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This work was carried out at my previous affiliation:
STEER Group, Ontario Tech University, Oshawa, Canada
Constant-Temperature Constant-Voltage (CT-CV)
Charging Technique for Lithium-Ion Batteries
Dr. Lalit Patnaik
Senior Fellow, CERN, Geneva, Switzerland
(present affiliation)
Webinar on 15 July 2020
1
IEEE PELS & IES Bangalore Chapter
Can we charge batteries faster without killing them?
Outline
2
1. Why lithium-ion batteries?
2. Existing charging methods
3. Proposed CT-CV charging method
4. Experimental setup and results
5. Future work and summary
Image: [Loveridge 2019]
3
Why Lithium-Ion Batteries?
Pros
+ High energy density: 250-700 Wh/L
+ High specific energy: 100-300 Wh/kg
+ Good cycle life: 400-1200 cycles
+ Low self-discharge: <3% per month
+ Affordable cost: 150 $/kWh
+ Reasonably safe operation
+ Environment friendly: no Pb and Cd
Cons
- Underutilization
- Capacity fade: 10-20% fade in 500 cycles
- Limited temperature range: 15-35°C
- Thermal runaway
4
Lithium-Ion Battery (LIB) Applications
Image: [Ding 2019]
5
The Nobel Prize in Chemistry 2019
Image: Niklas Elmehed, Nobel Media
6
Charging Methods for Li-ion Batteries
Charging technique Reference
Constant-current constant-voltage (CC-CV) [Cope 1999, Zhang 2006, Hoffart 2008]
Multistage constant current (MCC) [Liu 2005, Liu 2010, Liu 2011, Vo 2015,
Wang 2015, Min 2017, Kodali 2017]
4C-1C-CV [Fernandez 2016]
Pulse current [Chen 2007, Schalkwijk 2007, Savoye 2012]
Sinusoidal ripple current (SRC) [Chen 2013, Bessman 2018*]
Time [minutes]
Charging
current
1C
4C
Time [ms]
Charging
current
1C
2C Continue till
fully charged
Ripple frequency 900-1200 Hz
7
Motivation for New Charging Scheme
Shortcomings of existing methods
• Open-loop method based on manufacturer datasheet
➢ Does not adjust for aging/temperature of cells
➢ Tends to be conservative
• Cell degradation due to uncontrolled heating in poor cooling conditions
Key research question
What charging profile ensures the fastest charging time without hampering cell life?
8
CC-CV charging
• Lower temperature at beginning of CC mode
• Higher temperature towards end of CC mode
• Temperature rise, ΔT = 2-8 °C
CT-CV charging
• Cell is charged faster
• Same temperature rise as CC-CV
• Custom current profile for each cell
• Current profile adjusts for cell aging
Closed-Loop CT-CV Charging Concept
Premises:
1. Pumping energy into a battery: If it is not stored, it is dissipated!
2. Cell temperature is a key degradation metric [Amine 2005, Leng 2015, Kabir 2017]
3. Charging current ≤1C for SOC>70% to avoid Li plating [Zhang 2006]
9
CT-CV Charging: Block Diagram
• Validation of charging technique
➢ First at cell level
➢ Then at pack level
• Large thermal time constant (∼minutes)
➢ Slow control loop permissible
10
PLECS Simulation for Various Rint
• Parameters: Kp = 0.9, Ki = 0.0005, Kd = 0.05, Iff = 0, Tset = 28.5°C, Ci = 30 J/K,
Cs = 55 J/K, Ris = 10 K/W, Rsa = 18 K/W
• Higher Rint ⇒ Faster heating ⇒ Lower charging current
• Exponential approximation of charging current can serve as Iff
• PLECS Model of the Month – June 2018:
https://www.plexim.com/support/videos/mom_june_2018_ctcvcharge
[Gao 2002]
[Chen 2006]
[He 2011]
[Forgez 2010]
Caveat: 1st order model
does NOT work!
Rint
Ploss = Ich
2 Rint
Annotated Rint values are in Ω
USB
Keysight oscilloscope
Experimental Set-up for Charging
11
Samsung 18650 cell
LM335
Solid-state sensor
Rigol power supply
USB
Popular form factor:
From laptops to EVs
Scope in
the loop!
