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

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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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