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 2
*
Institute of Vehicle System Technology, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany;
[email protected] (M.G.);
[email protected] (F.G.) 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]. Figure 1 demonstrates a typical discharge characteristic curve of a lithium-ion battery. The battery voltage extends between an upper and lower voltage limits V 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 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 V nom voltage is reached. Not only is the battery voltage
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influenced by the discharge rate, but the battery capacity is also diminished at high discharge rates. 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 This occurs as a sharp voltage drop at the end of the discharge process, as indicated in Figure 1. At rate the discharge terminates at V cut-off [4]. that rate the discharge terminates at V cut‐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. Lithium iron phosphate cells are characterized by their flat open circuit voltage curve (OCV). Hence, The vehicle under test (VUT) is equipped with battery cells of a cathode type LiFeMgPO4 . the cell stays almost constant over the complete charge (SOC) voltage range [2,3,6]. Lithium ironvoltage phosphate cells are characterized by theirstate flat of open circuit curveThe (OCV). battery pack of the VUT consists of 19 modules. Each module comprises six cell blocks connected in Hence, the cell voltage stays almost constant over the complete state of charge (SOC) range [2,3,6]. series; a single cell block is constructed out of 50 LiFeMgPO4–graphite cells, connected in parallel. In The battery pack of the VUT consists of 19 modules. Each module comprises six cell blocks connected 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 LiFeMgPO4 –graphite cells, connected in parallel. V, amounting to a total voltage of 19.2 V. The battery specifications are given in Table 1. A Controller In total, there are 300 cells within the single battery module. Each cell block has a nominal voltage of Area Network (CAN) communication environment is used for the control and management of the 3.2 V, battery modules. More technical information about the VUT is available in the Appendix. 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 Table 1. Technical data of LiFeMgPO Battery [7]. battery modules. More technical information about the VUT 4is available in the Appendix. Parameter (Unit) Value Table 1. Technical data of LiFeMgPO4 Battery [7]. Nominal Module Voltage (V) 19.2 Nominal Module Capacity (Ah) 69 Parameter (Unit) Value Max Continuous Load Current (A) 120 Nominal Module Voltage (V) 19.2 Peak Current for 30 s (A) 200 Nominal Module Capacity (Ah) 69 Continuous Current (A) modeling 120 methods to decide which In this paper, we will Max investigate the Load different battery Peak Current for 30 s (A) 200 approach will be the most appropriate for modeling the battery pack of VUT. Then, we will select a group of the most thorough models for Li‐ion batteries. These models will contribute to the development of the proposed battery model, which will be considered for modeling actual battery In this paper, we will investigate the different battery modeling methods to decide which 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 proposed battery model, which will be considered for modeling actual battery pack voltage response Section 3. In Section 4 the thermal behavior of the battery is elaborated. The experimental tests are whendescribed the VUT in undergoes driving Section 5. severe The models are maneuvers. evaluated and a new, improved model is developed and The paper is organized as follows. Section 2 presents the different modeling techniques of Li-ion proposed in Section 6. Finally, the conclusions are stated at the end of the paper.
batteries. Three models are elected from the reviewed models and are discussed in more details in Section 3. In Section 4 the thermal behavior of the battery is elaborated. The experimental tests are described in Section 5. The models are evaluated and a new, improved model is developed and proposed in Section 6. Finally, the conclusions are stated at the end of the paper.
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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:
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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) et al. [1] (battery model 3) Wijewardana Wijewardana et al. [1] (battery model 3)
3.1. Tremblay Battery Model (Battery Model 1) 3.1. Tremblay Battery Model (Battery Model 1) Tremblay andand Dessaint [5] improved their own model in Reference [21]. The new model is is shown Tremblay Dessaint [5] improved their own model in Reference [21]. The new model shown in Figure 2. Only three points on the steady state manufacturer’s discharge curve are required in Figure 2. Only three points on the steady state manufacturer’s discharge curve are required to to parametrize the model, which are the full voltage, the end point of exponential voltage region, and parametrize the model, which are the full voltage, the end point of exponential voltage region, and the the nominal voltage. The variation of the OCV from a reference constant voltage (E ) is related to SOC nominal voltage. The variation of the OCV from a reference constant voltage0(E 0 ) is related to SOC changes by incorporating a polarization constant (K). changes by incorporating a polarization constant (K).
Figure 2. Tremblay and Dessaint battery discharge model. Figure 2. Tremblay and Dessaint battery discharge model.
