ELECTRIC POWER GRID
INTERDICITION
Javier Salmeron and Kevin Wood, Naval Postgraduate School
Ross Baldick, University of Texas at Austin
Sponsored by DoJ, Office of Domestic Preparedness
1
Purpose
In this presentation we will...
•
Show the importance of analyzing vulnerabilities of electric
power systems to terrorist attacks
•
Present our models, and exact and heuristic algorithms to
carry out this analysis
•
Present results on standard IEEE Reliability Test Networks
2
A Long-Recognized Issue (I)
“One can hardly imagine a target more ideal than the U.S. domestic
energy” (A.B. and L.H. Lovins, 1983)
“Any U.S. region could suffer lasting and widespread blackouts if three or
more substations were targeted.” (OTA, 1990)
 “The U.S. is at, or is fast approaching, a crisis stage with respect to
reliability of transmission grids.” (NERC, 2001)
 “The U.S. electric power systems must clearly be made more resilient to
terrorist attack.” (Committee on Science and Technology for Countering
Terrorism, NRC, 2002)
3
A Long-Recognized Issue (II)
 (On Ahmed Ressam) “They were specifically trained to attack critical
infrastructure, including electric power plants.” (CNN, 2002)
 “And the threat isn't simply academic. U.S. occupation forces in
Afghanistan discovered Al Qaeda documentation about the facility that
controls power distribution for the eastern U.S., fueling fears that an attack
on the power grid may one day become a reality.” (Energy Pulse, 2003)
 “Blue Cascades” project (simulated terrorist attack on the Pacific
Northwest's power grid). The study showed that such an attack, if successful,
could wreak havoc on the nation's economy, shutting down power and
productivity in a domino effect that would last weeks. (Energy Pulse, 2003)
4
Terrorist Threat
Potential targets:
 Generating plants
Transmission and distribution lines
 Substations
Easy disruption + Widespread damage + Difficult recovery
5
Our Approach
•
Assumes Information Transparency: Same information is available
to both sides
•
Uses optimization to assess worst-case disruptions
•
Goal:
To provide insight on physical vulnerabilities and protective plans
that proactively hedge against disruption caused by terrorist attacks
6
Mathematical Analysis of the Problem
 In order to better defend the electric grid it is valuable to
understand how to attack it!
-
Optimal power flow model (minimizing load shedding)
-
Interdiction model (maximize disruption)
 Additional features of the problem are:
-
Time scale: Very short-, short-, medium- and long-term
-
Customer types; ability to “share the pain”
-
Uncertainty about terrorist resources
-
Assumptions on protection resources
7
Power Flow Model (DC Approx.)
DC-OPF:
P
min
Gen
Line
,P
, S ,
Gen Gen
Shed
c
P

c
 ic g  ic Si c
g
i
c
Pl Line  Bl (o( l )  d ( l ) ),
P
gGi
s.t.
Gen
g


l |o ( l ) i
Pl Line 

l | d ( l ) i
l  L
Pl Line   (di c  Si c ),
c
i
l  L
 Pl Line  Pl Line  Pl Line ,
PgGen  PgGen  PgGen ,
g  G
 i, c
0  Si c  d i c ,
i: bus, l: line, g: generator, c: customer sector
PLine, PGen: power (MW)
S: power shed
 : bus phase
8
Interdiction Model
I-DC-OPF:

max
Gen Line
,
, Bus
G(δ Gen ,δ Line ,δ Bus )
Gen Gen
Line
Line
Bus
Bus
M
δ

M
δ

M
δ
  g g  l l  i i M
iI gGi*
lL*
All δ  {0,1}
iI *
Where:
G (δ Gen ,δ Line ,δ Bus ) 
P
min
Gen
Line
,P
, S ,
Gen Gen
Shed
c
P

c
 ic g  ic Si c
g
i
c
Bus
Pl Line  Bl (o( l )  d ( l ) ) (1  δ lLine ) (1 δ oBus
)(1

