Optimization through rapid meta-model based transient thermal simulation of lithium ion battery cells Kerler Matthias, Hoffmann Felix, Lienkamp Markus Technical University of Munich (TUM) Dept. of Mechanical Engineering, Institute of automotive Technology
[email protected] Abstract—Today's battery electric vehicles (BEVs) use a broad variety of shapes and sizes of lithium-ion battery cells. One of the major concerns about a BEV battery pack is the process of aging, and the loss of driving range over the years of utilization. The phenomenon of capacity loss of lithium-ion batteries has been under scientific investigation for many years. Meanwhile, it is commonly accepted that the effects of temperature play an important role in this context [1–6]. Moreover, among others, the dynamic temperature behavior dictates the performance of the battery pack. The dimensioning of the cooling plays an important role in this manner [7]. In the early concept phase of a BEV and in this case the battery pack, many decisions must be made which have a major influence on the aforementioned aspects. Normally, simulation models are created to answer essential initial questions and to assist the cell selection process, as well as more general conceptual questions regarding the whole battery pack. More complex simulation models like 3D electrochemical or electrothermal finite element models require a great deal of computational power, especially when transient simulations are needed to answer important questions [8]. Therefore, a method is developed, which can speed up those simulations by a factor of more than 1,000 without losing to much accuracy of result. By creating metamodels with standardized pre-simulations of the models, the dynamic behavior can be emulated. It is shown, that by evaluating these meta-models in sequence, transient simulations can be executed without the time-consuming solving process of finite element models. Hence, it is possible to investigate a multitude of possible configurations in a much shorter and less computational expensive way. Keywords – lithium, ion, battery, meta-model, simulation, transient, optimization, cell size, thermal
I.
INTRODUCTION
In the early stage of the concept phase for a new battery electric vehicle’s (BEV) battery pack, an important part of the development is the decision on the correct battery cell (cell size, cell shape and chemistry). It has a major influence on many of the following components decisions, like the cooling system or the internal interconnections or the performance which all influence the aging behavior etc. [7]. In [9] is shown, that parallel interconnections within the battery, for example, lead to a more efficient energy utilization. Looking more closely at today's BEV market, a
bright variety (shape and capacity) of cells installed in BEV's battery packs can be found [10]. On the one hand, it is mainly larger OEMs which are using large cells in accordance with the German Association of the Automotive Industry (VDA) standard, with up to a 60–66 Ah capacity. When such cells are used to reach a voltage level of 300– 400 V, usually only a serial connection is necessary to get sufficient battery capacity of 20 kWh (e.g. BMW i3). On the other hand, Tesla Motors is using 18650 (and 21700 from now on) battery cells to build up packs under the use of a massively parallel connection. At this point, questions emerge as to whether a rather simple battery pack layout with large cells is the best solution, or it is Tesla Motors’ greater effort, with its use of a large quantity of small cells. To answer this question, the influence of the cell size on efficiency, safety, weight, cost, thermal behavior and aging will be investigated. Thus, a method emerges to define the optimum cell size for given boundary conditions. In [11] a method is shown to optimize the geometry of a battery cell under the aspects of the maximum temperature and temperature distribution in a battery cell. Furthermore, it was shown that the cell size optimization process took quite a while because many finite element simulation runs (of one cell) were necessary until the optimization algorithm found a solution to the problem. Therefore, the simulated driving cycle had to be simplified, to speed up the transient thermal simulations. Anyway, the optimization of larger cells (30 Ah and more) took sometimes 1–2 weeks on a quad core workstation (Intel Xeon E5-1620). Thus, a way must be found, to reduce the computational complexity of the problem. Unfortunately, methods like model order reduction (MOR) were found to be unsuitable for the problem, because it is impossible to reduce input or output dimensions beforehand, since maximum temperature could emerge anywhere in the model, for example. Therefore, a method is created to speed up this process, by developing a meta-model based transient thermal simulation of lithium ion battery cells. II.
OPTIMAL CELL SIZE
The VDA, together with German automakers, has developed DIN 91252. This standard describes different shapes of battery cells that can be used in PHEVs and BEVs. But recently one can see a transition away from these
standards, once again raising the question of which shape and capacity is the right choice for a vehicle or a modular battery pack design. To answer this question many aspects must be considered. •
Package
•
Production
•
Cost
•
Safety (thermal runaway, propagation etc.)
•
Electrical aspects (efficiency, behavior etc.)