In case of discharging the output voltage reads:
In case of discharging the output voltage reads: ∙
∙
∗
∙
(1)
Q Vbatt “ E0 ´ R ¨ i ´ K ¨ pit ` i˚ q ` Ae´B ¨ it and for charging, the equation becomes: Q ´ it and for charging, the equation becomes: ∙
0.1
∙
∗
∙
∙
(1)
(2)
Q Q the variables and constants in Equations (1) and (2) are defined in Table A1 in the Appendix A. Vbatt “ E0 ´ R ¨ i ´ K ¨ i˚ ´ K ¨ it ` Ae´B ¨ it (2) Although, the charging and discharging characteristics Qare extensively modeled, some other it ´ 0.1Q ´ it influential factors like the variations in internal resistance (R) and temperature influence are not the variables and constants in Equations (1) and (2) are defined in Table A1 in the Appendix A.1. considered. The capacity fading effect is not taken into account in this model as well. Although, the charging and discharging characteristics are extensively modeled, some other 3.2. Lam and Bauer Battery Model (Battery Model 2) influential factors like the variations in internal resistance (R) and temperature influence are not
considered. capacity fading effectequivalent is not taken into model accountis inshown this model as well. The The Lam and Bauer battery circuit in Figure 3. The model demonstrates the VOC as a function of SOC, a variable ohmic resistance Ro, and two variable
3.2. Lam and Bauer Battery Model (Battery Model 2) RC‐networks: R SCS and RlCl for the short and the long time transient responses, respectively. Lam
and also showed the relation between to aging and model different stress The Bauer Lam and Bauer battery equivalent circuitcapacity model isfading showndue in Figure 3. The demonstrates influences, which are the cell’s temperature, C‐rate, SOC and intensity of discharge. Lam and Bauer the V OC as a function of SOC, a variable ohmic resistance Ro , and two variable RC-networks: RS CS parametrized their equations through curve fitting of experimental measurements. They employed and Rl Cl 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 relation between capacity fading due to aging and different stress influences, which are the cell’s temperatures from 20 °C and above are detailed in Equations (7)–(28) in Reference [20]. We refer also temperature, C-rate, SOC and intensity of discharge. Lam and Bauer parametrized their equations to the VOC equation with the corrected constants as proposed in Reference [20]:
through curve fitting of experimental measurements. They employed in their tests the LiFePO4 battery . (3) SOC resistors 0.5863 3.414 0.1102 for SOCtemperatures 0.1718 20 ˝ C and cell. The equivalent circuit and capacitors equations from 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]: 8ˆ10´3
VOC pSOCq “ ´0.5863 e´21.9 SOC ` 3.414 ` 0.1102 SOC ´ 0.1718 e´ 1´SOC
(3)
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Figure 3. Lam and Bauer battery circuit model.
Figure 3. Lam and Bauer battery circuit model.
3.3. Wijewardana Battery Model
3.3. Wijewardana Battery Model
Figure 3. Lam and Bauer battery circuit model.
A different perception, than the two previous models, is adopted in this model. The electrical components, R S, CS, RL, Cthan L are functions of SOC and independent of the temperature. Only the series A3.3. Wijewardana Battery Model different perception, the two previous models, is adopted in this model. The electrical internal is a function of SOC temperature of(Rthe intS(SOC,T)). The temperature components, RSresistance , CS , RL , resistor CL are functions of SOC andand independent temperature. Only the series A different perception, than the two previous models, is adopted in this model. The electrical influence is considered by adding potential correction terms, which are voltage due to electrode film components, R 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 (RintS (SOC,T)). The temperature formation (ΔE) and voltage due to electrolyte transfer (R formation (ΔVChe). The capacity internal resistance resistor is a function of SOC electrons and temperature intS(SOC,T)). The temperature influence is considered by adding potential correction terms, which are voltage due to electrode film fading effect is modeled as an additional series resistance R cyc. The battery output voltage is computed influence is considered by adding potential correction terms, which are voltage due to electrode film formation (∆E) and voltage due to electrolyte electrons transfer formation (∆V Che ). The capacity by subtracting the voltage drop of each circuit element from the V OC value. Figure 4 demonstrates formation (ΔE) and voltage due to electrolyte electrons transfer formation (ΔVChe). The capacity fading effect is modeled as an additional series resistance Rcyc . The battery output voltage is computed Wijewardana battery model. 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. Figure 4 demonstrates by subtracting the voltage drop of each circuit element from the V OCOC value. Figure 4 demonstrates Wijewardana battery model. Wijewardana battery model.
Figure 4. Wijewardana battery circuit model.
The battery output voltage of this model reads [1]: Figure 4. Wijewardana battery circuit model. Figure 4. Wijewardana battery circuit model. ∆ ∆ The battery output voltage of this model reads [1]: The battery output voltage of this ∆ model1reads ∆[1]: ∆ ∆ ∆
(4) (5) (4)
Vbatt “ VOC ´ i RintS⁄` Rcyc ´ V1 ´ V2 ´ ∆E pTq ´ ∆VChe pTq `
∆
β ∆
˘
∆1
∆
∆
∆
1
β ∆
(5) (6)
(4)
ˇ dVr ˇˇ ∆E pTq “ ∆T ∆ 1 β ∆ (5) The values of the model parameters are listed in the Appendix A. ⁄ p1 ` CE1 ∆Tq ∆ β ∆ (6) dT ˇT“Tcell ˇ 3.4. Assessment of Battery Models Qualities dV The values of the model parameters are listed in the Appendix A. Che ˇˇ pC ∆VChe pTq “ βw expp´1{tq ∆T ` ` CChe1 ∆Tq p1 ` βq ∆T (6) Three different highly dynamic to model Li‐ion batteries have been proposed. Each model has dT ˇT“Tcell Che 3.4. Assessment of Battery Models Qualities its dominant features. Table 2 summaries the qualities of each model. The (+) sign implies that the
The values of the model parameters are listed inmodel. the Appendix. corresponded feature is considered in the Whereas, a (++) sign denotes an extensive
Three different highly dynamic to model Li‐ion batteries have been proposed. Each model has consideration to the related feature. In contrast, the (‐) sign means that the related feature was its dominant features. Table 2 summaries the qualities of each model. The (+) sign implies that the 3.4. Assessment Models assigned of as Battery a feature constant it Qualities is not considered at all in the model. Battery 2 considers more corresponded is or considered in the model. Whereas, a (++) sign model denotes an extensive factors than the other models. However, each model must be evaluated with experimental data to Three differentto highly dynamic to model Li-ion have been proposed. Each model consideration the related feature. In contrast, the batteries (‐) sign means that the related feature was has investigate its accuracy. assigned as a constant or it 2is not considered in the of model. Battery considers more its dominant features. Table summaries theat all qualities each model.model The 2 (+) sign implies that factors than the other models. However, each model must be evaluated with experimental data to the corresponded feature is considered in the model. Whereas, a (++) sign denotes an extensive investigate its accuracy.
