NEW COMPUTATIONAL TECHNIQUES TO REDUCE THE VULNERABILITY OF POWER GRIDS

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NEW COMPUTATIONAL TECHNIQUES TO REDUCE THE
VULNERABILITY OF POWER GRIDS

• Chen-Ching Liu
• Electrical and Computer Engineering
• Iowa State University
• 2007 Seminar at University College Dublin

Sponsored by U.S. NSF, EPRI, U.S. DoD
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CATASTROPHIC POWER OUTAGES
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Eastern Interconnection August 14th, 2003
Blackout
Initiating events
System becomes unstable
Blackout
107 p.m. FE turns off their state estimator for
troubleshooting.
265 power plants tripped off line and 50 million
people are without power.
40557 p.m. The loss of 138-kV lines overloads
the Sammis-Star line.
131 p.m. Eastlake 5 generation unit trips and
shuts down. 202 p.m. Stuart-Atlanta 345-kV line
tips off due to contact with a tree.
40859 p.m. Galion-Ohio and Central-Muskinghun
345-kV lines trip on Zone 3 causing major power
swings through New York and Ontario and into
Michigan.
214 p.m. FEs control room lost alarm functions
followed by a number of the EMS consoles.
Low voltage/ high load conditions and system
disturbances propagate through the system
tripping transmission lines and generators.
ME
ND
VT
MN
NH
MI
NY
SD
MA
WI
CT
RI
254 p.m. The primary and secondary alarms
servers failed.
IA
PA
NE
NJ
OH
DE
IL
IN
MD
WV
VA
KS
MO
KY
30541-35735 p.m. 3 345-kV lines trip due to
contact with trees. This overloads the
underlying 138-kV system and depressed voltages.
413 p.m. most of the North East and parts of
Canada blacked out. There are only a few islands
which remain operating.
NC
TN
OK
AR
SC
GA
AL
MS
LA
FL
33917-40859 p.m. 16 138-kV lines trip due to
overloading.
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Hydro-Québec Blackout-April 18th, 1988
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El Paso Electric Blackout-January 31st 2001
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Planned Generation Capacity Transmission
Enhancement in U.S.
Planned Capacity ( 25 increase )
Projected Demand ( 18 increase )
Estimated Capacity Margin (5 increase
)
Planned Transmission ( 3.5 increase )
Actual data (19992000)
Source Reliability Assessment 2001-2010 Report
by NERC, 2001. Information Administration
Website http//www.eia.doe.gov/cneaf/electricity
/page/fact_sheets/transmission.html
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Strategic Power Infrastructure Defense (SPID)
Hidden failure monitoring
Fast and on-line power comm. system assessment
Adaptive load shedding, generation rejection,
islanding, protection
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Multi-Agent System Architecture for SPID
DELIBERATIVE LAYER
COORDINATION LAYER
REACTIVE LAYER
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CONTROL AND COMPUTATIONAL TECHNIQUES

• Adaptive Load Shedding
• Flexible Configuration
• Analysis of interdependency between power and
  communication systems

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LOAD SHEDDING

• Studies have shown that the August 10th 1996
  blackout could have been prevented if just 0.4
  of the total system load had been dropped for 30
  minutes.
• According to the Final NERC Report on August 14,
  2003, Blackout, at least 1,500 to 2,500 MW of
  load in Cleveland-Akron area had to be shed,
  prior to the loss of the 345-kV Sammis-Star line,
  to prevent the blackout.

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Adaptive Self-HealingLoad Shedding Agent
WECC 179 bus system
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Adaptive Self-HealingLoad Shedding Agent
Frequency
Time (multiples of 0.02 sec)
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Adaptive Self-HealingLoad Shedding Agent
Expected normalized system frequency that makes
the system stable
Normalized frequency
The load shedding agent is able to find the
proper control action in an adaptive manner based
on responses from the power system
Number of trials
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PARTITIONING A SYSTEM INTO SELF-SUFFICIENT
ISLANDS
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Simulated Cascading Events (179 Bus System Model)

• Compute Power Flows after Tripping
• Six lines are found on limit violation
• Trip these lines
• Identify New Network Configuration and Solve
  Power Flows Again
• Fifteen lines are found with limit violations
• Trip these lines
• Continue This Simulation Procedure
• Finally system collapses most transmission
  lines are tripped and most loads are lost

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2-Area Partitioning Algorithm (from VLSI)

• Spectral 2-way Ratio-Cut Partitioning
• Theorem Given an edge-weighted graph G (V, E),
  the second smallest eigenvalue ?2 of the graphs
  Laplacian matrix Q yields a lower bound on the
  cost c of the optimal ratio cut partition, with c
  e(U,W)/(UW) (?2/n)
• Cut-Size e(U,W) (?2/n) (UW)

