Mode Estimation using Synchrophasors Arezoo Rajabi and Rakesh B. - PowerPoint PPT Presentation

A Resilient Algorithm for Power System Mode Estimation using Synchrophasors Arezoo Rajabi and Rakesh B. Bobba 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Outline • Introduction • Background and Problem • Prony Algorithm • Standard ADMM • False Data Injection • Related Work • Our Proposed Method • Evaluation • Analytical Intuition • Conclusion 1 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Power System Introduction Large synchronous distributed system of interconnected electrical components used for generation, transmission and distribution of electric power • Generators • Transmission (and distribution) lines • Transformers • Substations Basic structure of Power System * 2 * Image Source: http://www2.econ.iastate.edu 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Stability In Power Systems Introduction • The ability of operating an AC power network with: • All generators in synchronism and • Retaining synchronism even after a large disturbance • Faults can lead to instability in power systems • Instability problems in power systems can lead to brownouts or in extreme cases blackouts 3 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Northeast Blackout – August 2003 Introduction • Impacted 50 million people • Estimated loss: $4-$10 billion • At least 2 deaths in New York city attributed to the blackout Northeast Blackout Map * 4 * Image Source: http://naturalhistory.si.edu/exhibits 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Inter-Area Oscillation Modes Introduction • In the presence of a fault, two or more coherent groups of generators may start swinging against each other leading to frequency oscillations • It is important to detect unstable oscillations and take corrective action Unstable Power Oscillations Stable Power Oscillations 5 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Oscillation Mode Detection Approaches Introduction Model-Based Measurements- Methods Methods Time Efficiency × Scalability × On-line × Accuracy × Topology × Independency 6 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Background and Prony Algorithm [Hauer 1990] Problem • Prony algorithm is a popular measurement-based method • Consider a power system with 𝑛 synchronous generators • Assume that each synchronous generator is modeled by a second-order swing equation • [𝑧 𝑗 𝑢 0 , … , 𝑧 𝑗 (𝑢 𝑜 )] is a set of measurements provided by 𝑗 𝑢ℎ Phasor Measurement Units at time 𝑢 2𝑛 𝑗,𝑙 𝑓 𝜏 𝑙 +𝑘Ω 𝑙 + 𝑠′ 𝑗,𝑙 𝑓 𝜏 𝑙 −𝑘Ω 𝑙 𝑧 𝑗 𝑢 = ෍ 𝑠 𝑙=1 7 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Prony Algorithm Background and Problem • Goal: To estimate damping factors( 𝜏 𝑙 ) and , frequencies ( Ω 𝑙 ) of oscillation modes • Finds coefficient vector Ԧ 𝑏 : ⋯ 𝑏 1 𝑧 𝑗 (𝑢 0 + 𝑜𝑈) 𝑧 𝑗 𝑢 0 + 𝑜 − 1 𝑈 𝑧 𝑗 (𝑢 0 + (𝑜 − 1)𝑈) 𝑧 𝑗 (𝑢 0 ) 𝑏 2 ⋯ 𝑧 𝑗 (𝑢 0 + (𝑜 + 1)𝑈) 𝑧 𝑗 (𝑢 0 + 𝑜𝑈) 𝑧 𝑗 (𝑢 0 + (𝑜 − 2)𝑈) 𝑧 𝑗 (𝑢 0 + 𝑈) = ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 𝑏 𝑜 ⋯ 𝑧 𝑗 (𝑢 0 + (𝑜 + 𝑚)𝑈) 𝑧 𝑗 (𝑢 0 + (𝑜 + 𝑚 − 2)𝑈) 𝑧 𝑗 (𝑢 0 + 𝑚𝑈) ถ 𝑧 𝑗 (𝑢 0 + (𝑜 + 𝑚 − 1)𝑈) 𝑏 𝐼 Ԧ 𝐷 • Obtains the roots 𝑎 1 , … , 𝑎 𝑜 of discrete-time characteristic polynomial equation 𝑎 𝑜 + 𝑏 𝑜 𝑎 𝑜−1 + 𝑏 𝑜−1 𝑎 𝑜−2 + ⋯ + 𝑏 1 = 0 𝜏 𝑗 ± Ω 𝑗 = log 𝑎 𝑗 𝑈 8 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Power Grid: A Large Distributed Network Background and Problem • Power systems are usually divided into multiple areas of control North American Interconnections* 9 *Image source: [Andersson (2005)] 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Power Grid: A Large Distributed Network Background and Problem • Power systems are usually divided into multiple areas of control • Using Alternating Direction Method of Multipliers (ADMM) to implement Prony Algorithm in a distributed fashion [Wei 2013] : • Local objective function of 𝑗 𝑢ℎ area: ( 𝑔 𝑗 𝑏 = 𝐼 𝑗 𝑏 − 𝐷 𝑗 ) • Goal: to find a solution for: 𝑂 ෍ 𝐼 𝑗 𝑏 𝑗 − 𝐷 𝑗 min 𝑏 𝑗=1 𝑡. 