consideration to the 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.
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Table 2. Comparison between the battery models. Feature Charge-Discharge hysteresis Open circuit voltage Internal resistance (R) Temperature influence Capacity fading
Battery Model 1
Battery Model 2
-
Considered in the output voltage Constant value for E0 Constant value
+ ++
-
Not considered
+
-
Not considered
+
++
Total Assessment
2
+
Battery Model 3
Considered in the internal resistance (R) equations V OC (SOC) R(SOC,T,C-rate) Considered in the internal resistance model
-
Charge-discharge
+ +
Considered in the battery’s used capacity estimation
+
V OC (SOC) R(SOC,T) Considered as potential correction terms Considered in the battery’s internal resistance (R) estimation 4
+
6
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: mC p
´ ¯ dTcell 4 4 “ i pVOC ´ Vbatt q ´ hAcell ∆T ´ σAcell Tcell ´ Tamp dt
(7a)
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: MC p
´ ¯ dTcell 4 4 “ I pVOC ´ Vbatt q ´ hA∆T ´ σA Tcell ´ Tamp dt
(7b)
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: Ploss = Icell 2 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. Figure 5 demonstrates the charge and discharge OCV curves
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over the SOC for various temperatures. It is noticeable that the lower the operating temperatures, the higher the difference between charging and discharging. Energies 2016, 9, 563 7 of 18
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OCV[V]
OCV[V]
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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 Testsobjective on the Real Vehicle of a real test is to find a real driving maneuver reference signal to validate the
Battery pack voltage [V] pack voltage [V] Battery
100 50 250 200 0
150 -50
100 -100 0 50
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250
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(a)
0 -50 250
Battery current [A] Battery current [A]
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100 -50 0 50
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Battery voltage Battery [V] voltage [V]
Battery pack current [A] Battery pack current [A]
battery model performance. Nevertheless, the battery model should be able to simulate the actual Figure 5. The objective of a real test is to Charge and discharge OCV curves over SOC. find a real driving maneuver reference signal to validate the system in real operating conditions, not merely charging‐discharging cycles. Two driving tests were battery performed model performance. Nevertheless, the battery model should be able to simulate the actual 5.2. Driving Tests on the Real Vehicle with the test vehicle for the purpose of investigation the system and collecting the system experimental data. The tests were executed on the testing ground at Karlsruhe Institute of Technology in real operating conditions, not merely charging-discharging cycles. Two driving tests The objective of a real test is to find a real driving maneuver reference signal to validate the were performed with the test vehicle for the purpose of investigation the system and collecting the (KIT). The experimental data attained from the CAN bus are displayed in Figures B1 and B2 in the battery model performance. Nevertheless, the battery model should be able to simulate the actual Appendix B. Then, the data were processed in MATLAB. In the first test, the vehicle was driven in a experimental data. The tests were executed on the testing ground at Karlsruhe Institute of Technology system in real operating conditions, not merely charging‐discharging cycles. Two driving tests were counterclockwise circular direction for about 230 s. Then the direction for driving was reversed and performed with test attained vehicle for the purpose of bus investigation the system and collecting the A2 in the (KIT). The experimentalthe data from the CAN are displayed in Figures A1 and the test was resumed. A variable pedal input was implemented in order to cover a broader range of experimental data. The tests were executed on the testing ground at Karlsruhe Institute of Technology Appendix A.2. Then, the data were processed in MATLAB. In the first test, the vehicle was driven data. This test represents an aggressive driving scenario, leading to discharge rate of up to 3.4 C. The (KIT). The experimental data attained from the CAN bus are displayed in Figures B1 and B2 in the in a counterclockwise circular direction for about 230 s. Then the direction for driving was reversed second test was implemented by subjecting the vehicle to a sequence of sudden accelerations and Appendix B. Then, the data were processed in MATLAB. In the first test, the vehicle was driven in a and thedecelerations. These tests were performed this way to create highly fluctuating signals in the battery test was resumed. A variable pedal input was implemented in order to cover a broader range counterclockwise circular direction for about 230 s. Then the direction for driving was reversed and the test was resumed. A variable pedal input was implemented in order to cover a broader range of which are shown Figure 6. The dynamic responses of battery voltage can be used of data.system, This test represents anin aggressive driving scenario, leading to discharge rate of upto to 3.4 C. data. This test represents an aggressive driving scenario, leading to discharge rate of up to 3.4 C. The evaluate the battery models, discussed above. The second test was implemented by subjecting the vehicle to a sequence of sudden accelerations second test was implemented by subjecting the vehicle to a sequence of sudden accelerations and and decelerations. These tests were performed this way to create highly fluctuating signals in the decelerations. These tests were performed this way to create highly fluctuating signals in the battery 250 380 battery system, which areshown shownin in Figure 6. The dynamic responses of battery canto be used to 200 system, which are Figure 6. The dynamic responses of battery voltage voltage can be used 370 evaluate evaluate the battery models, discussed above. the150battery models, discussed above. 360