12
Experimental Set-up for Charging
• Rigol DP831A programmable DC power supply serves as charger
• 3-channel data acquisition using Keysight DSOX3014T oscilloscope
• USB interface to PC for control and long-time (2 hours) data logging
• Control using MATLAB Instrument Control Toolbox and SCPI commands
13
Experimental Set-up for Discharging
• Turnigy Reaktor balance charger/discharger
• Up to 20 A discharge current
• Appreciable current ripple: 0.5 A (pk-pk)
• Test discharge capacity in order to compare charging techniques
0.5 A
14
Experimental Results: 20% Faster Charging
[Patnaik 2019]
15
Experimental Results: 20% Faster Charging
In most EV applications, charging is done up to 70–80% SOC
16
Experimental Results: 20% Lower ΔT
[Patnaik 2019]
17
Experimental Results for Different Cooling Conditions
• Charging current dynamically adjusts to available cooling
• Better cooling ⇒ Higher charging current in CT mode
⇒ Shorter charging time
• Good cooling: Forced air
• Average cooling: Natural convection
• Poor cooling: Thermally insulated
18
Towards “Sensorless” CT-CV Charging
1.4℃
• Replace temperature sensor with
estimator?
• 1.4℃ temperature error based on
➢ Constant Rint
➢ 2nd order thermal model
• More accurate temperature
estimator required
19
No apparent capacity fade
[Marcis 2020]
(For NMC cells)
20
Comparison with other charging methods
[Liu 2010]
[Chen 2007]
[Chen 2013]
*
*
*Not for the same cell type as other measurements
21
Future Work
1. Testing for different types of Li-ion cells (and beyond?)
• Pouch, prismatic, built-in temperature sensors
• Cathode materials: LFP, LCO, LMO, LTO
2. Cycle-life and calendar-life testing
• Capacity fade / SOH implications
• Thousands of charge/discharge cycles
• Requires automated cell cycle tester
3. Sensorless CT-CV charging
• Detailed modeling: internal resistance, thermal
• Accurate temperature estimation
22
4. CT-CV fast charging
• Requires elaborate cooling systems
➢ Collaboration with thermal experts
• Modeling and experiments on degradation mechanisms
➢ Collaboration with electrochemistry experts
5. Extension to battery pack level
• Integration with Battery Management System (BMS)
• 2S, 4S, … nS configurations
Future Work
Summary
1. Closed-loop charging scheme
• Adjusts charging current in response to battery condition
• Corrects for aging and thermal environment
2. Faster charging for given amount of degradation
• 20% lesser time with same ΔT as CC-CV technique
3. Lower temperature rise for given charge time
• 20% lower ΔT with same charge time as CC-CV technique
4. Enables controlled aging/degradation based on value of set
battery temperature
5. Simple, low band-width PID control with feedforward aid
23
24
Thank You Very Much
Merci Beaucoup
Twitter: @lalitpatnaik
LinkedIn: lalitpatnaik
25
Relevant Publications
• [Patnaik 2019] L. Patnaik, A.V.J.S. Praneeth, and S.S. Williamson, “A Closed-Loop
Constant-Temperature Constant-Voltage Charging Technique to Reduce Charge
Time of Lithium-Ion Batteries,” IEEE Transactions on Industrial Electronics, vol.
66, no. 2, pp.1059-1067, 2019.
https://ieeexplore.ieee.org/document/8353785
• [Marcis 2020] V.A. Marcis, A.V.J.S. Praneeth, L. Patnaik, S.S. Williamson, "Analysis
of CT-CV Charging Technique for Lithium-Ion and NMC 18650 Cells Over
Temperature Range," IEEE International Conference on Industrial Technology
(ICIT), 2020.
https://ieeexplore.ieee.org/abstract/document/9067186
26
• [Loveridge 2019] M.J. Loveridge, C.C. Tan, F.M. Maddar, G. Remy, M. Abbott, S. Dixon, R. McMahon, O. Curnick, M. Ellis,
M. Lain, and A. Bara. “Temperature Considerations for Charging Li-Ion Batteries: Inductive versus Mains Charging
Modes for Portable Electronic Devices,” ACS Energy Letters, vol. 4, no. 5, pp. 1086–1091, 2019.