•
Thermal aspects (performance, aging etc.)
NCR18650PF), this leads to a capacity range from 2.9 Ah to 19.92 Ah. TABLE 1 VALUES AND FORMULAS OF THE PARAMETRIC CYLINDRICAL CELL MODEL
Label ljellyroll lisolation
All aspects are more or less connected with each other. Thermal aspects with safety, electrical aspects (efficiency) with thermal ones, etc. In this paper, however thermal aspects are of interest. First, the question of what a thermally optimum cell size is must be treated. Two parameters are often named in this context: The maximum temperature within a battery cell and the temperature difference, especially within the jellyroll or active material, respectively. The maximum temperature must be kept below a certain value and so does the temperature difference in the cell. Various reasons can be cited and are described here [3, 4, 12–17]. Assuming that the manner of cooling is already defined, the size and the shape of the cell are the determining factors of the thermal behavior. Making the cell smaller reduces the maximum temperature, because of lower currents at a given C-rate. Furthermore, the cooling gets more effective because of shorter distances from the cell’s core to the surface, where the cooling is normally applied. The same reasons can be stated for the explanation of a smaller temperature difference in the cell with shrinking cell dimensions. It is the other way around with larger cells, where maximum temperature and temperature difference rises [16, 18]. Thus, the question is, what the limit of the cell dimension is, under given boundaries like the cell shape, way of cooling, load, etc. Hence, the objective function is to maximize the cell’s dimension or the cell’s capacity, respectively. Restrictions are the maximum temperature and the temperature gradient within the cell.
lpositive terminal lexcess rpositive terminal rexcess rjellyroll inside rjellyroll outside rinner cylinder dcasing dinner cylinder disolation
cell
Based on the [19] and our own disassemblies of 11 different 18650 cell brands, a fully parametric simplified model of a cylindrically shaped lithium ion cell (Fig. 1) is built, using APDL (Ansys Parametric Design Language). The length can be varied in a rage from 30 mm to 150 mm, and the diameter from 18 mm to 30 mm. The remaining geometrical parameters (Fig. 1) are calculated based on these inputs (Table 1). Based on a chosen reference cell (Panasonic
∙ Ah =
=
(1)
for a particular technology. This means, with knowledge of CR (in ΩAh) for a particular technology, it is possible to determine the resistance Rcell depending on the cell’s capacity, and vice versa. In this case [20] refers to the resistance that is used to calculate the thermal losses. Therefore, the model automatically updates electrical parametrization to reproduce this relationship. Independently if radius or length is altered, based on the reference cell (Panasonic NCR18650PF) the specific resistance of the jelly-roll’s material is altered so as to meet the resistance calculated based on eq. (1). B. Meta-modelling A meta-model is a mathematical representation of a computationally much more complex model [21]. [21] describes it as “model of a model”. Using meta-models often makes sense when computationally demanding models need to be evaluated multiple times, such as for optimization problems.
MODELING
A. Parametric cell models The process of optimization by the meta-model based rapid simulation technique shall be demonstrated, using the example of cylindrically shaped lithium ion cells.
0.936(length – dcasing – dIsolation – lexcess) 0.03(length – dcasing – dIsolation – lexcess) 0.034(length – dcasing – dIsolation – lexcess) 0.64725 mm radius – dIsolation – dcasing 0.6(radius – dcasing) rinner cylinder + dinner cylinder radius – dcasing 2.0 mm 0.275 mm 0.275 mm 0.2 mm
Moreover, depending on the chosen cell dimensions, electrical parameters must be updated according to [20]. [20] describes that it is reasonable to assume that
radius rpositive terminal rexcess rinner cylinder
III.
Values/Formula
jellyroll positive terminal isolation inner cylinder casing positive tab
dinner cylinder lexcess lpositive terminal lisolation
dcasing ljellyroll length
Fig. 1 2-dimensional illustration of the parametric model
dIisolation
According to [21] the original model can be seen as a function : ℝ → ℝ which maps a number of k real inputs (x) to another set of real outputs l (y).
Development of a parametric cell model
Further on, for each scalar response y, a meta-model can be built to approximate the true response:
Validation of the simulation model
= ( ) (2) where s(x) describes the meta-model that tries to predict the response of the real model. The approximation of s(x) is generally not exactly the same and will differ from y.
