particle filter and its potential applications in smart grid
DESCRIPTION
Particle filter and its potential applications in smart grid. Zhiguo Shi. Outline. Introduction to Zhejiang University Fundamental concept Particle filter algorithm Application to SOC/SOH of battery charge Discussion. Outline. Introduction to Zhejiang University Fundamental concept - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/1.jpg)
Particle filter and its potential applications in smart grid
Zhiguo Shi
![Page 2: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/2.jpg)
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
![Page 3: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/3.jpg)
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
![Page 4: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/4.jpg)
23/4/19
Goal: Estimate a stochastic process given some noisy observations
Concepts:– Bayesian filtering– Monte Carlo sampling
sensort
Observed signal 1
t
Observed signal 2
ParticleFilter
t
Estimation
Big picture
![Page 5: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/5.jpg)
23/4/19
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 functionuk process noise with known
distribution
Step 1: Build system dynamic model
State equation: xk=fx(xk-1, uk)
xk state vector at time instant k
fx state transition functionuk process noise with known
distribution
![Page 6: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/6.jpg)
23/4/19
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 kfx observation functionvk observation noise with known
distribution
Step 2: Build observation model
Observation equation: zk=fz(xk, vk)
zk observations at time instant kfx observation functionvk observation noise with known
distribution
![Page 7: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/7.jpg)
23/4/19
Problem formulations
• Estimate a stochastic process given some noisy observations
• How?
Step 3: Use particle filterStep 3: Use particle filter
x
Posterior
![Page 8: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/8.jpg)
23/4/19
Motivations
• The trend of addressing complex problems continues
• Large number of applications require evaluation of integrals
• Non-linear models• Non-Gaussian noise
![Page 9: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/9.jpg)
23/4/19
Applications
• Signal processing– Image processing and
segmentation– Model selection– Tracking and navigation
• Communications– Channel estimation– Blind equalization– Positioning in wireless
networks
• Other applications1)
– Biology & Biochemistry– Chemistry– Economics & Business– Geosciences– Immunology– Materials Science– Pharmacology &
Toxicology
– Psychiatry/Psychology– Social Sciences
![Page 10: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/10.jpg)
An Example
x
y
T rajec to ry
xk xk + 1
ykyk + 1
zkzk + 1
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
![Page 11: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/11.jpg)
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
![Page 12: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/12.jpg)
23/4/19 ISEE, ZJU
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
( ) ~ { , | 1,..., }i it t t tBel x S x w i n
itw
![Page 13: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/13.jpg)
23/4/19
Particle filter illustration
Step 0: initialization
Each particle has the same weight
Step 1: updating weights. Weights are proportional to p(z|x)
![Page 14: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/14.jpg)
23/4/19
Particle filter illustration (Continued)
Particles are more concentrated in the region where the person is more likely to be
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.
![Page 15: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/15.jpg)
23/4/19
Particle filtering algorithm
Initialize particles
Output
Output estimates
1 2 M. . .
Particlegeneration
New observation
Exit
Normalize weights
1 2 M. . .
Weigthcomputation
Resampling
More observations?
yes
no
![Page 16: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/16.jpg)
23/4/19
Resampling
M
m
mk M
x1
)(1
1,
x
M
mm
km
k wx 1)()( ,
M
m
m
kM
x1
)(~ 1,
M
m
mk M
x1
)(1
1,
M
mm
km
k wx 1)(1
)(1 ,
M
m
m
kM
x1
)(
1
~ 1,
M
m
mk M
x1
)(2
1,
![Page 17: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/17.jpg)
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
![Page 18: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/18.jpg)
23/4/19
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.
![Page 19: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/19.jpg)
23/4/19
Battery capacity under different discharging rates
![Page 20: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/20.jpg)
23/4/19
System model
• State Transition function
• Observation function
Proportion coefficientt related to discharge rate
Nominal capacity of batteryInstantaniously discharge current
![Page 21: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/21.jpg)
23/4/19
Simulation results
![Page 22: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/22.jpg)
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
![Page 23: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/23.jpg)
23/4/19
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.
![Page 24: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/24.jpg)
23/4/19
Battery Charge Management
![Page 25: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/25.jpg)
23/4/19
Smart Grid Network Status Control
![Page 26: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/26.jpg)
23/4/19
Short Term Electricity Price Prediction for Home Appliance Control
![Page 27: Particle filter and its potential applications in smart grid](https://reader038.vdocuments.us/reader038/viewer/2022102818/56812da9550346895d92cde5/html5/thumbnails/27.jpg)
23/4/19