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Statistical Model Checking for Distributed Probabilistic-Control Hybrid Automata with Smart Grid Applications ao Martins 1 , 2 e Platzer 1 ao Leite 2 Jo Andr Jo 1 Computer Science Department, Carnegie Mellon University, Pittsburgh PA 2

  1. Statistical Model Checking for Distributed Probabilistic-Control Hybrid Automata with Smart Grid Applications ao Martins 1 , 2 e Platzer 1 ao Leite 2 Jo˜ Andr´ Jo˜ 1 Computer Science Department, Carnegie Mellon University, Pittsburgh PA 2 CENTRIA and Departamento de Inform´ atica, FCT, Universidade Nova de Lisboa 13th International Conference on Formal Engineering Methods J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 1 / 51

  2. Introduction Summary 1 Introduction The Power Grid The Smart Grid Model for the Smart Grid 2 Model Discrete-Time Hybrid Automata Distributed Probabilistic-Control Hybrid Automata 3 Verification Specifying properties Statistical Model Checking 4 Case Study: network properties 5 Conclusions J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 2 / 51

  3. Introduction The Power Grid The Grid is a hierarchical “graph” with sources and sinks Image from the TCIPG Education applet J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 3 / 51

  4. Introduction The Power Grid Power consumption follows well-known patterns Image from The Impact of Daylight Savings Time on Electricity Consumption in Indiana, J. Basconi, J. Kantor J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 4 / 51

  5. Introduction The Smart Grid Smart Meters + Smart Appliances The Grid predicts load, becomes more stable, cost-effective, energy-efficient, secure, resilient J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 5 / 51

  6. Introduction The Smart Grid Even today, utilities deploy networks that transmit several thousands of bits... per day . J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 6 / 51

  7. Introduction The Smart Grid Even today, utilities deploy networks that transmit several thousands of bits... per day . Is reliability the most significant factor for the Grid? How about bandwidth? RTT? J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 6 / 51

  8. Introduction The Smart Grid Even today, utilities deploy networks that transmit several thousands of bits... per day . Is reliability the most significant factor for the Grid? How about bandwidth? RTT? Deployment and testing of technologies is extremely expensive. J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 6 / 51

  9. Introduction The Smart Grid Answer: formal verification Test, evaluate and tweak technologies - then deploy. J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 7 / 51

  10. Introduction Model for the Smart Grid Model What are the properties of the Smart Grid? It’s a cyber-physical system It’s a distributed system It is a stochastic system J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 8 / 51

  11. Introduction Model for the Smart Grid Model What are the properties of the Smart Grid? It’s a cyber-physical system It’s a distributed system It is a stochastic system Plan: 1 Develop hybrid, distributed and probabilistic model 2 Develop logic for stating properties 3 Verify properties using existing statistical model-checking techniques J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 8 / 51

  12. Model Summary 1 Introduction The Power Grid The Smart Grid Model for the Smart Grid 2 Model Discrete-Time Hybrid Automata Distributed Probabilistic-Control Hybrid Automata 3 Verification Specifying properties Statistical Model Checking 4 Case Study: network properties 5 Conclusions J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 9 / 51

  13. Model Discrete-Time Hybrid Automata DTHA [12]: Washing machine c = 1 , w ′ = 1 c = 0 , w ′ = − 2 T ′ T ′ 1 = g n i k Fill up Flush r o w Standby working=0 w o r k i n w g = o 0 r k i n g = 1 c = 0 . 8 , w ′ = 0 . 8 c = 0 , w ′ = − 2 T ′ T ′ T c is total water consumed, w is water currently in the machine J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 10 / 51

  14. Model Discrete-Time Hybrid Automata Washing machine c = 1 , w ′ = 1 c = 0 , w ′ = − 2 T ′ T ′ 1 = g n i k Fill up Flush r o w Standby working=0 w o r k i n w g = o 0 r k i n g = 1 c = 0 . 8 , w ′ = 0 . 8 c = 0 , w ′ = − 2 T ′ T ′ Control graph � Q , E � J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 11 / 51