50
100 Time[s]
(c)
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330 0 350 340
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(d)
Figure 6. CAN bus measurements: (a) Battery pack current for the circular driving test; (b) Battery -50 330 0 50 100 150 200 0 50 100 150 200 Time[s] pack voltage for the circular driving test; (c) Battery pack current for the Time[s] rapid acceleration and (d) deceleration driving (c) test; (d) Battery pack voltage for the rapid acceleration and deceleration driving test. Figure 6. CAN bus measurements: (a) Battery pack current for the circular driving test; (b) Battery
Figure 6.pack CANvoltage bus measurements: (a) Battery pack current the circular driving test; (b) and Battery pack for the circular driving test; (c) Battery pack for current for the rapid acceleration voltage for the circular driving (c) Battery current forrapid the rapid acceleration and deceleration deceleration driving test; test; (d) Battery pack pack voltage for the acceleration and deceleration driving test. driving test; (d) Battery pack voltage for the rapid acceleration and deceleration driving test.
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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 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. We validated both V 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. The influence of the temperature variation on the OCV curves is defined as dVOC {dT. From the measurements shown in Figure 6, the value of this term was found to be 1.25 mV in case of discharge and 0.69 mV for charging. The V 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. a6 VOC,discharge pSOC, Tq “ a1 e´a2 SOC ` a3 ` a4 SOC ` a5 e´ 1´SOC ` T dVOC,d {dT
(8)
b6 VOC,charge pSOC, Tq “ b1 e´b2 SOC ` b3 ` b4 SOC ` b5 e´ 1´SOC ` T dVOC,c {dT
(9)
Table 3. V OC parameter values. Constant
Value
Constant
Value
a1 a2 a3 a4 a5 a6
´1.166 ´35 3.344 0.1102 ´0.1718 ´2 ˆ 10´3 0.00125
b1 b2 b3 b4 b5 b6
´0.9135 ´35 3.484 0.1102 ´0.1718 ´8 ˆ 10´3 0.00069
dV OC,d /dT
dV OC,c /dT
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 Section 4 is employed for all models. The battery currents in Figure 6a,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 Figure 6b,d. The V 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. Figures 9 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
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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 ascribed to the fact that the test conditions were nearly matching the standard condition for defining Energies 2016, 9, 563 9 of 18 ˝ the constant voltage (E0 ). E0 is equal to the nominal voltage at 20 C, which is equal to 3.21 V and the ascribed to the fact that the test conditions were nearly matching the standard condition for defining ascribed to the fact that the test conditions were nearly matching the standard condition for defining initial voltage of the single0). E battery cell is estimated as 3.25 V. When the test second driving test was the constant voltage (E 0 is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the the constant voltage (E 0). E0 is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the performed at different circumstances, the outcome was not as good as it in the first case. Figure 10a initial voltage of the single battery cell is estimated as 3.25 V. When the test second driving test was initial voltage of the single battery cell is estimated as 3.25 V. When the test second driving test was reveals a relatively large offset error in the response of battery model 1 with a mean square error (MSE) performed at different circumstances, the outcome was not as good as it in the first case. Figure 10a 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 of about 2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. The offset reveals a relatively large offset error in the response of battery model 1 with a mean square error errors(MSE) of about 2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. between the reference signal and initial voltage value of both battery models 2 and 3 were minor, (MSE) of about 2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. The Equation offset errors between the reference signal and voltage value models 2 of whereas (3) is employed in both models for initial the estimation of Vof of both . both Thebattery simulation results The offset errors between the reference signal and initial voltage value OC battery models 2 and 3 were minor, whereas Equation (3) is employed in both models for the estimation of V OC. The model 3 indicate less dynamic response than the other two models. It could not conduct the drastic 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 changes in the battery current input signal. 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. conduct the drastic changes in the battery current input signal. 4.5
4.5 4
OCV[V] OCV[V]
4 3.5
3.5 3
3 2.5
2.5 2 0
20
2 0
20
Discharge measured at T=20°C Charge measured at T=20°C Voc of battery model 2 at T=20°C Discharge measured Voc of battery modelat3T=20°C Charge measured Voc 2 40 60 of battery model 80 100 SOC[%] Voc of battery model 3
40
60
80
100
SOC[%] Figure 7. Comparing the Voc model with measured experimental results.
Figure 7. Comparing the Voc model with measured experimental 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 V OC model.
