Dynamic Decomposition forMonitoring and Decision Making

in Electric Power Systems

Contributed Talk at NetSci 2007

May 20, 2007

Le Xie (lx@ece.cmu.edu)

Advisor: Marija Ilic

Outline• Motivation• Problem Statement• Proposed Methodologies

– Performance index (PI)– Decomposition method

• Example• Conclusions

U.S National Power Grid

Data Source: FERC

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

Goal of Research

Physical interaction

Normal Operating Conditions

Goal of Research

Abnormal Operating Conditions

Physical interaction

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

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0.500

00.20.2

000.3

1

2

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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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'

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=

b

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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

l

u

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

Normal Conditions

Control Area II(24 Nodes)

Control Area III(25 Nodes)

Control Area I(24 Nodes)

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

Thank you!