Download Li-Ion Battery State Estimation and Prognosis

Li-Ion Battery State Estimation and
Prognosis
Mutasim Salman
Xidong Tang
Xiaofeng. Mao
GM Research and Development
Outline
• Background
• Battery State of Charge Estimation
• Battery State of Health Estimation
( Capacity Estimation)
• Battery Life Models & Prognosis
• Summary & Conclusions
Technology Drivers for Sustainability
Challenges
Stretch Goals
Energy
Low-cost renewable energy

Emissions
No tailpipe environmental impact

Safety
Vehicles that don’t crash

Congestion
Congestion-free routing

Affordability
Vehicle for every purse & purpose

Battery Technology Improvements
Battery capacity
and vehicle range
35
Motivation
•
•
•
Battery State of Charge (SOC) defines the remaining charge as a percentage of the stored charge in a
fully charged battery
The knowledge of SOC is critical for PHEV/EV applications; however SOC is not measurable given
existing onboard sensing technologies
SOC can be calculated through current integration
–
–
–
–
–
•
Battery Open Circuit Voltage (OCV) can be correlated to SOC, and SOC can be estimated through
estimating OCV
–
–
–
•
A correct initial value of SOC needs to be known
A correct value of battery capacity needs to be known
Error accumulates over time due to the measurement error
Not able to recover from a wrong SOC value
Can capture the details of dynamic SOC movement rustled from vehicle operation
OCV needs to be estimated online during vehicle operation
OCV based SOC estimation can recover from a wrong SOC value
OCV based SOC estimation is robust to initial values and measurement error, and is adaptive to changes in
operation conditions, and battery aging and variation
Combining the current based SOC and voltage based SOC provides a more accurate and robust SOC
estimate
Approach
• Based on HPPC data, a second order battery model is established
• Apply the Recursive Least Square method to extract battery parameters by matching
model input I and output V with measured data
• Based on the equivalent RC circuit model in the literature, infer open circuit voltage
from extracted battery parameters
• Obtain the thermodynamic voltage Vo by subtracting the hysteresis voltage Vh from
the open circuit voltage VOC
• Correlate Vo and SOCV in terms of temperature
• Determine validity of SOCV
• Adjust weights for SOCV and SOCI to obtain the SOC
Battery Model Identification
• The discrete time model in terms of a difference equation: V (k )   T  (k )
–
–
–
–
V: the measured battery terminal voltage
Φ(k): the vector of measured data and known signals
θ = [θ1,θ2,…,θn]T: the vector of parameters to be estimated
k: time step
3.8
3.8
3.7
3.7
3.6
3.6
3.5
3.5
Voltage (v)
Voltage (v)
• Matching of the output of the second-order model and HPPC data
3.4
3.3
3.4
3.3
3.2
3.2
3.1
3.1
Measured Voltage
Model Output
3
0
10
20
30
40
50
Time (sec)
60
70
Measured Voltage
Model Output
3
80
A manganese-based Li-ion battery at 20°C and 5% SOC
0
10
20
30
40
50
Time (sec)
60
70
80
An iron phosphate Li-ion battery at 25°C and 65% SOC
Equivalent Circuit Model
• A two-RC-pair equivalent circuit model:
Voltage equation
Cdl
Cdf
Rohm
V0
{
Voc
V0
+
Vh
Rct
I
+
I = terminal current
V0 = thermodynamic voltage
Rohm = ohmic resistance
Rct = charge transfer resistance
Rdiff = diffusion resistance
Rdf
V
V = terminal voltage
VH = hysteresis voltage
Cdl = double layer capacitance
Cdiff = diffusion capacitance
VOC = open circuit voltage
Control Oriented Model
• Transform the voltage equation of the equivalent circuit model into a standard
control oriented second order difference equation:
V (k )  VOC  I (k ) Rohm  Vdl (k )  Vdf (k )
 (a1  a2 )V (k  1)  a1a2V (k  2)  RohmI (k )  b1  b2  Rohm (a1  a2 )I (k  1)
 (a1a2 Rohm  b1a2  b2 a1 ) I (k  2)  (1  a1  a2  a1a2 )VOC
 [1 , 2 , 3 , 4 , 5 , 6 ]T [V (k  1),V (k  2), I (k ), I (k  1), I (k  2),1]
where a1  e  t Rct Cdl , b1  Rct (1  e  t Rct Cdl ), a2  e
•
The parameters to be estimated are
• The open circuit voltage is
 t Rdf C df
, b2  Rdf (1  e
 t Rdf Cdf
)
Battery Parameter Estimation
• Estimate θ by minimizing a cost function of the error between the
actual V(k) and the predicted Vˆ (k )
k