Temperature °C Table 4. Accuracy of the proposed V MSE in Discharge Model % MSE in Charge Model % OC model. 10 0.5232 0.8914 ˝ Temperature C MSE in Discharge Model % MSE in Charge Model % Temperature °C MSE in Discharge Model % MSE in Charge Model % 20 0.5320 0.5719 10 0.5232 0.8914 10 0.5232 0.8914 40 0.5751 0.4522 20 0.5320 0.5719 20 0.5320 0.5719 40 0.5751 0.4522 40 0.5751 0.4522
(a)
(b)
(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.
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10
MSE = 0.9453%
105 Error [%] Error [%]
Battery pack voltage [V]
Battery pack voltage [V]
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MSE = 0.9453%
50 0
-5
-5
-10 0
50
-10 0
(a) (a)
50
100 100
150 150
200 Time[s]
200 Time[s]
250
250
(b)
(b)
10
350
350
MSE = 1.75%
10
MSE = 1.75%
5 Error [%][%] Error
300
300
5
0 0
-5 -5
-10
-10 0 0
50
50
100
100
150
150
250
300
300
350
350
(d) (d) 10 10
Battery pack voltage [V]
= 1.7841% MSEMSE = 1.7841%
55 Error [%] Error [%]
Battery pack voltage [V]
(c)(c)
200
200 Time[s]250 Time[s]
00 -5-5
-10 -10 0
50
0
50
100
100
150
200
250
150 Time[s]200 Time[s]
300
250
350
300
350
(f)
(e)
(f)
(e)
Figure 9. Battery simulation models and reference voltage signal for circular driving test: (a) Battery
Figure 9. Battery simulation models and reference voltage signal for circular driving test: (a) Battery 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 model 1 response; (b) Mean square error of battery model 1; (c) Battery model 2 response; (d) Mean 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. square error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3. square error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3. 10
MSE = 2.2373%
Error [%]
Error [%]
5 0
0 -5
-5
-10 0
-10 0
(a)
50
100 Time[s]
50
10
(a) Error [%]
200
150
Time[s]
(b)
200
MSE = 1.0347%
MSE = 1.0347%
Error [%]
05 -5 0
-10 -5 0
(c)
150
(b) 100
10 5
Battery voltage [V]
Battery voltage [V]
MSE = 2.2373%
5
Battery voltage [V]
Battery voltage [V]
10
-10 0
(c)
50
100 Time[s]
200
(d) 50
100 Time[s]
(d) Figure 10. Cont.
150
150
200
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MSE = 1.5176%
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10 5
Error [%]
(e)
MSE = 1.5176%
0 -5 0
-10 0
-5
-10 0
50
100 Time[s]
150
200
(f) 50
100
150
200
Time[s] Figure 10. Battery simulation models and reference voltage signal for rapid acceleration and Figure 10. Battery simulation models and reference voltage signal for(f) rapid acceleration and (e) 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; Figure 10. Battery simulation models and reference voltage signal for rapid acceleration and (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response deceleration driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1; (f) Mean square error in battery model 3. (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
(f) Mean square error in battery model 3. 6.3. The Proposed Synthesized Battery Model 6.3. The Proposed Synthesized Battery Model It is explicable that each model has some flaws, as determined in Table 2. The simulation results 6.3. The Proposed Synthesized Battery Model It is explicable that each model has some flaws, as determined in Table 2. 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 results in Figures 9 and 10 prove that even the best performing models need to be further improved. Accordingly, a synthesized model that holds the best qualities of each model has been developed. in Figures 9 and 10 prove that that even holds the best models need model to be further improved. Accordingly, a synthesized model theperforming best qualities of each has been developed. First, the charge‐discharge characteristics of model 1 are considered. Additionally, the discharging Accordingly, a synthesized model that holds the best qualities of each model has been developed. First, the charge-discharge characteristics of model 1 are considered. Additionally, the discharging part part our proposed V OC(SOC,T) is employed instead of constant (E0) value. Then, the highly detailed First, the charge‐discharge characteristics of model 1 are considered. Additionally, the discharging our proposed V (SOC,T) is employed instead of constant (E ) value. Then, the highly detailed internal OC internal resistance model of battery model 2 in case of 0discharging, which is represented by part our proposed V OC(SOC,T) is employed instead of constant (E 0) value. Then, the highly detailed resistance model of battery model 2 in case of discharging, which is represented by Equations (7)–(11), Equations (7)–(11), (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal internal resistance model of battery model 2 in case of discharging, which is represented by (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal resistance (R). resistance (R). The capacity fading effect is considered by adding R cyc from battery model 3 to the internal Equations (7)–(11), (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal The capacity fading effect is considered by adding R from battery model 3 to the internal resistance. cyc 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‐ The empirical in case of discharging implemented because the charging-discharging resistance. equations The empirical equations in case of are discharging are implemented because the charging‐ discharging hysteresis is properly modeled by model 1. The synthesized model is shown in Figure 11. discharging hysteresis is properly modeled by model 1. The synthesized model is shown in Figure 11. hysteresis is properly modeled by model 1. The synthesized model is shown in Figure 11.
Figure 11. The proposed synthesized battery model. Figure 11. The proposed synthesized battery model. Figure 11. The proposed synthesized battery model.
