# New Electro-Thermal Battery Pack Model of an Electric Vehicle

^{1}

^{2}

^{*}

## Abstract

**:**

_{4}) battery type at different temperatures. It also considers both charging and discharging cases. The most remarkable features from different models, in addition to the proposed OCV model, are integrated in a single hybrid electrical model. A lumped thermal model is implemented to simulate the temperature development in the battery cell. The synthesized electro-thermal battery cell model is extended to model a battery pack of an actual electric vehicle. Experimental tests on the battery, as well as drive tests on the vehicle are performed. The proposed model demonstrates a higher modeling accuracy, for the battery pack voltage, than the constituent models under extreme maneuver drive tests.

## 1. Introduction

_{full}and V

_{cut-off}, respectively. V

_{cut-off}represents the empty state of the battery where the minimum allowable voltage is reached. This restriction is meant to protect the battery from deep depletion. The section formed between V

_{full}, V

_{exp}and the correspondences capacity rates (C-rate) 0 and Q

_{exp}is identified as the exponential region of the discharge characteristic curve, at which the discharged voltage changes exponentially regarding to the battery capacity. The voltage holds an approximately steady value for C-rates beyond Q

_{exp}up to the nominal C-rate Q

_{nom}, where the nominal V

_{nom}voltage is reached. Not only is the battery voltage influenced by the discharge rate, but the battery capacity is also diminished at high discharge rates. This occurs as a sharp voltage drop at the end of the discharge process, as indicated in Figure 1. At that rate the discharge terminates at V

_{cut-off}[4].

_{4}. Lithium iron phosphate cells are characterized by their flat open circuit voltage curve (OCV). Hence, the cell voltage stays almost constant over the complete state of charge (SOC) range [2,3,6]. The battery pack of the VUT consists of 19 modules. Each module comprises six cell blocks connected in series; a single cell block is constructed out of 50 LiFeMgPO

_{4}–graphite cells, connected in parallel. In total, there are 300 cells within the single battery module. Each cell block has a nominal voltage of 3.2 V, amounting to a total voltage of 19.2 V. The battery specifications are given in Table 1. A Controller Area Network (CAN) communication environment is used for the control and management of the battery modules. More technical information about the VUT is available in the Appendix.

## 2. Existing Battery Models

_{4}–graphite battery by coupling the empirical equations of the modified Shephard’s battery model with a lumped thermal model for the battery cell. The temperature development of a complete vehicle battery pack under different driving cycles was simulated in [23]. Tan et al. [24] have incorporated the thermal losses to Shephard’s model for Li-ion battery cells by adding temperature dependent correction terms to the model. Wijewardana et al. [1] proposed a generic electro-thermal model for Li-ion batteries. The model considers potential correction terms accounting for electrode film formation and electrolyte electron transfer chemistry. In addition, the constant values in the empirical equations that represent the equivalent circuit components of the battery were adjusted. These equations were employed to model the electrical components in dependence of SOC and temperature. Wijewardana et al. consider the C-rate effect in the estimation of SOC by employing an extended Kalman filter technique. Computational thermal models and temperature distribution estimations were proposed in References [25,26,27,28]. Additionally, finite element analysis models to estimate the temperature distribution in the battery were presented in References [25,27,28,29]. This kind of simulation requires knowledge of thermal properties of the battery cell materials, such as thermal capacity, density, mechanical construction and cooling of the battery. For an accurate parameterization intensive and precise measurements are necessary.

## 3. Overview of Selected Dynamic Battery Models

#### 3.1. Tremblay Battery Model (Battery Model 1)

_{0}) is related to SOC changes by incorporating a polarization constant (K).

#### 3.2. Lam and Bauer Battery Model (Battery Model 2)

_{OC}as a function of SOC, a variable ohmic resistance R

_{o}, and two variable RC-networks: R

_{S}C

_{S}and R

_{l}C

_{l}for the short and the long time transient responses, respectively. Lam and Bauer also showed the relation between capacity fading due to aging and different stress influences, which are the cell’s temperature, C-rate, SOC and intensity of discharge. Lam and Bauer parametrized their equations through curve fitting of experimental measurements. They employed in their tests the LiFePO

_{4}battery cell. The equivalent circuit resistors and capacitors equations for temperatures from 20 °C and above are detailed in Equations (7)–(28) in Reference [20]. We refer also to the V

