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Topic 6: Wide Area Measurements 1 Networking and Distributed Systems Department of Electrical & Computer Engineering Texas Tech University Spring 2012

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Page 1: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Topic 6: Wide Area Measurements

1Networking and Distributed Systems

Department of Electrical & Computer EngineeringTexas Tech University

Spring 2012

Page 2: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Wide-Area Measurement

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 2

• We would like to deploy several sensors across the grid:

• To monitor the operation of the grid (almost) in real‐time.

• Applications:

• Angle and frequency monitoring

• Post‐mortem analysis (disturbances and system failures)

• Voltage and voltage stability monitoring

• Improved state estimation

• Steady‐state benchmarking

Page 3: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Wide-Area Measurement for Situational Awareness

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 3

• WAM can help us achieve Wide‐area Situational Awareness:

• Situational Awareness:

• To be able to optimally and yet robustly operate the grid.

• Key Sensor: Phasor Measurement Unit (PMU)

Understanding the current environment and being able to accurately anticipate future problems to enable effective actions.

Page 4: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Synchronized Measurements

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 4

• A PMU at a substation measures voltage and current phasors:

• Very precise synchronization with μs accuracy.

• Compute MW/MVAR and frequency.

• Measurements are reported at a rate of 20‐60 times a second.

• Can track grid dynamics in real time

• Traditional SCADA refresh rate is seconds to minutes

Page 5: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Synchronized Measurements

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 5

•Each utility has its own Phasor Data Concentrator (PDC) to

• Aggregate/align data from various PMUs based on time tag

PMU 1

PMU 2

PMU 3

PDC / Vector Processor

Page 6: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Synchronized Measurements

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 6

• Measurements from each utility’s PDC is sent to the Central Facility:

• Where the measurements are synchronized across utilities

Page 7: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Comparison Between SCADA and PMUs

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 7

• PMUs have much faster sampling rate:

Page 8: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Synchrophasor Definition

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 8

• Synchrophasor:

• Time‐tagged sequence phasor measured at different locations.

Page 9: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Architecture

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 9

• A GPS receiver is used to time‐stamp measurements:

Measurements from all PMUs will be synchronized

Page 10: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Measurement Synchronization

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 10

• It is achieved via:

• 24 Satellites

• 12 Hour Orbit Time

• Signal: Position, Velocity, Time

• Visibility:

• 5 to 8 Satellites from

• Any point at any time!

Page 11: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Measurement Synchronization

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 11

• Performance:

• 95% Reliable

• 100 nanosecond time accuracy

• Q: Good enough?

• Positioning is not a concern in PMUs.

Page 12: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Preventing Blackouts

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 12

• An application of PMUs and Situational Awareness:

• Quickly respond to emergencies

• Prevent disturbance propagation

• Planned islanding, if needed

• Limited scope load shedding, if needed

• Faster system restoration

• In general, we have no idea what happened after blackout.

Page 13: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts 2003

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 13

• Affected:

• About 10 Million People in Ontario, Canada

• About 45 Million People in 8 U.S. States

• Initiated in Ohio because of

• A device and also human error.

• A sequence of events finally led to the blackout.

Page 14: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Map of the Areas Affected

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 14

Some of the Major Cities Affected: New York, Toronto, Detroit, Cleveland, Ottawa

Page 15: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Map of the Areas Affected

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 15

Evening of August 14, 2003

Downtown Toronto

• Video: http://www.youtube.com/watch?v=6nt0njgVmv4.

Page 16: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 16

• 12:15:00 EDT: Some error in State Estimator in Northern Ohio

• 13:31:00 EDT: The Eastlake, Ohio generating plant shuts down

• 16:05:57 EDT: Last point blackout could have been prevented!

• 16:13:00 EDT: A total of 256 power plants are offline

• Restoration: It took up to 6 days in some locations.

Page 17: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 17

Rate of Line and Generator Trips During the Cascade

Page 18: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 18

Page 19: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 19

Page 20: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 20

Page 21: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 21

Page 22: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 22

Page 23: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Northeast Blackouts: Brief Timeline

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 23

Page 24: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Measurements Could Warn Instability

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 24

Page 25: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Measurements Could Warn Instability

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 25

• We can also use analytical models to capture:

• Dynamics of the phase angles and frequency.

• Usually we aim to reach linear models.

• The models can be used to

• Analyze stability as we collect PMU readings

• Find stability regions using simulations

Page 26: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 26

• Consider a network of n generators connected to each other:

• Connections are throughm tie‐lines, withm ≤ n (n‐1) / 2

Example: with n = 6 generators and m = 9 tie‐lines

Ref: A. Chakraborttyet al.

Page 27: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 27

• The internal voltage phasor of the ith generator is denoted as:

• For the link connecting pth and qth generators, impedance is:

• And we have

.,,2,1, niE ii

.pqpqpq jxrz

.11

pqpqpqpq jxrz

y

Page 28: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 28

• The dynamic electro‐mechanical model of the ith generator:

where

iNk ikik

ik

ikkiikikkiiki

ii

sii

xrrxxrEErE

PH 22

1222 tancos(2

ii

s

Generator ofVelacity Angular Rotor Hz 60at Velacity Angular Nominal120

Page 29: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 29

• A linear model around an initial equilibrium :

Assuming that a disturbance u enters the system at node j:

.,11

nn

),( 00 ii

uL

I

j

0

00

Page 30: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 30

• A linear model around an initial equilibrium :

where

),( 00 ii

uL

I

j

0

00

matrix identity ldimensiona-nI

1 iselement theand zero elements allr with unit vectoA thj j

Page 31: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 31

• A linear model around an initial equilibrium :

where

),( 00 ii

uL

I

j

0

00

ik

ikki

Nk ikik

kiii r

xxr

EELi

10022

tansin

otherwise 0

iftansin 10022 i

ik

ikki

ikik

ki

ikNk

rx

xrEE

L

Page 32: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 32

• So far we have only modeled angle and angular velocity.

