Reduced-Order Electro-Thermal Battery Model Ready for Software-in-the-Loop and Hardware-in-the-Loop BMS Evaluation for an Electric Vehicle
Abstract
:1. Introduction
2. Electrochemical Model
3. Reduced-Order Electro-Thermal Model
- Firstly, the equivalent circuit models are intensively studied in the literature. They commonly share a similar structure with electrical or electrochemical elements: (1) a voltage source to represent the open circuit voltage; (2) an ohmic resistance to represent the instantaneous voltage drop when a current is applied to the battery; (3) a diffusion impedance to capture the dynamic behavior related to the diffusion of lithium-ion inside the battery. The diffusion impedance can be represented by a network of RC circuits connected in series [7,8,9,10,11,12,13,14], by an electrochemical impedance such as the constant phase element (CPE) or Warburg impedance [15,16,17], or by other circuit structures including resistances and capacitors [11,18]. The equivalent circuit models are mostly calibrated with temporal test data. Frequency data from the electrochemical impedance spectroscopy (EIS) has also been used to identify the diffusion impedance [16,17]. The equivalent circuit models can be easily coupled with a simplified thermal model to estimate the temperature change during the battery operation [7,9,10,11,14]. The simplified thermal models reported in the literature commonly include one or several equivalent thermal capacitors to represent the specific heat of the battery cell, one or several equivalent thermal resistances to represent the heat conduction inside the cell and the heat convection with the ambient environment. The equivalent circuit models are compatible with aging modeling [19] and thermal runaway modeling [20]. These models have also been implemented in some of the simulation software, such as Simcenter Amesim which is a multi-physical simulation software of Siemens.
- Secondly, the single particle (SP) model, which is a simplified version of the p2D electrochemical model, is also widely studied in the literature [21,22,23]. The SP model shares many parameters with the p2D model. Compared to the equivalent circuit model, the SP model requires considerable effort in experimental tests and parameter identification. The computation cost of the SP model is higher than that of the equivalent circuit model.
- Finally, some black box models based on the neural network have been reported in the literature [24,25]. While they could capture the battery dynamic behavior, specific sets of data are needed to train the neural network model so that the model gives correct estimation in the expected operating range. Since the parameter values of the black box models do not have explicit physical meaning like in the equivalent circuit model and the electrochemical model, the black box models require higher effort to find out the exact reason when there is a significant difference between the model estimation and the battery test data.
3.1. Proposed Model
- The OCV is calculated with the following equation to consider the hysteresis behavior of the OCV in battery:
- The ohmic voltage drop ΔUohm is calculated with equation:
- The voltage drop ΔUdiff_i for each of the RC circuits (i = 1, 2, …, NRC) is calculated with the following equation:
3.2. Model Calibration
- Test 1: Pulses test. As shown in Figure 4a, this profile discharges the cell from 100% to 0% SoC. It includes several groups of short-duration (<2 s) charge and discharge pulses at different current levels. Between two groups of pulses, a long-duration discharge with a constant current is used to decrease 5% SoC of the cell. Two levels of current are used alternatively for the long-duration discharge (1 C and 0.5 C). Each long-duration discharge is followed by a long rest period (1800 s) to stabilize the cell voltage and temperature.
- Test 2: Charge test. As shown in Figure 4b, this profile consists of long-duration charges with two levels of current used alternatively (1 C and 0.5 C) to charge the cell from 0% to 95% SoC. Each long-duration charge increases the SoC of the cell by 5% and is followed by a long rest period (1800 s).
3.2.1. OCVd and OCVc
3.2.2. ΔSoChys
3.2.3. dU/dT
3.2.4. Rohm_d and Rohm_c
3.2.5. RC Circuits
- Evaluate the possibility of removing the current dependency, so that faster simulation time and simpler lookup table implementation could be achieved;
- Include the relaxation phase after the current pulse into the parameter identification, so that the dynamic behavior during the relaxation phase could also be properly represented in case the battery dynamic behavior in the relaxation phase is significantly different from the one during the current pulse;
- Search for an optimal function, such as a polynomial used in [9], to represent the parameter value in function of the SoC or the current. It could help to guarantee smooth parameter value change along the SoC and current axis. The smooth parameter value change during the simulation has several benefits. It will allow to have faster model simulation. It will also minimize the risk of simulation failure due to the discontinuity issue in which there is a sharp change of the parameter value during the simulation [29].