• [Ding 2019] Y. Ding, Z.P. Cano, A. Yu, J. Lu, and Z. Chen, “Automotive Li-ion batteries: current status and future
perspectives,” Electrochemical Energy Reviews, vol. 2, no. 1, pp.1–28, 2019.
• [Cope 1999] R. C. Cope and Y. Podrazhansky, “The art of battery charging,” in Proc. IEEE 4th Annu. Battery Conf. Appl.
Adv., pp. 233–235, 1999.
• [Zhang 2006] S. S. Zhang, “The effect of the charging protocol on the cycle life of a Li-ion battery,” J. Power Sources, vol.
161, no. 2, pp. 1385–1391, 2006.
• [Hoffart 2008] F. Hoffart, “Proper care extends Li-ion battery life,” Power Electron. Technol. Mag., vol. 34, pp. 24–28,
2008.
• [Liu 2005] Y. H. Liu, J. H. Teng, and Y. C. Lin, “Search for an optimal rapid charging pattern for lithium-ion batteries using
ant colony system algorithm,” IEEE Trans. Ind. Electron., vol. 52, no. 5, pp. 1328–1336, Oct. 2005.
• [Liu 2010] Y. H. Liu and Y. F. Luo, “Search for an optimal rapid-charging pattern for Li-ion batteries using the Taguchi
approach,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 3963–3971, Dec. 2010.
• [Liu 2011] Y. H. Liu, C. H. Hsieh, and Y. F. Luo, “Search for an optimal five-step charging pattern for Li-ion batteries using
consecutive orthogonal arrays,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 654–661, Jun. 2011.
References
27
• [Vo 2015] T. T. Vo, X. Chen, W. Shen, and A. Kapoor, “New charging strategy for lithium-ion batteries based on the
integration of Taguchi method and state of charge estimation,” J. Power Sources, vol. 273, pp. 413–422, 2015.
• [Wang 2015] S.-C. Wang and Y.-H. Liu, “A PSO-based fuzzy-controlled searching for the optimal charge pattern of Li-
ion batteries,” IEEE Trans. Ind. Electron., vol. 62, no. 5, pp. 2983–2993, May 2015.
• [Min 2017] H. Min et al., “Research on the optimal charging strategy for Li-ion batteries based on multi-objective
optimization,” MDPI Energies, vol. 10, no. 5, p. 709, 2017.
• [Kodali 2017] S. P. Kodali and S. Das, “Implementation of five level charging scheme in lithium ion batteries for
enabling fast charging in plug-in hybrid electric vehicles,” in Proc. Nat. Power Electron. Conf., pp. 147–152, 2017.
• [Fernandez 2016] V. M. G. Fernandez, C. B. Viejo, D. A. Gonzalez, M. G. Vega, Y. F. Pulido, and J. C. A. Anton, “Thermal
analysis of a fast charging technique for a high power lithium-ion cell,” MDPI Batteries, vol. 2, no. 4, p. 32, 2016.
• [Chen 2007] L. R. Chen, “A design of an optimal battery pulse charge system by frequency-varied technique,” IEEE
Trans. Ind. Electron., vol. 54, no. 1, pp. 398–405, Feb. 2007.
• [Schalkwijk 2007] W. A. Van Schalkwijk and R. S. Penn, “Lithium ion rapid charging system and method,” US Patent
7227336B1, Jun. 5, 2007.
• [Savoye 2012] F. Savoye, P. Venet, M. Millet, and J. Groot, “Impact of periodic current pulses on Li-ion battery
performance,” IEEE Trans. Ind. Electron., vol. 59, no. 9, pp. 3481–3488, Sep. 2012.
References
28
• [Chen 2013] L. R. Chen, S. L. Wu, D. T. Shieh, and T. R. Chen, “Sinusoidal-ripple current charging strategy and optimal
charging frequency study for Li-ion batteries,” IEEE Trans. Ind. Electron., vol. 60, no. 1, pp. 88–97, Jan. 2013.
