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 capacityand 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

– 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

• Battery Open Circuit Voltage (OCV) can be correlated to SOC, and SOC can be estimated through

estimating OCV

– 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: 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

• Matching of the output of the second-order model and HPPC data

0 10 20 30 40 50 60 70 80

3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

Time (sec)

Vo

ltag

e (

v)

Measured Voltage

Model Output

0 10 20 30 40 50 60 70 80

3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

Time (sec)

Vo

ltag

e (v

)

Measured Voltage

Model Output

A manganese-based Li-ion battery at 20°C and 5% SOC An iron phosphate Li-ion battery at 25°C and 65% SOC

)()( kkV T

• A two-RC-pair equivalent circuit model:

Voltage equation

Equivalent Circuit Model

Rohm

Cdl

Rct

Cdf

Rdf

V

V0

Rohm

V+ -

Cdl

Rct

C

R

h

0

Voc

I{ +

-

V0

I = terminal current V = terminal voltage

V0 = thermodynamic voltage VH = hysteresis voltage VOC = open circuit voltage

Rohm = ohmic resistance

Rct = charge transfer resistance Cdl = double layer capacitance

Rdiff = diffusion resistance Cdiff = diffusion capacitance

• Transform the voltage equation of the equivalent circuit model into a standard

control oriented second order difference equation:

• The parameters to be estimated are

• The open circuit voltage is

Control Oriented Model

)1(,),1(, where

]1),2(),1(),(),2(),1([],,,,,[

)1()2()(

)1()()()2()1()(

)()()()(

2211

654321

2121122121

21212121

dfdfdfdfdlctdlctCRt

df

CRtCRt

ct

CRt

T

OCohm

ohmohm

dfdlohmOC

eRbeaeRbea

kIkIkIkVkV

VaaaakIababRaa

kIaaRbbkIRkVaakVaa

kVkVRkIVkV

• Estimate θ by minimizing a cost function of the error between the

actual V(k) and the predicted

– The cost function often takes a quadratic form

• 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

Battery Parameter Estimation

)(ˆ kV

k

i

i iViVwJ1

2

)(ˆ)(

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 manganese-

based Li-ion battery pack

0 1000 2000 3000 4000 5000 6000

40

50

60

70

80

Time (sec)

SO

C (

%)

Estimated SOC

Calculated SOC

Results (cont’d)

• SOC estimation of a charge depletion-sustaining-increase drive for a

45AH manganese-based Li-ion battery pack

0 500 1000 1500 2000 2500 300020

30

40

50

60

70

80

90

Time (sec)

SO

C (

%)

Estimated SOC

Calculated SOC

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– Energy capability SOH

– Power capability SOH

• 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

– Predetermined usage models

– Have limited adaptability in the real life operation

• Capacity estimation based on electrochemical and thermodynamic models

– 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

• 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– 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

• 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

Approach

Voc

AH

1/C=Slope

Voc(k)

1/C

Voc

Aging

Aging

h h

S

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

– Compute capacity as

– Advantage: simple and robust to current noise

– Disadvantage: less accurate in case of insufficient data points

)(SOC)(SOC

)(SOC/

1

jk

tiISQ

k

ji

Result of Two Stage Estimation

• Two stage capacity estimation in the driving mode for a 13.3AH

module

1500 2000 2500 3000 3500 40000

2

4

6

8

10

12

14

Time (sec)

Ca

pa

cit

y (

AH

)

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

– R is a lump-sum resistance:

• SOC is inferred from VOC and capacity is estimated by

)(SOC)(SOC

)(SOC/

1

jk

tiISQ

k

ji

RkIkVkVOC )()()(

dfctohm RRRR

Result of Estimation in PIC

• Capacity estimation in the PIC mode for a 45AH pack

0 5000 10000 1500040

45

50

Time (s)

Ca

pa

cit

y (

AH

)

0 5000 10000 15000-1

0

1

2

Time (s)

Va

lid

ity

(B

oo

lea

n)

Result of Capacity Degradation Tracking

• Evaluation results with accelerated aging data

12

12.5

13

13.5

14

14.5

15

15.5

16

1 2 3 4 5 6

Cap

acit

y (A

H)

Test Iteration Number

Estimated Capacity v.s. Measured Capacity (25 C)After Multiple Aging Cycles

Measured Capacity

Estimated Capacity

Battery Life Modeling & Prognosis

• 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

Customer Expectation of Battery Life

• There three main modeling approaches to develop battery life

models:

• Empirical Models

• Physics Based Models

• Semi-Empirical Models

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

Empirical Battery Life Models

• 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.

Prognosis Approach

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