New Electro-Thermal Battery Pack Model of an Electric Vehicle

energies

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

Muhammed Alhanouti 1,*, Martin Gießler 1, Thomas Blank 2 and Frank Gauterin 1

1 Institute of Vehicle System Technology, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany; [email protected] (M.G.); [email protected] (F.G.) 2 Institute of Data Processing and Electronics, Eggenstein-Leopoldshafen 76344, Germany; [email protected] * Correspondence: [email protected]; Tel.: +49-721-608-45328

Academic Editor: Michael Gerard Pecht Received: 30 May 2016; Accepted: 12 July 2016; Published: 20 July 2016

Abstract: Since the evolution of the electric and hybrid vehicle, the analysis of batteries’ characteristics and inﬂuence on driving range has become essential. This fact advocates the necessity of accurate simulation modeling for batteries. Different models for the Li-ion battery cell are reviewed in this paper and a group of the highly dynamic models is selected for comparison. A new open circuit voltage (OCV) model is proposed. The new model can simulate the OCV curves of lithium iron magnesium phosphate (LiFeMgPO4) 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.

Keywords: temperature inﬂuence; new OCV model; battery circuit model; synthesized battery model; thermal model; electric vehicle

1. Introduction The global climate change, escalation in fuel cost, and the energy consumption, urged the necessity to replace the fossil fuel with renewable and environment friendly energy sources. Battery electric vehicles (BEV) are one major application, demonstrating the replacement of fossil fuel by renewable energy. Li-ion batteries have become the preferable energy storage for the future electric vehicles [1]. They receive greater attention than other battery types, such as lead-acid and nickel-cadmium batteries, due to their practical physical characteristics. They have a high specific energy, specific power, power density and a long life cycle. Moreover, their self-discharge rate is lower compared to other types of batteries [1–3]. Figure1 demonstrates a typical discharge characteristic curve of a lithium-ion battery. The battery voltage extends between an upper and lower voltage limits Vfull and Vcut-off, respectively. Vcut-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 Vfull, Vexp and the correspondences capacity rates (C-rate) 0 and Qexp 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 Qexp up to the nominal C-rate Qnom, where the nominal Vnom voltage is reached. Not only is the battery voltage

Energies 2016, 9, 563; doi:10.3390/en9070563 www.mdpi.com/journal/energies Energies 2016, 9, 563 2 of 17

Energies 2016, 9, 563 2 of 18 inﬂuencedinfluenced by the by the discharge discharge rate, rate, but but the the battery battery capacity is is also also diminished diminished at high at high discharge discharge rates. rates. This occursThis occurs as a sharpas a sharp voltage voltage drop drop at the at the end end of theof the discharge discharge process, process, as as indicated indicated inin FigureFigure 11.. AtAt that rate thethat discharge rate the discharge terminates terminates at Vcut-off at V[cut4‐].off [4].

Figure 1. Typical discharge characteristic curve of Li‐ion battery [4,5]. Figure 1. Typical discharge characteristic curve of Li-ion battery [4,5].

The vehicle under test (VUT) is equipped with battery cells of a cathode type LiFeMgPO4. TheLithium vehicle iron phosphate under test cells (VUT) are characterized is equipped by with their flat battery open cellscircuit of voltage a cathode curve (OCV). type LiFeMgPO Hence, 4. Lithiumthe cell iron voltage phosphate stays almost cells areconstant characterized over the complete by their state ﬂat of open charge circuit (SOC) voltage range [2,3,6]. curve The (OCV). Hence,battery the cell pack voltage of the VUT stays consists almost of constant19 modules. over Each the module complete comprises state ofsix charge cell blocks (SOC) connected range in [2 ,3,6]. The batteryseries; a pack single of cell the block VUT is consists constructed of 19 out modules. of 50 LiFeMgPO Each module4–graphite comprises cells, connected six cell blocksin parallel. connected In total, there are 300 cells within the single battery module. Each cell block has a nominal voltage of 3.2 in series; a single cell block is constructed out of 50 LiFeMgPO –graphite cells, connected in parallel. V, amounting to a total voltage of 19.2 V. The battery specifications4 are given in Table 1. A Controller In total,Area there Network are 300 (CAN) cells communication within the single environment battery module. is used for Each the cell control block and has management a nominal of voltage the of 3.2 V,battery amounting modules. to a totalMore voltagetechnical of information 19.2 V. The about battery the speciﬁcations VUT is available are in given the Appendix. in Table1 . A Controller Area Network (CAN) communication environment is used for the control and management of the battery modules. More technicalTable information 1. Technical aboutdata of LiFeMgPO the VUT4 is Battery available [7]. in the Appendix. Parameter (Unit) Value Table 1. Technical data of LiFeMgPO Battery [7]. Nominal Module Voltage (V) 4 19.2 Nominal Module Capacity (Ah) 69 Max ContinuousParameter Load (Unit) Current (A) Value120 NominalPeak Current Module for Voltage 30 s (A) (V) 19.2200 Nominal Module Capacity (Ah) 69 In this paper, we willMax investigate Continuous the Loaddifferent Current battery (A) modeling120 methods to decide which approach will be the most appropriatePeak Current for modeling for 30 s the (A) battery pack 200 of VUT. Then, we will select a group of the most thorough models for Li‐ion batteries. These models will contribute to the Indevelopment this paper, of we the will proposed investigate battery the model, different which battery will modeling be considered methods for modeling to decide actual which battery approach pack voltage response when the VUT undergoes severe driving maneuvers. will be the most appropriate for modeling the battery pack of VUT. Then, we will select a group of the The paper is organized as follows. Section 2 presents the different modeling techniques of Li‐ion most thorough models for Li-ion batteries. These models will contribute to the development of the batteries. Three models are elected from the reviewed models and are discussed in more details in proposedSection battery 3. In Section model, 4 which the thermal will be behavior considered of the for battery modeling is elaborated. actual battery The experimental pack voltage tests response are whendescribed the VUT in undergoes Section 5. severe The models driving are maneuvers. evaluated and a new, improved model is developed and Theproposed paper in is Section organized 6. Finally, as follows. the conclusions Section2 are presents stated at the the different end of the modeling paper. techniques of Li-ion batteries. Three models are elected from the reviewed models and are discussed in more details in Section 3. In Section4 the thermal behavior of the battery is elaborated. The experimental tests are described in Section5. The models are evaluated and a new, improved model is developed and proposed in Section6. Finally, the conclusions are stated at the end of the paper. Energies 2016, 9, 563 3 of 17