𝑢 𝑏 𝑗 − 𝑨 = 0 10 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Standard ADMM (S-ADMM) [Nabavi 2015] Background and Problem Local Phasor Data Concentrator (PDC): • Gathers measurements to create Henkel matrix 𝐼 𝑗 and vector 𝐷 𝑗 PMUs y 11 (t) ... y 1n1 (t) • Updates the local optimal estimate value Disadvantage: S-ADMM is not robust PDC 1 (𝑙+1) ) ( 𝑏 𝑗 against false data injection z a 1 • Shares its local optimal estimate value with PMUs Compromised areas can send PMUs y 21 (t) ... y 2n2 (t) central PDC and obtains the global optimal y 51 (t) .. y 5n5 (t) 5 z central corrupted data to mislead other PDC 2 estimate value ( 𝑨 𝑙+1 ) from Central PDC a z PDC 5 a PDC 2 areas or disrupt convergence Central PDC: z a 3 z a 4 • Gathers local optimal estimates from local PMUs PMUs PDCs y 41 (t) ... y 4n4 (t) y 31 (t) ... y 3n3 (t) • Computes the global optimal estimate vale PDC 4 PDC 3 ( 𝑨 𝑙+1 ) and shares it with local PDCs 11 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Impact of False Data Injection on Convergence Background and Problem Without Attack With Attack 12 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Potential Adversary Goals Background and Problem • Disrupting the mode estimation by preventing convergence : • Random Value Attack • Driving the estimate away from the real modes (potentially to desired modes) • Desired Value Attack • Remaining Undetected • Periodic Attack 13 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Related Work Related Work • Round-Robin ADMM [Liao 2016] • Central PDC updates the global optimal estimate value by using a local optimal estimate value from only one area in each iteration ( 𝑨 𝑙+1 = 𝑙+1 ) 𝑏 𝑗 • Central PDC removes the local optimal estimate which causes the most change in global optimal • D-ADMM [Nabavi 2015] • Fully distributed version of S-ADMM • Areas send their local optima estimate values to each other • Each area uses its objective function to detect compromised area • CON: • They need two runs: one for compromised area detection and one for mode estimation • Not robust against periodic attack 14 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Our Contributions Our Proposed Method • Unlike previous methods that localize the false data, our approach aims to tolerate the false data • Our approach needs only one run to estimate oscillation modes • We considered different attack scenarios to evaluate our methods 15 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Fault Tolerance Approach Our Proposed Method • Central PDC will identify outlier and remove it 𝑙+1 𝑏 𝑗 from 𝑨 𝑙+1 calculation (𝑙+1) = 𝑏 𝑗 (𝑙+1) − 𝑨 𝑙 points to the • Direction of 𝑤 𝑗 v 5(k+1) location of optimal value from view of area i 𝑨 𝑙 • Dissimilarity matrix (𝑁 𝑒𝑗𝑡 (𝑗, 𝑘)) keeps the angle (k+1) v 3 (k+1) v 4 𝑙+1 and 𝑤 𝑘 𝑙+1 between 𝑤 𝑗 θ 3 θ 2 θ 1 • To resist against periodic attacks, central PDC has 0 𝜄 5 𝜄 1 𝜄 1 + 𝜄 2 + 𝜄 3 𝜄 1 + 𝜄 2 (k+1) θ 4 v 1 𝜄 5 0 𝜄 4 + 𝜄 2 + 𝜄 3 𝜄 4 a local memory with size W to track attacker. 𝜄 4 + 𝜄 3 θ 5 𝜄 1 𝜄 4 + 𝜄 2 + 𝜄 3 𝑁 𝑒𝑗𝑡 = 0 𝜄 2 + 𝜄 3 𝜄 2 𝜄 1 + 𝜄 2 + 𝜄 3 𝜄 4 𝜄 2 + 𝜄 3 0 𝜄 3 (k+1) v 2 𝜄 1 + 𝜄 2 𝜄 4 + 𝜄 3 𝜄 2 𝜄 3 0 16 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Fault Tolerance Approach’s Impact Our Proposed Method on Convergence Without Attack and No Tolerance Approach No Attack and With Using Attack Tolerance Approach With Attack and Without Tolerance Approach With Attack and With Using Attack Tolerance Approach 17 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Evaluation Evaluation • IEEE 68-bus power system divided into 5 areas • Generated measurements using Power System Toolbox (PST) • Generators in this model are 6 𝑢ℎ order • Many of modes have small residues • Inter-area oscillation modes have small frequency • Therefore, we consider about 40 modes IEEE 68-bus* 18 *Image Source: [Nabavi 2015] 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Evaluation (Cont.) Evaluation Different Attack Scenarios Periodic Desired Value Attack 19 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016

Evaluation (Cont.) Evaluation Different Attack Scenarios Periodic Random Value Attack 20 2 nd Industrial Control System Security (ICSS) Workshop, December 6 th 2016