Pre-simulations (simulated time duration 1 s), of 25 different cell sizes and 8 different C-rates in Ansys Classic Writing result file
= +ℇ= ( )+ℇ (3) ε can be used as a stopping criterion while building the model. C. SUMO-Toolbox Because of its handling simplicity, it is decided to use the SUMO Toolbox from [22, 23] to build the needed metamodels. This Toolbox can be used with Matlab and can work with different data sources, such as scattered datasets from a text file, Matlab models that are directly executed and controlled by the SUMO Toolbox, or complied simulation models in the form of executable files. As described later, scattered datasets are used as input source which are processed by the toolbox. Thus, the toolbox does not have the control over the input values but simply processes the data. The data is presented to the toolbox by a simple text file where the input and output data are arranged in columns. Every row in the data file represents one dataset. In the toolbox’s configuration files, the number of in- and outputs are configured. Also, the names, type and range of the input values are configured as well as the type of model builder. In this case it has been decided to use kriging as model builder because it is used in many engineering applications [21]. The stopping criteria for the model builder can either be the maximum number of datasets or the aforementioned error criterion. In the early stage of development generation of enough datasets is tried to enable the error stopping criterion before the dataset is depleted. A more efficient way for the future would be direct control by the SUMO toolbox of the input variables, which led in the first stage of development to some, so far unsolved, problems with Ansys Classic. For future use and automation of model building this is definitely a topic to solve. IV.
APPROACH
Fig. 2 describes the overall approach which is presented in the following. A. FEM-simulation Based on the previously developed parametric thermal model in [11], it was extended to a thermal-electrical one (simulation parameter can be found in Table 2). This model considers Joule heat generation, which is implemented in ANSYS 15. For cell optimization, high current loads are of particular relevance. Since, in this case, the component of Joule heat outweighs reversible and irreversible heat generation, those components are ignored.
Reading result file Building of three meta-models (Tavg, Tdelta,max, Tdelta,min) with MatLab and SUMO-Toolbox Using meta-model based rapid simulation technique for thermal cell optimization for three different driving scenarios Fig. 2 General Approach
A homogeneously abstracted jellyroll is used for the adaptation of the cell’s electrical behavior. For this, measurements were carried out on a battery test system, BaSyTec CTS. Charging and discharging current pulses at various SOC and temperatures were performed on the reference cell Panasonic NCR18650PF. Resulting voltage drops and jumps were evaluated after 1 s, out of which the respective electrical resistances can be calculated. A duration of 1 s was chosen, because the meta-models are designed for 1 s intervals. Using ANSYS Workbench, the specific resistance of the jellyroll was parameterized to generate an electrical resistance that is equal to the real reference cell. As mentioned before, in order to comply with the requirement of Pistoia according to eq. (1), the parameterization for different cell sizes is dependent on the length and the radius. B. Thermal measurement Before using the FEM-model to build meta-models, the thermal behavior had to be validated by comparing it to the reference cell. To perform the measurements, the battery test system BaSyTec CTS was used. Five highly accurate PT100 sensors were fixed on the terminals and the lateral cell surface. The electrical load on the cell is the “Artemis Urban” current cycle. It is a fictitious driving cycle with a duration of 980 s, which is very dynamic due to the frequently changing charging (max. 1C) and discharging (max. 1.7C) phases. Both, the measurement and the FEM-simulation repeated the Artemis cycle five times, so that each experiment has a total duration of 4,900 s. To validate the model, two different approaches are used. In the first approach with adiabatic test conditions, the best possible thermal insulation is sought during the experiment. Therefore, the cell is embedded in a Styrofoam housing. In return, in the simulation any heat exchange with the environment is suppressed.
As Fig. 3 shows, in the first 1,200 s the two curves are well in agreement. After that, the simulated temperature rises steadily with the same slope, while the measured temperature starts to saturate.