2. Existing Battery Models Different modeling approaches are found in the literature. The most prominent battery modeling techniques are: Electrochemical, analytical, and circuit-based models [8]. Electrochemical models employ non-linear differential equations to model the chemical and electrical behavior of the cell [4,9]. Detailed knowledge of the battery chemistry, material structure and other physical characteristics are essential to achieve high accuracy and cover a large number of different operating points. However, the producers of batteries will rarely reveal the full parameters set of their products. Another shortcoming of electrochemical models is the high computational effort required to solve the non-linear partial differential equations [8]. Electrochemical models are better suited for research in battery’s components fabrication, like electrodes and electrolyte [4,10]. The analytical modeling, on the other hand, reduces the computational complexity for the battery. However, that would be on the expense of capturing the circuit physical features of the battery, such as open circuit voltage, output voltage, internal resistance, and transient response [8]. Lumped electrical circuit models offer low complexity combined with high accuracy and robustness in simulating batteries dynamics [11–13]. Models with single or double resistor-capacitor (RC) networks are the best candidates for simulating the battery module [12–14]. RC parameters employed to model the battery characteristic show a dependency on temperature, charge/discharge rates and the SOC. Several techniques had been discussed in literature [1,15–19] for SOC estimation. Lam and Bauer [20] proposed a circuit model for the Li-ion battery with variable open circuit voltages, resistances and capacitances. The equivalent circuit components were represented as empirical functions of the current direction, the SOC, the battery temperature and the C-rate. Tremblay et al. [5,21] proposed an improved version Shepherd’s model [22]. This model considers the influence of SOC on the OCV by considering the polarization voltage in the discharge-charge model. Different dynamic models for Li-ion, lead-acid, NiMH and NiCd battery typed were presented in Reference [5]. However, neither the temperature effect nor the variation of the internal resistance were considered. Saw et al. [23] investigated the thermal behavior for a LiFePO4–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 [25–28]. Additionally, finite element analysis models to estimate the temperature distribution in the battery were presented in References [25,27–29]. 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 The equivalent circuit battery model provides a generic, dynamic way of modeling Li-ion batteries with moderate complexity. The moderate model complexity supports the integration of the model in a multiphysical simulation, allowing to analyze dynamic effects of the electric drive train. Three models are selected from the literature as the best candidates for Li-ion battery modeling, since they are the most thorough among the reviewed models. These models are: Energies 2016, 9, 563 4 of 17

Energies 2016, 9, 563 4 of 18 ‚ Tremblay et al. [5] (battery model 1)  Tremblay et al. [5] (battery model 1) ‚ Lam and Bauer [20] (battery model 2)  Lam and Bauer [20] (battery model 2) ‚ Wijewardana Wijewardana et al. et al. [1] [1] (battery (battery model model 3) 3)

3.1. Tremblay3.1. Tremblay Battery Battery Model Model (Battery (Battery Model Model 1) 1) TremblayTremblay and and Dessaint Dessaint [5] improved[5] improved their their own own model model in Referencein Reference [21 [21].]. The The new new model model is is shown in Figureshown2. in Only Figure three 2. Only points three on points the on steady the steady state state manufacturer’s manufacturer’s discharge discharge curvecurve are are required required to parametrizeto parametrize the model, the model, which which are the are fullthe full voltage, voltage, the the end end point point of of exponential exponential voltage voltage region, region, and and the the nominal voltage. The variation of the OCV from a reference constant voltage (E0) is related to SOC nominal voltage. The variation of the OCV from a reference constant voltage (E0) is related to SOC changeschanges by incorporating by incorporating a polarizationa polarization constant constant ( (KK).).

FigureFigure 2. 2.Tremblay Tremblay andand Dessaint battery battery discharge discharge model. model.

In case of discharging the output voltage reads: In case of discharging the output voltage reads: ∗ ∙ ∙ ∙ (1) Q V “ E ´ R ¨ i ´ K ¨ pit ` i˚q ` Ae´B ¨ it (1) and for charging, the equationbatt becomes:0 Q ´ it and for charging, the equation becomes:∙ ∙∗ ∙∙ (2) 0.1 the variables and constants in Equations (1) andQ (2) are defined Qin Table A1 in the Appendix A. V “ E ´ R ¨ i ´ K ¨ i˚ ´ K ¨ it ` Ae´B ¨ it (2) Although, thebatt charging0 and dischargingit ´ 0.1 characteristicsQ Q are´ itextensively modeled, some other influential factors like the variations in internal resistance (R) and temperature influence are not the variablesconsidered. and The constants capacity fading in Equations effect is (1)not and taken (2) into are account defined in in this Table model A1 as in well. the Appendix A.1. Although, the charging and discharging characteristics are extensively modeled, some other influential3.2. Lam factors and Bauer like Battery the variationsModel (Battery in Model internal 2) resistance (R) and temperature influence are not considered.The TheLam capacity and Bauer fading battery effect equivalent is not taken circuit into model account is inshown this model in Figure as well. 3. The model demonstrates the VOC as a function of SOC, a variable ohmic resistance Ro, and two variable 3.2. LamRC‐networks: and Bauer R BatterySCS and ModelRlCl for (Battery the short Model and 2)the long time transient responses, respectively. Lam andThe Bauer Lam and also Bauer showed battery the relation equivalent between circuit capacity model isfading shown due in Figureto aging3. Theand modeldifferent demonstrates stress influences, which are the cell’s temperature, C‐rate, SOC and intensity of discharge. Lam and Bauer the V as a function of SOC, a variable ohmic resistance Ro, and two variable RC-networks: R C parametrizedOC their equations through curve fitting of experimental measurements. They employed S S and RlCl for the short and the long time transient responses, respectively. Lam and Bauer also showed in their tests the LiFePO4 battery cell. The equivalent circuit resistors and capacitors equations for the relationtemperatures between from capacity 20 °C and fading above are due detailed to aging in andEquations different (7)–(28) stress in Reference influences, [20]. which We refer are also the cell’s temperature,to the VOC C-rate,equation SOC with andthe corrected intensity constants of discharge. as proposed Lam andin Reference Bauer parametrized [20]: their equations through curve fitting of experimental measurements. They employed in their tests the LiFePO4 battery . ˝ (3) cell. The equivalent circuitSOC resistors 0.5863 and capacitors 3.414 equations 0.1102 for SOC temperatures 0.1718 from 20 C and above are detailed in Equations (7)–(28) in Reference [20]. We refer also to the VOC equation with the corrected constants as proposed in Reference [20]:

´3 ´21.9 SOC ´ 8ˆ10 VOC pSOCq “ ´0.5863 e ` 3.414 ` 0.1102 SOC ´ 0.1718 e 1´SOC (3) Energies 2016, 9, 563 5 of 17 Energies 2016, 9, 563 5 of 18

Energies 2016, 9, 563 5 of 18

Figure 3. Lam and Bauer battery circuit model. Figure 3. Lam and Bauer battery circuit model.