• [Bessman 2018] A. Bessman et al., “Challenging sinusoidal ripple-current charging of lithium-ion batteries,” IEEE
Trans. Ind. Electron., vol. 65, no. 6, pp. 4750–4757, Jun. 2018.
• [Amine 2005] K. Amine, J. Liu, and I. Belharouak, “High-temperature storage and cycling of C-LiFePO4/graphite Li-
ion cells,” Electrochem. Commun., vol. 7, no. 7, pp. 669–673, 2005.
• [Leng 2015] F. Leng, C. M. Tan, and M. Pecht, “Effect of temperature on the aging rate of Li-ion battery operating
above room temperature,” Nature Sci. Rep., vol. 5, Art no. 12967, 2015.
• [Kabir 2017] M. Kabir and D. E. Demirocak, “Degradation mechanisms in Li-ion batteries: A state-of-the-art review,”
Wiley Int. J. Energy Res., vol. 41, pp. 1963–1986, 2017.
• [Gao 2002] L. Gao, S. Liu, and R. A. Dougal, “Dynamic lithium-ion battery model for system simulation,” IEEE Trans.
Compon. Packag. Technol., vol. 25, no. 3, pp. 495–505, Sep. 2002.
• [Chen 2006] M. Chen and G. A. Rincon-Mora, “Accurate electrical battery model capable of predicting runtime and
IV performance,” IEEE Trans. Energy Convers., vol. 21, no. 2, pp. 504–511, Jun. 2006.
• [He 2011] H. He, R. Xiong, and J. Fan, “Evaluation of lithium-ion battery equivalent circuit models for state of charge
estimation by an experimental approach,” MDPI Energies, vol. 4, no. 4, pp. 582–598, 2011.
• [Forgez 2010] C. Forgez, D. V. Do, G. Friedrich, M. Morcrette, and C. Delacourt, “Thermal modeling of a cylindrical
LiFePO4/graphite lithium-ion battery,” J. Power Sources, vol. 195, no. 9, pp. 2961–2968, 2010.
References

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Constant Temperature Constant Voltage (CT-CV) Charging Technique for Lithium-Ion Batteries

  • 1. This work was carried out at my previous affiliation: STEER Group, Ontario Tech University, Oshawa, Canada Constant-Temperature Constant-Voltage (CT-CV) Charging Technique for Lithium-Ion Batteries Dr. Lalit Patnaik Senior Fellow, CERN, Geneva, Switzerland (present affiliation) Webinar on 15 July 2020 1 IEEE PELS & IES Bangalore Chapter Can we charge batteries faster without killing them?
  • 2. Outline 2 1. Why lithium-ion batteries? 2. Existing charging methods 3. Proposed CT-CV charging method 4. Experimental setup and results 5. Future work and summary
  • 3. Image: [Loveridge 2019] 3 Why Lithium-Ion Batteries? Pros + High energy density: 250-700 Wh/L + High specific energy: 100-300 Wh/kg + Good cycle life: 400-1200 cycles + Low self-discharge: <3% per month + Affordable cost: 150 $/kWh + Reasonably safe operation + Environment friendly: no Pb and Cd Cons - Underutilization - Capacity fade: 10-20% fade in 500 cycles - Limited temperature range: 15-35°C - Thermal runaway
  • 4. 4 Lithium-Ion Battery (LIB) Applications Image: [Ding 2019]
  • 5. 5 The Nobel Prize in Chemistry 2019 Image: Niklas Elmehed, Nobel Media
  • 6. 6 Charging Methods for Li-ion Batteries Charging technique Reference Constant-current constant-voltage (CC-CV) [Cope 1999, Zhang 2006, Hoffart 2008] Multistage constant current (MCC) [Liu 2005, Liu 2010, Liu 2011, Vo 2015, Wang 2015, Min 2017, Kodali 2017] 4C-1C-CV [Fernandez 2016] Pulse current [Chen 2007, Schalkwijk 2007, Savoye 2012] Sinusoidal ripple current (SRC) [Chen 2013, Bessman 2018*] Time [minutes] Charging current 1C 4C Time [ms] Charging current 1C 2C Continue till fully charged Ripple frequency 900-1200 Hz
  • 7. 7 Motivation for New Charging Scheme Shortcomings of existing methods • Open-loop method based on manufacturer datasheet ➢ Does not adjust for aging/temperature of cells ➢ Tends to be conservative • Cell degradation due to uncontrolled heating in poor cooling conditions Key research question What charging profile ensures the fastest charging time without hampering cell life?