• Q: What if we measure voltage phasors using PMUs?

qqE pqpqV ppE

Measurement is done somewhere between two generators.

Ref: A. Chakraborttyet al.

Page 33: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 33

• Voltage magnitude is obtained as

where

)cos()1(2)1( 2222qppqpqqppqppqqpq EEEEV

pq

pqpq z

z

location PMU tonode reference from Impedancepqz

Page 34: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 34

• The linearized model around becomes:

where

q

p

q

p

C

qpqpqppq

pqpqpq

pq

EEV

aaV

0011)sin(),()1(

0000

),( 00 ii

00

00

and at Model Voltage

Nonlinear of Evaluation),(

qp

qppqV

Page 35: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Dynamic Models

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 35

• Finally, the state space model becomes:

• The model can be used for

• Stability Analysis

• System Identification

• Closed‐loop controller / stabilizer design.

q

p

q

p

pqpq CV

uL

I

j

0

00

Page 36: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Region of Stability

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 36

• Using the non‐linear/linear models and simulations:

• We obtain regions for PMU readings that assure stability

• Contingency and security scenarios can also be considered.

PMU 1 Reading

PMU 2 Reading

Update Stability Boundary with SCADA data rate

Update Trajectory Pointswith PMU data rate

Page 37: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

Region of Stability

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 37

• Alarm is triggered as the trajectory approaches boundaries.

• Stability regions can also be used to visualize stability status.

• There can be several such two‐dimensional regions.

• One challenge: where are the optimal locations for PMUs?

Page 38: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 38

• PMU devices are available from many vendors:

• ABB, Schweitzer, AMETEK, Arbiters, GE, Macrodyne, SEL

• New IEEE C37.118 standard has been approved.

• Partly covered that in Topic 2.

• There are systems that are already installed and operating.

Page 39: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 39

• Eastern Interconnection Phasor Project (EIPP):

Source: EIPP

Page 40: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 40

• Eastern Interconnection Phasor Project (EIPP):

Source: EIPP

Page 41: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 41

• CCET Discovery Across Texas Project:

Source: C

CET

Page 42: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 42

• FNET (Frequency Monitoring Network) Project:

• University of Tennessee

• Virginia Tech

• They use a special type of PMU:

• Frequency Disturbance Recorder (FDR)

Page 43: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 43

• FDR measures

• Measure frequency, phase angle, and voltage

• Of the power system at ordinary 120 V outlets

• It is a single phase PMU.

• FDRs send data to the FNET servers over the Internet.

• Video: www.youtube.com/watch?v=9Vt2OlVoBJc (From 0:40)

Page 44: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 44

• Locations of current FDRs installed:

Page 45: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 45

• They have monitored frequency at some recent events:

• Visualization of the Eastern Interconnection powersystem frequency before, during, and after a generator tripat the John Amos plant in Nitro, West Virginia. (8/6/2007).

• Video: http://www.youtube.com/watch?v=f0rdFy1f4t4

• They have also simulated some other major events:

• Blackout of 2003 (8/14/2003).

• Video: http://www.youtube.com/watch?v=eBucg1tX2Q4

Page 46: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

PMU Deployment Status

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 46

• Link to FNET website:

• http://www.tntech.edu/cesr/fnet

• http://fnetpublic.utk.edu/

• Link to more captured events:

• http://fnetpublic.utk.edu/sample_events.html

• Link to more simulations:

• http://www.youtube.com/PowerITLabUTK

Page 47: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

References

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid

• North American Electric Reliability Council, "Technical Analysis of the August 14, 2003, Blackout: What Happened, Why, and What Did We Learn?", Report to the NERC Board of Trustees by the NERC Steering Group, July 2004. http://www.nerc.com/docs/docs/blackout/NERC_Final_Blackout_Report_07_13_04.pdf.

• M. Vaiman, M. Vaiman, S. Maslennikov, E. Litvinov, and X. Luo,"Calculation and Visualization of Power System Stability MarginBased on PMU Measurements", in Proc. of IEEE Smart GridCommunications Conference (Smart Grid Comm’10),Gaithersburg, MD, October 2010.

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Page 48: Topic 6: Wide Area Measurementshamed/Smart_Grid_Topic... · Wide-Area Measurement for Situational Awareness Dr. Hamed Mohsenian-Rad Communications and Control in Smart Grid Texas

References

Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid

• D. Novosel, "Tutorial on PMU Technology and Applications", In Proc. of the International Conference on SynchrophasorMeasurement Applications, Brazil, June 2006.

• A. Chakrabortty and C. F. Martin, "Optimal measurementallocation for parametric model identification of electricalnetworks", IEICE Transactions on Nonlinear Theory and ItsApplications, vol. 2, no. 3, pp. 302‐319, 2010.

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