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Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with Jianhui Wang 1 and Ahmad F. Taha 2 1 Energy Systems Division, Argonne National Laboratory 2 University of Texas at San Antonio Funded by DOE Cybersecurity of Energy Delivery Systems (CEDS) March 24, 2016

Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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Page 1: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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

Page 2: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

Outline

1 Dynamic State Estimation

2 Challenges

3 Estimation Approaches

4 Case Studies

5 Conclusion

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Page 3: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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

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Page 4: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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

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Page 5: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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

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Page 6: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 7: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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.

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Page 8: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 9: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 10: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 11: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 12: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 13: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 14: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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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Page 15: Secure Dynamic State Estimation Using PMU data under … · Secure Dynamic State Estimation Using PMU data under Model Uncertainty and Cyber Attacks Junjian Qi 1 A joint work with

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