  • 8. 8 CC-CV charging • Lower temperature at beginning of CC mode • Higher temperature towards end of CC mode • Temperature rise, ΔT = 2-8 °C CT-CV charging • Cell is charged faster • Same temperature rise as CC-CV • Custom current profile for each cell • Current profile adjusts for cell aging Closed-Loop CT-CV Charging Concept Premises: 1. Pumping energy into a battery: If it is not stored, it is dissipated! 2. Cell temperature is a key degradation metric [Amine 2005, Leng 2015, Kabir 2017] 3. Charging current ≤1C for SOC>70% to avoid Li plating [Zhang 2006]
  • 9. 9 CT-CV Charging: Block Diagram • Validation of charging technique ➢ First at cell level ➢ Then at pack level • Large thermal time constant (∼minutes) ➢ Slow control loop permissible
  • 10. 10 PLECS Simulation for Various Rint • Parameters: Kp = 0.9, Ki = 0.0005, Kd = 0.05, Iff = 0, Tset = 28.5°C, Ci = 30 J/K, Cs = 55 J/K, Ris = 10 K/W, Rsa = 18 K/W • Higher Rint ⇒ Faster heating ⇒ Lower charging current • Exponential approximation of charging current can serve as Iff • PLECS Model of the Month – June 2018: https://www.plexim.com/support/videos/mom_june_2018_ctcvcharge [Gao 2002] [Chen 2006] [He 2011] [Forgez 2010] Caveat: 1st order model does NOT work! Rint Ploss = Ich 2 Rint Annotated Rint values are in Ω
  • 11. USB Keysight oscilloscope Experimental Set-up for Charging 11 Samsung 18650 cell LM335 Solid-state sensor Rigol power supply USB Popular form factor: From laptops to EVs Scope in the loop!
  • 12. 12 Experimental Set-up for Charging • Rigol DP831A programmable DC power supply serves as charger • 3-channel data acquisition using Keysight DSOX3014T oscilloscope • USB interface to PC for control and long-time (2 hours) data logging • Control using MATLAB Instrument Control Toolbox and SCPI commands
  • 13. 13 Experimental Set-up for Discharging • Turnigy Reaktor balance charger/discharger • Up to 20 A discharge current • Appreciable current ripple: 0.5 A (pk-pk) • Test discharge capacity in order to compare charging techniques 0.5 A
  • 14. 14 Experimental Results: 20% Faster Charging [Patnaik 2019]
  • 15. 15 Experimental Results: 20% Faster Charging In most EV applications, charging is done up to 70–80% SOC
  • 16. 16 Experimental Results: 20% Lower ΔT [Patnaik 2019]
  • 17. 17 Experimental Results for Different Cooling Conditions • Charging current dynamically adjusts to available cooling • Better cooling ⇒ Higher charging current in CT mode ⇒ Shorter charging time • Good cooling: Forced air • Average cooling: Natural convection • Poor cooling: Thermally insulated
  • 18. 18 Towards “Sensorless” CT-CV Charging 1.4℃ • Replace temperature sensor with estimator? • 1.4℃ temperature error based on ➢ Constant Rint ➢ 2nd order thermal model • More accurate temperature estimator required
  • 19. 19 No apparent capacity fade [Marcis 2020] (For NMC cells)
  • 20. 20 Comparison with other charging methods [Liu 2010] [Chen 2007] [Chen 2013] * * *Not for the same cell type as other measurements
  • 21. 21 Future Work 1. Testing for different types of Li-ion cells (and beyond?) • Pouch, prismatic, built-in temperature sensors • Cathode materials: LFP, LCO, LMO, LTO 2. Cycle-life and calendar-life testing • Capacity fade / SOH implications • Thousands of charge/discharge cycles • Requires automated cell cycle tester 3. Sensorless CT-CV charging • Detailed modeling: internal resistance, thermal • Accurate temperature estimation
