weighting (not applicable) No deficiency in the presence of

leverage measurements, with scaling.

Exact cancellations in [G]

L1 (LAV): Linear programming (single solution)

computationally competitive in s-s

Does not require bad-data analysis[*]

No deficiency in the presence of leverage

measurements, with scaling.

[*] Kotiuga W. W. and Vidyasagar M., Bad Data Rejection Properties of WeightedLeast Absolute Value Techniques Applied to Static State Estimation, IEEE

Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 4, April 1982,

pp. 844-851.

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Talk Outline

Background and terminologyState estimation

Phasor measurements





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Further motivation

Develop a state estimator capable of solvingstate estimation for three-phase unbalanced

operating conditions,

yet:

Utilize existing, well developed and tested

software as much as possible.

47

Proposed approach:


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Proposed approach:

Modal decomposition revisited

Decompose phasor measurements into theirsymmetrical components

Estimate individual symmetrical components

of states separately ( in parallel if such

hardware is available )

Transform the estimates into phase domain to

obtain estimated phase voltages and flows.

48

Modal decomposition of


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Modal decomposition ofmeasurement equations

eHVZ +=

][ TIT

V

T ZZZ =

PS TVV = PS TII =

=

T

T

T

TZ

000

0

00

eTHVTZT ZZZ +=

Phasor domain measurement representationH: 3mx3n

V: 3nx1

Z: 30x1

&Modal domain vectors

T: 3x3

VS and IS: 3x1

T: 3mx3m

49

Modal decomposition of


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=

1

11

00

00

00

T

TT

TV

MVVTV=

MMMM eVHZ +=

eTe

HTTH

ZTZ

ZM

VZM

ZM

===

0000 eVHZ += rrrr eVHZ +=

0

1

00

1

00 ZRHGV T =

rr

T

rrr ZRHGV 11 =

01

000 HRHG T =

Zero sequence Positive/ Negative sequence

Z0, Zr : mx1

V0, Vr: nx1

H0, Hr: mxn!

rrTrr HRHG

1=

Fully decoupled three relations

Smaller size (Jacobian) matrices

Modal decomposition ofmeasurement equations

50

Large scale 3-phase system example:


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Large scale 3 phase system example:

3625-buses and 4836-branches

Case a Case b Case c

LAV WLS LAV WLS LAV WLS

Zero Seq. 3.52 s. 2.32 s. 3.65 s. 9.28 s. 3.78 s. 25.51 s.

Positive Seq. 3.61 s. 2.62 s. 3.63 s. 9.41 s. 3.66 s. 26.01 s.

Negative Seq. 3.21 s. 2.22 s. 3.45 s. 9.01 s. 3.62 s. 24.82 s.

Case a: No bad measurement.

Case b: Single bad measurement.

Case c: Five bad measurements.

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No reference bus or reference PMU


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No reference bus or reference PMUis needed or should be used

Eliminate the reference phase angle from the

SE formulation.

Bad data in SCADA as well as phasor

measurements can be detected and identified

with sufficiently redundant measurement sets.

PMU

Meas.

SCADA

Meas.

State

Estimator &

Bad Data

Processor

Estimated/Corrected

PMU&SCADA Meas.

Estimated State

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Numerical Example

: Power Injection : Power Flow : Voltage Magnitude

: PMU54

Numerical Example


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Numerical ExampleError in bus 1 phase angle

TEST A

Bus 1 is used as the reference bus

TEST B

No reference is used

Measurement

Normalized

residual Measurement

Normalized

residual

7.5 10.53

5.73 7.2

5.6 5.48

5.2 5.35

4.53 4.96

Test A Test B

8 1

74p 8

65p 74p

12

65p

1V 12

55

M i Ob bl I l d


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Merging Observable Islands

PMUs can be placed at any bus in theobservable island.

SCADA pseudo-measurements can merge

observable islands only if they are incident tothe boundary buses.