3.3. Wijewardana Battery Model Figure 3. Lam and Bauer battery circuit model. 3.3. Wijewardana Battery Model A different perception, than the two previous models, is adopted in this model. The electrical A3.3.components, different Wijewardana perception, RS Battery, CS, RL ,Model C thanL are functions the two previousof SOC and models, independent is adopted of the temperature. in this model. Only Thethe series electrical internal resistance resistor is a function of SOC and temperature (RintS(SOC,T)). The temperature components,A differentRS, CS, Rperception,L, CL are functionsthan the two of SOCprevious and models, independent is adopted of the in this temperature. model. The Only electrical the series influence is considered by adding potential correction terms, which are voltage due to electrode film internalcomponents, resistance RS resistor, CS, RL, C isL are a function functions of SOC SOC and and independent temperature of the (R temperature.intS(SOC,T)). Only The the temperature series formation (ΔE) and voltage due to electrolyte electrons transfer formation (ΔVChe). The capacity inﬂuenceinternal is considered resistance resistor by adding is a potentialfunction of correction SOC and temperature terms, which (R areintS(SOC, voltageT)). The due temperature to electrode ﬁlm influencefading effect is considered is modeled by as adding an additional potential series correction resistance terms, Rcyc which. The battery are voltage output due voltage to electrode is computed film formationby subtracting (∆E) and the voltage voltage due drop to of electrolyte each circuit electrons element from transfer the V formationOC value. Figure (∆V Che4 demonstrates). The capacity formation (ΔE) and voltage due to electrolyte electrons transfer formation (ΔVChe). The capacity fading effectWijewardana is modeled battery as model. an additional series resistance Rcyc. The battery output voltage is computed fading effect is modeled as an additional series resistance Rcyc. The battery output voltage is computed by subtracting the voltage drop of each circuit element from the V value. Figure4 demonstrates by subtracting the voltage drop of each circuit element from the VOCOC value. Figure 4 demonstrates WijewardanaWijewardana battery battery model. model.

Figure 4. Wijewardana battery circuit model.

The battery output voltage of this model reads [1]: FigureFigure 4. 4.Wijewardana Wijewardana battery circuit circuit model. model. ∆ ∆ (4) The battery output voltage of this model reads [1]: The battery output voltage of this∆ model 1 reads∆ [1]: ∆ ∆ ∆ (5) (4) “ ´ ` ´ ´ ´ p q ´ p q Vbatt VOC i RintS⁄ RcycV1 V2 ∆E T ∆VChe T (4) ∆ β ∆ ∆1 ∆ ∆ ∆1β∆ (5)(6) ` ˘ dVr ∆E pTq “⁄ p1 ` C ∆Tq ∆T (5) The values of the∆ model β parameters are ∆ listed inE1 the Appendix A. ∆1β∆ dT T“T (6) ˇ cell ˇ 3.4. Assessment of Battery Models Qualities The values of the model parameters are listeddV in the Appendixˇ A. ∆V pTq “ βw expp´1{tq∆T ` Che pˇC ` C ∆Tq p1 ` βq ∆T (6) Three Chedifferent highly dynamic to modeldT Li‐ion batteriesChe have beenChe1 proposed. Each model has ˇT“Tcell 3.4.its Assessmentdominant features.of Battery Table Models 2 Qualitiessummaries the qualitiesˇ of each model. The (+) sign implies that the The values of the model parameters are listed in theˇ Appendix. correspondedThree different feature highly is considereddynamic to modelin the Limodel.‐ionˇ batteries Whereas, have a been(++) proposed.sign denotes Each an model extensive has consideration to the related feature. In contrast, the (‐) sign means that the related feature was 3.4. Assessmentits dominant of Batteryfeatures. Models Table 2 Qualities summaries the qualities of each model. The (+) sign implies that the correspondedassigned as a featureconstant is or considered it is not considered in the model. at all inWhereas, the model. a (++) Battery sign modeldenotes 2 considersan extensive more Threeconsiderationfactors different than theto highly theother related models. dynamic feature. However, to modelIn contrast, each Li-ion model the batteries (must‐) sign be means haveevaluated beenthat with the proposed. relatedexperimental feature Each data model was to has its dominantassignedinvestigate features.as aits constant accuracy. Table or it2 issummaries not considered the qualitiesat all in the of model. each model.Battery model The (+)2 considers sign implies more that the correspondedfactors than the feature other models. is considered However, in each the model model. must Whereas, be evaluated a (++) with sign experimental denotes andata extensive to considerationinvestigate to its the accuracy. related feature. In contrast, the (-) sign means that the related feature was assigned as a constant or it is not considered at all in the model. Battery model 2 considers more factors than the other models. However, each model must be evaluated with experimental data to investigate its accuracy. Energies 2016, 9, 563 6 of 17

Table 2. Comparison between the battery models.

Feature Battery Model 1 Battery Model 2 Battery Model 3 Charge-Discharge Considered in the Considered in the internal ++ + - Charge-discharge hysteresis output voltage resistance (R) equations Open circuit voltage - Constant value for E0 + VOC(SOC) + VOC(SOC) Internal resistance (R) - Constant value ++ R(SOC,T,C-rate) + R(SOC,T) Temperature Considered in the internal Considered as potential - Not considered + + inﬂuence resistance model correction terms Considered in the Considered in the battery’s Capacity fading - Not considered + + battery’s internal used capacity estimation resistance (R) estimation Total Assessment 2 6 4

4. Battery Thermal Model A general energy balance is applied to estimate the battery cell temperature. It is assumed that the thermal distribution inside the cell is uniform and that the conduction resistance inside the battery cell is negligible compared with the convection and radiation heat transfer [1,23,27,28]. The change in temperature depends signiﬁcantly on the battery thermal capacity (Cp) 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:

dT mC cell “ i pV ´ V q ´ hA ∆T ´ σA T4 ´ T4 (7a) p dt OC batt cell cell cell amp ´ ¯ where ∆T is the difference between the battery cell and the ambient temperatures (Tcell ´ Tamp), h is the natural convection coefﬁcient, m is the cell mass, i is the cell current, Acell 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:

dT MC cell “ I pV ´ V q ´ hA∆T ´ σA T4 ´ T4 (7b) p dt OC batt cell amp ´ ¯ where M is the total cells mass, I is the battery current, A is the surface area of the cells blocks in the single battery module. Saw et al. [23] has pointed out to the contribution of the contact resistance in heat generation. The contact resistance can be neglected in the investigated batteries, since the cells are realizing low ohmic over wide cell connectors by means of welded connections. Fifty individual cells are connected in parallel and we have a nominal current about 1.4 A per cell. The resistance of the single contact is 0.2 mΩ. With four welding points per cell connectors, the contact resistance for the single battery cell became 50 µΩ. The power loss in the single cell due to contact resistance is determined as: 2 Ploss = Icell Rcontact = 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

In order to characterize the LiFeMgPO4-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. Figure5 demonstrates the charge and discharge OCV curves Energies 2016, 9, 563 7 of 17 over the SOC for various temperatures. It is noticeable that the lower the operating temperatures, the higherEnergies the 2016 difference, 9, 563 between charging and discharging. 7 of 18