2
ˆ
J

w
V
(
i
)

V
(
i
)
– The cost function often takes a quadratic form
 i
i 1
• Apply the U-D factorization-based RLS estimation method
– The covariance matrix P can be factored as P=UDUT where U is an upper
triangular matrix and D is a diagonal matrix
– Instead of updating P(k), update D(k) and U(k)
– Benefit
• Increase stability
SOC Estimation
• The final SOC estimate combines SOCV and SOCI
– SOCV is the voltage-based estimate resulted from Vo
– SOCI is the current-based estimate through current
integration
– w is a weighting factor tuned based on the signal
excitation level
Results
• SOC estimation of a charge depletion drive for a 30AH manganesebased Li-ion battery pack
Estimated SOC
Calculated SOC
80
SOC (%)
70
60
50
40
0
1000
2000
3000
4000
Time (sec)
5000
6000
Results (cont’d)
• SOC estimation of a charge depletion-sustaining-increase drive for a
45AH manganese-based Li-ion battery pack
90
Estimated SOC
Calculated SOC
80
SOC (%)
70
60
50
40
30
20
0
500
1000
1500
2000
Time (sec)
2500
3000
Capacity Estimation for Li-ion Batteries
Background
•
•
Battery management needs to be adjusted based on battery State of Health (SOH)
The knowledge of battery SOH is required for diagnostics and prognostics
–
–
•
•
•
Capacity, which defines how much energy in terms of Ampere-Hours can be stored into a fully charged
battery, reflects the energy capability of a battery
Battery capacity determines the achievable electric range for PHEV/EV
The conventional offline method to measure capacity
–
–
•
Deplete a fully charged battery with a certain current rate at a specific temperature
Time consuming and impractical for in-vehicle applications
Capacity estimation based on usage models
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–
•
Energy capability SOH
Power capability SOH
Predetermined usage models
Have limited adaptability in the real life operation
Capacity estimation based on electrochemical and thermodynamic models
–
–
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Study battery degradation mechanism at the micro scale
Apply finite element analysis methods to describe the Li-ion battery dynamics
Difficult to use for online battery capacity estimation directly
Motivation
• Develop a practical, low cost, efficient, and effective approach to
–
–
–
–
Estimate capacity in real time within an acceptable range of error
Ensure robustness to battery, environment and usage variations
Closely track capacity degradation due to battery aging
Monitor capacity degradation for onboard diagnostics
• The challenge lies in the accuracy of the capacity estimation and its
robustness to battery and operation variations
Approach
• Model the Li-ion battery as a time-varying linear dynamic system
• Based on the definition of SOC, capacity is calculated by Q=ΔS/ΔSOC
– S is the current integration or charge accumulation
• Define a battery parameter
to represent the change rate of open circuit
voltage under a certain amount of current integration
Voc
Aging
h
1/C=Slope
h
1/C
Voc (k)
Aging
AH
Voc
• Estimate the battery parameter h from measured terminal voltage and current based
on the battery models for different operation modes
• Infer capacity from the battery parameter h
• Determine the validity of the capacity estimate
Estimation
• Estimate capacity in the driving mode
– The frequent power transfer to/from batteries in the driving mode offers rich
signal excitation to estimate the model parameters
– Two algorithms
• Two stage estimation
• One stage estimation
• Estimate capacity in the plug-in charge (PIC) mode
– The current can be considered as a DC current in the PIC mode
– Regression method cannot be applied because of low excitation
• The capacity estimates are normalized with temperature
• The normalized capacity estimates are fused for updating a stored
capacity value based on the validity flag
Estimation in the Driving Mode
• Two stage estimation
–
–
–
–
–
Use the second order equivalent circuit to model the battery
On the first stage, estimate VOC based on the model equation
Determine the validity of VOC
Find the SOC from VOC through a lookup table
On the second stage, calculate ΔSOC=SOC(k)-SOC( j) between two time
instants based on the validity of VOC

