Optimal Power Flow: Closing the Loop over Corrupted Data

1. Optimal Power Flow: Closing the Loop over Corrupted Data André Teixeira, Henrik Sandberg, GyörgyDán, and Karl H. Johansson ACCESS Linnaeus Centre, KTH Royal Institute of Technology American Control Conference Montréal, June 28th, 2012

2. Motivation • Networkedcontrol systems arebecomingmorepervasive • Increasing use of ”open” networks and COTS • Infrastructures are becoming more vulnerable to cyber-threats! • Several attack points • Nature-driven events areknowntohavecausedseveredisruptions • A major concern is the possible impact of cyber threats on these systems ACCESS Linnaeus Centre KTH-Royal Institute of Technology

3. Power Transmission Networks • Previous work • Vulnerabilities of current SCADA/EMS systems to data attacks on measurements • Current work • Consequences on system operation: Optimal Power Flow ACCESS Linnaeus Centre KTH-Royal Institute of Technology SCADA: Supervisory Control and Data Acquisition

4. Cyber Security of State Estimator in Power Networks • State Estimator: estimates the state and unmeasuredvariables • Bad Data Detector: detects and removescorruptedmeasurements • Can data attacks affect the SE withoutbeingdetected? • Yes! [Liu et al, 2009] ACCESS Linnaeus Centre KTH-Royal Institute of Technology

5. DC Network Model • Measurement model: • LinearLeast Squares Estimator: • Measurementresidual: • Bad Data Detector: • Simplifications: • No resistances or shunt elements • Only active power: • Similar to a DC resistive network ACCESS Linnaeus Centre KTH-Royal Institute of Technology

6. Attacker Model • Corrupted measurements: • Attacker’sobjectives: • Attack is stealthy (undetectable) • Target measurementsarecorrupted • Least-effort attacks aremorelikely • Largereffortincreasedsecurity • Minimum effort attacks: • : set ofstealthy attacks • : set ofgoals • : set ofconstraints • and are scenario specific ACCESS Linnaeus Centre KTH-Royal Institute of Technology

7. Security Metric for Stealthy Attacks • is the securitymetric for the k-thmeasurement • is the optimal solution of • Minimum numberofattackedmeasurements so that • Attack is stealthy • Measurement is corrupted [Sandberg et al, 2010] [Sou et al, 2011] ACCESS Linnaeus Centre KTH-Royal Institute of Technology

8. Cyber Security of Optimal Power Flow in Power Networks • How do stealthy attacks affectthe powersystem’soperation? • Relatedwork: [Xie et al, 2010], [Yuan et al, 2011] • Optimal Power Flow • Computes generator setpointsminimizing operation costs • Ensures operation constraints ACCESS Linnaeus Centre KTH-Royal Institute of Technology

9. $ DC-Optimal Power Flow • DC-Optimal Power Flowconsiders the lossless DC model • powerdemand • power generation $ $ $ • Operation costs: • Generation costs • Transmission losses • Optimal power generation • Howevermay not be measured ACCESS Linnaeus Centre KTH-Royal Institute of Technology

10. DC-Optimal Power FlowNominal Operation • Lagrangian function: • At optimality, the KKT conditions hold: ACCESS Linnaeus Centre KTH-Royal Institute of Technology

11. DC-Optimal Power Flow under attack • The estimate is given by the State Estimator • vulnerableto cyber attacks • Suppose the system is in optimalitywith and • Operation under Data Attacks Proposedcontrol action Ficticious operating conditions • Whenwould an operator apply the proposedcontrol action? • Whatwould be the resulting operating cost? ACCESS Linnaeus Centre KTH-Royal Institute of Technology

12. DC-Optimal Power Flow under attack • Assume the attack does not change the active constraints • thus are known • The proposed control action is given by • is an affine map w.r.t ACCESS Linnaeus Centre KTH-Royal Institute of Technology

13. Estimated Re-Dispatch Profit Proposedcontrol action Ficticious operating conditions • Consider the corruptedestimates and • : estimated operation cost • : estimated optimal operation cost given • : estimated re-dispatch profit • Largeestimated profit maylead the operator toapply ACCESS Linnaeus Centre KTH-Royal Institute of Technology

14. True Re-Dispatch Profit Slack generators Proposedcontrol action True generation profile • Mismatchesbetween and arecompensated by slack generators • can be modeled as an affinemap w.r.t : • : true operation costafter re-dispatch • : true re-dispatch profit • Largemeansmore ”dangerous” attacks (largerimpact) ACCESS Linnaeus Centre KTH-Royal Institute of Technology

15. VIKING Benchmark: Impact of Data Attacks • Costfunctioncorrespondsto the total resistivelosses • Sparse attacks arecomputed from the previoussecuritymetric • is computed for eachsparse attack ACCESS Linnaeus Centre KTH-Royal Institute of Technology

16. VIKING Benchmark: Impact of Data Attacks • Securitymetric • Are all the sparse attacks equallydangerous? • Impactof Data Attacks • Most sparse attacks havelowimpact on operation cost ACCESS Linnaeus Centre KTH-Royal Institute of Technology Target measurement index Target measurement index

17. Impact-Aware Security Metric • is the impact-awaresecuritymetric for the k-thmeasurement • is the optimal solution of • Similarto the previoussecuritymetric • Sensitive to the choice of parameters ACCESS Linnaeus Centre KTH-Royal Institute of Technology

18. Summary • The effectsof data attacks on the DC-OPF wereanalyzedand analyticallycharacterized • The estimated and true profit wereintroduced • A novelimpact-awaresecuritymetricwasproposed Thankyou Questions? ACCESS Linnaeus Centre KTH-Royal Institute of Technology