δ
(l )
d (l ) )
s.t.
DC-OPF after
interdiction
 Pl Line(1  δ lLine )  Pl Line  Pl Line (1  δ lLine ),
Etc...
9
Heuristic
Solve the DC-OPF Power
Flow Model given the
current grid configuration
Interdict the assets that
maximize “Total Value”
max
Gen Line
δ ,δ ,
δ Bus ,δ Sub
V
Gen ,t
g
g*
Based on the current and
previous flow patterns,
assign a “Value” (V) to
each interdictable asset
 gGen   Vl Line,t lLine   Vi Gen ,t iGen   VsSub ,t sSub
lL*
iI*
sS*
 lLine   iBus  1,
 iBus   sSub  1,
....

s.t.   (ˆlLine,t '   lLine )   (ˆiBus ,t '   iBus ) ......  1,
lL* |
iI* |
 Line
ˆiBus ,t ' 1
ˆl ,t ' 1
t   t
10
Exact Linearization of the Model
max min c P
 
P
 g ( , P )  0
s.t. 
P  0
max max b   b 
 

s.t. A  c
( P)
 P12  B( a   b )  M (1   2 )
P12  B(a  b )(1  1 )(1   2 ) 
 P12  B( a   b )   M (1   2 )



v    



v  


v 

v     (1   ) 

0 

v0

(  )
(  )
MIP : max b   bv v
 , , v
s.t.
A  c

 B  Cv  d  D
  {0,1}

11
IEEE Reliability Test System 96-99
Total load: 2,850 MW
Interdiction resource: 6 terrorists
Line x1
Single transformer x2
Bus or substation x3
Load shedding: 1,258 MW
Load shedding: 1,373 MW
Salmeron, Wood and Baldick (2004),
IEEE Transactions on Power Systems
12
IEEE Reliability Test System 96-99
Load: 5,700 MW
12 terrorists
Shedding:
2,516 MW
Salmeron, Wood and Baldick (2004), IEEE Transactions on Power Systems
13
System Restoration
Trafos with
$  ($ / MWh)  MW dt
spares
Lines
MW
shedding
t
No repair
(Attack)
E.g.:
One to several
days
Slow repair
Days to one week
Weeks
Grid
Component
Interdictable
Resources M
(no. of
terrorists)
Outage Duration
(h)
Lines (overhead)
YES
1
72
Lines
(underground)
NO
N/A
N/A
Transformers
YES
2
768
Buses
YES
3
360
Generators
NO
N/A
N/A
Substations
YES
3
768
>1 months
14
t
IEEE Reliability Test System 96-99
Total Load: 2,850 MW
Plan
Time
Power
Energy
Period
Shed (MW)
Shed
(MWh)
1,373
98,856
Total: 98,856 MWh
0-72 h
0-72 h
902
64,944
72-768 h
708
492,768
Substation
Protected
Substation
Protected
Total: 557,712 MWh
0-360 h
756
272,160
Total: 272,160 MWh
MW
2
3
Attack
+72h
4
3
+360h
+768h
t
Salmeron, Wood and Baldick (2004),
IEEE Transactions on Power Systems
15
Results for the Linearized MIP
Case/Algorithm
Directly Interdicted Components
RTS-TwoAreas (M=12)
HEURISTIC
Substations: Sub-A1, Sub-A2, Sub-B1, SubB2
RTS-TwoAreas (M=12)
MIP
Lines: A23, B23
Transformers: A7, B7
Substations: Sub-A2, Sub-B2
Case/Algorithm
Directly Interdicted Components
RTS-Two-Areas
(M=24)
HEURISTIC
RTS-Two-Areas
(M=24)
MIP
Buses: 116, 118, 215, 218
Substations: Sub-A1, Sub-A2, Sub-B1, SubB2
Lines: A30, A33-2
Transformers: A7, B7
Buses: 115, 118, 215, 218
Substations: Sub-A2, Sub-B2
Time
Period
Power
Shed (MW)
0-768
1,416
Energy
Shed
(MWh)
1,087,488
Total: 1,087,488
0-72 h
1,804
129,888
72-768 h
1,416
985,536
Total: 1,115,424
Time
Period
Power
Shed (MW)
Energy
Shed (MWh)
0-360 h
2,693
969,480
360-768 h
1,416
577,728
Total: 1,547,208
0-72 h
3,164
227,808
72-360 h
2,716
782,208
360-720 h
1,416
577,728
Total: 1,587,744
16