Energies 2016, 9, 563 7 of 18 OCV[V] OCV[V]

Figure 5. Charge and discharge OCV curves over SOC. Figure 5. Charge and discharge OCV curves over SOC. 5.2. Driving Tests on the Real Vehicle 5.2. DrivingThe Tests objective on the Realof a real Vehicle test is to find a real driving maneuver reference signal to validate the Thebattery objective model of performance. a real testFigure Nevertheless, is 5. to Charge find and a the real discharge battery driving OCV model maneuvercurves should over SOC.be reference able to simulate signal the to actual validate the system in real operating conditions, not merely charging‐discharging cycles. Two driving tests were battery model performance. Nevertheless, the battery model should be able to simulate the actual performed5.2. Driving with Tests the on thetest Real vehicle Vehicle for the purpose of investigation the system and collecting the system in real operating conditions, not merely charging-discharging cycles. Two driving tests experimentalThe objective data. The of a tests real were test isexecuted to find ona real the drivingtesting groundmaneuver at Karlsruhe reference Institutesignal to ofvalidate Technology the were performed(KIT).battery The model experimental with performance. the test data vehicle Nevertheless,attained for from the the the purpose battery CAN bus model of investigationare shoulddisplayed be ablein the Figures to system simulate B1 and and the B2 actual collecting in the the experimentalAppendixsystem data. in B. real Then, The operating tests the data were conditions, were executed processed not merely on in the MATLAB. charging testing‐discharging In ground the first at test,cycles. Karlsruhe the Two vehicle driving Institute was tests driven of were Technology in a (KIT). Thecounterclockwiseperformed experimental with circularthe data test direction attainedvehicle for for from the about purpose the 230 CAN s. ofThen businvestigation the are direction displayed the for system driving in Figuresand was collecting reversed A1 and the and A2 in the the test was resumed. A variable pedal input was implemented in order to cover a broader range of Appendixexperimental A.2. Then, data. the The data tests were were executed processed on the in testing MATLAB. ground In at Karlsruhe the first Institute test, the of vehicle Technology was driven data.(KIT). This The test experimental represents andata aggressive attained fromdriving the scenario, CAN bus leading are displayed to discharge in Figures rate ofB1 up and to B2 3.4 in C. the The in a counterclockwise circular direction for about 230 s. Then the direction for driving was reversed secondAppendix test B.was Then, implemented the data were by processedsubjecting in the MATLAB. vehicle toIn athe sequence first test, of the sudden vehicle accelerations was driven in and a and thedecelerations. testcounterclockwise was resumed. These circular tests A variable were direction performed pedal for about inputthis 230 way wass. toThen create implemented the highlydirection fluctuating for in driving order signals towas cover reversed in the a broaderbattery and range of data.system, Thisthe test test which was represents resumed. are shown A an variable in aggressive Figure pedal 6. inputThe driving dynamic was implemented scenario, responses leading in of order battery to cover discharge voltage a broader can rate be range used of upof to to 3.4 C. The secondevaluatedata. test This the was test battery represents implemented models, an discussedaggressive by subjecting above. driving scenario, the vehicle leading to to discharge a sequence rate of up sudden to 3.4 C. accelerations The and decelerations.second test was These implemented tests were by subjecting performed the thisvehicle way to a to sequence create highlyof sudden fluctuating accelerations signals and in the decelerations.250 These tests were performed this way to create380 highly fluctuating signals in the battery battery system, which are shown in Figure6. The dynamic responses of battery voltage can be used to system,200 which are shown in Figure 6. The dynamic 370responses of battery voltage can be used to 150 evaluateevaluate the battery the battery models, models, discussed discussed above. above. 360 100 350 50250 380 340 2000 370 330

Battery pack current [A] 150 -50 Battery pack voltage [V] 360 -100100 320 0 50 100 150 200 250 300 350 3500 50 100 150 200 250 300 350 50 Time[s] Time[s] 340 0 (a) (b) 330 Battery pack current [A] -50250 Battery pack voltage [V] 380

-100 320 2000 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time[s] 370 Time[s] 150 (a) 360 (b) 100250 380 350 50200 370 Battery current [A] Battery voltage [V] 1500 340 360 -50100 330 0 50 100 150 200 0 50 100 150 200 Time[s] 350 Time[s] 50 Battery current [A] (c) Battery voltage [V] (d) 0 340

Figure-50 6. CAN bus measurements: (a) Battery pack current330 for the circular driving test; (b) Battery 0 50 100 150 200 0 50 100 150 200 pack voltage for the circularTime[s] driving test; (c) Battery pack current for theTime[s] rapid acceleration and deceleration driving (test;c) (d) Battery pack voltage for the rapid acceleration(d) and deceleration drivingFigure test. 6. CAN bus measurements: (a) Battery pack current for the circular driving test; (b) Battery Figure 6. CAN bus measurements: (a) Battery pack current for the circular driving test; (b) Battery pack pack voltage for the circular driving test; (c) Battery pack current for the rapid acceleration and voltage fordeceleration the circular driving driving test; test;(d) Battery (c) Battery pack packvoltage current for the for rapid the rapidacceleration acceleration and deceleration and deceleration driving test;driving (d) test. Battery pack voltage for the rapid acceleration and deceleration driving test.

Energies 2016, 9, 563 8 of 17

6. Battery Models Validation

6.1. Evaluating the Open Circuit Voltage Models (VOC) Wijewardana et al. [1] have employed a common model for VOC that is widely used and found in literature. Lam and Bauer [20] have redefined the model equation to suit the LiFeMgPO4 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 LiFeMgPO4 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 LiFeMgPO4-cathode type. Its OCV curves are presented earlier in Figure6. 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. We validated both VOC models in References [1,20] by comparing the simulation results with our own measurements, as shown in Figure7. We selected the charge-discharge curves at T = 20 ˝C to be the references for validation. The VOC model utilized in battery model 3 does not fit our measurements. The VOC 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. The influence of the temperature variation on the OCV curves is defined as dVOC{dT. From the measurements shown in Figure6, the value of this term was found to be 1.25 mV in case of discharge and 0.69 mV for charging. The VOC model 2 model is modified for better fitting of the OCV curve along the SOC range and the temperature influence is considered. The new VOC is modeled by Equations (8) and (9) and the constants values of the new VOC are presented in Table3. The validation results are shown in Figure8 and in Table4.

a6 ´a2SOC ´ ´ VOC,discharge pSOC, Tq “ a1 e ` a3 ` a4 SOC ` a5 e 1 SOC ` T dVOC,d{dT (8)

b6 ´b2SOC ´ ´ VOC,charge pSOC, Tq “ b1 e ` b3 ` b4 SOC ` b5 e 1 SOC ` T dVOC,c{dT (9)

Table 3. VOC parameter values.