For the simulation model, parameters in Table 2 were used. The values indicated with "ref" refer to the reference cell and are automatically adapted for deviating cell geometries. TABLE 2 SIMULATION PARAMETERS
40 simulation
temperature in °C
38
Component
measurement
kg
m3
36 valid
34
invalid
Jellyroll
32 30
Pos. terminal Casing
28 26 24 0
1000
2000 3000 time in s
4000
5000
Fig. 3 Adiabatic thermal comparison between FEM-simulation and measurement
The second approach (Fig. 4) is a comparison between a non-isolated cell and a simulation with adapted parameters. The influence of the free convection is taken into account with a heat transfer coefficient α of 10 W/ (m2 K) on the entire lateral surface [24]. A heat transfer coefficient a of 80 W/(m2 K) on the surfaces of the positive and negative terminals represents the heat conduction through the power cables. During the first 700 s, the temperatures of the experiment and the simulation are almost identical. In phases of high current loads the differences of the two curves increase and sink again at low currents. As the number of cycles increases, a convergence takes place. The diabatic comparison shows satisfying results regarding the intended purpose. 30
10 simulation
29
measurement
Current cycle
8
28
4
Phase with high current load
26
2
25
0
24
-2
23 22 0
1000
2000
3000
4000
-4 5000
time in s
Fig. 4 Diabatic thermal comparison between FEM-simulation and measurement
current in A
6
27
Inner cylinder Isolation Positive tab
This behavior can be explained by the fact, that the experimental conditions are not ideal adiabatic. Despite the low thermal conductivity of foamed polystyrene, heat exchange with the environment obviously takes place. Previous measurements show that the sensors fixed at the terminals have the lowest temperatures. It is assumed, that the welded power cables allow heat flux from the interior of the cell to the outside of the experimental setup.
temperature in °C
Density
Heat capacity
Thermal conductivity
kg K
m K
J
W
Electrical resistivity Ω m
2965.5
1480.7
λ0 = 55.0 λ90 = 5.0
7900.0
477.0
42.0
1.8 10-7
7900.0
477.0
42.0
1.8 10-7
7900.0
477.0
42.0
950.0
2100.0
0.42
1.0 1030
2700.0
896.0
235.0
ρref = 1.02 10-7
ρref = 0.0084
ρref = 1.8 10-7
C. Ansys-MatLab The general procedure developed is the evaluation of the thermal-electrical behavior of the simulation model within one second and its representation in a mathematical metamodel. The status change during the simulated second depends on several parameters (boundary conditions): •
Cell size
•
Cooling parameters
•
Start temperature
•
Temperature gradient
•
C-rate
These parameters are combined to full-factorial variations. Each combination is simulated for one second and represents a dataset that ANSYS automatically writes to a new row of a scattered text file. Fig. 5 shows the schematic approach to meta-modeling the FEM-simulation. The upper part represents the presimulation phase, whereas the lower part describes the metamodel based thermal simulation using meta-models, which is explained further below. The critical and relevant values for optimization are the jellyroll’s maximum temperature Tmax and its maximum temperature difference Tdiff. Attempting to create metamodels for these temperatures and to generate a wellperforming thermal simulation out of it failed. The reason for this is the dynamic behavior of Tmax, which occurs at local, varying spots. To avoid this problem, the average cell temperature is considered in the first step. Therefore, the element temperatures calculated by ANSYS have to be averaged in two levels. The component temperature Tc is the average of all its elements (with temperature Te) weighted according to the respective element volume Ve:
=
∑
(4)
∑
The weighted average of all components’ temperatures Tc, according to their heat capacities CC (which is calculated from the components mass mc and its specific heat capacity cc), leads to the average cell temperature Tavg: =
∑
∑
(5)
By using the cell’s average temperature, it is ensured that the entire heat energy change during the simulation is taken into account. This allows a sufficient representation of the thermal behavior in meta-models. In order to be able to reproduce Tmax and Tmin, the differences between the extreme values and Tavg are additionally considered:
Tdelta,max =Tmax - Tavg
(6)
Tdelta,min =Tavg - Tmin
(7)
The entire handling of simulation and data generation is controlled by Matlab. Several loops combine the input parameters with each other and then executes ANSYS in batch mode. This lowers the effort of the user. For each cell size three result files are generated. For Tavg, Tdelta,max and Tdelta,min, they contain the input and output variables for each parameter variation. D. SUMO The result files created by ANSYS represent the data required for generating the meta-models in the SUMO toolbox. For a specific cell size and a specific cooling scenario, the text file of Tavg consists of two inputs and one output per data set. The inputs are the C-rate and the initial average temperature before the simulation (Tavg,start). The final temperature after the simulation (Tavg,end) is used as the output (Table 3).
