A Consensus Algorithm for Multi-Objective Battery Balancing
Abstract
:1. Introduction
- Model-based: they rely on the mathematical model of the battery modules, often based on equivalent electric circuits. Battery models can be just used to estimate the current battery state, such in conventional OCV- and SOC-based balancing methods [12], but also to predict the future behavior of the battery pack, aiming to synthesize a control policy that fulfills the balancing goals, such as minimization of SOC or thermal unbalances, enforcing actuation and safety constraints. Model-predictive control [21], or linear state feedback [22] represent paradigmatic examples of this approach.
- Machine learning: in this case, the control policy is derived based on interactions with the real battery pack or with a simulation model. It usually decreases modeling efforts and domain knowledge expertise but at the expense of higher data needs and computational effort (especially during training). Reinforcement learning [23] is a good example of this approach, which has been gaining increased attention over the last few years.
- Fuzzy logic: in contrast with previous approaches, it relies mainly on expert knowledge to derive control algorithms [24], but this also means that there is no single systematic approach or implementation framework.
2. System Modeling and Control Algorithm
2.1. Electro-Thermal Battery Model
2.1.1. Electrical Model
2.1.2. Statistical Model of Cell-to-Cell Variations
2.1.3. Thermal Model
2.2. Balancing System Model
2.3. Battery Power Profiles Generation
2.3.1. Aggressive Driving Power Profiles
2.3.2. Fast Charging Power Profiles
2.4. Multi-Agent Consensus Algorithm
3. Results
- On the other hand, the next results are presented for the fast charging scenarios:
- Figure 19: a comparison of single and dual controllers with different fast charging profiles.
3.1. Aggressive Driving Results
3.2. Fast Charging Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- The Paris Agreement, United Nations Framework Convention on Climate Change (UNFCCC). Available online: https://unfccc.int/process-and-meetings/the-paris-agreement/the-paris-agreement (accessed on 26 October 2020).
- International Energy Agency (IEA). Global EV Outlook 2020; International Energy Agency (IEA): New York, NY, USA, 2020. [Google Scholar]
- BloombergNEF. BNEF Electric Vehicle Report (EVO) Report 2020; BloombergNEF: New York, NY, USA, 2020. [Google Scholar]
- Diaz, L.B.; He, X.; Hu, Z.; Restuccia, F.; Marinescu, M.; Barreras, J.V.; Patel, Y.; Offer, G.J.; Rein, G. Meta-Review of Fire Safety of Lithium-Ion Batteries: Industry Challenges and Research Contributions. J. Electrochem. Soc. 2020, 167, 090559. [Google Scholar] [CrossRef]
- Barreras, J.V. Practical Methods in Li-ion Batteries: For Simplified Modeling, Battery Electric Vehicle Design, Battery Management System Testing and Balancing System Control. Ph.D. Thesis, The Faculty of Engineering and Science, Aalborg University, Aalborg, Denmark, 2017. [Google Scholar] [CrossRef]
- Sun, Y.; Saxena, S.; Pecht, M. Derating Guidelines for Lithium-Ion Batteries. Energies 2018, 11, 3295. [Google Scholar] [CrossRef] [Green Version]
- Sowe, J.; Few, S.; Barreras, J.V.; Schimpe, M.; Wu, B.; Nelson, J.; Candelise, C. How Can Insights from Degradation Modelling Inform Operational Strategies to Increase the Lifetime of Li-Ion Batteries in Islanded Mini-Grids? ECS Meet. Abstr. 2020, MA2020-02, 3780. [Google Scholar] [CrossRef]
- Schimpe, M.; Barreras, J.V.; Wu, B.; Offer, G.J. Novel Degradation Model-Based Current Derating Strategy for Lithium-Ion-Batteries. ECS Meet. Abstr. 2020, MA2020-02, 3808. [Google Scholar] [CrossRef]
- Schimpe, M.; Barreras, J.V.; Wu, B.; Offer, G.J. Battery Degradation-Aware Current Derating: An Effective Method to Prolong Lifetime and Ease Thermal Management. J. Electrochem. Soc. 2021, 168, 060506. [Google Scholar] [CrossRef]
- Pelletier, S.; Jabali, O.; Laporte, G.; Veneroni, M. Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models. Transp. Res. Part B Methodol. 2017, 103, 158–187. [Google Scholar] [CrossRef]
- Barreras, J.V.; Raj, T.; Howey, D.A. Derating Strategies for Lithium-Ion Batteries in Electric Vehicles. In Proceedings of the IECON 2018—44th Annual Conference of the IEEE Industrial Electronics Society, Washington, DC, USA, 21–23 October 2018; pp. 4956–4961. [Google Scholar]
- Fleischer, C.; Sauer, D.U. Simulative comparison of balancing algorithms for active and passive cell balancing systems for lithium-ion batteries. In Proceedings of the Advanced Automotive Battery Conference (AABC), Detroit, MI, USA, 15–19 June 2014. [Google Scholar]
- Barreras, J.V.; Frost, D.; Howey, D. Smart Balancing Systems: An Ultimate Solution to the Weakest Cell Problem? IEEE Veh. Technol. Soc. Newsl. 2018. Available online: https://dokumen.tips/documents/capacitors-in-power-electronics-applications-reliability-and-.html (accessed on 10 June 2021).