_{OC}equation with the corrected constants as proposed in Reference [20]:

#### 3.3. Wijewardana Battery Model

_{S}, C

_{S}, R

_{L}, C

_{L}are functions of SOC and independent of the temperature. Only the series internal resistance resistor is a function of SOC and temperature (R

_{intS}(SOC,T)). The temperature influence is considered by adding potential correction terms, which are voltage due to electrode film formation (ΔE) and voltage due to electrolyte electrons transfer formation (ΔV

_{Che}). The capacity fading effect is modeled as an additional series resistance R

_{cyc}. The battery output voltage is computed by subtracting the voltage drop of each circuit element from the V

_{OC}value. Figure 4 demonstrates Wijewardana battery model.

#### 3.4. Assessment of Battery Models Qualities

## 4. Battery Thermal Model

_{p}) and the difference between the generated heat and the dissipated heat. The dissipation of the heat to the battery surrounding is performed by convection and radiation. Generated heat comprises two sources, irreversible heat generation by means of the effective ohmic resistance of the cell’s material, and reversible generated heat due to the entropy change in both cathode and anode. The total entropy changes in the battery cell can be considered as zero according to References [1,29,30]. The temperature development inside the battery cell is described as:

_{cell}− T

_{amp}), h is the natural convection coefficient, m is the cell mass, i is the cell current, A

_{cell}is the surface area of the single battery cell, σ is Stefan-Boltzmann constant, and ε is the emissivity of heat. Assuming that the temperature differences between the cells in the single battery module are small, Equation (7a) can be generalized for the whole battery module as:

_{loss}= I

_{cell}

^{2}R

_{contact}= 0.098 mW/cell, which is a negligible amount, thermally, as well as electrically.

## 5. Experimental Characterization of the Battery and the Vehicle under the Test

#### 5.1. Battery Measurements

_{4}-battery, several experimental tests were implemented on the battery at different conditions. OCV vs. SOC measurements were performed at 10, 20 and 40 °C. The battery was discharged until the cut-off voltage of 2 V was reached and then recharged up to the nominal capacity. A Low C-rate of C/10 was used to minimize the dynamic effects and to achieve a good approximation to an open circuit. Figure 5 demonstrates the charge and discharge OCV curves over the SOC for various temperatures. It is noticeable that the lower the operating temperatures, the higher the difference between charging and discharging.

#### 5.2. Driving Tests on the Real Vehicle

## 6. Battery Models Validation

#### 6.1. Evaluating the Open Circuit Voltage Models (V_{OC})

_{4}cathode type batteries. They concluded that the OCV is temperature independent. They justified this conclusion based on small changes of the OCV measurements due to temperature variations, which were in the range 2–8 mV [20]. An absolute error of 30 mV for LiFeMgPO

_{4}battery cell will lead to an uncertainty of 13% in the SOC estimation at 1 C discharge and 25 °C, according to Blank et al. [31]. The battery of our vehicle is LiFeMgPO

_{4}-cathode type. Its OCV curves are presented earlier in Figure 6. According to our measurements, the OCV temperature alteration is from 15 to 90 mV, which is about 10 times higher than the result presented in Reference [20]. In our study, we use a battery module that contains 6 cellblocks in series, with 50 cells in parallel for each. Moreover, the vehicle’s battery pack has 19 modules. With this combination of battery cells, the range of voltage alteration becomes 1.71–10.26 V, which is a considerable change in the battery pack output voltage.

_{OC}models in References [1,20] by comparing the simulation results with our own measurements, as shown in Figure 7. We selected the charge-discharge curves at T = 20 °C to be the references for validation. The V

_{OC}model utilized in battery model 3 does not fit our measurements. The V

_{OC}of battery model 2 better fits the experimental data. The deviation in an SOC range spanning from 10% to 90% is about 0.03 V. This deviation increases at low temperature.

_{OC}model 2 model is modified for better fitting of the OCV curve along the SOC range and the temperature influence is considered. The new V

_{OC}is modeled by Equations (8) and (9) and the constants values of the new V

_{OC}are presented in Table 3. The validation results are shown in Figure 8 and in Table 4.