  15. Model Discrete-Time Hybrid Automata Washing machine c = 1 , w ′ = 1 c = 0 , w ′ = − 2 T ′ T ′ 1 = g n i k Fill up Flush r o w Standby working=0 w o r k i n w g = o 0 r k i n g = 1 c = 0 . 8 , w ′ = 0 . 8 c = 0 , w ′ = − 2 T ′ T ′ Jump relation jump e : R n × R n J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 12 / 51

  16. Model Discrete-Time Hybrid Automata Washing machine c = 1 , w ′ = 1 c = 0 , w ′ = − 2 T ′ T ′ 1 = g n i k Fill up Flush r o w Standby working=0 w o r k i n w g = o 0 r k i n g = 1 c = 0 . 8 , w ′ = 0 . 8 c = 0 , w ′ = − 2 T ′ T ′ Flows ϕ q : R ≥ 0 × R d → R d J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 13 / 51

  17. Model Discrete-Time Hybrid Automata Washing machine: scheduler w = 0 c = 1 , w ′ = 1 c = 0 , w ′ = − 2 working = 1 T ′ T ′ working = 1 working=1 Fill up Flush w = 0 working = 0 Standby working=0 working = 2 • w w = 0 o r k i n working=2 g = working = 2 0 c = 0 . 8 , w ′ = 0 . 8 c = 0 , w ′ = − 2 T ′ T ′ J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 14 / 51

  18. Model Discrete-Time Hybrid Automata Washing machine: scheduler w = 0 c = 1 , w ′ = 1 c = 0 , w ′ = − 2 working = 1 T ′ T ′ working = 1 1 = g n i k Fill up Flush w = 0 r o w working = 0 Standby working=0 working = 2 w w = 0 o r k i n working=2 g = working = 2 0 • c = 0 , w ′ = − 2 c = 0 . 8 , w ′ = 0 . 8 T ′ T ′ J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 15 / 51

  19. Model Discrete-Time Hybrid Automata Washing machine: scheduler w = 0 c = 1 , w ′ = 1 c = 0 , w ′ = − 2 working = 1 T ′ T ′ working = 1 1 = g n i k Fill up Flush w = 0 r o w working = 0 Standby working=0 working = 2 w w = 0 o r k i n working=2 g = working = 2 0 t = 2 • w = 1.6 c = 0 , w ′ = − 2 working = 2 c = 0 . 8 , w ′ = 0 . 8 T ′ T ′ J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 16 / 51

  20. Model Discrete-Time Hybrid Automata Washing machine: probabilistic scheduler w = 0 c = 1 , w ′ = 1 c = 0 , w ′ = − 2 working = 1 T ′ T ′ p = 0.5 working=1 Fill up Flush w = 0 working = 0 Standby working = 0 p = 0.3 • w o w = 0 r k i n g working=2 = working = 2 0 c = 0 . 8 , w ′ = 0 . 8 c = 0 , w ′ = − 2 T ′ T ′ J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 17 / 51

  21. Model Distributed Probabilistic-Control Hybrid Automata Multiple washing machines? J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 18 / 51

  22. Model Distributed Probabilistic-Control Hybrid Automata Multiple washing machines? J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 18 / 51

  23. Model Distributed Probabilistic-Control Hybrid Automata What if they leave? J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 18 / 51

  24. Model Distributed Probabilistic-Control Hybrid Automata What if they leave? J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 18 / 51

  25. Model Distributed Probabilistic-Control Hybrid Automata Actions Washing machines behave like Petri Net markings. new [ N ] jmp die create new entity makes entity disappear jump e given by N J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 19 / 51

  26. Model Distributed Probabilistic-Control Hybrid Automata Actions They can also communicate asynchronously . recv [ l ][ R ] snd [ l ][ T ] Channel l , reacts with R Channel l , message content T J. Martins, A. Platzer, J. Leite (CMU, FCT/UNL) Statistical Model Checking for DPCHA and the Smart Grid ICFEM’11 20 / 51

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