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
Big picture
Observed signal 1
sensor
t
Observed signal
2
Particle
Filter
Estimation
t
t
 Goal: Estimate a stochastic
process given some noisy
observations
 Concepts:
–
–
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Bayesian filtering
Monte Carlo sampling
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
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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
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Problem formulations
• Estimate a stochastic process given some
noisy observations
• How?
Step 3: Use particle filter
Posterior
x
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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
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• Other applications1)
– Biology & Biochemistry
– Chemistry
– Economics & Business
– Geosciences
– Immunology
– Materials Science
– Pharmacology &
Toxicology
– Psychiatry/Psychology
– Social Sciences
An Example
y
 States: position and velocity xk=[xk, Vxk, yk, Vyk]T
 Observations: angle
yk
yk+1
Trajectory
zk
 Observation equation:
zk+1
xk xk+1
x
 State equation:

Blue – True trajectory

Red – Estimates
zk
zk=atan(yk/ xk)+vk
xk=Fxk-1+ Guk
Outline
•
•
•
•
•
Introduction to Zhejiang University
Fundamental concept
Particle filter algorithm
Application to SOC/SOH of battery charge
Discussion
Basic Idea
• Representing belief by sets of samples or
particles
Bel ( xt ) ~ St  { x , w | i  1,..., n}
i
t
•
i
t
are nonnegative weights called
importance factors
• Updating procedure is sequential
importance sampling with re-sampling
i
t
w
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ISEE, ZJU
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)
Step 2: predicting.
Predict the new
locations of particles.
Step 3: updating
weights. Weights are
proportional to p(z|x)
Step 4: predicting.
Predict the new
locations of particles.
Particles are more concentrated in the
region where the person is more likely to be
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Particle filtering algorithm
Initialize
particles
New observation
Particle
generation
1
2
... M
1
2
... M
Weigth
computation
Normalize weights
Output estimates
Resampling
Output
yes
More
observations?
no
Exit
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Resampling
M
M
 ~ ( m) 1 
 x k 1 , 
M m 1

 (m) 1 
 xk  2 , 
M  m 1

x
(m)
k 1
, wk( m1)

M
m 1
M
M
 ~ ( m) 1 
xk , 
M m 1

 (m) 1 
 xk 1 , 
M  m 1

x
(m)
k
, wk( m )

M
m 1
M
 (m) 1 
 xk 1 , 
M  m 1

x
2015/4/8
Outline
•
•
•
•
•
Introduction to Zhejiang University
Fundamental concept
Particle filter algorithm
Application to SOC/SOH of battery charge
Discussion
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
Proportion coefficientt related to discharge rate
Nominal capacity of battery
Instantaniously discharge current
• Observation function
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Simulation results
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Outline
•
•
•
•
•
Introduction to Zhejiang University
Fundamental concept
Particle filter algorithm
Application to SOC/SOH of battery charge
Discussion
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
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