Optimizing Battery Charging Using Neural Networks in the Presence of Unknown States and Parameters
Abstract
:1. Introduction
2. Model
3. Methodology
3.1. Model Predictive Control
3.2. State-Based Deep MPC
3.3. Output-Based Deep MPC
4. Training of the Controller
4.1. Optimal Battery Charging
4.2. Dataset Generation
4.3. Training Phase and Model Selection
5. Results
5.1. Approximation of the Optimal Charging Profile in the Presence of Unknown States and Parameters
5.2. Implementation Details
6. Discussion
- The proposed methodology is designed to be robust with respect to uncertainty in the battery parameters. However, it should be highlighted that a high performance can be achieved in a practical scenario only under the assumption that all of the relevant physical phenomena have been considered in the battery model used to generate the synthetic dataset. Although this assumption is more realistic than assuming perfect knowledge of states and parameters, it is important to investigate the consequences of its violation and develop countermeasures to mitigate the effects of potential inaccuracies in the modeling phase.
- The output-based deep MPC predicts the optimal input for charging a battery based on previous measurements. However, at the start of the charging process, there are only a limited number of previous measurements available, making it challenging to effectively use the proposed algorithm. To address this challenge, a rough guess for the initial control actions is utilized. This guess is computed offline as the average current applied at the beginning of the charging phase, based on the available data in our training set. Unfortunately, if the guess input deviates from the optimal one, the controller’s performance during the first stage of charging may be affected, potentially leading to safety issues. To mitigate this issue, multiple output-based deep MPC algorithms can be employed during the first stage of charging. Each algorithm utilizes a different number of previous measurements, starting from no previous measurements, then gradually incorporating one, two, and so on, until a certain number of measurements are available.
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Lu, L.; Han, X.; Li, J.; Hua, J.; Ouyang, M. A review on the key issues for Lithium-Ion battery management in electric vehicles. J. Power Sour. 2013, 226, 272–288. [Google Scholar] [CrossRef]
- Shen, W.; Vo, T.T.; Kapoor, A. Charging algorithms of Lithium-Ion batteries: An overview. In Proceedings of the 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA), Singapore, 18–20 July 2012; pp. 1567–1572. [Google Scholar]
- Chaturvedi, N.A.; Klein, R.; Christensen, J.; Ahmed, J.; Kojic, A. Algorithms for advanced battery-management systems. IEEE Control Syst. 2010, 30, 49–68. [Google Scholar]
- Hsieh, G.C.; Chen, L.R.; Huang, K.S. Fuzzy-controlled Li-ion battery charge system with active state-of-charge controller. IEEE Trans. Ind. Electron. 2001, 48, 585–593. [Google Scholar] [CrossRef]
- Wang, S.C.; Liu, Y.H. A PSO-based fuzzy-controlled searching for the optimal charge pattern of Li-ion batteries. IEEE Trans. Ind. Electron. 2014, 62, 2983–2993. [Google Scholar] [CrossRef]
- Purushothaman, B.; Landau, U. Rapid charging of Lithium-Ion batteries using pulsed currents a theoretical analysis. J. Electrochem. Soc. 2006, 153, A533–A542. [Google Scholar] [CrossRef]
- Chen, L.R.; Hsu, R.C.; Liu, C.S. A design of a grey-predicted Li-ion battery charge system. IEEE Trans. Ind. Electron. 2008, 55, 3692–3701. [Google Scholar] [CrossRef]
