PMU Placement to Ensure Observable Frequency and q yVoltage Dynamics: A Structured System Approachy pp

Qixing Liu

(Joint work with Sergio Pequito, Prof. Soummya Kar and Prof. Marija Ilic)

Electrical and Computer EngineeringCarnegie Mellon UniversityInstituto Superior Técnico

8th ANNUAL CMU CONFERENCE ON THE ELECTRICITY INDUSTRY 

1DATA‐DRIVEN SUSTAINABLE ENERGY SYSTEMS

March 12‐14, 2012

O liOutline

S i O i i i O i iStatic Observability vs Dynamic ObservabilityThe key role of Phasor Measurement UnitsCoupled Frequency-Voltage Dynamic ModelStructural SystemsStructural SystemsPMU Placement

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Static Observability vs Dynamic Observabilityy y y

Topological Static Observability [Abur 1995]Topological Static Observability [Abur 1995]

Covering problem (IEEE 14 Example)

14 Buses, 3 PMUs

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Static Observability vs Dynamic Observability

Mutual Information to Improve Static Observability [Li 2011]

y y y

p y [ ]

Mutual information (MI): the amount of information that PMU i b hPMU measurement carries about the system state

Placement Objective: Maximize mutual informationPlacement Objective: Maximize mutual information

Total uncertainty

Remaining uncertainty with PMU measurements

Reduction in uncertainty from PMU measurements

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IEEE 14-Bus: 3 PMUs

y

Static Observability vs Dynamic Observabilityy y y

T l i l Ob bilit

Mutual information

Topological ObservabilityStatic Observability

Dynamic ObservabilityDynamic ObservabilityA system is said to be observable if, for any possible sequence of state and control vectors, the current state can be determined in finite time using only the outputs.f g y p

(Descriptor form) Our modelDAEs vs ODEs

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The Key Role of Phasor Measurement y fUnits

Real-time synchronized measurements for geographically large-scale systems

Enable systematically designed dynamic observerobserver

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Modeling Power Systemsg yCoupled frequency-voltage dynamics

Load

‐Induction Machine

Network coupling constraints‐Linear Algebraic Equations (KCL

States of generator-Electromechanics: [∆δG, ∆ωG]

Linear Algebraic Equations (KCL, KVL and Ohm’s Law)

-Electromagnetics: [E’D, E’Q]

-Speed-governor: [∆PT, ∆a]

Excitation control: [V efd V ]

Standard state‐space model

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-Excitation control: [VR , efd, VF]

Problem Statement

Given only the dynamics/structure

How to design

Such that (A,C) is observable, I.e, PMUPlacement

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Structural SystemsStructural SystemsRepresentation of the dynamics as digraph

From

To

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Given the system DigraphGiven the system Digraph

Does it have a substructure as follows

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11Cactus

PMUCactus

PMU

# PMU = # Cacti

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C St d 5 bCase Study: 5 bus

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Is this system dynamically observable?y y y

14Number of states: 37

Compute one tree [Node 1-Tree (Path 1-37)]p ( )

Measured States 1, 22, 30, 34root

InterpretationGovernor Hydro (1)

Governor Diesel (22) Load 1 Angle (30)g ( )Load 2 Angle (34)

Buses 1, 3, 4, 5# PMUs 4

PMU

15Do it for all nodes...

endend

Compute one tree [Node 4-Tree (Path 4-22)]

Measured States 4, 30, 34

p ( )

InterpretationHydro G1 Angle (4)Load 1 Angle (30)Load 2 Angle (34)

root

Buses 1, 4, 5# PMUs 3

end

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Fi l bi ti ith i i b fFinal combinations with minimum number of sensors

Measured States 4, 30, 34

InterpretationHydro G1 Angle (4)Load 1 Angle (30)Load 2 Angle (34)Load 2 Angle (34)

Buses 1, 4, 5

# PMUs 3

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Conclusions and Further ResearchConclusions and Further Research

l hi f k i / / bImplement this framework in IEEE 14/20/30 bus

R b l i d i i l iRobustness analysis and quantitative analysis

User friendly toolboxUser friendly toolbox

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References

[1] Ali Abur, Optimal Plancement of Phasor Measurement Units forState Estimation. PSERC Report, 2005

[2] Qiao Li, Tao Cui, Yang Weng, Rohit Negi, Franz Franchetti, MarijaIlic, An Information-Theoretic Approach to PMU Placement in ElectricPower SystemsPower Systems

[3] PMU Placement to Ensure Observable Frequency and VoltageDynamics: A Structured System Approach 8th CMU ElectricityDynamics: A Structured System Approach, 8th CMU ElectricityConference. http://www.ece.cmu.edu/~electriconf/index.html

4 S i i S A A i A i[4] Sergio Pequito, S. Kar, A. Pedro Aguiar, Actuator Placement DesignStrategies for Controllability of Large Scale Systems: Minimalitythrough Structured Systems, To be submitted to Transactions of

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Automatic Control

Questions?

Sergio Pequito : spequito@andrew.cmu.edu

Qixing Liu: lqx@cmu eduQixing Liu: lqx@cmu.edu

Prof. Soummya Kar: soummyak@andrew.cmu.eduProf Marija Ilic: milic@ece cmu eduProf. Marija Ilic: milic@ece.cmu.edu

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Thank you!