k 1
– Compute capacity as
Q  S / SOC 
i j
I (i)t
SOC(k )  SOC( j )
– Advantage: simple and robust to current noise
– Disadvantage: less accurate in case of insufficient data points
Result of Two Stage Estimation
• Two stage capacity estimation in the driving mode for a 13.3AH
module
14
Capacity (AH)
12
10
8
6
4
2
0
1500
2000
2500
3000
Time (sec)
3500
4000
Estimation in the PIC Mode
• The current can be considered as a constant DC current
• Regression methods cannot be applied because of low signal
excitation
• Use the same equivalent circuit to model the battery
• The model equation is reduced to
VOC (k )  V (k )  I (k ) R
R  Rohm  Rct  Rdf
– R is a lump-sum resistance:
• SOC is inferred from VOC and capacity is estimated by

k 1
Q  S / SOC 
i j
I (i)t
SOC(k )  SOC( j )
Result of Estimation in PIC
• Capacity estimation in the PIC mode for a 45AH pack
Capacity (AH)
50
45
Validity (Boolean)
40
0
5000
10000
Time (s)
15000
0
5000
10000
Time (s)
15000
2
1
0
-1
Result of Capacity Degradation Tracking
• Evaluation results with accelerated aging data
Capacity (AH)
Estimated Capacity v.s. Measured Capacity (25 C)
After Multiple Aging Cycles
16
15.5
15
14.5
14
13.5
13
12.5
12
Measured Capacity
Estimated Capacity
1
2
3
4
Test Iteration Number
5
6
Battery Life Modeling & Prognosis
Customer Expectation of Battery Life
• Battery life is the same as vehicle life.
• Minimal Loss of battery functionality (in terms of power and
energy) over the life of the battery
• Customer expectation requires accurate estimation of battery
state and adaptive control to compensate for any degradation
Customer Expectation of Battery Life
• Li-Ion Battery degradation can impact the customer experience
in several ways:
• Electric range decrease
• Fuel economy reduction
• Acceleration from stop or while passing is weaker
• The ability to drive on grade is reduced
Battery Life Models
• There three main modeling approaches to develop battery life
models:
• Empirical Models
• Physics Based Models
• Semi-Empirical Models
Empirical Battery Life Models
• Based on accelerated aging of the cell.
• Different temperature profiles, SOC profiles are used to age the
cell. Cell capacity and resistance are monitored and measured.
• Regression models are developed to reflect the aging of the cell
Prognosis Approach
• There are several battery health monitoring algorithms, based on component health
signatures.
• Several degradation models of batteries, based on usage information are being
developed.
• We need to integrate both approaches to estimate more robust and consistent
component prognosis.
• Several methodologies to integrate component health signatures, usage information
and degradation model.
Conclusions and Future Work
• Algorithms are developed for onboard SOC and capacity estimation
• The developed algorithms have been verified through simulation, HIL
and in-vehicle testing, showing good accuracy and robustness
• The evaluation results with accelerated aging data demonstrate the
close tracking of the measured capacity for different ages of batteries
• More work is needed to develop battery aging models based on
Physics and data
• Research work is needed to predict battery pack life model from
battery cell aging data
• Interaction of component aging models and the effect on system
function require more work
• More research is required to have a prognosis integrated framework
that incorporates aging models, SOH and usage information