In case of discharging, the output voltage reads: In case of discharging, the output voltage reads: In case of discharging, the output voltage reads: ∗
∙
∙ ∙ ∗ ∙ (10) (10) ˘∙ Q ∙ ˚ ´ B ¨ it Vbatt “ VOC,discharge pSOC, Tq ´ RO ` Rcyc ` VS ` VL ¨ i ´ K ¨ pit ` i q ` Ae (10) Q ´ it and for charging, the equation expressed as: and for charging, the equation expressed as: ∙ and for charging, the equation expressed as: ∙ ∙ ∗ ∙ (11) OC,discharge SOC, ∙ 0.1 ∙ ∗ ∙ ∙ (11) OC,discharge SOC, 0.1Q ` ˘ Q ˚ ´ B ¨ it Vwhere (11) batt “ VOC,discharge pSOC, Tq ´ RO ` Rcyc ` VS ` VL ¨ i ´ K it´0.1Q ¨ i ´ K Q´it ¨ it ` Ae where where (12) dVS i VS (12) “ ´ (12) dt CS RS CS SOC, OC,discharge SOC,
OC,discharge
`
dVL i VL “ ´ dt CL R L CL
(13)
(13) (13)
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The resistances and capacitors values are determined through Equations (14)–(18): ´ ¯ Rs pSOC, ϑq “ c1 epc2 SOCq ` c3 ` c4 SOC ` c5 ∆ϑ ` c6 SOC∆ϑ
(14)
´ ¯ Cs pSOC, ϑq “ c7 SOC3 ` c8 SOC2 ` c9 SOC ` c10 ` c11 SOC∆ϑ ` c12 ∆ϑ
(15)
´ ¯ ` ˘ 12 of 18 IC´rate q “ pc13 epc14 SOCq ` c15 ` c16 SOCq ` c17 ∆ϑepc18 SOCq ` c19 ∆ϑ ˆ c20 pIC´rate qc21 ` c22 Rl pSOC, ϑ,Energies 2016, 9, 563
(16)
´ ¯ The resistances and capacitors values are determined through Equations (14)–(18): Cl pSOC, ϑq “ c23 SOC6 ` c24 SOC5 ` c25 SOC4 ` c26 SOC3 ` c27 SOC2 ` c28 SOC ` c29 ` c30 ec31 {ϑ
(17)
SOC,
SOC
∆
SOC ∆
(14)
´ ¯ 3 c38 {pϑ´c39 q (15) SOC SOC` ∆ c36 c∆ Ro pSOC, ϑq “SOC,c32 SOC4SOC ` c33 SOC ` c34SOC SOC2 ` c35 SOC 37 e SOC, ,
SOC
∆
∆
(18)
where ϑ is the battery cell temperature in Kelvin (˝ K) and c1 –c39 are constants, which (16) their values are listed in Table 5. SOC,
SOC
SOC
SOC
SOC
SOC
SOC
(17)
/
Table 5. Constants values of Equations (14)–(18).
/ (18) SOC, SOC SOC SOC SOC 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 c31 c1 c11 ´6.580 c21 1.080 ˆ 10´2 ´6.919 ˆ 10´1 ´2.398 ˆ 103 listed in Table 5. c2 ´11.03 c12 12.11 c22 c32 2.902 ˆ 10´1 1.298 ˆ 10´1 c3 c13 c23 c33 1.827 ˆ 10´2 2.950 ˆ 10´1 2.130 ˆ 106 ´2.892 ˆ 10´1 Table 5. Constants values of Equations (14)–(18). c14 ´20.00 c24 c34 c4 ´6.462 ˆ 10´3 ´6.007 ˆ 106 2.273 ˆ 10´1 ´4 Constant Constant Value Value c5 c15Constant 4.722 ˆValue c25 c35 ´3.697 ˆ 10Value 10´2 6.271 ˆ 106 Constant ´7.216 ˆ 10´2 −2 ´4 c2.225 1 1.080 × 10 c16 c11 ´2.420 ˆ −6.580 c21 −6.919 × 10 6 c31 c36 −2.398 × 10 c6 c26 ˆ 10 10´2 ´2.958 ˆ−110 8.9803 ˆ 10´2 −1 −1 2 ´3 5 c 2 −11.03 c 12 12.11 c 22 2.902 × 10 c 32 1.298 × 10 c7 c17 c27 c37 1.697 ˆ 10 6.718 ˆ 10 5.998 ˆ 10 7.613 ˆ 10´1 −2 c13 2.950 × 10−1 c23 2.130 × 106 4 c33 −2.892 × 10−1 c3 c8 c ´20.00 c c 10.14 ´1.007 ˆ1.827 × 10 103 ´3.102 ˆ 10 18 28 38 −6.462 × 10−3 c14 −20.00 c24 −6.007 × 106 3 c34 2.273 × 10−1 c4 c9 c19 c29 c39 1.408 ˆ 103 ´5.967 ˆ 10´4−2 2.232 ˆ 610 2.608 ˆ 102 −4 −2 c5 −3.697 × 10 c15 4.722 × 10 c25 6.271 × 10 3 c35 −7.216 × 10 2 ´1 c10 c c 3.897 ˆ 10 6.993 ˆ 10 3.128 ˆ 10 −4 −2 6 −2 20 30 2.225 × 10 c16 −2.420 × 10 c26 −2.958 × 10 c36 8.980 × 10 c6
1.697 × 102 c17 6.718 × 10−3 c27 5.998 × 105 c37 c7 −1.007 × 103 c18 −20.00 c28 −3.102 × 104 c38 c8 The new model shows a 3significant improvement inc29the simulation 1.408 × 10 c19 −5.967 × 10−4 2.232 × 103 response, c39 c9 3.897 × 102 c20 6.993 × 10−1 c30 3.128 × 103 c10
7.613 × 10−1 10.14 2 in Figure 12. as2.608 × 10 shown
The mean square error was reduced to only 0.256%. The new model shows also the best result when it The new model significant improvement in the simulation response, shown it in had employed for simulating theshows rapida acceleration and deceleration driving test, as though a small Figure 12. The mean square error was reduced to only 0.256%. The new model shows also the best offset error at the beginning of 3.2 V. This error yielded from an absolute voltage error of 0.028 V in result when it employed for simulating the rapid acceleration and deceleration driving test, though proposed VOC model, represented by Equation (8), at the specified SOC and temperature values. it had a small offset error at the beginning of 3.2 V. This error yielded from an absolute voltage error of 0.028 V in simulated proposed VOC model, represented by Equation (8), at the specified SOC and The battery models are in MATLAB/Simulink environment. Figure 13 shows 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%
Error [%]
5 0 -5 -10 0
50
100
150
200 Time[s]
250
300
350
(b)
(a)
10
MSE = 0.7862%
Error [%]
5 0 -5
(c)
-10 0
50
100 Time[s]
150
200
(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.