  • 22. 22 4. CT-CV fast charging • Requires elaborate cooling systems ➢ Collaboration with thermal experts • Modeling and experiments on degradation mechanisms ➢ Collaboration with electrochemistry experts 5. Extension to battery pack level • Integration with Battery Management System (BMS) • 2S, 4S, … nS configurations Future Work
  • 23. Summary 1. Closed-loop charging scheme • Adjusts charging current in response to battery condition • Corrects for aging and thermal environment 2. Faster charging for given amount of degradation • 20% lesser time with same ΔT as CC-CV technique 3. Lower temperature rise for given charge time • 20% lower ΔT with same charge time as CC-CV technique 4. Enables controlled aging/degradation based on value of set battery temperature 5. Simple, low band-width PID control with feedforward aid 23
  • 24. 24 Thank You Very Much Merci Beaucoup Twitter: @lalitpatnaik LinkedIn: lalitpatnaik
  • 25. 25 Relevant Publications • [Patnaik 2019] L. Patnaik, A.V.J.S. Praneeth, and S.S. Williamson, “A Closed-Loop Constant-Temperature Constant-Voltage Charging Technique to Reduce Charge Time of Lithium-Ion Batteries,” IEEE Transactions on Industrial Electronics, vol. 66, no. 2, pp.1059-1067, 2019. https://ieeexplore.ieee.org/document/8353785 • [Marcis 2020] V.A. Marcis, A.V.J.S. Praneeth, L. Patnaik, S.S. Williamson, "Analysis of CT-CV Charging Technique for Lithium-Ion and NMC 18650 Cells Over Temperature Range," IEEE International Conference on Industrial Technology (ICIT), 2020. https://ieeexplore.ieee.org/abstract/document/9067186
  • 26. 26 • [Loveridge 2019] M.J. Loveridge, C.C. Tan, F.M. Maddar, G. Remy, M. Abbott, S. Dixon, R. McMahon, O. Curnick, M. Ellis, M. Lain, and A. Bara. “Temperature Considerations for Charging Li-Ion Batteries: Inductive versus Mains Charging Modes for Portable Electronic Devices,” ACS Energy Letters, vol. 4, no. 5, pp. 1086–1091, 2019. • [Ding 2019] Y. Ding, Z.P. Cano, A. Yu, J. Lu, and Z. Chen, “Automotive Li-ion batteries: current status and future perspectives,” Electrochemical Energy Reviews, vol. 2, no. 1, pp.1–28, 2019. • [Cope 1999] R. C. Cope and Y. Podrazhansky, “The art of battery charging,” in Proc. IEEE 4th Annu. Battery Conf. Appl. Adv., pp. 233–235, 1999. • [Zhang 2006] S. S. Zhang, “The effect of the charging protocol on the cycle life of a Li-ion battery,” J. Power Sources, vol. 161, no. 2, pp. 1385–1391, 2006. • [Hoffart 2008] F. Hoffart, “Proper care extends Li-ion battery life,” Power Electron. Technol. Mag., vol. 34, pp. 24–28, 2008. • [Liu 2005] Y. H. Liu, J. H. Teng, and Y. C. Lin, “Search for an optimal rapid charging pattern for lithium-ion batteries using ant colony system algorithm,” IEEE Trans. Ind. Electron., vol. 52, no. 5, pp. 1328–1336, Oct. 2005. • [Liu 2010] Y. H. Liu and Y. F. Luo, “Search for an optimal rapid-charging pattern for Li-ion batteries using the Taguchi approach,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 3963–3971, Dec. 2010. • [Liu 2011] Y. H. Liu, C. H. Hsieh, and Y. F. Luo, “Search for an optimal five-step charging pattern for Li-ion batteries using consecutive orthogonal arrays,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 654–661, Jun. 2011. References
