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Vulnerability Analysis Of Optimal Power Flow Problem Under Cyber-Physical Security Attacks

Devendra Shelar and Saurabh Amin

Massachusetts Institute of Technology

INFORMS November 15th, 2016

Vulnerable Electricity Networks: Key issues

§ In addition to reliability failures, power

grids are increasingly vulnerable to cyber-physical security (CPS) attacks

§ Such CPS attacks can be modeled as

bilevel optimization problems

§ We present two CPS attack scenarios

§ Dynamic Line Rating (DLR)

Manipulation

§ Distributed Energy Resource (DER)

disruption

§ Structural insights allow for greedy and

efficient (approximate) algorithms Two motivating attack models California Sniper Attack Ukraine Cyber Attack

Related work

§ A. Verma, D. Bienstock: N-k vulnerability problem

§ Attacker disrupts generators or manipulates line impedances to

maximinimize load shedding

§ DC Power Flow approximation

§ S.Wright et al.: Vulnerability Analysis of Power Systems

§ Attacker increases the line impedances to maximinimize § Loss of voltage regulation, OR Load shedding § Use both active and reactive power

§ R. Baldick, K. Wood, D. Bienstock: Network Interdiction, Cascades

Use bilevel optimization models with outer problem as attack model, and the inner problem being optimal power flow (OPF) problem

§ Ensure demand is fully met while minimizing costs subject to

generator, capacity, supply-demand balance, power flow constraints

DLR Manipulations in Transmission Networks

Line capacity violations have cause cascading failures in the past, e.g., July 2012 blackout in India

Bilevel problem (Stackelberg game)

§ Leader: Attacker compromises the DLRs using false data injection attack; § Follower: Defender’s economic dispatch solution is optimal for new

manipulated system, but possibly infeasible for the old actual system. Problem statement:

§ Determine an optimal attack plan to maximinimize line rating violations

Solution Approaches

Benders Decomposition (Kevin Wood et al.)

§ Alternately consider follower problem, with fixed attacker actions, and

master problem with fixed defender actions

§ Sequentially generate Benders cut for the Master Problem until zero

• ptimality gap

§ Results in systematic vertex enumeration of the inner problem

Kuhn-Tucker Single-level reformulation (Bard et al.)

§ Apply KKT optimality conditions for the inner problem, and

reformulate complementarity constraints

§ Use Branch-n-Bound techniques to solve the resulting Mixed-Integer

Linear Program (MILP)

Insights

G1 G2

L

f12 f13 f23

β23 β13

p2 p1 u13 u23 = β12 u12 ua

23

ud

23

§ Attacker strategy, by and large,

exhibits a bang-bang policy

§ Some DLRs are set to

maximum

§ Other DLRs are set to

minimum (as long as feasible

• perating point exists)

§ Similar results hold for larger

(118 node) testcase

5 10 15 20

Time (in hours)

100 150 200 250 300

Actual DLR (in MW)

200 400 600 800 1000

Demand (in MW)

ud

13

ud

23

us

13, us 23

Demand

5 10 15 20

Time (in hours)

100 150 200 250 300

Manipulated DLR (in MW)

ua

13

ua

23

f13 f23

Implementation of attack in Powerworld simulator

06410AE0 01 00 00 00 C0 65 49 09 00 00 00 00 00 00 00 00 06410AF0 00 00 00 00 00 00 00 00 00 00 00 00 00 FE 00 00 06410B00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 06410B10 00 00 00 00 00 00 C0 3F E1 FA C7 42 E1 FA C7 42 06410840 01 00 00 00 A0 64 49 09 00 00 00 00 00 00 00 00 06410850 00 00 00 00 00 00 00 00 00 00 00 00 00 FE 00 00 06410860 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 06410870 00 00 00 00 00 00 C0 3F E1 FA C7 42 E1 FA C7 42

(c) Pre-attack system state (safe).

06410AE0 01 00 00 00 C0 65 49 09 00 00 00 00 00 00 00 00 06410AF0 00 00 00 00 00 00 00 00 00 00 00 00 00 FE 00 00 06410B00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 06410B10 00 00 00 00 9A 99 19 40 E1 FA C7 42 E1 FA C7 42 06410840 01 00 00 00 60 65 49 09 00 00 00 00 00 00 00 00 06410850 00 00 00 00 00 00 00 00 00 00 00 00 00 FE 00 00 06410860 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 06410870 00 00 00 00 9A 99 99 3F E1 FA C7 42 E1 FA C7 42

(d) Post-attack system state (unsafe).