- Perez, H.E.; Hu, X.; Dey, S.; Moura, S.J. Optimal charging of Li-ion batteries with coupled electro-thermal-aging dynamics. IEEE Trans. Veh. Technol. 2017, 66, 7761–7770. [Google Scholar] [CrossRef]
- Romagnoli, R.; Couto, L.D.; Kinnaert, M.; Garone, E. Control of the state-of-charge of a Li-ion battery cell via reference governor. IFAC-PapersOnLine 2017, 50, 13747–13753. [Google Scholar] [CrossRef]
- Camacho, E.F.; Alba, C.B. Model Predictive Control; Springer Science & Business Media: Berlin, Germany, 2013. [Google Scholar]
- Klein, R.; Chaturvedi, N.A.; Christensen, J.; Ahmed, J.; Findeisen, R.; Kojic, A. Optimal charging strategies in Lithium-Ion battery. In Proceedings of the 2015 American Control Conference (ACC), San Francisco, CA, USA, 29 June–1 July 2011; pp. 382–387. [Google Scholar]
- Zou, C.; Manzie, C.; Nešić, D. Model predictive control for Lithium-Ion battery optimal charging. IEEE/ASME Trans. Mechatron. 2018, 23, 947–957. [Google Scholar] [CrossRef]
- Torchio, M.; Wolff, N.A.; Raimondo, D.M.; Magni, L.; Krewer, U.; Gopaluni, R.B.; Paulson, J.A.; Braatz, R.D. Real-time model predictive control for the optimal charging of a Lithium-Ion battery. In Proceedings of the 2015 American Control Conference (ACC), Chicago, IL, USA, 1–3 July 2015; pp. 4536–4541. [Google Scholar]
- Torchio, M.; Magni, L.; Braatz, R.D.; Raimondo, D. Design of piecewise affine and linear time-varying model predictive control strategies for advanced battery management systems. J. Electrochem. Soc. 2017, 164, A949. [Google Scholar] [CrossRef]
- Lucia, S.; Torchio, M.; Raimondo, D.M.; Klein, R.; Braatz, R.D.; Findeisen, R. Towards adaptive health-aware charging of Li-ion batteries: A real-time predictive control approach using first-principles models. In Proceedings of the 2017 American Control Conference (ACC), Seattle, WA, USA, 24–26 May 2017; pp. 4717–4722. [Google Scholar]
- Pozzi, A.; Torchio, M.; Raimondo, D.M. Assessing the performance of model-based energy saving charging strategies in Li-ion cells. In Proceedings of the 2018 IEEE Conference on Control Technology and Applications (CCTA), Copenhagen, Denmark, 21–24 August 2018; pp. 806–811. [Google Scholar]
- Mrugalska, B.; Stetter, R. Health-aware model-predictive control of a cooperative AGV-based production system. Sensors 2019, 19, 532. [Google Scholar] [CrossRef]
- Kakouche, K.; Rekioua, T.; Mezani, S.; Oubelaid, A.; Rekioua, D.; Blazek, V.; Prokop, L.; Misak, S.; Bajaj, M.; Ghoneim, S.S. Model predictive direct torque control and fuzzy logic energy management for multi power source electric vehicles. Sensors 2022, 22, 5669. [Google Scholar] [CrossRef]
- Tian, N.; Fang, H.; Wang, Y. Real-Time Optimal Charging for Lithium-Ion Batteries via Explicit Model Predictive Control. In Proceedings of the 2019 IEEE 28th International Symposium on Industrial Electronics (ISIE), Vancouver, BC, Canada, 12–14 June 2019; pp. 2001–2006. [Google Scholar]
- Alessio, A.; Bemporad, A. A survey on explicit model predictive control. In Nonlinear Model Predictive Control; Springer: New York, NY, USA, 2009; pp. 345–369. [Google Scholar]
- Karg, B.; Lucia, S. Efficient representation and approximation of model predictive control laws via deep learning. IEEE Trans. Cybern. 2020, 50, 3866–3878. [Google Scholar] [CrossRef]
- Parisini, T.; Zoppoli, R. A receding-horizon regulator for nonlinear systems and a neural approximation. Automatica 1995, 31, 1443–1451. [Google Scholar] [CrossRef]
- Bemporad, A.; Oliveri, A.; Poggi, T.; Storace, M. Ultra-fast stabilizing model predictive control via canonical piecewise affine approximations. IEEE Trans. Autom. Control 2011, 56, 2883–2897. [Google Scholar] [CrossRef]
