Robustness Analysis of Power Grid under False Data Attacks Against AC State Estimation

Transcription

1 Robustness Analysis of Power Grid under False Data Attacks Against AC State Estimation Presenter: Ming Jin INFORMS 2017 Ming Jin, Prof Javad Lavaei, and Prof Karl Johansson 1

2 Power system resilience against cyber attack has become a critical issue 2

3 Outline Power system modeling and state estimation False data injection attack (FDIA) framework Semidefinite programming relaxation Experiments Conclusion 3

4 Power system modeled as a graph A power system G = (N, L) Transmission lines, buses, and transformers Complex voltage: v = v *, v +,, v -. C - Nodal current injection: i = Yv Injected complex power: p + qj = diag(vi ) 4

5 Nodal and line measurements p G,H Bus k Bus k v = p = Voltage magnitude and nodal power injections: v = + = Tr(E = vv ), p = = Tr(Y =,? vv ), q = = Tr(Y =,? vv ) where E = = e = e =., Y =,? = * + (Y E = + E = Y), Y =,@ = A + (E =Y Y E = ) ~ Branch active and reactive power flows: p G,H = Tr(Y G,?I vv ), p G,J = Tr(Y G,?K vv ) q G,H = Tr(Y G,@I vv ), q G,J = Tr(Y G,@K vv ) All quantities are quadratic functions of complex voltage, which is the state of the system 5

6 Power system state estimation Problem statement: Given noisy measurements m N = vv, M N + w N + b N measurement unknown state noise bad data estimate the unknown state v. Why state estimation? Provides real-time power system conditions Constitutes the core of online security analysis Provides diagnostics for modeling and maintenance (Zhang, Madani, Lavaei, 2017) 6

7 Cyber attack vs.resilience Adversary Generators, DERs Substations Telemetry & communication Breaker/switch status indications Network topology Analog measurements Generator outputs Automatic generation control System updates State estimator BDD Securityconstrained optimal power flow (SC-OPF) Outputs: power system states Security analysis Overload & voltage Contingency analysis Contingency selection

8 FDIA is stealthy if the spurious data correspond to a valid state State estimation: Quadratic measurements subject to noise and bad data m N = vv, M N + w N + b N measurement unknown state noise adversarial data Can be solved by Gauss-Newton or SDP Stealth attack: Bad data detection Residuals: m N vrvr, M N b N = m N vsvs, M N 8

9 FDIA causes spurious state estimation by tampering sensor data DC-based: (Liu et al., 2010) (Kosut et al., 2010) (Sandberg et al., 2010) (Dan and Sandberg, 2010) (Yuan et al., 2011) (Sou et al., 2013) (Hendrickx et al., 2014) Negative impact: Electricity market (Xie et al., 2010), Load redistribution (Yuan et al., 2011) AC-based (Rahman and Mohsenian- Rad, 2013) (Hug and Giampapa, 2012) Stealth vs. sparsity 9

10 State estimation can be falsified.. 10

11 ..with sparse sensor data attack 11

12 Would it be possible for an adversary to attack the state estimator by tampering few sensor data in stealth? 12

13 General FDIA framework with cardinality / stealth constraints min vs C Z h vs [,b RZ^ s.t. b N = m N vsvs, M N b ` k Objective function h(vs) Target state attack: h vs = vs v JU + + Voltage collapse attack: h vs = vs + + State deviation attack: h vs = vs v JNVW

14 Semidefinite programming (SDP) SDP standard form: min C, W s.t. x f = W, M N W 0 Definition: a Hermitian matrix W H - is positive semidefinite (PSD), W 0 iff: All eigenvalues of W are non-negative x Wx 0 for all x C - Wide applications in systems and control theory, robust optimization, nonconvex optimization 14

15 Convexification procedure min vsvs, M JU s.t. b N = m N vsvs, M N b ` k + 2Re{v JU vs} min W, M JU + 2Re{v JU vs} Transformation: Replace vsvs with W The augmented matrix Z = 1 vs vs is positive semidefinite and rank 1 W Relaxation: relax the rank 1 constraint Penalty: add penalty for the rank and cardinality constraint s.t. b N = m N W, M N 1 vs vs W b ` k min W, M JU 0, rank=1 + 2Re{v JU vs} + α b * + W, M?W-vGJw s.t. b N = m N W, M N 1 vs vs W 0 If the rank-1 constraint is satisfied, then we can recover a near-global stealthy attack solution 15

16 Key result: rank penalty design and performance bounds Theorem: For carefully designed M?W-vGJw and α, if the measurements include real and reactive branch power flows, and nodal voltage magnitudes, we have The attack b is stealthy, and sparse for large α The performance difference compared to an oracle by solving the original nonconvex problem is bounded Relation to compressed sensing: the trace penalty is equivalent to choosing M?W-vGJw as the identity matrix Extends the low-rank optimization method to deal with the augmented matrix rank 1 vs = 1, needed in a wide vs W range of problems 16

17 Experiment on IEEE 30-bus Target attack: h vs = vs v JU + + Solve for the stealth attack b using SDP relaxation Estimate the spurious state using Gauss-Newton in MATPOWER Check for BDD 17

18 FDIA tricks the operator to believe a potential voltage sag Falsified phase Falsified V Actual phase FDIA on voltage phase FDIA on voltage magnitude Falls out of the normal operation region Actual V 18

19 The sparsity is controlled by the l1 penalty weight α Upper bound by (Hug and Gimpapa 2012) 60 Attack sparsity vs. regularization Card(b) Upper bound SDP-FDIA regularization 19

20 FDIA is triggered by tampering a small set of sensors system α Rank(Z) Card(b) Upper bound Pass BDD 6-bus Yes 14-bus Yes 30-bus Yes 39-bus Yes 57-bus Yes 20

21 Our results analyze the potential threat of cyber attack on power grid AC-based state estimation. It should be used to inform new designs of Bad Data Detection. 21

22 Theoretical contributions Formulation of the nonconvex FDIA problem for AC grid Convex relaxation of the problem with cardinality constraint using Semidefinite programming design proper penalty matrix to induce rank 1 solution Prove performance bounds of the nearoptimal solution compared to the original problem 22