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2-Area Partitioning Example

• Illustration of Theorem

6-Bus System
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2-Area Partitioning Example
Partition Results of 6-Bus System
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WECC 179-bus model
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Split System into Two Areas
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Flexible Grid Configuration to Absorb the Shock

• Solve Power Flows of Area One
• All 35684.71 MW loads are supplied, no line flow
  constraints violations
• Solve Power Flows of Area Two
• Seven lines on limit violation
• (Bus158-Bus164), (163-8), (64-163), double lines
  (16-19), and double lines (150-154)

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Power Redispatching Load Shedding Algorithm

• For Each Area,
• Minimize (Load Shedding) min
• Subject to
• 
  (power balance)
• (generator limits)
• 
  (line flow limits)

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Flexible Grid Configuration to Absorb the Shock

• Use Power Redispatching Load Shedding in Area
  Two
• Totally, 188 64.4 60 312.4 MW load are shed

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Flexible Grid Configuration to Absorb the Shock

• Shed Load vs. System Total Load
• K1
• K2
• K3

?
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K-Area Partitioning Algorithm (from VLSI)

• Spectral k-way Ratio-Cut Partitioning
• The sum of the smallest k eigenvalues of the
  Laplacian Q of a weighted graph G is a lower
  bound on for any k-way partition of
  G
• where is a k-way
  partition of the nodes of graph G, ? is the set
  of all k-way partitions of graph G, and is
  the total weight of the edges in G having exactly
  one endpoint in

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K3 Case (Three Areas)
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DEPENDENCY ON THE COMMUNICATION INFRASTRUCTURE

• NERC data 1979-1995 for analysis of initial
  faults and contributing factors
• Leading initial fault categories severe weather,
  faults and equipment failures
• Real time monitoring and operating control
  system, communication system, and delayed
  restoration contribute to a very high percentage
  of large failures

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Analyzing the Impact of Communications on Power
Grids

• Modeling of Interaction of Infrastructures
• Analysis of Hydro-Québec Special Protection System

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Petri Net Analysis

• A single model that can span multiple
  infrastructures.
• Analytic evaluation of events.
• Calculation of the probability of a sequence of
  operations occurring Total Transition
  Probability (TTP).
• Calculation of the time required for a sequence
  of operations to occur Total Transition Time
  (TTT).
• Determination of Redundancy.

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Petri Net Structure
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Petri Net Example
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Algebraic Representation
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Hydro-Québec Special Protection Scheme
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Redundancy (Cont.)
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Redundancy

• By reordering the coincidence matrix the various
  infrastructures can be isolated.
• The rank of the sub-matrices is an indication of
  controllability.
• A fully controllable sub-matrix indicates no
  redundancy.
• In this way the communications section of the
  power system can be analyzed for redundancy.

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Redundancy (Cont.)
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Redundancy (Cont.)
Rank1
Rank3
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Total Transition Probabilityand Total Transition
Time
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Remarks on Hydro-Québec

• TTP and TTT have adequate values.
• Analysis of the redundancy identified 2 potential
  vulnerabilities.
• The first of the potential vulnerabilities is
  mitigated.
• The second potential vulnerability should be
  addressed.
• The second potential vulnerability is what
  contributed to the April 18th blackout.

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FURTHER INFORMATION

• Z. Xie, G. Manimaran, V. Vittal, A. Phadke and V.
  Centeno, An Information Architecture for Future
  Power Systems and Its Reliability Analysis, IEEE
  Trans. Power Systems, Aug 2002.
• K. Schneider, C. C. Liu, and J.-P. Paul,
  Assessment of Interactions between Power and
  Telecommunications Infrastructures, IEEE Trans.
  Power Systems, Aug. 2006.
• C. C. Liu, J. Jung, G. Heydt, V. Vittal, and A.
  Phadke, The Strategic Power Infrastructure
  Defense (SPID) System, IEEE Control Systems
  Magazine, Aug. 2000.
• H. Li, G. Rosenwald, J. Jung, and C. C. Liu,
  Strategic Power Infrastructure Defense,
  Proceedings of the IEEE, May 2005.
• J. Jung, C. C. Liu, S. Tanimoto, and V. Vittal,
  Adaptation in Load Shedding Under Vulnerable
  Operating Conditions, IEEE Trans. Power Systems,
  Nov. 2002.
• T. Nye, C. C. Liu, and M. Hofmann, Adaptation of
  Relay Operations in Real-Time, 15th PSCC, Aug.
  2005.