BMS State-Of-Charge estimation for I posted a presentation concerning an adaptative strategy for SOC estimation of LiFePO4/C technology.

Renewable energies | Eco-friendly production | Innovative transport | Eco-efficient processes | Sustainable resources

An Adaptive Strategy for Li-ion Battery
SOC Estimation
D. Di Domenico , E. Prada , Y. Creff
IFP Energies nouvelles
© 2011 - IFP Energies nouvelles

Technology, Computer Science and Applied Mathematics division

Outline of the presentation

Context and objectives
Li-ion cells modeling procedure
Estimation strategy
Filter design
Robustness analysis
Weight scheduling

Experimental results

Conclusion and future developments

2 18th IFAC World Congress - Milan, August 31, 2011

R&D objectives

Increasing demand for nontraditional vehicles (HEVs, PHEVs
and EVs) has resulted in increasing research effort on battery
management system (BMS)
BMS has to ensure the appropriate use of the battery in providing
the electrical power demand, while guaranteeing feasible and
safe operations
avoiding the overcharge and the thermal abuse
cell balancing
cooling system management

recharge management


BMS functional description

Battery Management System

Battery
Battery SOC
SOC Cell balancing
Cell balancing
state
state estimation
estimation
SOH
SOH Cooling
Cooling
estimation
estimation management
management
SOP //SOF
SOP SOF HV relays
HV relays

estimation
management
Core temperature
Core temperature Charger setpoint
Charger setpoint
Faults detection
Faults detection estimation
management


Batteries SOC estimation
The battery dynamics strongly depends on the state of charge (SOC).
The main battery operations are then related to the SOC estimation
which is usually a key task for BMS

Non-model
Black-box model-based
based

Artificial neural
Ah Counting Kalman filter
networks

Luenberger
Fuzzy-logic
observer
Sliding mode
estimator

Cell modeling

Mathematical Experimental Experimental Model
Model Applications
complexity identification environment precision

Map based +++ +++ Simple - -

EIS (frequency
Equivalent circuit + ++ = ++
domain)

Electrochemical 0D = +

Multi level
- +++
single-electrode
Electrochemical +++
-
1D/pseudo2D


Modeling procedure

Equivalent circuit models are based on Electrochemical Impedance
Spectroscopy (EIS)
Spectra analysis
Based on the equivalence between electrochemical impedance and
electric impedance, an electric circuit can be inferred from the
electrochemical spectrum. The Nyquist diagrams are analyzed and an
appropriate electric circuit is selected.
The equivalent electric circuit parameters, function of SOC and
temperature are then automatically fitted from the data
Based on the range of frequencies and on the impedance electric

equivalent elements, specific techniques have been elaborated to
frequency- resistor-
approximate the frequency-domain element with a resistor-
capacitance network


EIS based model
C dl
U0
RΩ Z diff

V = U 0 + ηΩ + ηct + ηdiff i (t )

Rct

Randles Electrical Circuit of the cell
-3 Nyquist
x 10
1.2

1
Medium, High-
0.8

frequencies
Low-frequencies
-Im(Z)

domain
0.6 domain
0.4

0.2

0
1.8 2 2.2 2.4 2.6 2.8 3 3.2
Re(Z) -3
x 10

Diffusion impedance examples
tanh( j ωτ d )
Z CPE ( jω ) = 1 α Z W ( jω ) = Rd
Q ( jω ) j ωτ d
x 10
-3 Nyquist -4 Nyquist
1.5 x 10
1.5

1 1
-Im(Z)

-Im(Z)
0.5 0.5

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4
Re(Z) -3
x 10 Re(Z) -4
x 10
x 10
-3 Bode MODULE Bode PHASE -4 Bode MODULE Bode PHASE
1.5 -0.9737 x 10
4 0

3

module(Z)

1 -0.9737
module(Z)
phase(Z)

phase(Z)
2 -0.5
0.5 -0.9737
1

0 -5 0 5
-0.9737 -5 0 5 0 -5 -1 -5
0 5 0 5
10 10 10 10 10 10 10 10 10 10 10 10
omega omega omega omega


LFP/C model
Transposition to time-domain

tanh( j ωτ d )
Z ( jω ) = R Ω +
R ct
+ Rd
1 + j ω R ct C dl j ωτ d

C dl C diff 1 C diffN

U0 RΩ
Rct Rdiff 1 RdiffN


State-space formulation
 1
&=
q C I
 nom

 1  V ct 
& =
V ct I − 
 C dl (q , T ) 
 R ct ( q , T , I ) 


V = 1  Vd 
& I − 
 C d (q , T )  R d (T ) 
d

 
&
T =
1
(Q gen (q , T , I ) − q n (T ) )

 mC p
Medium, High-
frequencies Low-frequencies
domain domain

V = U 0 (q , T ) + R Ω (T )I + V ct + V d


Model performance
50
current [A]

0

-50
0 5000 10000 15000
4 3.3
experimental
3.25 model
5450 5500 5550
3.5
voltage [V]