- Pinto, C.; Barreras, J.V.; Schaltz, E.; Araújo, R.E. Evaluation of Advanced Control for Li-ion Battery Balancing Systems Using Convex Optimization. IEEE Trans. Sustain. Energy 2016, 7, 1703–1717. [Google Scholar] [CrossRef]
- Daowd, M.; Omar, N.; Bossche, P.V.D.; Van Mierlo, J. Passive and active battery balancing comparison based on MATLAB simulation. In Proceedings of the 2011 IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, 6–9 September 2011. [Google Scholar]
- Altaf, F.; Egardt, B.; Mardh, L.J. Load Management of Modular Battery Using Model Predictive Control: Thermal and State-of-Charge Balancing. IEEE Trans. Control. Syst. Technol. 2016, 25, 47–62. [Google Scholar] [CrossRef] [Green Version]
- Altaf, F.; Johannesson, L.; Egardt, B. Simultaneous Thermal and State-of-Charge Balancing of Batteries: A Review. In Proceedings of the 2014 IEEE Vehicle Power and Propulsion Conference (VPPC), Coimbra, Portugal, 27–30 October 2014; pp. 1–7. [Google Scholar]
- Barreras, J.V.; Pinto, C.; De Castro, R.; Schaltz, E.; Andreasen, S.J.; Araújo, R.E. Multi-Objective Control of Balancing Systems for Li-Ion Battery Packs: A Paradigm Shift? In Proceedings of the 2014 IEEE Vehicle Power and Propulsion Conference (VPPC), Coimbra, Portugal, 27–30 October 2014; pp. 1–7. [Google Scholar]
- Pinto, C.; De Castro, R.; Barreras, J.V.; Araujo, R.E.; Howey, D.A. Smart Balancing Control of a Hybrid Energy Storage System Based on a Cell-to-Cell Shared Energy Transfer Configuration. In Proceedings of the 2018 IEEE Vehicle Power and Propulsion Conference (VPPC), Chicago, IL, USA, 27–30 August 2018; pp. 1–6. [Google Scholar]
- De Castro, R.P.; Pinto, C.; Barreras, J.V.; Araujo, R.E.; Howey, D.A. Smart and Hybrid Balancing System: Design, Modeling, and Experimental Demonstration. IEEE Trans. Veh. Technol. 2019, 68, 11449–11461. [Google Scholar] [CrossRef]
- De Castro, R.; Pereira, H.; Araujo, R.E.; Barreras, J.V.; Pangborn, H.C. Multi-Layer Control for Hybrid Balancing System. In Proceedings of the 2021 5th IEEE Conference on Control Technology and Applications (CCTA), San Diego, CA, USA, 9–11 August 2021. [Google Scholar]
- Docimo, D.J.; Fathy, H.K. Multivariable State Feedback Control as a Foundation for Lithium-Ion Battery Pack Charge and Capacity Balancing. J. Electrochem. Soc. 2016, 164, A61–A70. [Google Scholar] [CrossRef]
- Sui, Y.; Song, S. A Multi-Agent Reinforcement Learning Framework for Lithium-ion Battery Scheduling Problems. Energies 2020, 13, 1982. [Google Scholar] [CrossRef] [Green Version]
- Ma, Y.; Duan, P.; Sun, Y.; Chen, H. Equalization of Lithium-Ion Battery Pack Based on Fuzzy Logic Control in Electric Vehicle. IEEE Trans. Ind. Electron. 2018, 65, 6762–6771. [Google Scholar] [CrossRef]
- Olfati-Saber, R.; Murray, R. Consensus Problems in Networks of Agents with Switching Topology and Time-Delays. IEEE Trans. Autom. Control. 2004, 49, 1520–1533. [Google Scholar] [CrossRef] [Green Version]
- Abhinav, S.; Binetti, G.; Davoudi, A.; Lewis, F.L. Toward consensus-based balancing of smart batteries. In Proceedings of the 2014 IEEE Applied Power Electronics Conference and Exposition—APEC 2014, Fort Worth, TX, USA, 16–20 March 2014; pp. 2867–2873. [Google Scholar]