#### 6.2. Evaluating the Battery Models Output Voltage

_{OC}of model 3 [1] showed a large deviation from the actual curve, as shown in Figure 7. Therefore, the V

_{OC}derived from model 2 [20] will be also utilized in model 3. Figure 9 and Figure 10 demonstrate the responses of the three models for both driving test. The simulation results gained from model 1 reveal the highest accuracy for the first test. The mean squared error between the measured voltage and the simulated voltage by model 1 is less than 1%. However, it performed the worst in the second test. The good performance of model 1 in the first test ascribed to the fact that the test conditions were nearly matching the standard condition for defining the constant voltage (E

_{0}). E

_{0}is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the initial voltage of the single battery cell is estimated as 3.25 V. When the test second driving test was performed at different circumstances, the outcome was not as good as it in the first case. Figure 10a reveals a relatively large offset error in the response of battery model 1 with a mean square error (MSE) of about 2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. The offset errors between the reference signal and initial voltage value of both battery models 2 and 3 were minor, whereas Equation (3) is employed in both models for the estimation of V

_{OC}. The simulation results of model 3 indicate less dynamic response than the other two models. It could not conduct the drastic changes in the battery current input signal.

#### 6.3. The Proposed Synthesized Battery Model

_{OC}(SOC,T) is employed instead of constant (E

_{0}) value. Then, the highly detailed internal resistance model of battery model 2 in case of discharging, which is represented by Equations (7)–(11), (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal resistance (R). The capacity fading effect is considered by adding R

_{cyc}from battery model 3 to the internal resistance. The empirical equations in case of discharging are implemented because the charging-discharging hysteresis is properly modeled by model 1. The synthesized model is shown in Figure 11.

_{1}–c

_{39}are constants, which their values are listed in Table 5.

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## Appendix

#### Appendix A.1. Nomenclature

Parameter (Unit) | Symbol | Value |
---|---|---|

Constant voltage (V) | E_{0} | 3.21 [23] |

Constant internal resistance (Ω) | R | 0.0833 |

Polarization constant (V/(Ah)) or polarization resistance (Ω) | K | 0.0119 [23] |

Battery capacity (Ah) | Q | Variable |

Actual battery charge (Ah) | it | Variable |

Exponential zone amplitude (V) | A | 0.2711 [23] |

Exponential zone time constant inverse (Ah)^{−1} | B | 152.130 [23] |

Battery current (A) | i | Variable |

Filtered current (A) | i* | Variable |

Voltage change due to electrolyte electrons transfer formation | ΔV_{Che} | Variable |

