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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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 : [email protected]
Qixing Liu: lqx@cmu eduQixing Liu: [email protected]
Prof. Soummya Kar: [email protected] Marija Ilic: milic@ece cmu eduProf. Marija Ilic: [email protected]
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Thank you!