- Ouyang, Q.; Chen, J.; Zheng, J.; Fang, H. Optimal Cell-to-Cell Balancing Topology Design for Serially Connected Lithium-Ion Battery Packs. IEEE Trans. Sustain. Energy 2018, 9, 350–360. [Google Scholar] [CrossRef]
- Barreras, J.V.; Raj, T.; Howey, D.A.; Schaltz, E. Results of Screening over 200 Pristine Lithium-Ion Cells. In Proceedings of the 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), Belfort, France, 11–14 December 2017; pp. 1–6. [Google Scholar]
- Zheng, Y.; Han, X.; Lu, L.; Li, J.; Ouyang, M. Lithium ion battery pack power fade fault identification based on Shannon entropy in electric vehicles. J. Power Sources 2013, 223, 136–146. [Google Scholar] [CrossRef]
- An, F.; Chen, L.; Huang, J.; Zhang, J.; Li, P. Rate dependence of cell-to-cell variations of lithiumion cells. Sci. Rep. 2016, 6, 35051. [Google Scholar] [CrossRef]
- Rothgang, S.; Baumhöfer, T.; Sauer, D.U. Diversion of Aging of Battery Cells in Automotive Systems. In Proceedings of the 2014 IEEE Vehicle Power and Propulsion Conference (VPPC), Coimbra, Portugal, 27–30 October 2014; pp. 1–6. [Google Scholar]
- Paul, S.; Diegelmann, C.; Kabza, H.; Tillmetz, W. Analysis of ageing inhomogeneities in lithium-ion battery systems. J. Power Sources 2013, 239, 642–650. [Google Scholar] [CrossRef]
- An, F.; Huang, J.; Wang, C.; Li, Z.; Zhang, J.; Wang, S.; Li, P. Cell sorting for parallel lithium-ion battery systems: Evaluation based on an electric circuit model. J. Energy Storage 2016, 6, 195–203. [Google Scholar] [CrossRef]
- Rumpf, K.; Naumann, M.; Jossen, A. Experimental investigation of parametric cell-to-cell variation and correlation based on 1100 commercial lithium-ion cells. J. Energy Storage 2017, 14, 224–243. [Google Scholar] [CrossRef]
- Zou, H.; Zhan, H.; Zheng, Z. A Multi—Factor Weight Analysis Method of Lithiumion Batteries Based on Module Topology. In Proceedings of the 2018 International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), Xi’an, China, 15–17 August 2018; pp. 61–66. [Google Scholar]
- Baumann, M.; Wildfeuer, L.; Rohr, S.; Lienkamp, M. Parameter variations within Li-Ion battery packs—Theoretical investigations and experimental quantification. J. Energy Storage 2018, 18, 295–307. [Google Scholar] [CrossRef]
- Devie, A.; Baure, G.; Dubarry, M. Intrinsic Variability in the Degradation of a Batch of Commercial 18650 Lithium-Ion Cells. Energies 2018, 11, 1031. [Google Scholar] [CrossRef] [Green Version]
- Campestrini, C.; Keil, P.; Schuster, S.F.; Jossen, A. Ageing of lithium-ion battery modules with dissipative balancing compared with single-cell ageing. J. Energy Storage 2016, 6, 142–152. [Google Scholar] [CrossRef]
- Schuster, S.F.; Brand, M.J.; Berg, P.; Gleissenberger, M.; Jossen, A. Lithium-ion cell-to-cell variation during battery electric vehicle operation. J. Power Sources 2015, 297, 242–251. [Google Scholar] [CrossRef]
- Dubarry, M.; Truchot, C.; Cugnet, M.; Liaw, B.Y.; Gering, K.; Sazhin, S.; Jamison, D.; Michelbacher, C. Evaluation of commercial lithium-ion cells based on composite positive electrode for plug-in hybrid electric vehicle applications. Part I: Initial characterizations. J. Power Sources 2011, 196, 10328–10335. [Google Scholar] [CrossRef]
- Baumhöfer, T.; Brühl, M.; Rothgang, S.; Sauer, D.U. Production caused variation in capacity aging trend and correlation to initial cell performance. J. Power Sources 2014, 247, 332–338. [Google Scholar] [CrossRef]