3.2.6. Thermal Parameters
3.3. Model Validation
4. Battery Pack Model
4.1. Battery Pack Model in a Virtual Test Bench
4.2. Scenarios for Battery Pack Cooling
4.3. Real-Time Capability
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Doyle, M.; Fuller, T.F.; Newman, J.S. Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell. J. Electrochem. Soc. 1993, 140, 1526–1533. [Google Scholar] [CrossRef]
- Sturm, J.; Rheinfeld, A.; Zilberman, I.; Spingler, F.B.; Kosch, S.; Frie, F.; Jossen, A. Modeling and Simulation of inhomogeneities in a 18650 nickel-rich, silicon-graphite lithium-ion cell during fast charging. J. Power Sources 2019, 412, 204–223. [Google Scholar] [CrossRef] [Green Version]
- Sturm, J.; Ennifar, H.; Erhard, S.; Rheinfeld, A.; Kosch, S.; Jossen, A. State estimation of lithium-ion cells using a physicochemical model based extended Kalman filter. Appl. Energy 2018, 223, 103–123. [Google Scholar] [CrossRef]
- Subramanian, V.R.; Diwakar, V.D.; Tapriyal, D. Efficient Macro-Micro Scale Coupled Modeling of Batteries. J. Electrochem. Soc. 2005, 152, A2002. [Google Scholar] [CrossRef]
- Thomas, K.E.; Newman, J.; Darling, R.M. Mathematical Modeling of Lithium Batteries. In Advances in Lithium-Ion Batteries; Van Schalkwijk, W.A., Scrosati, B., Eds.; Springer: Boston, MA, USA, 2002; pp. 345–392. [Google Scholar]
- Brenan, K.E.; Campbell, S.L.; Petzold, L.R. (Eds.) Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations; Classics in Applied Mathematics; Society for Industrial and Applied Mathematics: Philadelphia, PA, USA, 1996; Volume 14. [Google Scholar]
- Mathew, M.; Mastali, M.; Catton, J.W.A.; Samadani, E.; Janhunen, S.; Fowler, M. Development of an Electro-Thermal Model for Electric Vehicles Using a Design of Experiments Approach. Batteries 2018, 4, 29. [Google Scholar] [CrossRef] [Green Version]
- Li, A.; Pelissier, S.; Venet, P.; Gyan, P. Fast Characterization Method for Modeling Battery Relaxation Voltage. Batteries 2016, 2, 7. [Google Scholar] [CrossRef] [Green Version]
- Lin, X.; Perez, H.E.; Mohan, S.; Siegel, J.B.; Stefanopoulou, A.G.; Ding, Y.; Castanier, M.P. A lumped-parameter electro-thermal model for cylindrical batteries. J. Power Sources 2014, 257, 1–11. [Google Scholar] [CrossRef]
- German, R.; Shili, S.; Sari, A.; Venet, P.; Bouscayrol, A. Characterization Method for Electrothermal Model of Li-Ion Large Cells. In Proceedings of the 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), Belfort, France, 11–14 December 2017; pp. 1–6. [Google Scholar]
- Saldaña, G.; Martín, J.I.S.; Zamora, I.; Asensio, F.J.; Onederra, O. Analysis of the Current Electric Battery Models for Electric Vehicle Simulation. Energies 2019, 12, 2750. [Google Scholar] [CrossRef] [Green Version]
- Meng, J.; Luo, G.; Ricco, M.; Swierczynski, M.; Stroe, D.-I.; Teodorescu, R. Overview of Lithium-Ion Battery Modeling Methods for State-of-Charge Estimation in Electrical Vehicles. Appl. Sci. 2018, 8, 659. [Google Scholar] [CrossRef] [Green Version]