3 3.35
3.3 3.2
3.25 3
2000 2500 3000 1.005 1.01
2.5 4
0 5000 10000 x 10 15000
time [s]


Model performance
50
current [A]

0

-50
0 5000 10000 15000
experimental
308.5 model

308
temperature [K]

307.5

307

306.5

306
0 5000 10000 15000
time [s]


Model order reduction
As the thermal dynamics are slower than the electric dynamics, the
temperature can be considered as a slowly varying parameter known
from the measurements
For the estimation purpose, charge transfer dynamics can be
approximated by the steady-state. The LFP/C cell model then reduces to

 1
&=
q C I
 nom

V = 1  I − V d 
&  

 C d (q ) 
 Rd 
d
 

V = U 0 (q ) + (R Ω + R ct (I ))I + V d

Extended Kalman filter design
System linearization
 x = Ax + Bu
&
Observability 
Filter implementation  y = Cx + Du
 0 0 
 1  Vd  dCd 
A = − I −  −
1

2 
 C
 d  Rd  dq
 Rd Cd 

 1 
 

 Cnom   dU 0  dRct
B= C =  dq 1  D = RΩ + Rct + I
 1    dI
−
 C 
 d 

Observability
Filter implementation

 dU 0 
 1 
 dq 
O=
 1  Vd  dCd 1 
− 2 I −  − 
 Cd 
 Rd  dq
 Rd Cd 

det(O ) = 2 ∀q Observability


Observability AP + PAT − PC T R −1CP + Q = 0
Filter implementation
K e = PCR −1

I Lithium-ion V
battery T
ˆ

Vd
EKF
&
x = Ax + Bu + K e ⋅ e
ˆ ˆ
ˆ
q
e = V ( x, u ) − V ( x, u )
ˆ


EKF performance in simulation
1
model
0.9 estimation
5% error
0.8

0.7

0.6
SOC

0.5

0.4 0.58

0.3 0.57

0.2 0.56

0.1 0.55
5600 5800 6000 6200 6400
0
0 5000 10000 15000
time [s]

Robustness analysis
Due to modeling errors, good filter performance in simulation does not
does
imply good performance in experimental test
model-
Several factors can heavily deteriorate the model-based estimation,
such as
Parameter uncertainties
Mismatch between measured voltage and model prediction
Neglected dynamics
A robustness analysis is thus required for a sounded simulation test
Several robustness indicators were considered, in particular the mean

square error, computed as

1 T
MSE = ∫ q(t ) − q (t ) dt
2
ˆ
T 0

Robustness analysis
model (nominal)
0.7
EKF

0.6
The effect on the
SOC estimation of
10% uncertainty on
0.5

0.4 one of the open
SOC

0.3 circuit voltage
0.2
parameters
0.1

0
0 2000 4000 6000 8000 10000 12000 14000 16000
time [s]

The filter sensitivity is non-homogeneous and depends on the
SOC value


Robustness analysis

For each parameter, a +10% variation is imposed.
The MSE is normalized with respect to the nominal SOC value.
The global robustness index (computed as the average of the indexes for each
parameter divided by 10) summarizes, for each SOC interval, the filter robustness with
respect to the main parameters indetermination.

Adaptive strategy

ˆ
q
I EKF
T
V ˆ
q0
weight
R,Q

and
In order to compensate for the filter sensitivity to the model and the
function
measurement uncertainties, the filter gain was scheduled function of
the estimated SOC value

actual
Furthermore, to preposition the SOC estimation close to the actual
value, an initialization module was added to the filter based on the
experimental OCV map .


Experimental results
1
model
estimation
0.9 5% error

0.8

0.7
0.025

0.6
0.02
SOC

0.5

SOC estimation error
0.015

0.4
0.01

0.3
0.005

0.2 0
0 5000 10000 15000
time [s]

0.1

0
0 5000 10000 15000
time [s]

A good compromise between estimation robustness and speed of convergence is
achieved
,
The filter pre-positioning, that predicts the initial condition within a 2% error range,
.
is able to decrease the filter convergence time

Conclusion and future developments

A semi-automatic procedure to obtain Li-ion battery models describing
thermal, physical and electrical battery properties was presented
Based on the model, a 2nd-order extended Kalman filter was designed
for the estimation of the state of charge
The filter showed high performance when tested in simulation but
exhibits a strong sensitivity to the parameters indetermination
In order to compensate for the model and the measurement
uncertainties, the filter was readapted by tuning its weight matrices
depending on the robustness degree, function of the SOC interval
Despite its simplicity, the filter shows good performance, with an error

within 2% − 3%
In order to further improve this work, the low frequencies accuracy of the
model is being improved by using a higher order transmission line to
approximate the diffusive impedance


Renewable energies | Eco-friendly production | Innovative transport | Eco-efficient processes | Sustainable resources

www.ifpenergiesnouvelles.com

BMS State-Of-Charge estimation for I posted a presentation concerning an adaptative strategy for SOC estimation of LiFePO4/C technology.

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BMS State-Of-Charge estimation for I posted a presentation concerning an adaptative strategy for SOC estimation of LiFePO4/C technology.