- Dubarry, M.; Vuillaume, N.; Liaw, B.Y. Origins and accommodation of cell variations in Li-ion battery pack modeling. Int. J. Energy Res. 2010, 34, 216–231. [Google Scholar] [CrossRef]
- Shin, D.; Poncino, M.; Macii, E.; Chang, N. A statistical model of cell-to-cell variation in Li-ion batteries for system-level design. In Proceedings of the International Symposium on Low Power Electronics and Design (ISLPED), Beijing, China, 4–6 September 2013; pp. 94–99. [Google Scholar]
- Barreras, J.V.; Pinto, C.; De Castro, R.; Schaltz, E.; Swierczynski, M.J.; Andreasen, S.J.; Araújo, R.E. An improved parametrization method for Li-ion linear static Equivalent Circuit battery Models based on direct current resistance measurement. In Proceedings of the 2015 International Conference on Sustainable Mobility Applications, Renewables and Technology (SMART), Kuwait City, Kuwait, 23–25 November 2015; pp. 1–9. [Google Scholar]
- Barreras, J.V.; Fleischer, C.; Christensen, A.E.; Swierczynski, M.J.; Schaltz, E.; Andreasen, S.J.; Sauer, D.U. An Advanced HIL Simulation Battery Model for Battery Management System Testing. IEEE Trans. Ind. Appl. 2016, 52, 5086–5099. [Google Scholar] [CrossRef]
- Barreras, J.V.; Swierczynski, M.J.; Schaltz, E.; Andreasen, S.J.; Fleischer, C.; Sauer, D.U.; Christensen, A.E. Functional analysis of Battery Management Systems using multi-cell HIL simulator. In Proceedings of the 2015 Tenth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte Carlo, Monaco, 31 March–2 April 2015; pp. 1–10. [Google Scholar]
- ASTM E1461-13 Standard Test Method for Thermal Diffusivity by the Flash Method. Available online: https://www.astm.org/Standards/E1461.htm (accessed on 13 October 2020).
- Zhu, C.; Li, X.; Song, L.; Xiang, L. Development of a theoretically based thermal model for lithium ion battery pack. J. Power Sources 2013, 223, 155–164. [Google Scholar] [CrossRef]
- Araújo, R.E.; De Castro, R.; Pinto, C.; Melo, P.; Freitas, D. Combined Sizing and Energy Management in EVs with Batteries and Supercapacitors. IEEE Trans. Veh. Technol. 2014, 63, 3062–3076. [Google Scholar] [CrossRef] [Green Version]
- Meng, L.; Dragicevic, T.; Roldan-Perez, J.; Vasquez, J.C.; Guerrero, J. Modeling and Sensitivity Study of Consensus Algorithm-Based Distributed Hierarchical Control for DC Microgrids. IEEE Trans. Smart Grid 2016, 7, 1504–1515. [Google Scholar] [CrossRef] [Green Version]
- Olfati-Saber, R.; Fax, J.A.; Murray, R. Consensus and Cooperation in Networked Multi-Agent Systems. Proc. IEEE 2007, 95, 215–233. [Google Scholar] [CrossRef] [Green Version]
- Xiao, L.; Boyd, S. Fast linear iterations for distributed averaging. Syst. Control. Lett. 2004, 53, 65–78. [Google Scholar] [CrossRef]
- Gu, G. Linear Feedback Control—Analysis and Design with MATLAB (by Dingyu Xue et al; 2007) [Bookshelf]. IEEE Control. Syst. 2009, 29, 128–129. [Google Scholar] [CrossRef]
- Wen, B.S. Cell Balancing Buys Extra Run Time and Battery Life; Power Management, Analog Applications Journal; Texas Instruments Incorporated: New York, NY, USA, 2009. [Google Scholar]
Capacity 1 [Ah] | Sample Size [–] | Chemistry | Format | Ageing State | Reference | Year |
---|---|---|---|---|---|---|
70 | 96 | C/LFP | Prismatic | BOL | Zheng [29] | 2011 |