Constant Value Constant Value

a1 ´1.166 b1 ´0.9135 a2 ´35 b2 ´35 a3 3.344 b3 3.484 a4 0.1102 b4 0.1102 a5 ´0.1718 b5 ´0.1718 ´3 ´3 a6 ´2 ˆ 10 b6 ´8 ˆ 10 dVOC,d/dT 0.00125 dVOC,c/dT 0.00069

6.2. Evaluating the Battery Models Output Voltage The accuracy of each model is yet to be proved. For objective comparison, the thermal model elaborated in Section4 is employed for all models. The battery currents in Figure6a,c are designated as the inputs for all models and the output voltage of each model is investigated against the voltage response signal, shown in Figure6b,d. The VOC of model 3 [1] showed a large deviation from the actual curve, as shown in Figure7. Therefore, the VOC derived from model 2 [20] will be also utilized in model 3. Figures9 and 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 Energies 2016, 9, 563 9 of 17 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 Energies 2016, 9, 563 9 of 18 ascribedEnergies to 2016 the, 9 fact, 563 that the test conditions were nearly matching the standard condition for9 defining of 18 the constant voltage (E ). E is equal to the nominal voltage at 20 ˝C, which is equal to 3.21 V and the ascribed to the fact 0that the0 test conditions were nearly matching the standard condition for defining initialascribed voltage to ofthe the fact single that the battery test conditions cell is estimated were nearly as 3.25matching V. When the standard the test condition second driving for defining test was the constant voltage (E0). E0 is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the the constant voltage (E0). E0 is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the performedinitial atvoltage different of the circumstances, single battery cell the is outcomeestimated as was 3.25 not V. asWhen good the as test it second in the firstdriving case. test Figure was 10a initial voltage of the single battery cell is estimated as 3.25 V. When the test second driving test was revealsperformed a relatively at different large offset circumstances, error in the the response outcome ofwas battery not as modelgood as 1 it with in the a first mean case. square Figure error 10a (MSE) performed at different circumstances, the outcome was not as good as it in the first case. Figure 10a of aboutreveals 2.24%. a relatively Model 2 large performed offset error moderately in the response with percentage of battery model errors 1 between with a mean 1% and square 2%. error The offset reveals a relatively large offset error in the response of battery model 1 with a mean square error errors(MSE) between of about the reference 2.24%. Model signal 2 performed and initial moderately voltage value with of percentage both battery errors models between 2 and 1% and 3 were 2%. minor, (MSE)The offsetof about errors 2.24%. between Model the 2 referenceperformed signal moderately and initial with voltage percentage value errorsof both between battery 1%models and 2%.2 whereas Equation (3) is employed in both models for the estimation of VOC. The simulation results of Theand offset 3 were errors minor, between whereas the Equation reference (3) signalis employed and initial in both voltage models value for the of estimation both battery of V modelsOC. The 2 model 3 indicate less dynamic response than the other two models. It could not conduct the drastic andsimulation 3 were minor, results whereasof model Equation3 indicate (3)less is dynamic employed response in both than models the other for thetwo estimation models. It couldof VOC not. The changessimulationconduct in the the results battery drastic of current changesmodel 3 inputin indicate the signal.battery less currentdynamic input response signal. than the other two models. It could not conduct the drastic changes in the battery current input signal. 4.5

4.5 4 4 3.5

3.5

OCV[V] 3

OCV[V] 3 Discharge measured at T=20°C 2.5 Charge measured at T=20°C VocDischarge of battery measured model 2 at T=20°C 2.5 VocCharge of battery measured model at 3 T=20°C 2 0 20 40 Voc60 of battery model80 2 100 SOC[%] Voc of battery model 3 2 0 20 40 60 80 100 SOC[%] FigureFigure 7. Comparing 7. Comparing the theV Vococ modelmodel with with measured measured experimental experimental results. results. Figure 7. Comparing the Voc model with measured experimental results. Table 4. Accuracy of the proposed VOC model. Table 4. Accuracy of the proposed VOC model. Temperature °C TableMSE 4. Accuracy in Discharge of the Model proposed % VOC MSEmodel. in Charge Model % 10 0.5232 0.8914 Temperature ˝C MSE in Discharge Model % MSE in Charge Model % Temperature20 °C MSE in Discharge0.5320 Model % MSE in 0.5719Charge Model % 101040 0.52320.52320.5751 0.4522 0.89140.8914 2020 0.53200.5320 0.57190.5719 4040 0.57510.5751 0.45220.4522

(a) (b)

(c)

Figure 8. The new Voc model and measured experimental data: (a) T = 10 °C; (b ) T = 20 °C; (c) T = 40 °C. (c)

Figure 8. The new Voc model and measured experimental data: (a) T = 10 °C; (b) T = 20 °C; (c) T = 40 °C. Figure 8. The new Voc model and measured experimental data: (a) T = 10 ˝C; (b) T = 20 ˝C; (c) T = 40 ˝C.

Energies 2016, 9, 563 10 of 18 Energies 2016, 9, 563 10 of 17

Energies 2016, 9, 563 10 10 of 18 MSE = 0.9453%

105 MSE = 0.9453%

50 Error [%] Error 0 -5 Error [%] Error

Battery pack voltage [V] pack voltage Battery -5 -10 0 50 100 150 200 250 300 350 Battery pack voltage [V] pack voltage Battery Time[s] -10 0 50 100 150 200 250 300 350 (a) Time[s](b)

(a) 10 (b) MSE = 1.75% 10 MSE = 1.75% 5 5 0 0 Error [%]Error

Error [%]Error -5 -5

-10 -10 0 50 100 150 200 250 300 350 0 50 100 150 200Time[s]250 300 350 Time[s] (d) (c()c ) (d) 10 10 MSEMSE = 1.7841% = 1.7841%

00 Error [%] Error Error [%] Error -5-5 Battery pack voltage [V] pack voltage Battery Battery pack voltage [V] pack voltage Battery -10 -100 50 100 150 200 250 300 350 0 50 100 150Time[s]200 250 300 350 Time[s] (e) (f) (e) (f) Figure 9. Battery simulation models and reference voltage signal for circular driving test: (a) Battery FigureFigure 9. 9.Battery Battery simulation simulation modelsmodels andand reference voltage signal signal for for circular circular driving driving test: test: (a ()a Battery) Battery model 1 response; (b) Mean square error of battery model 1; (c) Battery model 2 response; (d) Mean modelmodel 1 1 response; response; ( b(b)) Mean Mean squaresquare errorerror of battery model 1; 1; ( (cc)) Battery Battery model model 2 2 response; response; (d (d) )Mean Mean square error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3. squaresquare error error of of batterybattery model 2; 2; ( (ee) )Battery Battery model model 3 response 3 response (f) (Meanf) Mean square square error error in battery in battery model model 3. 3.

