Preliminary Results on Identification of an Electro-Thermal Model for Low Temperature

and High Power Operation of Cylindrical Double Layer Ultracapacitors

Yasha Parvini, Jason B. Siegel, Anna G. Stefanopoulou, Ardalan Vahidi

American Control Conference Portland, OR

June 4, 2014

1

Motivation

Ultracapacitor Advantages:

• High power density • Reliable performance in harsh environments (low and high temperatures) • Low impedance • Virtually unlimited cycle life

• Modelling the ultracapacitor at low temperatures and high power operation conditions to study cold start performance

2

Outline

Electric Model • Equivalent Electric Circuit Model • Parameterization & Results

Thermal Model • Linear Two State Model • Reversible and Irreversible Heat Generation • Electro-Thermal Coupling • Parameterization & Results

• Conclusion and Future Work

Capacity = 3000 F≈2.25 Ah Nominal Voltage = 2.7 V

3

Electrical Model of the Ultracapacitor

• Identification is done by minimizing the least square error between the measured and simulated voltages at each time instant.

𝐽 = 𝑚𝑖𝑛 (𝑉𝑚(𝑘) − 𝑉𝑇(𝑘))2

𝑘

• This study will also determine the number of RC pairs.

Equivalent Electric Circuit Model: Electrical

Model (Rs, Ri, Ci)

Current Terminal Voltage

4

0 100 200 300 400 500 600 700 800 900-200

-100

0

100

200

Time (s)

Cu

rren

t(A

)

0 100 200 300 400 500 600 700 800 900-1

0

1

2

3

Vo

lta

ge(V

)

Current

Voltage

Pulse-relaxation test at -40°C and 191A current

Test Procedure for Parameterization of the Electrical Model

• 5% Pulse-Relaxation which the battery is charged from 0% SOC with constant current to 5% SOC and then relaxed for 20 seconds. The procedure is repeated to 100% SOC and similarly for discharging.

Currents (Amps) 191, 135,

67.5,22.5

SOC Range (%) 0-100

Temperatures (℃) -40, -20, 0

5

Determination of the Cell Open Circuit Voltage and Capacity

• OCV and cell capacity are determined based on low current cycling test at a rate of C/5 (0.45Amps).

• Despite the ideal capacitor with a linear OCV The C/5 data shows that the OCV of the cell is actually nonlinear.

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

SOC

Vo

lta

ge (

V)

Experimental

Ideal

6

0 100 200 300 400 500 600 700 800 9000

0.5

1

1.5

2

2.5

Vo

lta

ge (

V)

Measurement

Model

0 100 200 300 400 500 600 700 800 900-0.03

-0.02

-0.01

0

0.01

0.02

Time (S)

Vo

lta

ge-E

rro

r (

V)

520 530 540 550

2.1

2.2

2.3

Vo

lta

ge (

V)

Model RMSE(mV)

Linear-OCV-Rs 81

Nonlinear-OCV-Rs 16

Nonlinear-OCV-Rs-RC 9

Parameterization Results

Results for the pulse test at -20°C and 135A

7

Thermal Model of the Ultracapacitor

* Youngki Kim, Jason B. Siegel and Anna G. Stefanopoulou, ” A Computationally Efficient Thermal Model of Cylindrical Battery Cells for the Estimation of Radially Distributed Temperatures ” In 2013 American Control Conference, June 2013.

*

Thermal Model

(Cp, h, kt, 𝜹)

Heat Generation Surface Temperature

Core Temperature Ambient Temperature

8

• Joule Heating (Irreversible) which is the heat generated due to resistive losses and is equal to :

• Reversible Heat Generation which is due to change of entropy in the

cell and is governed by:

Reversible and Irreversible Heat Generation

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-20

-18

-16

-14

-12

-10

-8

Time (S)

Tem

pera

tu

re (

oC

)

SOC(50-100),Rest=90s

SOC(0-100),Rest=90s

SOC(50-100),Rest=0s

SOC(0-100),Rest=0s

5200 5400 5600-9.4-9.2

-9-8.8-8.6-8.4

Thermal pulse tests at -20°C and 140A

Total heat generation consists of two parts:

9

Electro-Thermal Coupling

• The electrical and thermal models are coupled through total heat generation and temperature dependent electrical parameters.

10

• Constant current pulses (charging/discharging) with 90 and 0 second rest in between until the temperature reaches steady state are used to exercise the thermal model.

Currents(Amps) SOC Range (%) T(℃)

140, 100, 50 (0-100)&(50-100) -20

Test Procedure for Parameterization of the Thermal Model

11

Parameterization Problem Setup

• Thermal parameters (Cp, h, Kt ,𝛿) are identified by minimizing the least square error between the measured and simulated surface temperatures at each time instant.

𝐽 = 𝑚𝑖𝑛 (𝑇𝑚(𝑘) − 𝑇𝑠(𝑘))2

𝑘

• The minimization problem is solved using nonlinear optimization functions in Matlab.

12

Parameterization Results for the Thermal Model

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-20

-18

-16

-14

-12

-10

-8

Time (s)

Tem

pera

ture (

C)

Measured

Estimated

5000 5200-9.4

-9.2

-9

-8.8

-8.6

Result for -20°C, 140A, zero rest and SOC range of 0 to 100

13

Conclusion and Future Work

• Single RC model with non-linear OCV mapping is accurate enough in capturing the terminal voltage behavior of the UC at sub-zero temperatures, different current rates and the whole SOC range.

• Parameterization of the thermal model for ultracapacitor was developed considering the entropic heat generation effect.

• The electro-thermal model will allow studying the hybrid Battery/UC at low temperature operations and also cold starting applications and also the benefits of hybridizing on battery life.

14

ACKNOWLEDGMENT

• The authors wish to acknowledge the technical and financial support of automotive research center (ARC) in accordance to agreement W56HZV-04-2-0001 with TARDEC.

15

Thank You!

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