53 | 208 | C/NMC | Pouch | BOL | Barreras [28] | 2017 |
5.3 | 198 | C/NCA+NMC | - | BOL | An [30] | 2016 |
5 | 216 | C/NMC | Prismatic | BOL | Rothgang [31] | 2014 |
4.4 | 96 | C/LFP | Cylindrical | BOL | Paul [32] | 2013 |
3.35 | 2 | C/NCA | Cylindrical | MOL | An [33] | 2015 |
3 | 1100 | C/LFP | Cylindrical | BOL | Rumpf [34] | 2017 |
3 | 248 | - | - | BOL | Zou [35] | 2018 |
2.9 | 356 | C/NCA | Cylindrical | BOL, EOL | Baumann [36] | 2018 |
2.8 | 51 | C/LCO+NMC | Cylindrical | BOL | Devie [37] | 2018 |
2.8 | 112 | C/NCA | Cylindrical | BOL, MOL | Campestrini [38] | 2016 |
1.95 | 2392 | C/NMC | Cylindrical | BOL, MOL | Schuster [39] | 2015 |
1.9 | 10 | C/LMNC+LMO | Cylindrical | BOL | Dubarry [40] | 2011 |
1.85 | 48 | C/NMC | Cylindrical | BOL | Baumhöfer [41] | 2014 |
0.3 | 100 | C/LCO | Cylindrical | BOL | Dubarry [42] | 2010 |
~0.3 | 60 | C/LCO | Cylindrical | - | Shin [43] | 2013 |
[1.602 2.955 2.882 1.636 0.999 1.428 0.973 1.487] | [0.934 0.883 0.874 0.925 0.977 0.921 0.976 0.934] |
Balancing Scenario | [mV] | [°C] | [Wh] | [Wh] | Simulation Time [s] | |||
---|---|---|---|---|---|---|---|---|
No control | 94 | 1.5 | 3.5 | 54.2 | 0 | 121.1 | 5.86 | 2813 |
SOC ( | 84 | 0.1 | 3.3 | 52.8 | 0.9 | 127.0 | 5.27 | 3092 |
Temperature () | 82 | 7.9 | 0.7 | 41.4 | 13.4 | 87.9 | 0.43 | 2306 |
Voltage () | 57 | 3.4 | 1.8 | 46.8 | 5.0 | 110.5 | 2.26 | 2781 |
Balancing Scenario | [mV] | [°C] | [Wh] | Simulation Time [s] | ||||
---|---|---|---|---|---|---|---|---|
No control | 94 | 1.5 | 3.5 | 54.2 | 0 | 121.1 | 5.86 | 2813 |
SOC ( | 84 | 0.1 | 3.3 | 52.8 | 0.9 | 127.0 | 5.27 | 3092 |
Voltage () | 57 | 3.4 | 1.8 | 46.8 | 5.0 | 110.5 | 2.26 | 2781 |
Voltage () | 49 | 4.0 | 1.2 | 44.3 | 8.7 | 106.8 | 1.17 | 2738 |
Dual (SOC and voltage) (, ) | 59 | 1.6 | 1.7 | 46.2 | 7.5 | 116.4 | 1.38 | 2973 |
[–]. | [mV] | Simulation Time [s] | ||||||
---|---|---|---|---|---|---|---|---|
0 | 84 | 0.1 | 3.3 | 52.8 | 0.9 | 127.0 | 5.27 | 3092 |
0.2 | 78 | 0.7 | 3.1 | 52.3 | 1.2 | 124.3 | 4.47 | 3063 |
0.5 | 70 | 2.2 | 2.5 | 51.0 | 2.2 | 117.4 | 3.63 | 2834 |
0.8 | 64 | 5.1 | 1.7 | 45.2 | 5.3 | 102.0 | 1.59 | 2696 |
1 | 82 | 7.9 | 0.7 | 41.4 | 13.4 | 87.9 | 0.43 | 2306 |
Balancing Scenario | ||||||
---|---|---|---|---|---|---|
No control | 86 | 1.5 | 3.3 | 47.3 | 0 | 71.5 |
SOC ( | 74 | 0.1 | 2.7 | 45.5 | 0.7 | 70.0 |
Voltage () | 31 | 3.9 | 0.8 | 38.9 | 4.0 | 65.7 |
[–] | ||||||
---|---|---|---|---|---|---|
0 | 74 | 0.1 | 2.7 | 45.5 | 0.7 | 70.0 |
0.2 | 72 | 0.2 | 2.6 | 45.3 | 0.7 | 69.8 |
0.5 | 66 | 0.7 | 2.4 | 44.6 | 0.9 | 69.4 |
0.8 | 52 | 1.9 | 1.7 | 42.2 | 1.9 | 68.1 |
1 | 31 | 3.9 | 0.8 | 38.9 | 4.0 | 65.7 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Barreras, J.V.; de Castro, R.; Wan, Y.; Dragicevic, T. A Consensus Algorithm for Multi-Objective Battery Balancing. Energies 2021, 14, 4279. https://doi.org/10.3390/en14144279
Barreras JV, de Castro R, Wan Y, Dragicevic T. A Consensus Algorithm for Multi-Objective Battery Balancing. Energies. 2021; 14(14):4279. https://doi.org/10.3390/en14144279
Chicago/Turabian StyleBarreras, Jorge Varela, Ricardo de Castro, Yihao Wan, and Tomislav Dragicevic. 2021. "A Consensus Algorithm for Multi-Objective Battery Balancing" Energies 14, no. 14: 4279. https://doi.org/10.3390/en14144279