10 MSE = 2.2373% 10 MSE = 2.2373% 5 5 0

Error [%] 0 Battery voltage [V] voltage Battery -5 Error [%]

Battery voltage [V] voltage Battery -5 -10 0 50 100 150 200 Time[s] -10 (a) 0 50 (b) 100 150 200 Time[s] 10 (a) (b) MSE = 1.0347%

510 MSE = 1.0347%

05 Error [%] Battery voltage [V] -50 Error [%]

Battery voltage [V] -10 -50 50 100 150 200 Time[s] (c) (d) -10 0 50 100 150 200 Time[s] (c) (d)

Figure 10. Cont.

Energies 2016, 9, 563 11 of 17 Energies 2016, 9, 563 11 of 18

10 MSE = 1.5176% Energies 2016, 9, 563 11 of 18 5

10 MSE = 1.5176% 0

Error [%] 5 -5 0 Error [%] -10 0 50 100 150 200 -5 Time[s] (e) (f) -10 0 50 100 150 200 Figure 10. Battery simulation models and reference voltage signal for rapidTime[s] acceleration and Figure 10. Battery simulation(e) models and reference voltage signal for(f rapid) acceleration and deceleration driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1; deceleration driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1; (c) BatteryFigure model 10. Battery 2 response; simulation (d) Mean models square and errorreference of battery voltage model signal 2; (fore) Batteryrapid accelerationmodel 3 response and (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response (f) Meandeceleration square errordriving in batterytest: (a) modelBattery 3. model 1 response; (b) Mean square error of battery model 1; (f) Mean square error in battery model 3. (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response 6.3. The Proposed(f) Mean Synthesizedsquare error in Battery battery Model model 3. 6.3. The Proposed Synthesized Battery Model It6.3. is Theexplicable Proposed that Synthesized each model Battery has Model some flaws, as determined in Table 2. The simulation results It is explicable that each model has some ﬂaws, as determined in Table2. The simulation in Figures 9 and 10 prove that even the best performing models need to be further improved. It is explicable that each model has some flaws, as determined in Table 2. The simulation results resultsAccordingly, in Figures a synthesized9 and 10 prove model that that even holds the the best best performing qualities modelsof each needmodel to has be furtherbeen developed. improved. in Figures 9 and 10 prove that even the best performing models need to be further improved. Accordingly,First, the charge a synthesized‐discharge characteristics model that holds of model the best 1 are qualities considered. of each Additionally, model has the been discharging developed. First, theAccordingly, charge-discharge a synthesized characteristics model that of holds model the 1 best are considered.qualities of each Additionally, model has thebeen discharging developed. part part ourFirst, proposed the charge V‐OCdischarge(SOC,T )characteristics is employed ofinstead model of 1 constantare considered. (E0) value. Additionally, Then, the the highly discharging detailed our proposed VOC(SOC,T) is employed instead of constant (E0) value. Then, the highly detailed internal internalpart resistanceour proposed model VOC(SOC, of batteryT) is employed model instead2 in case of constant of discharging, (E0) value. Then,which the is highlyrepresented detailed by resistanceEquationsinternal model (7)–(11), resistance of battery(17)–(19), model model (21),of battery 2 (27) in case in modelReferance of discharging, 2 in [20],case isof which taking discharging, is the represented place which of the byis constantrepresented Equations internal (7)–(11), by (17)–(19),resistanceEquations (21),(R). The (7)–(11), (27) capacity in (17)–(19), Referance fading (21), effect [20 (27)], is is consideredin taking Referance the by [20], placeadding is taking of Rcyc the from the constant place battery of internalthemodel constant 3 to resistance the internal internal (R ). Theresistance. capacityresistance The fading (R empirical). The effect capacity isequations considered fading effect in bycase is addingconsidered of dischargingRcyc byfrom adding are battery R implementedcyc from model battery 3 to modelbecause the internal3 to the the charginginternal resistance. ‐ Thedischarging empiricalresistance. hysteresis equations The empirical is properly in case equations of modeled discharging in case by modelof aredischarging implemented1. The synthesized are implemented because model the because is charging-dischargingshown the in charging Figure 11.‐ hysteresisdischarging is properly hysteresis modeled is properly by model modeled 1. The by model synthesized 1. The synthesized model is shown model is in shown Figure in 11Figure. 11.

FigureFigureFigure 11. 11. The The proposed proposed proposed synthesized synthesized synthesized batterybattery battery model. model.

In caseIn caseof discharging, of discharging, the the output output voltage voltage reads: reads: In case of discharging, the output voltage reads: ∗ ∙ OC,dischargeSOC, ∙ ∙ ∗ ∙ (10) OC,dischargeSOC, ∙ ∙ (10) Q ˚ ´B ¨ it Vbatt “ VOC,discharge pSOC, Tq ´ RO ` Rcyc ` VS ` VL ¨ i ´ K ¨ pit ` i q ` Ae (10) and for charging, the equation expressed as: Q ´ it and for charging, the equation expressed` as: ˘ ∗ ∙ and for charging, OC,discharge the equationSOC, expressed as: ∙ ∙ ∙ (11) SOC, ∙ 0.1 ∙∗ ∙∙ (11) OC,discharge 0.1 Q ˚ Q ´B ¨ it Vwherebatt “ VOC,discharge pSOC, Tq ´ RO ` Rcyc ` VS ` VL ¨ i ´ K it´0.1Q ¨ i ´ K Q´it ¨ it ` Ae (11) where ` ˘ where (12) dVS i V S (12) “ ´ (12) dt C RC S S S (13) dV i V L “ ´ L (13)(13) dt CL RLCL

Energies 2016, 9, 563 12 of 17

The resistances and capacitors values are determined through Equations (14)–(18):

pc SOCq Rs pSOC, ϑq “ c1e 2 ` c3 ` c4SOC ` c5∆ϑ ` c6SOC∆ϑ (14) ´ ¯ 3 2 Cs pSOC, ϑq “ c7SOC ` c8SOC ` c9SOC ` c10 ` c11SOC∆ϑ ` c12∆ϑ (15) ´ ¯ Energies 2016, 9, 563 pc14SOCq pc18SOCq 12 ofc 2118 Rl pSOC, ϑ, IC´rateq “ pc13e ` c15 ` c16SOCq ` c17∆ϑe ` c19∆ϑ ˆ c20 pIC´rateq ` c22 (16) ´ ¯ The resistances6 and capacitors5 values are4 determined3 through Equations2 (14)–(18):` c {ϑ ˘ Cl pSOC, ϑq “ c23SOC ` c24SOC ` c25SOC ` c26SOC ` c27SOC ` c28SOC ` c29 ` c30 e 31 (17) SOC, SOC ∆ SOC ∆ (14) ´ ¯ 4 3 2 c {pϑ´c q Ro pSOC, ϑq “SOC,c32 SOC SOC` c33SOCSOC `c34SOCSOC `c35SOCSOC` ∆c36 c∆37e 38 39 (15) (18)

SOC, ,´ ˝ SOC ∆ ¯ ∆ where ϑ is the battery cell temperature in Kelvin ( K) and c1–c39 are constants, which(16) their values are listed in Table5. SOC, SOC SOC SOC SOC SOC SOC (17) / Table 5.Constants values of Equations (14)–(18).

