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Secure Dynamic State Estimation Using PMUdata under Model Uncertainty and Cyber Attacks
Junjian Qi 1
A joint work with Jianhui Wang1 and Ahmad F. Taha 2
1Energy Systems Division, Argonne National Laboratory
2University of Texas at San Antonio
Funded by DOE Cybersecurity of Energy Delivery Systems (CEDS)
March 24, 2016
Outline
1 Dynamic State Estimation
2 Challenges
3 Estimation Approaches
4 Case Studies
5 Conclusion
2 / 15
Dynamic State Estimation
I Discrete-time nonlinear system{xk = f(xk−1,uk−1) + qk−1
yk = h(xk,uk−1) + rk
I Dynamic state estimation:
given xk−1 and yk, estimate xk
I For power systems:
I x: internal states of generators
I y comes from synchrophasors
3 / 15
Challenge 1: Model Uncertainty
I Power system model can be inaccurate
I unknown inputsx = Ax + Bu + Bww + φ(x, u)
I unavailable inputs (not measured or difficult to measure)
I parameter inaccuracy
I Are more detailed models always better?
I difficult to validate and calibrate
I higher computational burden
4 / 15
Challenge 2: Cyber Attacks against PMU Measurements
I National Electric Sector Cybersecurity Organization Resource(NESCOR) failure scenarios
I measurement data compromised due to PDC authentication compromise
I communications compromised between PMUs and control center
I Different types of attacks against measurements
I data integrity attack
I denial of service attack
I replay attack
5 / 15
Kalman Filters
I Extended Kalman Filter
I used for linearized model
I need to calculate Jabobian
I Unscented Kalman Filter
I used for nonlinear model
I no need to calculate Jabobian
I numerical stability problem
I Cubature Kalman Filter
I used for nonlinear model
I large system with high nonlinearity
I better numerical stability
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Dynamic Observers
I Real system dynamics
x = Ax + Bu + Bww + φ(x,u)
I Observer dynamics
˙x = Ax + Bu + φ(x,u) + L(y− h(x)
)I Observer designA>P + PA + (ε1ρ+ ε2µ)In − σC>C P +
ϕε2 − ε1
2In(
P +ϕε2 − ε1
2In
)>−ε2In
< 0
L =σ
2P−1C>
W. Zhang, H. Su, H. Wang, and Z. Han, “Full-order and reducedorder observers for one-sided lipschitz nonlinearsystems using riccati equations,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 12, pp. 4968–4977, 2012.
7 / 15
A Realistic Scenario for Dynamic State Estimation
I 16-machine 68-bus system
I Power system is modeled as 10th order nonlinear system
I Gaussian Process noise and measurement noise
I Model uncertainty
I unknown Bww
w(t) =
0.5 cos(ωut)0.5 sin(ωut)0.5 cos(ωut)0.5 sin(ωut)
−e−5t
0.2 e−t cos(ωut)0.2 cos(ωut)0.1 sin(ωut)
I estimator only knows steady-state values of Tm and Efd
I reduced admittance matrix is the steady-state one within 1 second after fault
I Initial guess of the states is far from the real states
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Data Integrity Attack
Data integrity attack: 8 out of 64 measurements are scaled by k or 1/k(k = 0.6)
Time (second)0 2 4 6 8 10
eR1
0.6
0.8
1
1.2
1.4
1.6realcompromisedEKFSR-UKFCKFobserver
Time (second)0 2 4 6 8 10
Norm
ofRelative
Error
10-2
100
102
EKFSR-UKFCKFobserver
Compromised measurements eR1 Norm of relative error of states
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Data Integrity Attack (cont’d)
Time (second)0 2 4 6 8 10
e′ q
1
1.5
2
0 2 4 6 8 10
δ
0.5
1
1.5
Time (second)0 2 4 6 8 10
e′ d
0.2
0.6
1
1.40 2 4 6 8 10
ω
365
370
375
380
real statesEKFCKFobserver
Estimation from EKF, CKF, and observer
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Data Integrity Attack (cont’d)
time (second)0 2 4 6 8 10
e′ q
0
1
2
δ
0
500
1000
time (second)0 2 4 6 8 10
e′ d
-2
-1
0
ω
400
450
500
real statesSR-UKF
Estimation from SR-UKF
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Denial of Service Attack
8 measurements do not update for t ∈ [3s, 6s]
Time (second)0 2 4 6 8 10
Norm
ofRelative
Error
10-2
100
102
104EKFSR-UKFCKFobserver
Time (second)0 2 4 6 8 10
Absolute
Error
10-4
10-2
100
102
EKFSR-UKFCKFobserver
Norm of relative error of states Absolute error of measurements
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Replay Attack
8 measurements for t ∈ [3s, 6s] equal those t ∈ [0s, 3s]
Time (second)0 2 4 6 8 10
Norm
ofRelative
Error
10-2
100
102
EKFSR-UKFCKFobserver
Time (second)0 2 4 6 8 10
Absolute
Error
10-4
10-2
100
102
EKFSR-UKFCKFobserver
Norm of relative error of states Absolute error of measurements
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Conclusion
I We design a realistic scenario for DSE with significant modeluncertainty and cyber attacks
I We compare different estimation approaches
I observers are more robust to model uncertainty and cyber attacks
I observers have theoretical guarantee for convergence
I observers are easier to implement
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References
I J. Qi, A. F. Taha, and J. Wang, “Comparing Kalman filters and observers for dynamic state estimation withmodel uncertainty and malicious cyber attacks,” IEEE Trans. Power Systems, under review.
I A. F. Taha, J. Qi, J. Wang, and J. H. Panchal, “Risk mitigation for dynamic state estimation against cyberattacks and unknown inputs,” IEEE Trans. Smart Grid, under review.
I J. Qi and K. Sun, J. Wang, and H. Liu, “Dynamic state estimation for multi-machine power system byunscented Kalman filter with enhanced numerical stability,” IEEE Trans. Smart Grid, under review.
I K. Sun, J. Qi, and W. Kang, “Power system observability and dynamic state estimation for stabilitymonitoring using synchrophasor measurements,” Control Engineering Practice, in press.
I J. Qi, K. Sun, and W. Kang, “Adaptive optimal PMU placement based on empirical observability gramian,”IFAC NOLCOS 2016, under review.
I J. Qi, K. Sun, and W. Kang, “Optimal PMU placement for power system dynamic state estimation by usingempirical observability gramian,” IEEE Trans. Power Systems, vol. 30, no. 4, pp. 2041–2054, Jul. 2015.
I W. Zhang, H. Su, H. Wang, and Z. Han, “Full-order and reducedorder observers for one-sided lipschitznonlinear systems using riccati equations,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 12, pp.4968–4977, 2012.
THANK YOU!15 / 15