BMS: Review of approaches for the design of BMS functions

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A review of approaches for the
design of Li-ion BMS estimation
functions
D. Di Domenico, Y. Creff, E. Prada, P. Duchêne,
J. Bernard, V. Sauvant-Moynot
IFP Energies nouvelles
© 2010 - IFP Energies nouvelles, Rueil-Malmaison, France

Direction Technologie, Informatique et Mathématiques Appliquées

Outline of the presentation

Context and objectives
Model based approaches for SOC estimation
Ah Counting
Equivalent circuit models

Electrochemical models

A case-study
Conclusion and future developments

2 RHEVE 2011, 6-7 December IFP Energies nouvelles, Rueil-Malmaison

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 overcharge, overdischarge and thermal abuse
cell balancing
cooling system management

recharge management
inner state estimation
Accurate knowledge of the actual battery state is required for the vehicle
management, for achieving high efficiency, slow aging, no battery damaging
and for reducing pollutant emission
At steady state, a variation of 80% of SOC implies a typical variation of the
cell voltage smaller than 1V: if a high precision on the estimation is required
a high open loop precision of the model is necessary


Ah Counting

Easy to implement on-line
OCV vs SOC map-based
initialization ˆ
SOC
I cell Observer
Accumulation of the
measurement error during the
battery life ˆ

SO C0
Battery capacity degradation
with battery aging
Due to the large characteristic Tcell Init
time associated to the battery Vcell
relaxation, the OCV
measurement can be
SOC (t ) = SOC 0 + I cell (τ )d τ
1 t
unavailable in automotive
C nom ∫t0
applications

I/O measurement allows to C dl
U0
dynamically estimate the inner RΩ Z diff
cell state
The state initial condition is I cell
dynamically recovered by the Rct
observer
The modeling technique can
Randles Electrical Circuit of the cell
rigorously be applied only for low

demanded currents (system
linearization around an I cell ˆ
equilibrium at zero input) SOC
Tcell Observer
Circuit parameters dependence ˆ
on SOC, temperature, and Vcell ( SO C0 )
applied current needs to be
integrated in order to reach the
precision required for BMS
C nom
application
RHEVE 2011, 6-7 December IFP Energies nouvelles, Rueil-Malmaison
parameters
5

V = U 0 + ηΩ + ηct + ηdiff Z diff ( j ω ) =
1
1 + RQ ( j ω )
α

Z ( jω ) = RΩ +
R ct
Z diff ( j ω ) =
1
+ Z diff ( j ω )
1 + j ω R ct C dl Q ( jω )
α

tanh( j ωτ d )
Z diff ( j ω ) = R d
j ωτ

d
-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

Electrochemical model

I/O measurement allows to SOC (t )
dynamically estimate the
inner cell state
The state initial condition is c Li ( x , r , t )
estimated
The electrodes porous

morphology is integrated in
the model I cell
SOC
Physical meaning of the state Tcell Observer
The identification requires Vcell ( SOC 0 )
specific tests, such as single-
electrode analysis (with cell
disassembling) physical, chemical and geometrical
parameters

Electrochemical model
Fick’s equation, describing the solid concentrations diffusion
∂c Li r
( )
r
= ∇ Ds ∇ c Li c Li = c Li ( x , r , t )
∂t

electrolyte
electrode

electrode
negative
Simplified approaches

positive
P2D 1D

c Li = c Li ( x , t )
l neg l elect l pos x

P2D SPM and AV
c Li = c Li ( r , t )
cs (r )

cs ( R ) = cse

P2D 0D r1 r2 ......... rm = R
r

dc Li 3
Ds → ∞ ⇒ =− j Li
dt aFR

Cell modeling

The precision of the model and the range of applications increase with
the mathematical complexity and with the number of parameters.
When based on the input/output experimental data, the model
identification is moderately difficult for the equivalent circuit, but it suffers
from low robustness for the electrochemical model

A case study: modeling procedure
Due to the manufacturers restrictions imposed on the cell usage, a
semi-
semi-automatic procedure has been developed for a circuit equivalent
on-
model design, from the cell characterization to the on-line
experimental test
Li-
The procedure has been applied to a Li-ion cell for the collaborative
Citroë
project HYDOLE, led by PSA Peugeot Citroën and funded by the
"Agence de l’Environnement et de la Maîtrise de l’Energie" (ADEME)
Maî Energie"