/ SOC, SOC SOC SOC SOC (18) Constant Value Constant Value Constant Value Constant Value where ϑ is the battery cell temperature in Kelvin (°K) and c1–c39 are constants, which their values are ´2 ´1 3 c1 1.080 ˆ 10 c11 ´6.580 c21 ´6.919 ˆ 10 c31 ´2.398 ˆ 10 listed in Table 5. ´1 ´1 c2 ´11.03 c12 12.11 c22 2.902 ˆ 10 c32 1.298 ˆ 10 ´2 ´1 6 ´1 c3 1.827 ˆ 10 c13 2.950 ˆ 10 c23 2.130 ˆ 10 c33 ´2.892 ˆ 10 ´3 Table 5. Constants values of Equations (14)–(18). 6 ´1 c4 ´6.462 ˆ 10 c14 ´20.00 c24 ´6.007 ˆ 10 c34 2.273 ˆ 10 ´4 ´2 6 ´2 c5 Constant´3.697 ˆ 10Value c15Constant4.722 ˆValue10 Constantc25 6.271Valueˆ 10 Constantc35 Value´7.216 ˆ 10 ´4 −2 ´2 −1 6 3 ´2 c6 c2.2251 ˆ 101.080 × 10 c16 c11 −´2.420 ˆ6.58010 c26c21 −´6.9192.958 × 10ˆ 10 c31 −c36 2.3988.980 × 10 ˆ 10 −1 −1 c2 −211.03 c12 12.11´ 3 c22 2.902 × 10 5 c32 1.298 × 10 ´1 c7 1.697 ˆ 10 c17 6.718 ˆ 10 c27 5.998 ˆ 10 c37 7.613 ˆ 10 −2 −1 6 −1 c c´3 1.007 ˆ1.827103 × 10 c c13 ´2.95020.00 × 10 cc23 ´2.1303.102 × 10ˆ 104 c33 −c 2.892 × 1010.14 8 −3 18 28 6 38 −1 c4 −6.4623 × 10 c14 −20.00´ 4 c24 −6.007 × 10 3 c34 2.273 × 10 2 c9 1.408 ˆ 10 −4 c19 ´5.967 ˆ 10 −2 c29 2.232 ˆ 610 c39 2.608−2 ˆ 10 c5 −3.6972 × 10 c15 4.722 ×´ 101 c25 6.271 × 10 3 c35 −7.216 × 10 c 3.897 ˆ 10 −4 c 6.993 ˆ 10 −2 c 3.128 ˆ 106 −2 10 c6 2.225 × 10 20 c16 −2.420 × 10 30c26 −2.958 × 10 c36 8.980 × 10 2 −3 5 −1 c7 1.697 × 10 c17 6.718 × 10 c27 5.998 × 10 c37 7.613 × 10 3 4 c8 −1.007 × 10 c18 −20.00 c28 −3.102 × 10 c38 10.14 3 −4 3 2 The new modelc9 shows1.408 × a10 signiﬁcant c19 − improvement5.967 × 10 inc29 the simulation2.232 × 10 response,c39 as2.608 shown × 10 in Figure 12. 2 −1 3 The mean squarec10 error3.897 was × 10 reduced c20 to only6.993 0.256%. × 10 Thec30 new model3.128 × 10 shows also the best result when it employed for simulatingThe new model the shows rapid a accelerationsignificant improvement and deceleration in the simulation driving response, test, as though shown itin had a small Figure 12. The mean square error was reduced to only 0.256%. The new model shows also the best offset error atresult the when beginning it employed of for 3.2 simulating V. This errorthe rapid yielded acceleration from and an deceleration absolute driving voltage test, error though of 0.028 V in proposed VOCit had model, a small offset represented error at the beginning by Equation of 3.2 V. (8), This at error the yielded speciﬁed from an SOC absolute and voltage temperature error values. The battery modelsof 0.028 V are in simulatedproposed VOC in MATLAB/Simulinkmodel, represented by Equation environment. (8), at the Figure specified 13 showsSOC and the Simulink temperature values. The battery models are simulated in MATLAB/Simulink environment. Figure 13 model for the proposed battery model. shows the Simulink model for the proposed battery model.

10 MSE = 0.2559%

0 Error [%]Error -5

-10 0 50 100 150 200 250 300 350 Time[s] (a) (b)

10 MSE = 0.7862%

0 Error [%]

-5

-10 0 50 100 150 200 Time[s] (c) (d)

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. Energies 2016, 9, 563 13 of 18

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; Energies(c2016) Proposed, 9, 563 model response for the rapid acceleration and deceleration driving test; (d) Error of13 of 17 proposed model voltage for the rapid acceleration and deceleration driving test.

SOC0 3

K Ts z -K- f(u) z-1 OCV(SOC,T)_dis2 Gain4 Discrete-Time Integrator2 SOC U_R E0-R*i T[°C] 2 exp Actual battery e% Sim I_Crate Q(Capacitance) pack voltage PE Subsystem |u| -K- R I_cell Integrator Abs C-Rate Calculation Lam, Bauer 1/s it E_batt 6 RC Model Cell Blocks U Lowpass i* 19 Cells current Saturation Lowpass Filter number of 1 1/50 i Modules Measured battery pack current Discharge-Charge dynamics

V_cell

VOC

|u| i_cell Battery Temperature

4 Ambient Temp T_ambient 5 Tbatt0 T_Cell Battery Temperature Model

FigureFigure 13.13. The proposed synthesized battery simulation simulation model. model.

