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ELECTRIC POWER GRID INTERDICTION

Javier Salmeron and Kevin Wood, Naval Postgraduate School

Ross Baldick, University of Texas at Austin

Sponsored in part by Department of Homeland Security, Office of Domestic Preparedness

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What is VEGA?

• VEGA determines the worst possible disruption that could be caused by a terrorist attack,

• Compares multiple attack plans terrorists might undertake under different resource-constrained assumptions,

• Assesses security enhancement through preemptive measures, and

• VEGA is based on powerful optimization techniques.

VEGA is a tool for analyzing the vulnerability and defense of electric power systems under threats posed by terrorist attacks.

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“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)

Vulnerability of Electric Power Grids: A Long-Recognized Issue

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“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)

(On Ahmed Ressam) “They were specifically trained to attack critical

infrastructure, including electric power plants.” (CNN, 2002)

(On Colombian FARC) “They are leaving entire regions without service.

We can’t post a soldier at every tower” (ISA spokesman, 2002)

Terrorist Threat?

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Potential targets:

Generating plants

Transmission and distribution lines

Substations

Easy disruption + Widespread damage + Difficult recovery

Terrorist Threat? (cont.)

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• U.S. systems are operated so that a single failure does not disrupt the system (N–1 security)

• We investigate vulnerability to multiple, coordinated failures (N–m).

• Our approach uses optimization theory to:

- Mathematically represent a power grid and power flows

- Identify worst-case attacks to the grid (most “disruptive”)

- Provide insight into physical vulnerabilities, and help guide protective plans that will mitigate disruptions should attacks occur

(We maintain the assumption of information transparency)

Modeling Assumptions

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What are the best

- New investments (e.g., new facilities, lines, spare transformers)

- Upgrades (e.g., replacing conductors)

- Protective measures (e.g., hardening, surveillance...)

in

- Generating systems and/or

- Transmission and distribution systems

that substantially reduce system vulnerabilities?

“Best”= Improve Security + Affordable (+ Market Benefits???)

Key Questions

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To defend an electric grid, first learn how to attack it!

- Optimal power flow model (minimize load shedding)

- Interdiction model (maximize disruption, i.e., load shedding)

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

- (Protective measures???)

Mathematical Analysis

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- Level 1: Optimal power flow model to minimize “disruption”:

(disruption = load shedding + increased costs)

Data: Power grid data

Integrating Three Levels of Optimization

- Level 2: Interdiction model to maximize “Level-1 disruption”

Data: Power grid data and terrorist resources

- Level 3: Protective model to minimize “Level-2 interdiction”

Data: Power grid data, terrorist resource and counter-terrorist resources (budget for expansion, spares, upgrades, hardening)

(See mathematical details at the end of this presentation)

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t(Attack)

MW shedding

Other Factors: System Restoration, Demand Curves...

(months)

Slow repair

Grid Component Interdictable Resources (number of terrorists)

Outage Duration (h)

Lines (AC/DC) (overhead)

YES 1 72 (or 48)

Lines (underground) NO N/A N/A

Transformers YES 2 768 (or 168)

Buses YES 3 (or 2) 360 (or 168)

Generators NO N/A N/A

Substations YES 3 768 (or 360)

One to several days

No Repair

Days to one week

Lines

Weeks

Trafos with Spares

$$ MW

MWh t

dt

11Salmeron, Wood and Baldick (2004), IEEE Transactions on Power Systems

Total Load: 2,850 MW

IEEE Reliability Test System 96-99

BUS 24

BUS 15

BUS 14

230 kV

138 kV

BUS 22

BUS 23

BUS 18

BUS 21

BUS 16BUS 19 BUS 20

BUS 13

BUS 12

BUS 3

BUS 11

BUS 4

BUS 5

BUS 9

BUS 1 BUS 2BUS 7

BUS 8

BUS 6BUS 10

Synch.Cond.

cable

BUS 17

C

G A

E

F

D

B

cable

Time Power Energy

Period Shed (MW) Shed (MWh)

0-72 h 1,373 98,856

Plan

Total: 98,856 MWh

A

t

MW

+72hAttack

A A

A A

A

A

A0-72 h 902 64,944

72-768 h 708 492,768

Total: 557,712 MWh

B B+768h

B

B

B B0-360 h 756 272,160

Total: 272,160 MWh

C+360h

C

C

C

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VEGA

VEGA: Vulnerability of Electric

Power Grids Analyzer

Potential Users:

Utilities, ISOs...