the effective voltage gradient | dV_{Che}/dT | 0.0016 [1] |

Constant property of electrolyte | C_{Che} | 0.07 [1] |

Constant property of electrolyte | C_{Che1} | 0.001 [1] |

Constant property of electrolyte | b | 0.0012 [1] |

Constant property of electrolyte | w | 0.012 [1] |

Voltage change due to electrode film formation | ΔE | Variable |

voltage gradient | dV_{r}/dT | 0.00003 [1] |

Constant property | C_{E}_{1} | 0.00011 [1] |

Battery module surface area (m^{2}) | A | 0.283954 |

Battery cell mass (kg) | m | 0.04 [23] |

Battery module mass (kg) | M | 12 |

Specific heat capacity (J·kg^{−1}·K^{−1}) | C_{p} | 1360 [27] |

Stefane-Boltzmann constant (W·m^{−2}·K^{4}) | σ | 5.67 × 10^{−8} |

Emissivity of heat | ε | 0.95 |

Natural heat convection constant (W·m^{−2}·K^{−1}) | h | 4 |

#### Appendix A.2. Driving Tests

#### Appendix A.3. The Vehicle under the Test

Parameter | Value |
---|---|

Rated Power, PN | 45 kW |

Peak Power, Pmax | 68 kW |

Peak Torque, Tmax | 210 N·m |

Rated Speed, nN | 3000 rpm |

**Figure A4.**The basic drive train topology of the Mercedes A-Class research vehicle [30].

## References

- Wijewardana, S.; Vepa, R.; Shaheed, M.H. Dynamic battery cell model and state of charge estimation. J. Power Sources
**2016**, 308, 109–120. [Google Scholar] [CrossRef] - Doppebattery Model 2auer, M. Hybrid and Electric Vehicles—Lecture Notes; ETI-HEV, Karlsruhe Institute of Technology: Karlsruhe, Germany, 2014.
- Ivers-Tiffee, E. Batteries and Fuel Cells—Lecture Notes; IWE, Karlsruhe Institute of Technology: Karlsruhe, Germany, 2012. [Google Scholar]
- Illig, J. Physically Based Impedance Modelling of Lithium-Ion Cells. Ph.D. Thesis, Karlsruhe Institute of Technology, Karlsruhe, Germany, 2014. [Google Scholar]
- Tremblay, O.; Dessaint, L.-A. Experimental validation of a battery dynamic model for EV applications. World Electr. Veh. J.
**2009**, 3, 1–10. [Google Scholar] - Padhi, A.K.; Nanjundaswamy, K.S.; Goodenough, J.B.D. Phospho-olivines as positive-electrode materials for rechargeable lithium batteries. J. Electrochem. Soc.
**1997**, 144, 1188–1194. [Google Scholar] [CrossRef] - Valence Technology. U-Charge® XP Rev 2 User Manual; Valence Technology, Inc.: Austin, TX, USA, 2011. [Google Scholar]
- Lin, N.; Ci, S.; Li, H. An enhanced circuit-based battery model with considerations of temperature effect. In Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, USA, 14–18 September 2014; pp. 3985–3989.
- 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] - Dees, D.W.; Battaglia, V.S.; Bélanger, A. Electrochemical modeling of lithium polymer batteries. J. Power Sources
**2002**, 110, 310–320. [Google Scholar] [CrossRef] - He, H.; Xiong, R.; Guo, H.; Li, S. Comparison study on the battery models used for the energy management of batteries in electric vehicles. Energy Convers. Manag.
**2012**, 64, 113–121. [Google Scholar] [CrossRef] - Hu, X.; Li, S.; Peng, H. A comparative study of equivalent circuit models for Li-ion batteries. J. Power Sources
**2012**, 198, 359–367. [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] - Hussein, A.A.; Batarseh, I. An overview of generic battery models. In Proceedings of the 2011 IEEE Power and Energy Society General Meeting, San Diego, CA, USA, 24–29 July 2011; pp. 1–6.
- Kroeze, R.C.; Krein, P.T. Electrical battery model for use in dynamic electric vehicle simulations. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008; pp. 1336–1342.
- Liu, X.; Ma, Y.; Ying, Z. Research of SOC estimation for lithium-ion battery of electric vehicle based on AMEsim-simulink co-simulation. In Proceedings of the 32nd Chinese Control Conference (CCC), Xi’an, China, 26–28 July 2013; pp. 7680–7685.
- Szumanowski, A.; Chang, Y. Battery management system based on battery nonlinear dynamics modeling. IEEE Trans. Veh. Technol.
**2008**, 57, 1425–1432. [Google Scholar] [CrossRef] - Zhang, C.; Jiang, J.; Zhang, W.; Sharkh, S.M. Estimation of state of charge of lithium-ion batteries used in HEV using robust extended Kalman filtering. Energies
**2012**, 5, 1098–1115. [Google Scholar] [CrossRef] - Watrin, N.; Roche, R.; Ostermann, H.; Blunier, B.; Miraoui, A. Multiphysical lithium-based battery model for use in state-of-charge determination. IEEE Trans. Veh. Technol.
**2012**, 61, 3420–3429. [Google Scholar] [CrossRef] - Lam, L.; Bauer, P.; Kelder, E. A practical circuit-based model for Li-ion battery cells in electric vehicle applications. In Proceedings of the 2011 IEEE 33rd International Telecommunications Energy Conference (INTELEC), Amsterdam, The Netherlands, 9–13 October 2011; pp. 1–9.
- Tremblay, O.; Dessaint, L.A.; Dekkiche, A.I. A generic battery model for the dynamic simulation of hybrid electric vehicles. In Proceedings of the 2007 IEEE Vehicle Power and Propulsion Conference, Arlington, TX, USA, 9–12 September 2007; pp. 284–289.
- Shepherd, C.M. Design of primary and secondary cells II. An equation describing battery discharge. J. Electrochem. Soc.
**1965**, 112, 657–664. [Google Scholar] [CrossRef] - Saw, L.H.; Somasundaram, K.; Ye, Y.; Tay, A.A.O. Electro-thermal analysis of Lithium Iron Phosphate battery for electric vehicles. J. Power Sources
**2014**, 249, 231–238. [Google Scholar] [CrossRef] - Tan, Y.K.; Mao, J.C.; Tseng, K.G. Modelling of battery temperature effect on electrical characteristics of Li-ion battery in hybrid electric vehicle. In Proceedings of the 2011 IEEE Ninth International Conference on Power Electronics and Drive Systems (PEDS), Singapore, Singapore, 5–8 December 2011.
- Pesaran, A.A. Battery thermal models for hybrid vehicle simulations. J. Power Sources
**2002**, 110, 377–382. [Google Scholar] [CrossRef] - Kim, Y.; Siegel, J.B.; Stefanopoulou, A.G. A computationally efficient thermal model of cylindrical battery cells for the estimation of radially distributed temperatures. In Proceedings of the 2013 American Control Conference (ACC), Washington, DC, USA, 17–19 June 2013; pp. 698–703.
- Rad, M.S.; Danilov, D.L.; Baghalha, M.; Kazemeini, M.; Notten, P.H. Thermal modeling of cylindrical LiFeMgPO
_{4}Batteries. J. Mod. Phys.**2013**, 4, 1–7. [Google Scholar] [CrossRef] - Fan, L.; Khodadadi, J.M.; Pesaran, A.A. A parametric study on thermal management of an air-cooled lithium-ion battery module for plug-in hybrid electric vehicles. J. Power Sources
**2013**, 238, 301–312. [Google Scholar] [CrossRef] - Sun, Y. Construction and Validation of a Thermal FEM-Model of an Automobile Battery. Master’s Thesis, Karlsruhe Institute of Technology, Karlsruhe, Germany, 2011. [Google Scholar]
- Gießler, M.; Fritz, A.; Paul, J.; Sander, O.; Gauterin, F.; Müller-Glaser, K.D. Converted vehicle for battery electric drive: Aspects on the design of the software-driven vehicle control unit. In Proceedings of the 2nd International Energy Efficient Vehicle Conference (EEVC), Dresden, Germany, 18–19 June 2012.
- Blank, T.; Lipps, C.; Ott, W.; Hoffmann, P.; Weber, M. Influence of environmental conditions on the sensing accuracy of Li-Ion battery management systems with passive charge balancing. In Proceedings of the 17th European Conference on Power Electronics and Applications, Geneva, Switzerland, 8–10 September 2015; pp. 1–9.