7.7. Conclusions AA battery is is a sophisticated a sophisticated system, system, which which necessitates necessitates a detailed a model detailed for accurate model for simulation. accurate simulation.Many factors Many must factors be considered must be consideredin the battery in themodel battery for accurate model for simulation accurate results. simulation Charging results.‐ Charging-dischargingdischarging dynamics, dynamics, battery internal battery resistance, internal resistance,and open circuit and open voltage circuit are voltagethe most are significant the most significantaspects for aspects battery for modeling. battery modeling. Temperature Temperature is an influential is an influential factor for factor all of for these all of aspects. these aspects. The Thedifference difference between between the the charging charging and and discharging discharging in inthe the OCV OCV curves curves increases increases at at low low temperatures. temperatures. ThisThis phenomenon phenomenon occurs occurs duedue toto thethe decrement in battery capacity, capacity, which which in in turn turn appears appears as as a a result result ofof a a rise rise of of the the internal internal resistance.resistance. Neglecting the effect of of temperature temperature will will lead lead to to inaccuracy inaccuracy in in simulation.simulation. EvenEven thethe slightestslightest errors in the simulation results results of of the the battery battery cell cell model, model, would would grow grow significantlysignificantly when when the the model model isis extendedextended to the complete battery battery pack. pack. Battery Battery model model 1 1 has has two two flaws. flaws. Firstly,Firstly, it it assumes assumes the the initial initial voltage voltage valuevalue toto be the nominal battery cell cell voltage. voltage. This This assumption assumption led led toto large large offset offset from from the the actual actual value,value, whenwhen the vehicle was tested tested at at about about 30 30 °C.˝C. Secondly, Secondly, it it considers considers aa constant constant internal internal resistance resistance of of the the battery, battery, which which is is in in fact fact a verya very fluctuating fluctuating quantity quantity that that affects affects the batterythe battery cell current cell current and the and voltage the response voltage asresponse well. The as proposed well. The battery proposed model battery has compensated model has for thesecompensated shortages for and these it has shortages accurately and simulated it has accurately the battery simulated pack voltage the battery response pack on voltage the real response vehicle. on the real vehicle. Author Contributions: Author Contributions:Muhammed Muhammed Alhanouti Alhanouti made made the literaturethe literature review review on the on current the current battery models,battery proposedmodels, the synthesized battery model, developing the simulation models, and wrote the paper. Martin Gießler and Thomasproposed Blank the synthesized designed and battery performed model, the developing battery measurements, the simulation andmodels, they and helped wrote in the editing paper. the Martin paper Gießler content. Frankand Thomas Gauterin Blank supervised designed the and work performed of this paper the battery and approved measurements, the results and they helped in editing the paper content. Frank Gauterin supervised the work of this paper and approved the results Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. Appendix

Appendix A.1. Nomenclature

Table A1. Battery models parameters.

Parameter (Unit) Symbol Value

Constant voltage (V) E0 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 Energies 2016, 9, 563 14 of 17

Table A1. Cont.

Parameter (Unit) Symbol Value 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 ∆V Variable formation Che the effective voltage gradient dVChe/dT 0.0016 [1] Constant property of electrolyte CChe 0.07 [1] Constant property of electrolyte CChe1 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 ∆E Variable voltage gradient dVr/dT 0.00003 [1] Constant property CE1 0.00011 [1] Battery module surface area (m2) A 0.283954 Battery cell mass (kg) m 0.04 [23] Battery module mass (kg) M 12 ´1 ´1 Speciﬁc heat capacity (J¨ kg ¨ K ) Cp 1360 [27] Stefane-Boltzmann constant (W¨ m´2¨ K4) σ 5.67 ˆ 10´8 Emissivity of heat ε 0.95 Natural heat convection constant (W¨ m´2¨ K´1) h 4

Appendix A.2. DrivingEnergies 2016 Tests, 9, 563 15 of 18 Appendix B. Driving Tests Car Speed [km/h] Battery current [A] Battery voltage [V] SOC [%] Battery temperature [°C] temperature

Figure B1. The measured data of the circular drive test. Figure A1. The measured data of the circular drive test.

Energies 2016, 9, 563 16 of 18 Car Speed [km/h] Speed

Energies 2016, 9, 563 15 of 17

Energies 2016, 9, 563 16 of 18 Battery current [A] Car Speed [km/h] Speed Battery Battery current [A] voltage [V] Battery voltage [V] SOC [%] SOC [%] Battery Battery temperature [°C] temperature [°C]

Figure B2. The measured data of the rapid acceleration and deceleration drive test. Figure A2.B2. TheThe measured measured data of the rapid acceleration and deceleration drive test. Appendix C. The Vehicle under the Test An electric hydrogen front wheel passenger car (Figure C1) was modified by the institute for Appendix A.3.C. The The“FAhrzeug Vehicle Vehicle ‐underSystemTechnik” under the the Test Test (FAST) of the Karlsruhe Institute of Technology to a battery electric vehicle (BEV), [30]. A battery pack was installed in the vehicle. This vehicle is used for research in An electricdifferent hydrogen automotive front engineering wheel and passenger e‐mobility related car (Figure projects. The A3C1) propulsion) was modified modiﬁed systems comprises by the institute for “FAhrzeug-SystemTechnik”“FAhrzeug‐SystemTechnik”an induction motor (FAST)with(FAST) a single ofof gear thethe transmission. KarlsruheKarlsruhe The motor InstituteInstitute specifications of Technology are listed in Table to C1. a batterybattery electric vehicle (BEV), [[30].30]. A battery pack was installed in the vehicle. This vehicle is used for research in different automotive engineering and e-mobilitye‐mobility related projects. The propulsion systems comprises an induction motor with a single gear transmission. The motor speciﬁcationsspecifications are listedlisted inin TableTable A2C1..

Figure C1. Vehicle under test.

Figure A3.C1. Vehicle under test.

Table A2. Technical data of electric motor.

Parameter Value Rated Power, PN 45 kW Peak Power, Pmax 68 kW Peak Torque, Tmax 210 N¨ m Rated Speed, nN 3000 rpm Energies 2016, 9, 563 17 of 18

Table C1. Technical data of electric motor.

Parameter Value Rated Power, PN 45 kW Peak Power, Pmax 68 kW Peak Torque, Tmax 210 N∙m Energies 2016, 9, 563 16 of 17 Rated Speed, nN 3000 rpm

TheThe motor motor shown shown in in Figure Figure C2A4 isis powered powered by by the the AC AC current, current, delivered delivered from from the the power power electronicselectronics that that converts converts the the DC DC current current supplied supplied by by the the battery. battery. As As the the driver driver presses presses the the accelerator accelerator pedal,pedal, a a corresponding corresponding “torque “torque demand” demand” signal signal is isconverted converted by by the the vehicle vehicle control control unit unit (VCU) (VCU) to an to appropriatean appropriate signal signal for forthe the motor motor control control unit unit (power (power electronics), electronics), which which in inturn turn transforms transforms it into it into a currenta current frequency frequency signal. signal. The The motor motor control control unit unit (MCU) (MCU) is is incorporated incorporated with with a a thermal thermal derating systemsystem in in order order to to limit limit the the torque torque demand demand received received by by the the power power electronics electronics and and to to prevent prevent any any criticalcritical operating operating conditions conditions for for the the motor. motor. The The assigned assigned powertrain powertrain can can accelerate accelerate the the vehicle vehicle to toa maximuma maximum speed speed of of 120 120 km/h. km/h.

FigureFigure C2. A4. TheThe basic basic drive drive train train topology topology of of the the Mercedes Mercedes A A-Class‐Class research research vehicle vehicle [30]. [30].

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