kalman filter

Kalman Filter Analysis and Implementation for Battery State

Estimation using MATLAB &VHDLRatna Kumar Dasari

Supervisor : Univ.Ass. Dipl.-Ing. Christoph Unterrieder

Professor : Univ.-Prof. Dr. Mario Huemer

Contents

Introduction Battery Modeling

Simple Battery Model and Thevenin Model Impedance Model and Runtime-based Model

Battery State Estimation Techniques Kalman Filter Alternative forms of Kalman Filter

Sequential Filter Information Filter

Battery State Estimations in VHDL Conclusions

1

Problem Definition and Objectives

Aim of the thesis Research, design, evaluation and implement the Kalman Filter

based state estimation for the Li-ion battery model The Kalman Filter state estimation has to be done in Matlab and

VHDL

Objectives achieved in the course of thesis Understand clearly about different existing estimation methods Compare Kalman Filter estimation with existing approaches The Kalman Filter estimations must be evaluated Key arguments to improve accuracy Compare Kalman Filter estimations with Sequential, Information,

etc Implement Kalman Filter estimations in VHDL

2

Li-ion

Most commonly used battery Provides high specific power, low self-discharge

behaviour and more life cycles

Pb-acid NiMH Zn-air Li-ion

Nominal cell voltage

2 1.2 1.15 3.2

Specific Energy (Wh/kg)

30-40 30-80 100 160

Specific Power (W/kg)

180 250-1000 80-140 1800

Cycle Life 500-800 1500 200 1200

3

Battery Modeling

Used for battery design, performance estimation

Predicting-capability

Thevenin-Model Impedance –Modeal

Runtime-based Model

DC No No Yes

AC Limited Yes No

Transient Yes Limited Limited

Runtime No No Yes

4

Proposed Model

Capable of DC, transient responses and runtime

Battery model parameters [1]

5

Proposed Model (1)

Continuous time-variant state space (stsp) model

Continuous time-variant stsp model of the battery

)()()()()(

)()()()()(

tUtDtXtCtY

tUtBtXtAtX

uR

x

x

x

y

u

C

C

C

x

x

x

dt

dxdt

dxdt

dx

s

TL

TS

cap

3

2

1

110

1

1

1

3

2

1

2

100

01

10

000

3

2

1

6

Proposed Model (2)

Discrete time-variant stsp model

ks

k

k

k

k

k

T

TL

T

TS

cap

s

k

k

k

T

T

k

k

k

uR

x

x

x

Y

u

eR

eR

C

T

x

x

x

e

e

x

x

x

s

s

s

s

,3

,2

,1

1

1,3

1,2

1,1

,3

,2

,1

110

1

1

00

00

001

2

1

2

1

7

Battery State Estimation Techniques

Electrochemical approaches Electrochemical equations Not easy to implement

Partial differential algebric equations Specilized laboratory enviroments

Coulomb counting Easy to implement Depends on SOC0 and Ccap

T

bcap

t dttIC

SOCSOC0

0 )(1

8

Battery State EstimationTechniques (1)

Voltage based estimation SOC estimation based on open-circuit voltage Look up table approach

Kalman Filter estimation It accounts all noises To overcome inaccuracy in state estimation Offers system with multiple inputs and outputs Leads to the precise and robust estimations

9

Kalman Filter

System Description

Time update

Measurement update11,11,

11,11,ˆˆ

kT

kdkkdk

kkdkkdk

QAPAP

UBXAX

kkdkk

kkdkkkk

kT

kdkkdT

kdkk

PCKIP

XCYKXX

RCPCCPK

,

,

1,,,

ˆˆˆ

Linear system

Process model and measurement model

kkkdkkdk

kkkdkkdk

VUDXCY

WUBXAX

,,

111,11,

10

Selection of Q and R

When ‘Q‘ is high and ‘R‘ is low

When ‘R‘ is high and ‘Q‘ is low

11

Kalman Filter (1)

Recursive Algorithm The selection of noise

parameters is dependent on the better estimates

Gaussian noise ( Wk ,Vk )

Kalman gain (Kk )

Flow chart

12

Kalman Filter to Li-ion

The state variables are SOC, VTS and VTL

Intial state vetor is defined as X0 =[1;0;0]

Input uk = 2A

The values of Q and R selected based on the noise error The RMS error is used to analyze the estimation

accuracy

n

iiiRMS XX

ne

1

2ˆ1

13

Outputs

State variable : SOC RMS error : 0.026918

14

Outputs (1)

State variable : VTS

Transient response of the element RTSCTS

15

Outputs (2)

State variable : VTL

Transient response of the second RC element (RTLCTL)

16

Outputs (3)

Battery output voltage

17

Alternative forms of Kalman Filter

Sequential Kalman Filter Kalman Filtering without matrix inversion Useful for embedded system application One iteration at once

Information Filter Using information matrix rather than state covariance matrix(I =P-

1) If I → 0, no knowledge of ‚x‘ and as I→∞, perfect knowledge of

x

18

Outputs (4)

State variable :SOC

19

Outputs (5)

Statate variable :VTS

20

Kalman Filter in VHDL

One –to-one comparison between two domains Block diagram:

21

Kalman Filter in VHDL (1)

22

Matlab vs VHDL

One-to-one comparison

23

Conclusions

Understand and evaluate different estimation approaches

The reasons to select the Kalman Filter estimation Kalman filter estimation under different noise

conditions Alternative forms of Kalman Filter and compare the

simulations VHDL implementation of Kalman Filter Comparison between Matlab and VHDL estimations

24

References

[1]. M.chen and G.Rincon-Mora, “Accurate Electrical battery model capable of predicting runtime and I-V performance‘‘, IEEE Transactions on energy conversion, vol. 26, no.4, pp.1172-1180, Dec.2011.

[2].D.W.Dees and B.V.S, “ Electro chemical modeling of lithium polymer batteries‘‘, Journal of Power Sources, vol 110, no.2, pp.310-320, Aug.2002.

[3]. D.Simon, “ Optimal state estimation: Kalman, H infinity and nonlinear approaches. Wiley-Interscience, New jersey, 2006.

Battery Modeling

Thevenin model One RC element Provides transient response

Impedence model Mass trasnport ( ohmic characterstics) Half circle (transient characterstics) Skin effect ( inductive characterstics)

Battery Modeling (1)

Runtime-based model Transient response (a) Battery runtime (SOC) (b)

Two RC elements

The dynamic characterstics represented very accurately

Proposed Model

Linearization

Discretization

Discretization (1)

RMS Error

RMS errors for different Kalman Filters

Method RMS Error Reasons

Discrete-time 0.02691 Linear modeal

Sequential 0.04329 Time consuming

Information 0.05537 Need more matrix inversion operations

Kalman Filter Evaluation

State initial conditions

Kalman Filter Evaluation (1)

Different state covariance and same intial conditions

Kalman Filter Evaluation (2)

Measurement noise

Outputs (3)

State variable :VTL .