P PS

S

56

R b t M t i


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Robust Metering

Bad data appearing in critical measurementscan NOT be detected.

Adding new measurements at strategic locationswill transform them, allowing detection of bad

data which would otherwise have been missed.

Note:

When a critical measurement is removed fromthe measurement set, the network will no longer beOBSERVABLE.

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Number of Critical Meas Number of PMU needed


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IEEE 57-bus systemCritical

Meas.

Type

1 F41-43

2 F36-35

3 F42-41

4 F40-56

5 I-11

6 I-24

7 I-39

8 I-37

9 I-46

10 I-48

11 I-56

12 I-57

13 I-34

P

P

Number of Critical Meas. Number of PMU needed

13 2

58

IEEE 118 b s s stemNumber of Critical Meas. Number of PMU needed


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IEEE 118-bus system29 13

P

P

P

P

P

P

P

P

P

P

P

P

P

59

Impact of PMUs on


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p

Parameter Error Identification

Are there cases where errors in certain

parameters can not be identified without

synchronized phasor measurements?

Cases where more than one set of parameters

satisfies all SCADA measurements.

60

Illustrative Example


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),,(),,( 2121 ppxJppxJ =

k lkl

klP x

=

lm

mllm

xP

=

' 'kl k l

kl k l

xx

=

' 'lm l m

lm l m

xx

=

l mlm

lm

Px

=

kl

lkkl

xP

=

Pl=Plm - Pkl

VkVl

Vm61



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),,(),,( 2121 ppxJppxJ =

k lkl

klP x

=

lm

mllm

xP

=

' 'kl k l

kl k l

xx

=

' 'lm l m

lm l m

xx

=

l mlm

lm

Px

=

kl

lkkl

xP

=

Pl=Plm - Pkl

Vk

Vl

Vm62

Remarks and Conclusions


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Remarks and Conclusions

LAV estimator will be a computationally viable and effective

alternative to WLS estimator when the measurement set

consists of only PMUs. Scaling can be a simple yet effective

tool in the presence of leverage measurements.

Use of phasor measurements for SE allows modaldecomposition of measurement equations.

WLS estimator implementation has built-in simplifications due

to exact cancellations in the gain [G] matrix.

Given sufficiently redundant phasor measurements, fast androbust state estimation is possible even for very large scale

power grids.

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Related Publications:

Gl, M. and Abur, A., A Hybrid State Estimator for Systems with Limited Number of PMUs, accepted for

publication in IEEE Transactions on Power Systems, 2014.

Gl, M. and Abur, A., LAV Based Robust State Estimation for Systems Measured by PMUs, IEEE Transactions

on Smart Grid, Vol. 5, No: 4, July 2014, pp.1808 -- 1814.

Gl, M. and Abur, A., A Robust PMU Based Three-Phase State Estimator Using Modal Decoupling, IEEE

Transactions on Power Systems, Nov. 2014, Vol. 29, No: 5, pp.2292-2299.

Gl, M. and Abur, A., Observability Analysis of Systems Containing Phasor Measurements, Proceedings of

the IEEE Power and Energy Society General Meeting, 22-26 July 2012.

Gl, M. and Abur, A., Effective Measurement Design for Cyber Security, Proceedings of the 18

th

PowerSystems Computation Conference, August 18-22, 2014, Wroclaw, Poland.

Gl, M. and Abur, A., PMU Placement for Robust State Estimation, Proceedings of the North American

Power Symposium, Sep. 22-24, 2013, Manhattan, KS.

Acknowledgements


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g

National Science Foundation NSF/PSERC

DOE/Entergy Smart Grid Initiative Grants

NSF/ERC CURENT

Jun Zhu, Ph.D. 2009

Jian Chen, Ph.D. 2008

Murat Gol , Ph.D. 2014

Former PhD Students:

Liuxi Zhang, Ph.D. 2014

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Thank You

Any Questions?
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phasor-only state estimation

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