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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(c) 2016, 9, 563 model response for the rapid acceleration and deceleration driving test; (d) Error of 13 of 17 Proposed proposed model voltage for the rapid acceleration and deceleration driving test. SOC0 3 -KGain4
K Ts z
f(u)
z-1 Discrete-Time Integrator2
OCV(SOC,T)_dis2
SOC T[°C]
|u| Abs
E0-R*i
U_R
-K-
I_cell
C-Rate Calculation
R
1/s
Lam, Bauer RC Model
Saturation
exp e% Sim
Subsystem
PE
Integrator it
6
E_batt
Cell Blocks Lowpass
1 Measured battery pack current
2 Actual battery pack voltage
Q(Capacitance)
I_Crate
Cells current
i*
19
i
number of Modules
Lowpass Filter
1/50
U
Discharge-Charge dynamics
V_cell VOC |u|
4 T_ambient 5 T_Cell
i_cell
Battery Temperature
Ambient Temp Tbatt0
Battery Temperature Model
Figure 13. The proposed synthesized battery simulation model. Figure 13. The proposed synthesized battery simulation model.
7.7. Conclusions Conclusions AA battery is a sophisticated system, which necessitates a detailed model for accurate simulation. battery is a sophisticated system, which necessitates a detailed model for accurate Many factors must be considered in the battery model for accurate simulation Charging‐ simulation. Many factors must be considered in the battery model for accurate results. simulation results. discharging dynamics, battery internal resistance, and open circuit voltage are the most significant Charging-discharging dynamics, battery internal resistance, and open circuit voltage are the most aspects for battery Temperature is an influential factor for all of The significant aspects formodeling. battery modeling. Temperature is an influential factor forthese all of aspects. these aspects. difference between the charging and discharging in the OCV curves increases at low temperatures. The difference between the charging and discharging in the OCV curves increases at low temperatures. This phenomenon occurs due to the decrement in battery capacity, which in turn appears as a result This phenomenon occurs due to the decrement in battery capacity, which in turn appears as a result rise ofof the the internal internal resistance. resistance. Neglecting Neglecting the ofof aa rise the effect effect of of temperature temperature will will lead leadto toinaccuracy inaccuracyin in simulation. Even the slightest errors in the simulation results of the battery cell model, would grow simulation. Even the slightest errors in the simulation results of the battery cell model, would grow significantly when the model is extended to the complete battery pack. Battery model 1 has two flaws. significantly when the model is extended to the complete battery pack. Battery model 1 has two flaws. Firstly, it assumes the initial voltage value to be the nominal battery cell voltage. This assumption led Firstly, it assumes the initial voltage value to be the nominal battery cell voltage. This assumption led toto large offset from the actual value, when the vehicle was tested at about 30 °C. Secondly, it considers large offset from the actual value, when the vehicle was tested at about 30 ˝ C. Secondly, it considers a constant internal resistance of the battery, which is in fact a very fluctuating quantity that affects a constant internal resistance of the battery, which is in fact a very fluctuating quantity that affects the the battery cell current the response voltage asresponse well. The proposed model has battery cell current and the and voltage well. Theas proposed battery model battery has compensated for compensated for these shortages and it has accurately simulated the battery pack voltage response these shortages and it has accurately simulated the battery pack voltage response on the real vehicle. on the real vehicle. Author Contributions: Muhammed Alhanouti made the literature review on theon current battery models, Author Contributions: Muhammed Alhanouti made the literature review the current battery proposed models, the synthesized battery model, developing the simulation models, and wrote the paper. Martin Gießler and proposed the synthesized battery model, developing the simulation models, and wrote the paper. Martin Gießler Thomas Blank designed and performed the battery measurements, and they helped in editing the paper content. and Thomas Blank designed and performed the battery measurements, and they helped in editing the paper Frank Gauterin supervised the work of this paper and approved the results 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) Constant internal resistance (Ω) Polarization constant (V/(Ah)) or polarization resistance (Ω) Battery capacity (Ah)
E0 R K Q
3.21 [23] 0.0833 0.0119 [23] Variable
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Table A1. Cont. Parameter (Unit)
Symbol
Value
