PMU Placement to Ensure Observable Frequency and q
y
Voltage Dynamics: A Structured System Approach
y
pp
Qixing Liu
(Joint work with Sergio Pequito, Prof. Soummya Kar and Prof. Marija Ilic)
Electrical and Computer Engineering
Carnegie Mellon University
Instituto Superior Técnico
8th ANNUAL CMU CONFERENCE ON THE ELECTRICITY INDUSTRY DATA‐DRIVEN SUSTAINABLE ENERGY SYSTEMS
March 12‐14, 2012
1
O li
Outline
Static
S
i Observability
O
i i vs Dynamic
i Observability
O
ii
The key role of Phasor Measurement Units
Coupled Frequency-Voltage Dynamic Model
Structural Systems
PMU Placement
2
Static Observabilityy vs Dynamic
y
Observabilityy
Topological Static Observability [Abur 1995]
Covering problem (IEEE 14 Example)
14 Buses, 3 PMUs
3
Static Observabilityy vs Dynamic
y
Observabilityy
Mutual Information to Improve
p
Static Observability
y [Li 2011]
Mutual information (MI): the amount of information that
PMU measurement carries
i about
b
the
h system state
Placement Objective: Maximize mutual information
Remaining uncertainty with PMU measurements
Total uncertainty
Reduction in uncertainty from PMU measurements
y
IEEE 14-Bus: 3 PMUs
4
Static Observabilityy vs Dynamic
y
Observabilityy
T l i l Observability
Topological
Ob
bilit
Static Observability
Mutual information
Dynamic Observability
A system is said to be observable if, for any possible sequence of state and control
vectors, the current state can be determined in ffinite time usingg onlyy the outputs.
p
Our model
(Descriptor form)
DAEs vs ODEs
5
The Keyy Role off Phasor Measurement
Units
Real-time synchronized measurements for
geographically large-scale systems
Enable systematically designed dynamic
observer
6
Modelingg Power Systems
y
Coupled frequency-voltage dynamics
Load
‐Induction Machine
States of generator
Network coupling constraints
‐Linear
Linear Algebraic Equations (KCL, Algebraic Equations (KCL
KVL and Ohm’s Law)
-Electromechanics: [∆δG, ∆ωG]
-Electromagnetics: [E’D, E’Q]
-Speed-governor: [∆PT, ∆a]
Standard state‐space model
-Excitation
Excitation control: [VR , efd,
efd VF]
7
Problem Statement
Given only the dynamics/structure
How to design
Such that (A,C) is observable, I.e,
PMU
Placement
8
Structural Systems
Representation of the dynamics as digraph
From
To
9
Given the system Digraph
Does it have a substructure as follows
10
Cactus
11
PMU
Cactus
# PMU = # Cacti
12
C
Case
St
Study:
d 5b
bus
13
Is this system
y
dynamically
y
y observable?
Number of states: 37
14
Compute
p
one tree [Node 1-Tree ((Path 1-37)]
)
Measured States
1, 22, 30, 34
Interpretation
Governor Hydro (1)
Governor Diesel (22)
g (30)
( )
Load 1 Angle
Load 2 Angle (34)
Buses
1, 3, 4, 5
# PMUs
4
root
PMU
Do it for all nodes...
end
end
15
Compute
p
one tree [Node 4-Tree ((Path 4-22)]
)
Measured States
4, 30, 34
Interpretation
Hydro G1 Angle (4)
Load 1 Angle (30)
Load 2 Angle (34)
Buses
1, 4, 5
# PMUs
3
root
end
16
Fi l combinations
Final
bi ti
with
ith minimum
i i
number
b off sensors
Measured States
4, 30, 34
Interpretation
Hydro G1 Angle (4)
Load 1 Angle (30)
Load 2 Angle (34)
Buses
1, 4, 5
# PMUs
3
17
Conclusions and Further Research
Implement
l
this
hi framework
f
k in
i IEEE 14/20/30
/ / bus
b
R b
Robustness
analysis
l i andd quantitative
i i analysis
l i
User friendly toolbox
18
References
[1] Ali Abur, Optimal Plancement of Phasor Measurement Units for
State Estimation. PSERC Report, 2005
[2] Qiao Li, Tao Cui, Yang Weng, Rohit Negi, Franz Franchetti, Marija
Ilic, An Information-Theoretic Approach to PMU Placement in Electric
Power Systems
[3] PMU Placement to Ensure Observable Frequency and Voltage
Dynamics: A Structured System Approach,
Approach 8th CMU Electricity
Conference. http://www.ece.cmu.edu/~electriconf/index.html
[4]
4 Sergio
S i Pequito,
i S.
S Kar, A.
A Pedro Aguiar,
A i Actuator
A
Placement Design
i
Strategies for Controllability of Large Scale Systems: Minimality
through Structured Systems, To be submitted to Transactions of
Automatic Control
19
Questions?
Sergio Pequito : spequito@andrew.cmu.edu
Qixing Liu: lqx@cmu.edu
lqx@cmu edu
Prof. Soummya Kar: soummyak@andrew.cmu.edu
Prof Marija Ilic: milic@ece.cmu.edu
Prof.
milic@ece cmu edu
Thank you!
20