- Csekö, L.H.; Kvasnica, M.; Lantos, B. Explicit MPC-based RBF neural network controller design with discrete-time actual Kalman filter for semiactive suspension. IEEE Trans. Control Syst. Technol. 2015, 23, 1736–1753. [Google Scholar] [CrossRef]
- Hertneck, M.; Köhler, J.; Trimpe, S.; Allgöwer, F. Learning an approximate model predictive controller with guarantees. IEEE Control Syst. Lett. 2018, 2, 543–548. [Google Scholar] [CrossRef]
- Pozzi, A.; Moura, S.; Toti, D. A Neural Network-Based Approximation of Model Predictive Control for a Lithium-Ion Battery with Electro-Thermal Dynamics. In Proceedings of the 2022 IEEE 17th International Conference on Control & Automation (ICCA), Naples, Italy, 27–30 June 2022; pp. 160–165. [Google Scholar]
- Pozzi, A.; Moura, S.; Toti, D. Deep Learning-Based Predictive Control for the Optimal Charging of a Lithium-Ion Battery with Electrochemical Dynamics. In Proceedings of the 2022 IEEE Conference on Control Technology and Applications (CCTA), Bridgetown, Barbados, 16–18 August 2022; pp. 785–790. [Google Scholar]
- Park, S.; Kato, D.; Gima, Z.; Klein, R.; Moura, S. Optimal experimental design for parameterization of an electrochemical Lithium-Ion battery model. J. Electrochem. Soc. 2018, 165, A1309. [Google Scholar] [CrossRef]
- Waag, W.; Fleischer, C.; Sauer, D.U. Critical review of the methods for monitoring of Lithium-Ion batteries in electric and hybrid vehicles. J. Power Sources 2014, 258, 321–339. [Google Scholar] [CrossRef]
- Santhanagopalan, S.; Guo, Q.; Ramadass, P.; White, R.E. Review of models for predicting the cycling performance of lithium ion batteries. J. Power Sources 2006, 156, 620–628. [Google Scholar] [CrossRef]
- He, H.; Xiong, R.; Fan, J. Evaluation of Lithium-Ion battery equivalent circuit models for state of charge estimation by an experimental approach. Energies 2011, 4, 582–598. [Google Scholar] [CrossRef]
- Nejad, S.; Gladwin, D.; Stone, D. A systematic review of lumped-parameter equivalent circuit models for real-time estimation of Lithium-Ion battery states. J. Power Sources 2016, 316, 183–196. [Google Scholar] [CrossRef]
- Gomadam, P.M.; Weidner, J.W.; Dougal, R.A.; White, R.E. Mathematical modeling of Lithium-Ion and nickel battery systems. J. Power Sources 2002, 110, 267–284. [Google Scholar] [CrossRef]
- Ramadesigan, V.; Northrop, P.W.; De, S.; Santhanagopalan, S.; Braatz, R.D.; Subramanian, V.R. Modeling and simulation of Lithium-Ion batteries from a systems engineering perspective. J. Electrochem. Soc. 2012, 159, R31. [Google Scholar] [CrossRef]
- Moura, S.J. Estimation and control of battery electrochemistry models: A tutorial. In Proceedings of the 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, 15–18 December 2015; pp. 3906–3912. [Google Scholar]
- Zou, C.; Manzie, C.; Anwar, S. Control-oriented modeling of a Lithium-Ion battery for fast charging. IFAC Proc. Vol. 2014, 47, 3912–3917. [Google Scholar] [CrossRef]
- Zou, C.; Manzie, C.; Nešić, D. A framework for simplification of PDE-based Lithium-Ion battery models. IEEE Trans. Control. Syst. Technol. 2015, 24, 1594–1609. [Google Scholar] [CrossRef]
- Doyle, M.; Fuller, T.F.; Newman, J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. J. Electrochem. Soc. 1993, 140, 1526–1533. [Google Scholar] [CrossRef]
- Pozzi, A.; Xie, X.; Raimondo, D.M.; Schenkendorf, R. Global Sensitivity Methods for Design of Experiments in Lithium-ion Battery Context. IFAC-PapersOnLine 2020, 53, 7248–7255. [Google Scholar] [CrossRef]