  • 27. 27 • [Vo 2015] T. T. Vo, X. Chen, W. Shen, and A. Kapoor, “New charging strategy for lithium-ion batteries based on the integration of Taguchi method and state of charge estimation,” J. Power Sources, vol. 273, pp. 413–422, 2015. • [Wang 2015] S.-C. Wang and Y.-H. Liu, “A PSO-based fuzzy-controlled searching for the optimal charge pattern of Li- ion batteries,” IEEE Trans. Ind. Electron., vol. 62, no. 5, pp. 2983–2993, May 2015. • [Min 2017] H. Min et al., “Research on the optimal charging strategy for Li-ion batteries based on multi-objective optimization,” MDPI Energies, vol. 10, no. 5, p. 709, 2017. • [Kodali 2017] S. P. Kodali and S. Das, “Implementation of five level charging scheme in lithium ion batteries for enabling fast charging in plug-in hybrid electric vehicles,” in Proc. Nat. Power Electron. Conf., pp. 147–152, 2017. • [Fernandez 2016] V. M. G. Fernandez, C. B. Viejo, D. A. Gonzalez, M. G. Vega, Y. F. Pulido, and J. C. A. Anton, “Thermal analysis of a fast charging technique for a high power lithium-ion cell,” MDPI Batteries, vol. 2, no. 4, p. 32, 2016. • [Chen 2007] L. R. Chen, “A design of an optimal battery pulse charge system by frequency-varied technique,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 398–405, Feb. 2007. • [Schalkwijk 2007] W. A. Van Schalkwijk and R. S. Penn, “Lithium ion rapid charging system and method,” US Patent 7227336B1, Jun. 5, 2007. • [Savoye 2012] F. Savoye, P. Venet, M. Millet, and J. Groot, “Impact of periodic current pulses on Li-ion battery performance,” IEEE Trans. Ind. Electron., vol. 59, no. 9, pp. 3481–3488, Sep. 2012. References
  • 28. 28 • [Chen 2013] L. R. Chen, S. L. Wu, D. T. Shieh, and T. R. Chen, “Sinusoidal-ripple current charging strategy and optimal charging frequency study for Li-ion batteries,” IEEE Trans. Ind. Electron., vol. 60, no. 1, pp. 88–97, Jan. 2013. • [Bessman 2018] A. Bessman et al., “Challenging sinusoidal ripple-current charging of lithium-ion batteries,” IEEE Trans. Ind. Electron., vol. 65, no. 6, pp. 4750–4757, Jun. 2018. • [Amine 2005] K. Amine, J. Liu, and I. Belharouak, “High-temperature storage and cycling of C-LiFePO4/graphite Li- ion cells,” Electrochem. Commun., vol. 7, no. 7, pp. 669–673, 2005. • [Leng 2015] F. Leng, C. M. Tan, and M. Pecht, “Effect of temperature on the aging rate of Li-ion battery operating above room temperature,” Nature Sci. Rep., vol. 5, Art no. 12967, 2015. • [Kabir 2017] M. Kabir and D. E. Demirocak, “Degradation mechanisms in Li-ion batteries: A state-of-the-art review,” Wiley Int. J. Energy Res., vol. 41, pp. 1963–1986, 2017. • [Gao 2002] L. Gao, S. Liu, and R. A. Dougal, “Dynamic lithium-ion battery model for system simulation,” IEEE Trans. Compon. Packag. Technol., vol. 25, no. 3, pp. 495–505, Sep. 2002. • [Chen 2006] M. Chen and G. A. Rincon-Mora, “Accurate electrical battery model capable of predicting runtime and IV performance,” IEEE Trans. Energy Convers., vol. 21, no. 2, pp. 504–511, Jun. 2006. • [He 2011] H. He, R. Xiong, and J. Fan, “Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach,” MDPI Energies, vol. 4, no. 4, pp. 582–598, 2011. • [Forgez 2010] C. Forgez, D. V. Do, G. Friedrich, M. Morcrette, and C. Delacourt, “Thermal modeling of a cylindrical LiFePO4/graphite lithium-ion battery,” J. Power Sources, vol. 195, no. 9, pp. 2961–2968, 2010. References