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
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
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
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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
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
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Problem formulations
• Estimate a stochastic process given some noisy observations
• How?
Step 3: Use particle filterStep 3: Use particle filter
x
Posterior
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Motivations
• The trend of addressing complex problems continues
• Large number of applications require evaluation of integrals
• Non-linear models• Non-Gaussian noise
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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
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
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
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
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Particle filter illustration
Step 0: initialization
Each particle has the same weight
Step 1: updating weights. Weights are proportional to p(z|x)
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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.
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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
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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,
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
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.
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Battery capacity under different discharging rates
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System model
• State Transition function
• Observation function
Proportion coefficientt related to discharge rate
Nominal capacity of batteryInstantaniously discharge current
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Simulation results
Outline
• Introduction to Zhejiang University
• Fundamental concept
• Particle filter algorithm
• Application to SOC/SOH of battery charge
• Discussion
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.
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Battery Charge Management
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Smart Grid Network Status Control
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Short Term Electricity Price Prediction for Home Appliance Control
23/4/19
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