Particle filter and its potential applications in smart grid

1. Particle filter and its potential applications in smart grid Zhiguo Shi

2. Outline • Introduction to Zhejiang University • Fundamental concept • Particle filter algorithm • Application to SOC/SOH of battery charge • Discussion

3. Outline • Introduction to Zhejiang University • Fundamental concept • Particle filter algorithm • Application to SOC/SOH of battery charge • Discussion

4. Big picture Observed signal 1 t Estimation Particle Filter sensor Observed signal 2 t t • Goal: Estimate a stochastic process given some noisy observations • Concepts: • Bayesian filtering • Monte Carlo sampling

5. Problem formulations • Estimate a stochastic process given some noisy observations • How? • Step 1: Build system dynamic model • State equation: xk=fx(xk-1, uk) • xk state vector at time instant k • fx state transition function • uk process noise with known distribution

6. Problem formulations • Estimate a stochastic process given some noisy observations • How? • Step 2: Build observation model • Observation equation: zk=fz(xk, vk) • zk observations at time instant k • fx observation function • vk observation noise with known distribution

7. Problem formulations • Estimate a stochastic process given some noisy observations • How? Step 3: Use particle filter Posterior x

8. Motivations • The trend of addressing complex problems continues • Large number of applications require evaluation of integrals • Non-linear models • Non-Gaussian noise

9. Applications • Other applications1) • Biology & Biochemistry • Chemistry • Economics & Business • Geosciences • Immunology • Materials Science • Pharmacology & Toxicology • Psychiatry/Psychology • Social Sciences • Signal processing • Image processing and segmentation • Model selection • Tracking and navigation • Communications • Channel estimation • Blind equalization • Positioning in wireless networks

10. An Example • States: position and velocity xk=[xk, Vxk, yk, Vyk]T • Observations: angle zk • Observation equation: zk=atan(yk/ xk)+vk • State equation: xk=Fxk-1+ Guk • Blue – True trajectory • Red – Estimates

11. Outline • Introduction to Zhejiang University • Fundamental concept • Particle filter algorithm • Application to SOC/SOH of battery charge • Discussion

12. Basic Idea • Representing belief by sets of samples or particles • are nonnegative weights called importance factors • Updating procedure is sequential importance sampling with re-sampling ISEE, ZJU

13. Step 0: initialization Each particle has the same weight Step 1: updating weights. Weights are proportional to p(z|x) Particle filter illustration

14. Step 3: updating weights. Weights are proportional to p(z|x) Step 4: predicting. Predict the new locations of particles. Step 2: predicting. Predict the new locations of particles. Particle filter illustration (Continued) Particles are more concentrated in the region where the person is more likely to be

15. Output estimates Output More observations? Particle filtering algorithm Initialize particles New observation Particle generation 1 2 M . . . 1 2 M . . . Weigth computation Normalize weights Resampling yes no Exit

16. Resampling x

17. Outline • Introduction to Zhejiang University • Fundamental concept • Particle filter algorithm • Application to SOC/SOH of battery charge • Discussion

18. Battery management in Electrical Vehicle[1] • The cost of the power system can reach up to 1/3 of the total cost of the electric vehicle. • The consistency of batteries is essential to the life and safety of the whole vehicle system [1] Gao, M., et al., Battery State of Charge online Estimation based on Particle Filter, Proceeding of the 4th International Congress on Image and Signal Processing, pp. 2233-2236, 2011.

19. Battery capacity under different discharging rates

20. System model • State Transition function Proportion coefficientt related to discharge rate Nominal capacity of battery Instantaniously discharge current • Observation function

21. Simulation results

22. Outline • Introduction to Zhejiang University • Fundamental concept • Particle filter algorithm • Application to SOC/SOH of battery charge • Discussion

23. Hope: my crude remarks may draw forth by abler people • Fundamentally, the particle filter can be applied to systems described by state equation representation with state transition function and observation function.

24. Battery Charge Management

25. Smart Grid Network Status Control

26. Short Term Electricity Price Prediction for Home Appliance Control