**Figure 6.**CAN bus measurements: (

**a**) Battery pack current for the circular driving test; (

**b**) Battery pack voltage for the circular driving test; (

**c**) Battery pack current for the rapid acceleration and deceleration driving test; (

**d**) Battery pack voltage for the rapid acceleration and deceleration driving test.

**Figure 8.**The new Voc model and measured experimental data: (

**a**) T = 10 °C; (

**b**) T = 20 °C; (

**c**) T = 40 °C.

**Figure 9.**Battery simulation models and reference voltage signal for circular driving test: (

**a**) Battery model 1 response; (

**b**) Mean square error of battery model 1; (

**c**) Battery model 2 response; (

**d**) Mean square error of battery model 2; (

**e**) Battery model 3 response (

**f**) Mean square error in battery model 3.

**Figure 10.**Battery simulation models and reference voltage signal for rapid acceleration and deceleration driving test: (

**a**) Battery model 1 response; (

**b**) Mean square error of battery model 1; (

**c**) Battery model 2 response; (

**d**) Mean square error of battery model 2; (

**e**) Battery model 3 response (

**f**) Mean square error in battery model 3.

**Figure 12.**The proposed synthesized battery model and reference voltage signal: (

**a**) Proposed model response for the circular driving test; (

**b**) Error of proposed model voltage for the circular driving test; (

**c**) Proposed model response for the rapid acceleration and deceleration driving test; (

**d**) Error of proposed model voltage for the rapid acceleration and deceleration driving test.

Parameter (Unit) | Value |
---|---|

Nominal Module Voltage (V) | 19.2 |

Nominal Module Capacity (Ah) | 69 |

Max Continuous Load Current (A) | 120 |

Peak Current for 30 s (A) | 200 |

Feature | Battery Model 1 | Battery Model 2 | Battery Model 3 | |||
---|---|---|---|---|---|---|

