Dr. Gregory L. Plett, 5 April 2005 [0/12]

Results of Temperature-Dependent LiPB Cell Modeling

for HEV SOC Estimation

Dr. Gregory L. PlettCompact Power Inc. (CPI), and the

University of Colorado at Colorado Springs

Dr. Gregory L. Plett, 5 April 2005 [1/12]

Overview Introduction. “Enhanced Self Correcting” (ESC) cell model. OCV modeling method. Dynamics modeling method. Results of fitting model to cell data. SOC estimation results using model. Conclusions.

Dr. Gregory L. Plett, 5 April 2005 [2/12]

Introduction Ultimate goal is accurate and precise SOC estimation for

HEV (high power) applications. Kalman filtering methods (e.g., EKF) have been shown

to work well. To make methods work, we need an accurate model of

cell dynamic behavior. Past work has used model fitted for 25ºC. Present work requires model accurate for – 30ºC…50ºC.

Dr. Gregory L. Plett, 5 April 2005 [3/12]

State-Space Cell Modeling To use KF, a dynamic cell model is required, which must

have a discrete-time nonlinear state-space form:

Coupled nonlinear dynamic equations: The first is the state equation, and describes the evolution

of the system state vector over time; The second is the output equation, and describes how the

system output may be formed if the state and input areknown.

.),(

,),(1

kkkk

kkkk

vuxhy

wuxfx

+=

+=+

Dr. Gregory L. Plett, 5 April 2005 [4/12]

ESC Cell Model The ESC cell model includes terms to describe:

Open circuit voltage (OCV); Voltage polarization time constants; Ohmic (I x R) voltage rise/drop; Hysteresis.

The state equation captures changing dynamic values ofvoltage polarization level, hysteresis level, and SOC.

The output equation mixes effects of OCV (as a functionof SOC), different voltage polarization time constants,ohmic voltage change, and hysteresis.

Dr. Gregory L. Plett, 5 April 2005 [5/12]

Cells Being Modeled Previous work used LG Chem “GEN3” cells:

Mn spinel/graphite LiPB chemistry; 7.5 ampere-hour capacity; High power (>20C capable).

Present work uses LG Chem “G4” cells: Mn spinel/blended-carbon LiPB chemistry; 5 ampere-hour capacity; Very high power (>30C capable).

Kim, S.W., Yu, J.S., Namgoong, J. Kim, J.H., Kim, M.H., “Progress in Li-ion Polymerbattery and Pack System of LG Chem. for Transportation Applications,” EVS20.

Dr. Gregory L. Plett, 5 April 2005 [6/12]

OCV Data Collection Method Use “super-cell” with nominal capacity 15 Ah.

Soak super-cell at 25ºC for at least two hours. Charge super-cell: CC @ 1C to 4.2V, CV @ 4.2V to 0.01A. Soak super-cell at test temperature for two hours. Discharge super-cell CC @ C/30 to 2.5V. Rest for 30 sec. Charge super-cell CC @ C/30 to 4.2V.

Steps 4–6 generate discharge and charge curves of cellat test temperature.

Dr. Gregory L. Plett, 5 April 2005 [7/12]

OCV Model Generation Charge and discharge curves averaged at each SOC to

get raw OCV estimate. OCV model structure is:OCV(SOC,T) = OCV0(SOC) + T x OCVrel(SOC).

Fit raw OCV estimates at each SOC and temperature to OCV0 table and OCVrel table using least-squares fitting.

Dr. Gregory L. Plett, 5 April 2005 [8/12]

Dynamics Data Collection Method UDDS drive cycles, generated by ADVISOR, conducted. Methodology similar to before:

Soak cell at 25ºC for at least two hours. Charge cell: CC @ 1C to 4.2V, CV @ 4.2V to 0.01A. Soak cell at the test temperature for two hours. Execute test profile, comprising 22 UDDS cycles

separated by discharges and 5 min rests.

Model parameters fit to cell data using an optimizationprogram written in Matlab. Polynomial data fitting:

.4

4

3

3

2

210TaTaTaTaa ++++=!

Dr. Gregory L. Plett, 5 April 2005 [9/12]

Cell-Model Fitting Results

RMS modeling error (mV) for tests at various temperatures (degrees Celsius)

Temp. –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30 35 40 45

GEN3 35.4 32.1 37.0 22.6 12.9 7.8 4.3 7.1 4.8 2.5 5.1 4.2 3.9 3.2 2.9 3.2

G4 35.3 — 16.4 — 16.7 — 11.7 — 12.6 — — 7.3 — 9.9 — 11.8

Dr. Gregory L. Plett, 5 April 2005 [10/12]

SOC Estimation: “Training”Results when testing nonlinear KF using training data and correct initializa-

tion.

Temperature –30ºC –20ºC –10ºC 0ºC 10ºC 25ºC 35ºC 45ºC

Max abs error 2.85% 3.18% 2.26% 1.96% 1.56% 1.36% 1.65% 3.09%

RMS error 0.38% 0.37% 0.47% 0.62% 0.40% 0.20% 0.40% 0.51%

Bounds error 0.21% 0% 0% 6.48% 0% 0.44% 0.21% 3.47%

Results testing nonlinear KF using training data and incorrect initialization.

Temperature –30ºC –20ºC –10ºC 0ºC 10ºC 25ºC 35ºC 45ºC

Converge time (s) to 2% 714 1039 937 289 137 101 471 241

RMS error after converge 0.36% 0.27% 0.38% 0.63% 0.44% 0.30% 0.46% 0.65%

Bounds error 0.93% 0.52% 0.01% 6.52% 0.01% 0.45% 0.25% 3.48%

SOC Estimate good; Bounds estimate good.

Dr. Gregory L. Plett, 5 April 2005 [11/12]

SOC Estimation: “Testing”Results when testing nonlinear KF using testing data and correct initialization.

Temperature –30ºC –20ºC –10ºC 0ºC 10ºC 25ºC 35ºC 45ºC

Max abs error 2.74% 4.99% 2.49% 2.01% 1.57% 2.57% 2.70% 2.43%

RMS error 0.61% 1.01% 0.91% 0.69% 0.41% 1.60% 1.36% 0.64%

Bounds error 61.52% 53.00% 57.54% 9.24% 0% 73.15% 84.53% 25.16%

Results testing nonlinear KF using testing data and incorrect initialization.

Temperature –30ºC –20ºC –10ºC 0ºC 10ºC 25ºC 35ºC 45ºC

Converge time (s) to 2% 416 2055 1071 303 137 339 652 246

RMS error after converge 0.60% 0.94% 0.85% 0.69% 0.44% 1.64% 1.43% 0.75%

Bounds error 63.05% 54.71% 55.61% 8.93% 0.01% 73.16% 87.21% 24.86%

SOC Estimate good; Bounds estimate too optimistic—needs improvement

Dr. Gregory L. Plett, 5 April 2005 [12/12]

Conclusions We have presented a general LiBP modeling technique. Applied to LG Chem “G4” cells. OCV relationship described. Dynamics modeling described. RMS error results of modeling presented. SOC estimation using model presented.

Steeper OCV curve of G4 vs. GEN3 helps, higher rates hurt. More importantly, RMS SOC estimation error very low

(very good estimates), both for training and testing data. Bounds estimate needs work still.