The procedure consists in the following steps:
Impedance Spectroscopy (EIS)
circuit
Spectra analysis and selection of the appropriate electric circuit
reproducing the experimental Nyquist diagrams
Automatic fit of the equivalent electric circuit parameters, as a function of
SOC and temperature, from the data
frequency- resistor-
Approximation of the frequency-domain element with a resistor-
capacitance network

A case study: diffusion impedance
For given SOC and temperature, an impedance diagram collects the
imaginary
wave response at different frequencies, in terms of real and imaginary
part of the system frequency response

Z ( jω ) = RΩ +
R ct 1
+
1 + j ω R ct C dl Q ( j ω ) α

RΩ = RΩ ( q , T ) Q = Q ( q, T )

R ct = R ct ( q , T ) α = α ( q, T )
C dl = C dl ( q , T )

The diagrams are analyzed and a frequency domain model is selected in
selected
order to reproduce the experimental spectra.
the
The parameters of the impedance are automatically fitted from the data,
function of SOC and temperature.

Equivalent circuit model
The transposition to the time-domain model can be performed by means of
time-
the fractional impedance representation method*
resistor-
The CPE impedance is approximated by a series of five resistor-
capacitance circuits whose characteristic times are computed in order to
ensure a satisfying accuracy in the limited frequency band corresponding
corresponding
to experimental frequencies range (5 mHz to10 kHz)

C dl C diff 1 C diffN

U0 RΩ
Rct Rdiff 1 RdiffN
*[Oustaloup et al., 2005]


State-space formulation

 1
 q=
& I cell
C nom

 1  Vct 
& =  I cell − 
Vct
 C dl (q , T )  Rct ( q , T )   V = U 0 (q, T ) + RΩ (q, T )I cell + Vct + ∑ Vd
  
V 1 V diff 1 Medium, High-

& =  I cell −  frequencies
Low-frequencies
 diff 1 C (q , T )  R diff 1 ( q , T )  domain
domain

 diff 1  
 .
 .
 .

V 1  V diff N 
&
diff N =
 I cell − 

 C diff N (q , T )  R diff N ( q , T ) 


Model performance
3.9
data 3.6
model
3.8
3.55

3.7 3.5
Cell Voltage [V]

3.6 3.45

3.5 3.4

3.4 3.35

3.3
3.3
3.25

3.2
0 500 1000 1500 2000 2500 3000 3500 4000 1300 1400 1500 1600 1700 1800 1900 2000
Time [s]

3.9 4.1
data data
EIS model model
3.8 static model
4

3.7
3.9
Voltage [V]

Voltage [V]
3.6
3.8
3.5

3.7
3.4

3.3 3.6

3.2 3.5
0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time [s] Time [s]

Extended Kalman filter

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

I Lithium-ion V
battery T

EKF ∑V
ˆ
d

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


Experimental results
0.1

Diffusion overpotential [V]
model
EKF
0.05
0.8
model
0
0.7 EKF
2% error
0.6 -0.05

0.5
SOC

-0.1

0 1000 2000 3000 4000
0.4 Time [s]
0.01

0.3 model
0 EKF
0.2
-0.01
0.1
0 1000 2000 3000 4000 -0.02
Time [s]
-0.03

-0.04
0 1000 2000 3000 4000
16 RHEVE 2011, 6-7 December IFP Energies nouvelles, Rueil-Malmaison Time [s]

Experimental results
0.1

model
EKF
0.05
1.2
0
1
-0.05
0.8
SOC

model -0.1

0 2000 4000
EKF Time [s]
0.6 0.02
3% error

model
EKF
0.4 0.01

0
0.2
0 1000 2000 3000 4000 5000
Time [s] -0.01

-0.02
0 2000 4000
17 RHEVE 2011, 6-7 December IFP Energies nouvelles, Rueil-Malmaison Time [s]

Conclusion
A short review of the main modeling techniques for the design of BMS
for automotive application has been presented
Ah counting, circuit equivalent model-based and electrochemical model-
based SOC observers have been considered
A case-test has been proposed to show the performance of a complete
procedure for the SOC estimator design, from the cell characterization to
the on-line experimental test
The model exhibits good performance, with an average prediction error

on the voltage less than 20mV
An extended Kalman filter was designed for the estimation of the state of
charge
The filter shows good performance, with an error within 2%-3%



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