Actual battery charge (Ah) Exponential zone amplitude (V) Exponential zone time constant inverse (Ah)´1 Battery current (A) Filtered current (A) Voltage change due to electrolyte electrons transfer formation the effective voltage gradient Constant property of electrolyte Constant property of electrolyte Constant property of electrolyte Constant property of electrolyte Voltage change due to electrode film formation voltage gradient Constant property Battery module surface area (m2 ) Battery cell mass (kg) Battery module mass (kg) Specific heat capacity (J¨ kg´1 ¨ K´1 ) Stefane-Boltzmann constant (W¨ m´2 ¨ K4 ) Emissivity of heat Natural heat convection constant (W¨ m´2 ¨ K´1 )
it A B i i*
Variable 0.2711 [23] 152.130 [23] Variable Variable
∆V Che
Variable
dV Che /dT CChe CChe1 b w ∆E dVr /dT CE1 A m M Cp σ ε h
0.0016 [1] 0.07 [1] 0.001 [1] 0.0012 [1] 0.012 [1] Variable 0.00003 [1] 0.00011 [1] 0.283954 0.04 [23] 12 1360 [27] 5.67 ˆ 10´8 0.95 4
Energies 2016, 9, 563 Appendix A.2. Driving Tests
15 of 18
Battery temperature [°C]
SOC [%]
Battery voltage [V]
Battery current [A]
Car Speed [km/h]
Appendix B. Driving Tests
Figure B1. The measured data of the circular drive test.
Figure A1. The measured data of the circular drive test.
Car Speed [k Battery current [A]
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Battery current [A] SOC [%]
Battery voltage [V] Battery temperature [°C]
Battery temperature [°C]
SOC [%]
Battery voltage [V]
Car Speed [km/h]
Energies 2016, 9, 563
Figure B2. The measured data of the rapid acceleration and deceleration drive test.
Figure A2. The measured data of the rapid acceleration and deceleration drive test. Figure B2. The 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. The Vehicle under the Test Appendix C. The Vehicle under the Test “FAhrzeug‐SystemTechnik” (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 automotive engineering and e‐mobility related projects. The propulsion systems comprises hydrogen front wheel passenger car (Figure A3) was modified by the institute for An electric hydrogen front wheel passenger car (Figure C1) was modified by the institute for an induction motor with a single gear transmission. The motor specifications are listed in Table C1. “FAhrzeug-SystemTechnik” “FAhrzeug‐SystemTechnik” (FAST) (FAST) of of the the Karlsruhe Karlsruhe Institute Institute of of Technology Technology to to aa battery battery electric electric vehicle (BEV), [30]. A battery pack was installed in the vehicle. This vehicle is used for research in vehicle (BEV), [30]. A battery pack was installed in the vehicle. This vehicle is used for research in different automotive engineering and e-mobility related projects. The propulsion systems comprises different automotive engineering and e‐mobility related projects. The propulsion systems comprises an induction motor with a single gear transmission. The motor specifications are listed in Table A2. an induction motor with a single gear transmission. The motor specifications are listed in Table C1.
Figure C1. Vehicle under test.
Figure C1. Vehicle under test. Figure A3. Vehicle under test. Table A2. Technical data of electric motor. Parameter
Value
Rated Power, PN Peak Power, Pmax Peak Torque, Tmax Rated Speed, nN
45 kW 68 kW 210 N¨ m 3000 rpm
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Parameter Rated Power, PN Peak Power, Pmax Peak Torque, Tmax Rated Speed, nN
Value 45 kW 68 kW 210 N∙m 3000 rpm
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The The motor motor shown shown in in Figure Figure C2 A4 is is powered powered by by the the AC AC current, current, delivered delivered from from the the power power electronics that converts the DC current supplied by the battery. As the driver presses the accelerator electronics that converts the DC current supplied by the battery. As the driver presses the accelerator pedal, a corresponding “torque demand” signal is converted by the vehicle control unit (VCU) to an pedal, a corresponding “torque demand” signal is converted by the vehicle control unit (VCU) to appropriate signal for the motor control unit (power electronics), which in turn transforms it into a an appropriate signal for the motor control unit (power electronics), which in turn transforms it into current frequency signal. a current frequency signal.The Themotor motorcontrol controlunit unit(MCU) (MCU)is isincorporated incorporatedwith with a a thermal thermal derating derating system in order to limit the torque demand received by the power electronics and to prevent any system in order to limit the torque demand received by the power electronics and to prevent any critical operating conditions for the motor. The assigned powertrain can accelerate the vehicle to a critical operating conditions for the motor. The assigned powertrain can accelerate the vehicle to maximum speed of 120 km/h. a maximum speed of 120 km/h.
Figure C2. The basic drive train topology of the Mercedes A‐Class research vehicle [30]. Figure A4. The basic drive train topology of the Mercedes A-Class research vehicle [30].
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