- Fotouhi, A.; Auger, D.J.; Propp, K.; Longo, S.; Wild, M. A review on electric vehicle battery modelling: From Lithium-ion toward Lithium–Sulphur. Renew. Sustain. Energy Rev. 2016, 56, 1008–1021. [Google Scholar] [CrossRef] [Green Version]
- Gao, Z.; Chin, C.S.; Woo, W.L.; Jia, J. Integrated Equivalent Circuit and Thermal Model for Simulation of Temperature-Dependent LiFePO4 Battery in Actual Embedded Application. Energies 2017, 10, 85. [Google Scholar] [CrossRef] [Green Version]
- Hafsaoui, J.; Scordia, J.; Sellier, P.; Aubret, P. Development of an Electrochemical battery model and Its Parameters Identification Tool. Int. J. Automot. Eng. 2012, 3, 27–33. [Google Scholar]
- Montaru, M.; Pelissier, S. Frequency and Temporal Identification of a Li-ion Polymer Battery Model Using Fractional Impedance. In Proceedings of the Proceedings in Advances in Hybrid Powertrains, Paris, France, 25–26 November 2008. [Google Scholar]
- Stroe, D.-I.; Swierczynski, M.J.; Stroe, A.-I.; Kær, S.K. Generalized Characterization Methodology for Performance Modelling of Lithium-Ion Batteries. Batteries 2016, 2, 37. [Google Scholar] [CrossRef] [Green Version]
- Urbain, M.; Hinaje, M.; Raël, S.; Davat, B.; Desprez, P. Energetical Modeling of Lithium-Ion Batteries Including Electrode Porosity Effects. IEEE Trans. Energy Convers. 2010, 25, 862–872. [Google Scholar] [CrossRef]
- Mesbahi, T.; Rizoug, N.; Bartholomeus, P.; Sadoun, R.; Khenfri, F.; Le Moigne, P. Dynamic Model of Li-Ion Batteries Incorporating Electrothermal and Ageing Aspects for Electric Vehicle Applications. IEEE Trans. Ind. Electron. 2018, 65, 1298–1305. [Google Scholar] [CrossRef]
- Petit, M.; Abada, S.; Mingant, R.; Bernard, J.; Desprez, P.; Perlo, P.; Biasiotto, M.; Introzzi, R.; Lecocq, A.; Marlair, G. Demobase project: Numerical simulation for seamless integration of battery pack in light electric vehicle. In Proceedings of the 32nd Electric Vehicle Symposium (EVS32), Lyon, France, 22 May 2019. [Google Scholar]
- Prada, E.; Di Domenico, D.; Creff, Y.; Bernard, J.C.; Sauvant-Moynot, V.; Huet, F. Simplified Electrochemical and Thermal Model of LiFePO4-Graphite Li-Ion Batteries for Fast Charge Applications. J. Electrochem. Soc. 2012, 159, A1508–A1519. [Google Scholar] [CrossRef] [Green Version]
- Bizeray, A.M.; Kim, J.-H.; Duncan, S.R.; Howey, D.A. Identifiability and Parameter Estimation of the Single Particle Lithium-Ion Battery Model. IEEE Trans. Control. Syst. Technol. 2019, 27, 1862–1877. [Google Scholar] [CrossRef] [Green Version]
- Chen, J.; Wang, R.; Li, Y.; Xu, M. A Simplified Extension of Physics-Based Single Particle Model for Dynamic Discharge Current. IEEE Access 2019, 7, 186217–186227. [Google Scholar] [CrossRef]
- Li, S.; Li, J.; He, H.; Wang, H. Lithium-ion battery modeling based on Big Data. Energy Procedia 2019, 159, 168–173. [Google Scholar] [CrossRef]
- Sarvi, M.; Masoum, M.A.S. A Neural Network Model for Ni-Cd Batteries. In Proceedings of the 43rd International Universities Power Engineering Conference, Padova, Italy, 1–4 September 2008. [Google Scholar]