- Pozzi, A.; Toti, D. Lexicographic model predictive control strategy in ageing-aware optimal charging procedure for Lithium-Ion batteries. Comput. Chem. Eng. 2022, 163, 107847. [Google Scholar] [CrossRef]
- Perez, H.E.; Hu, X.; Moura, S.J. Optimal charging of batteries via a single particle model with electrolyte and thermal dynamics. In Proceedings of the 2016 American Control Conference (ACC), Boston, MA, USA, 6–8 July 2016; pp. 4000–4005. [Google Scholar]
- Moura, S.J.; Argomedo, F.B.; Klein, R.; Mirtabatabaei, A.; Krstic, M. Battery state estimation for a single particle model with electrolyte dynamics. IEEE Trans. Control Syst. Technol. 2017, 25, 453–468. [Google Scholar] [CrossRef]
- Perez, H.; Dey, S.; Hu, X.; Moura, S. Optimal charging of li-ion batteries via a single particle model with electrolyte and thermal dynamics. J. Electrochem. Soc. 2017, 164, A1679. [Google Scholar] [CrossRef]
- Ecker, M.; Tran, T.K.D.; Dechent, P.; Käbitz, S.; Warnecke, A.; Sauer, D.U. Parameterization of a physico-chemical model of a Lithium-Ion battery I. Determination of parameters. J. Electrochem. Soc. 2015, 162, A1836–A1848. [Google Scholar] [CrossRef]
- Ecker, M.; Käbitz, S.; Laresgoiti, I.; Sauer, D.U. Parameterization of a physico-chemical model of a Lithium-Ion battery II. Model validation. J. Electrochem. Soc. 2015, 162, A1849–A1857. [Google Scholar] [CrossRef]
- Bemporad, A.; Morari, M. Robust model predictive control: A survey. In Robustness in Identification and Control; Springer: New York, NY, USA, 1999; pp. 207–226. [Google Scholar]
- Åkesson, B.M.; Toivonen, H.T. A neural network model predictive controller. J. Process Control 2006, 16, 937–946. [Google Scholar] [CrossRef]
- Patnaik, L.; Praneeth, A.; Williamson, S.S. A closed-loop constant-temperature constant-voltage charging technique to reduce charge time of Lithium-Ion batteries. IEEE Trans. Ind. Electron. 2018, 66, 1059–1067. [Google Scholar] [CrossRef]
- Park, S.; Pozzi, A.; Whitmeyer, M.; Perez, H.; Kandel, A.; Kim, G.; Choi, Y.; Joe, W.T.; Raimondo, D.M.; Moura, S. A Deep Reinforcement Learning Framework for Fast Charging of Li-ion Batteries. IEEE Trans. Transp. Electrif. 2022, 8, 2770–2784. [Google Scholar] [CrossRef]
Model | Measurements Window () | Mean Squared Error |
---|---|---|
DNN (Dense: ) | 10 | 0.256 |
DNN (Dense: ) | 15 | 0.212 |
DNN (Dense: ) | 20 | 0.199 |
RNN (LSTM: , Dense: ) | 10 | 0.202 |
RNN (LSTM: , Dense: | 15 | 0.182 |
RNN (LSTM: , Dense: | 20 | 0.124 |
RNN (LSTM: , Dense: | 10 | 0.193 |
RNN (LSTM: , Dense: | 15 | 0.133 |
RNN (LSTM: , Dense: | 20 | 0.109 |
Statistics | |||
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Mean | |||
Standard deviation |
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Pozzi, A.; Barbierato, E.; Toti, D. Optimizing Battery Charging Using Neural Networks in the Presence of Unknown States and Parameters. Sensors 2023, 23, 4404. https://doi.org/10.3390/s23094404
Pozzi A, Barbierato E, Toti D. Optimizing Battery Charging Using Neural Networks in the Presence of Unknown States and Parameters. Sensors. 2023; 23(9):4404. https://doi.org/10.3390/s23094404
Chicago/Turabian StylePozzi, Andrea, Enrico Barbierato, and Daniele Toti. 2023. "Optimizing Battery Charging Using Neural Networks in the Presence of Unknown States and Parameters" Sensors 23, no. 9: 4404. https://doi.org/10.3390/s23094404
APA StylePozzi, A., Barbierato, E., & Toti, D. (2023). Optimizing Battery Charging Using Neural Networks in the Presence of Unknown States and Parameters. Sensors, 23(9), 4404. https://doi.org/10.3390/s23094404