Kalman Filter
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Transcript of 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
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C
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dt
dxdt
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s
TL
TS
cap
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110
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6
Proposed Model (2)
Discrete time-variant stsp model
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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
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Linear system
Process model and measurement model
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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 .