- Siemens. Help Document of ESSBATCA01—Advanced Equivalent Circuit Model of Battery Cell; Simcenter Amesim V17; Siemens: Munich, Germany, 2018. [Google Scholar]
- Marongiu, A.; Nußbaum, F.G.W.; Waag, W.; Garmendia, M.; Sauer, D.U. Comprehensive study of the influence of aging on the hysteresis behavior of a lithium iron phosphate cathode-based lithium ion battery—An experimental investigation of the hysteresis. Appl. Energy 2016, 171, 629–645. [Google Scholar] [CrossRef]
- Siemens. Help Document of Strinitu Utility; Simcenter Amesim V17; Siemens: Munich, Germany, 2018. [Google Scholar]
- Siemens. Help Document of Discontinuity Handling—Impact of a Discontinuity on Simulation; Simcenter Amesim V17; Siemens: Munich, Germany, 2018. [Google Scholar]
Parameter | Description | Unit |
---|---|---|
Qcell | Cell capacity | Ah |
OCVc | OCV in charge at the reference temperature | V |
OCVd | OCV in discharge at the reference temperature | V |
ΔSoChys | SoC variation for full charge and discharge open circuit voltage transition | % |
dU/dT | Entropic coefficient | V/K |
Rohm | Ohmic resistance | Ohm |
Rdiff[i] | Diffusion resistance | Ohm |
Cdiff[i] | Diffusion capacitance | F |
Cp | Specific heat of the cell | J/kg/K |
hconv | Convective heat exchange coefficient | W/m2/K |
Sconv | Convective heat exchange area | m2 |
mcell | mass of the cell | kg |
OCVx | OCVd | OCVd | OCVd | OCVc | OCVc | OCVc |
---|---|---|---|---|---|---|
T1 (°C) | 5 | 25 | 45 | 5 | 25 | 45 |
T2 (°C) | 25 | 45 | 5 | 25 | 45 | 5 |
Parameter | Value | Unit |
---|---|---|
Cp | 791.86 | J/kg/K |
hcov | 27.5087 | W/m2/K |
Sconv | 0.00421525 | m2 |
mcell | 0.04622 | kg |
RMS Error of Voltage | 1 RC (mV) | 2 RC (mV) | 3 RC (mV) | 4 RC (mV) | 5 RC (mV) |
---|---|---|---|---|---|
5 °C | 36 | 36 | 35 | 35 | 36 |
25 °C | 29 | 29 | 29 | 29 | 29 |
45 °C | 29 | 28 | 28 | 28 | 28 |
RMS Error of Temperature | 1 RC (°C) | 2 RC (°C) | 3 RC (°C) | 4 RC (°C) | 5 RC (°C) |
---|---|---|---|---|---|
5 °C | 0.55 | 0.55 | 0.54 | 0.54 | 0.54 |
25 °C | 0.32 | 0.32 | 0.32 | 0.32 | 0.31 |
45 °C | 0.34 | 0.34 | 0.34 | 0.34 | 0.34 |
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Li, A.; Ponchant, M.; Sturm, J.; Jossen, A. Reduced-Order Electro-Thermal Battery Model Ready for Software-in-the-Loop and Hardware-in-the-Loop BMS Evaluation for an Electric Vehicle. World Electr. Veh. J. 2020, 11, 75. https://doi.org/10.3390/wevj11040075
Li A, Ponchant M, Sturm J, Jossen A. Reduced-Order Electro-Thermal Battery Model Ready for Software-in-the-Loop and Hardware-in-the-Loop BMS Evaluation for an Electric Vehicle. World Electric Vehicle Journal. 2020; 11(4):75. https://doi.org/10.3390/wevj11040075
Chicago/Turabian StyleLi, An, Matthieu Ponchant, Johannes Sturm, and Andreas Jossen. 2020. "Reduced-Order Electro-Thermal Battery Model Ready for Software-in-the-Loop and Hardware-in-the-Loop BMS Evaluation for an Electric Vehicle" World Electric Vehicle Journal 11, no. 4: 75. https://doi.org/10.3390/wevj11040075