Dynamic Decomposition forMonitoring and Decision Making
in Electric Power Systems
Contributed Talk at NetSci 2007
May 20, 2007
Le Xie ([email protected])
Advisor: Marija Ilic
Outline• Motivation• Problem Statement• Proposed Methodologies
– Performance index (PI)– Decomposition method
• Example• Conclusions
MotivationAnnual average growth rates in U.S. transmission
capacity and peak demand for three decades
(projected for 2002-2012)
0
0.5
1
1.5
2
2.5
3
1982-
1992
1992-
2002
2002-
2012
% per year
Transmission (GW-Miles) Summer Peak (GW)
Data Source: FERC
• Power system isoperated over amuch broaderrange than it wasoriginally designedfor.
• More and morestressed conditionsare encountered inreal-timeoperations.
Challenges for Power SystemOperation
• Goal: meet the continually changing loaddemand for both active and reactive powerwhile the desired system frequency andvoltage profile are maintained.
• Traditional power system operation isdesigned as a hierarchical structure.However, the assumptions underlying thishierarchical control design are not alwayssatisfied when system experience largedeviation from normal conditions.
P. Kundur, “Power System Stability and Control,” pp. 27, McGraw-Hill, 1994
Major Blackouts in the Past 30Years
year 1978
80% of France
Blackout
1983
Sweden Voltage Collapse
1987
FranceVoltage Collapse
1996
MexicoBlackout
2003 2005
LondonBlackout
Northeast USABlackout
ItalyMalaysia…
…. MoscowBlackout
2007
ColumbiaBlackout
Lessons from History
• Control devices are tuned and mosteffective under normal load conditions.
• Control devices may not function asdesigned when load level becomessevere and/or hierarchical assumptionsare violated.
• Need for intelligent online monitoringand decision making tools.
As more sensors are placed for thepower system
• Two basic questions– Who talks to whom and for what purpose?– Sensors communicate what data/information?
System-wide Coordinator
Component1
DecompositionLevel I Component
2 Componenti+1
Component3
Componenti
Interaction Physical
Sensor
Goal of Research
Dynamic re-grouping over time, space and organizational boundaries as the power system conditions vary
Offline Training
Set of Decomposition Strategy
Data Communication and Monitoring
Performance Indices (PI) Computation
PI<Threshold?YES
NO
Re-aggregate System Nodes
Adjust Data Communication StructureOffline
Online
• x- state variables, define system dynamics(such as rotor angles of generators)
• y- algebraic coupling variables (such as thevoltage magnitude and phase angle of all thebuses)
• p- system parameters (such as networktopology, load consumption)
Example: Monitoring ofStatic Voltage Stability
M. Ilic and J. Zaborszky, “Dynamics and Control of Large Electric Power Systems”, 2001
Proposed Performance Index
• The singularity of linearized system load flowequations (Jacobian matrix) indicates the staticvoltage instability.
• Sensitivity of minimum singular value of load flowJacobian with respect to the the load level
– Define Load Level as the algebraic sum of |apparent powerconsumption| at all nodes in a system
– Define PI for a system (subsystem)Min singular value
Load level
!! +==i
ii
i
i QPSS22
S
JSVPI
QV
!
!=
))(min(
Epsilon Decomposition• Clustering algorithm that decomposes
weakly coupled sub-groups
D. D. Siljak, Decentralized Control of Complex Systems. Academic Press, 1991
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&
0.23.00.2
2.00.51.0
4.02.00.3
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0.500
00.20.2
000.3
1
2
3
5.0
3.0 2.00.4
2.0
0.10.2 0.3
0.2
2.01
2
3
5.0
3.0
2.05.0=!
5.0=!
Epsilon Decomposition: cont.
• Row and column permutation to JQVs.t.
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In which and
IEEE Reliability Test System (RTS)
• 3 control areas• 5 tie line buses• Keep constant
power factorincreasing of theload at bus #308(in area III) untilstatic voltageinstability limit isreached
Grigg, et. al, “The IEEE Reliability Test System-1996 ”, IEEE Tran. Power Systems, 1996
Control Area II(24 Nodes)
Control Area III(25 Nodes)
Control Area I(24 Nodes)
Epsilon Decomposition Result
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 67
8
9
10
11
12
13
14
Normalized Load Level at Bus#308
M
i
n
(
S
i
n
g
u
l
a
r
V
a
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e
)
Area layer: overlapping decomposed JQV
for area III
Group-of-nodes layer: 6 nodes around bus #308
Local (node-by-node) layer: bus#308
Stressed Load Level
Abnormal (Stressed) Conditions
Control Area II(24 Nodes)
Control Area III(25 Nodes)
Control Area I(24 Nodes)
Conclusions• A dynamic decomposition method, which is
based on coupling strength among sub-groups, is proposed to monitor and controlthe power system over a broad range ofoperating conditions.
• A performance index is proposed as anexample to monitor the static voltage problemin a dynamical decentralized approach.
• Dynamic decomposition could potentially formthe framework for adaptive real-time powersystem operation.
References• Xie, et. al. “Novel Performance Index and Multi-layered Information
Structure for Monitoring Quasi-static Voltage Problems”, Proceedings ofIEEE Power Engineering Society General Meeting, 2007 (to appear)
• Ilic, et. al. “Dynamics and Control of Large Electric Power Systems”, JohnWiley & Sons, 2000
• Ilic, et. al. “Preventing Future Blackouts by Means of Enhanced ElectricPower System Control: From Complexity to Order”, IEEE Proceedings,vol 93, no 11, pp 1920-1941, Nov. 2005
• Siljak, “Decentralized Control of Complex Systems”, Academic Pr, Jan.1991
• Sauer, et. al. “Power System Steady State Stability and the Load-FlowJacobian”, IEEE Transactions on Power Systems, vol 5, no 4, pp 1374-1383, Nov. 1990
• A. Tiranuchit, et. al. “Towards a Computationally Feasible On-line VoltageInstability Index”, IEEE Transactions on Power Systems, vol 3, no 2, pp669-675, May 1988
• Lof, et. al. “Voltage Stability Indices for Stressed Power System”, IEEETransactions on Power Systems, vol 8, no 1, pp 326-335, Feb 1993