Charge-Discharge hysteresis | ++ | Considered in the output voltage | + | Considered in the internal resistance (R) equations | - | Charge-discharge |

Open circuit voltage | - | Constant value for E_{0} | + | V_{OC}(SOC) | + | V_{OC}(SOC) |

Internal resistance (R) | - | Constant value | ++ | R(SOC,T,C-rate) | + | R(SOC,T) |

Temperature influence | - | Not considered | + | Considered in the internal resistance model | + | Considered as potential correction terms |

Capacity fading | - | Not considered | + | Considered in the battery’s used capacity estimation | + | Considered in the battery’s internal resistance (R) estimation |

Total Assessment | 2 | 6 | 4 |

Constant | Value | Constant | Value |
---|---|---|---|

a_{1} | −1.166 | b_{1} | −0.9135 |

a_{2} | −35 | b_{2} | −35 |

a_{3} | 3.344 | b_{3} | 3.484 |

a_{4} | 0.1102 | b_{4} | 0.1102 |

a_{5} | −0.1718 | b_{5} | −0.1718 |

a_{6} | −2 × 10^{−3} | b_{6} | −8 × 10^{−3} |

dV_{OC,d}/dT | 0.00125 | dV_{OC,c}/dT | 0.00069 |

Temperature °C | MSE in Discharge Model % | MSE in Charge Model % |
---|---|---|

10 | 0.5232 | 0.8914 |

20 | 0.5320 | 0.5719 |

40 | 0.5751 | 0.4522 |

Constant | Value | Constant | Value | Constant | Value | Constant | Value |
---|---|---|---|---|---|---|---|

c_{1} | 1.080 × 10^{−2} | c_{11} | −6.580 | c_{21} | −6.919 × 10^{−1} | c_{31} | −2.398 × 10^{3} |

c_{2} | −11.03 | c_{12} | 12.11 | c_{22} | 2.902 × 10^{−1} | c_{32} | 1.298 × 10^{−1} |

c_{3} | 1.827 × 10^{−2} | c_{13} | 2.950 × 10^{−1} | c_{23} | 2.130 × 10^{6} | c_{33} | −2.892 × 10^{−1} |

c_{4} | −6.462 × 10^{−3} | c_{14} | −20.00 | c_{24} | −6.007 × 10^{6} | c_{34} | 2.273 × 10^{−1} |

c_{5} | −3.697 × 10^{−4} | c_{15} | 4.722 × 10^{−2} | c_{25} | 6.271 × 10^{6} | c_{35} | −7.216 × 10^{−2} |

c_{6} | 2.225 × 10^{−4} | c_{16} | −2.420 × 10^{−2} | c_{26} | −2.958 × 10^{6} | c_{36} | 8.980 × 10^{−2} |

c_{7} | 1.697 × 10^{2} | c_{17} | 6.718 × 10^{−3} | c_{27} | 5.998 × 10^{5} | c_{37} | 7.613 × 10^{−1} |

c_{8} | −1.007 × 10^{3} | c_{18} | −20.00 | c_{28} | −3.102 × 10^{4} | c_{38} | 10.14 |

c_{9} | 1.408 × 10^{3} | c_{19} | −5.967 × 10^{−4} | c_{29} | 2.232 × 10^{3} | c_{39} | 2.608 × 10^{2} |

c_{10} | 3.897 × 10^{2} | c_{20} | 6.993 × 10^{−1} | c_{30} | 3.128 × 10^{3} |

© 2016 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alhanouti, M.; Gießler, M.; Blank, T.; Gauterin, F.
New Electro-Thermal Battery Pack Model of an Electric Vehicle. *Energies* **2016**, *9*, 563.
https://doi.org/10.3390/en9070563

**AMA Style**

Alhanouti M, Gießler M, Blank T, Gauterin F.
New Electro-Thermal Battery Pack Model of an Electric Vehicle. *Energies*. 2016; 9(7):563.
https://doi.org/10.3390/en9070563

**Chicago/Turabian Style**

Alhanouti, Muhammed, Martin Gießler, Thomas Blank, and Frank Gauterin.
2016. "New Electro-Thermal Battery Pack Model of an Electric Vehicle" *Energies* 9, no. 7: 563.
https://doi.org/10.3390/en9070563