Government analysts

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VEGA: Main Menu

• File mgmt.

• Grid data

• Optimization

• Results

• One-Line GUI

• Help

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Power Grid Data

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One-Line GUI: Power Flow After Optimal Interdiction

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, , ,min

Gen Line

Gen Shedic ic

g i cP P S

c c

Geng i cP SDC-OPF:

i: bus, l: line, g: generator, c: customer sector

PLine, PGen: power (MW) S: power shed : bus phase

Power Flow Model (DC Approx.)

( ) ( )( ),Linel o dl l lB P l L

| ( ) | ( )

( ),i

i cg G l o l i l d l i c

d

Gen Line Lineg l l i cP P P S i

,Line Linel lP P Line

lP l L

,Gen Geng gP P Gen

gP g G

0 ,i cd i cS ,i c

s.t.

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Interdiction Model

WHERE: Disruption( ) Load Shedding Cost

(from DC-OPF as modified by attacks )

δ

δ

{0,1}Disrupt n ,io ( )

Gen Line Bus Subδ ,δ ,δ δδmaxI-DC-OPF:

Gen Line Bus SubLine Bus SubM M M M M Genδ δ δ δs.t.

max min

( ) 0s.t.

0

,P

c

g

P

P

P

I-DC-OPF:

Interdiction max-min problem

, ,MIP : max

A

s.t.

{0,1}

v

vb b

c

B v d

v

C D

Can be converted into a standard mixed-integer model

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Solve the DC-OPF Power Flow Model given the

current grid configuration ()Based on present and

previous flow patterns, assign a “Value” (V) to each interdictable asset

Interdiction Model Heuristic

Interdict the assets that maximize “Total Value”

* * * *L I S, ,,

maxGen Line

Bus Sub

Gen Line Bus Subg

Gen Line Gen Sl i s

g

ubg l

l i si sV V V V

δ δδ δ

, ' , 'ˆ ˆ| 1 | 1

1, 1, ....s.t. (1 ) (1 ) ...... 1,

Line t Bus till i

Line Bus Bus Subl i i s

Line Busl i t t

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Exact (Mixed-Integer) Linearization of I-DC-OPF

max min

( ) 0s.t.

0

,P

c

g

P

P

P

12 1 2( )(1 )(1 )a bP B 12 1 2

12 1 2

( ) ( ) ( )

( ) ( ) ( )

a b

a b

B

B

P

P

MM

(1 )

0

0

v

v

v v

v

max max

s.t. A ( )

b

P

b

c

, ,MIP : max

A

s.t.

{0,1}

v

vb b

c

B v d

v

C D

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Results for the Linearized MIP

Case/Algorithm Directly Interdicted Components TimePeriod

PowerShed (MW)

EnergyShed (MWh)

RTS-Two-Areas (M=24)HEURISTIC

Buses: 116, 118, 215, 218Substations: Sub-A1, Sub-A2, Sub-B1, Sub-

B2

0-360 h 2,693 969,480

360-768 h 1,416 577,728

Total: 1,547,208

RTS-Two-Areas (M=24)

MIP

Lines: A30, A33-2Transformers: A7, B7

Buses: 115, 118, 215, 218Substations: Sub-A2, Sub-B2

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

Case/Algorithm Directly Interdicted Components TimePeriod

PowerShed (MW)

EnergyShed

(MWh)

RTS-Two-Areas (M=12)HEURISTIC

Substations: Sub-A1, Sub-A2, Sub-B1, Sub-B2

0-768 1,416 1,087,488

Total: 1,087,488

RTS-Two-Areas (M=12)

MIP

Lines: A23, B23Transformers: A7, B7

Substations: Sub-A2, Sub-B2

0-72 h 1,804 129,888

72-768 h 1,416 985,536

Total: 1,115,424

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The VEGA Team

Javier Salmeron, NPSjsalmero@nps.edu

Ross Baldick, UT Austinbaldick@ece.utexas.edu

Kevin Wood, NPSkwood@nps.edu

http://www.nps.navy.mil/orfacpag/resumePages/projects/VEGA.htm