Unlike Tavg, the transient behavior of Tmax and Tmin is not independent of the temperature distribution within the cell, due to their local occurrence. An exemplary comparison illustrates this: An applied current load I1 on a cell, with a homogeneous temperature distribution (which equals Tambient), always leads to an increase of Tmax. However, if there is a large temperature gradient within the cell (Tmax>Tambient) due to a high preceding current I2>I1, a low current intensity I1 can even lead to a reduction of Tmax. Therefore, the metamodel Tdelta,max additionally requires the input value Tdelta,max,start. TABLE 3 META-MODEL INPUTS AND OUTPUTS
Meta-model Tavg Tdelta,max Tdelta,min
Input 1 C-rate C-rate C-rate
Input 2 Tavg,start Tavg,start Tavg,start
Input 3 Tdelta,max,start Tdelta,min,start
Output 1 Tavg,end Tdelta,max,end Tdelta,min,end
After settings (e.g. range of values, stopping criterion and parameter names) are made, the model builder is started by the SUMO-Toolbox. It iteratively reads data sets from the scattered input file and uses them for building and training the meta-model. This is done until the desired error stopping criterion is reached. Regarding Tavg the error score is set to ε = 0.001, for Tdelta,max/min it is ε = 0.01. Once all three meta-models of a cell size are generated, a first thermal simulation run based thereon, can be executed. As with the FEM-simulation, a current cycle and a starting temperature must be specified. The C-rate is defined through the chosen current cycle. For the first time step, the entered start values represent the input variables for the evaluation of the meta-models. The results generated act as input values for the following time step (Fig. 5). This iteration continues until the end of the current cycle is reached. By summing the values of Tavg and Tdelta,max, the maximum temperature Tmax can be reproduced. The procedure for Tmin is the same. V.
META-MODELS
In first investigations, only one cooling variant is modeled. A heat transfer coefficient α of 70 W/(m2 K) on the entire lateral surface represents forced air cooling [24]. Also, 20 °C is assumed for the coolant temperature. The considered temperature range of the cell is between 20 °C and 45 °C. Maximum current load of the cell is limited by a charging rate of 1 C and a discharging rate of 3 C, of which 8 subdivisions turned out to be a sufficient resolution. At this level of development, no SOC and current-direction dependency is integrated into the meta-model based simulation. Although it is successfully implemented in the FEM-model, a takeover into the meta-model method leads to significantly longer model building effort. The utilized specific resistance is an average value of a SOC between 30 % and 80 %. Since the cells of an electric vehicle are operated in this range for most of the time, this is a valid simplification. Fig. 5 Procedure for generating meta-models based on thermal FEsimulations
In order to analyze the behavior of the average temperature, a closer look in a 2-dimensional section of the Tavg meta-model at Tavg,start = 25 °C is shown in Fig. 7. Increasing the current load leads to a quadratic increase of the average cell temperature. For this exemplary scenario, at least a discharging rate of -2.1C is necessary to keep the temperature at 25 °C. With a lower current load, the temperature drops due to the cooling settings. VI.
22.2 22 21.8 21.6 21.4 21.2 21 20.8 0
VALIDATION
For validation the FEM-simulation and the meta-model based simulation have to be compared. All settings (meshing, current load, cooling, etc.) are the same as the settings used to create the meta-models. At the model boundaries (20 °C), inaccuracies can occur. Therefore, the starting temperatures are 21 °C in each case. The current cycle used is based on a fictitious highway scenario and consists of three parts. At the beginning, constant travel (300 s) takes place, which discharges the batteries with 1 C. Subsequently, braking occurs for a period of 10 s. The battery system recuperates with 1 C. Immediately thereafter, an acceleration phase, which also lasts for 10 s, discharges the cells at the maximum permissible C-rate of 3 C. In total, the duration of one period is 320 s. Figure 6 shows the course of both Tmax and Tmin for the simulation and the meta-models, for a duration of 1500 s. As shown in Fig. 6, there is good agreement between both methods. Both the overall course and the temperature peaks are almost equal. •
Tmax,FEM = 22.24 °C; Tmax,meta = 22.26 °C
•
Tdiff,FEM = 0.60 °C; Tdiff,meta = 0.60 °C VII. PERFORMANCE-COMPARISON
The main reason why the meta-model-based method is developed is the long computational time for the FEM25.02
25.01 Tavg,end in °C
22.4
temperature in °C
In total, 25 different cell sizes were examined. Five radial gradations between 9 and 15 mm, and five grades in the longitudinal direction of 65 to 150 mm. Since there are three meta-models for each geometry, in total 75 meta-models.
200
400
600
800 time in s
1000
1200
simulation T_max
meta-model T_max
simulation T_min
meta-model T_min
1400
Fig. 6 Comparison of Tmax and Tdiff between meta-models and FEMsimulation
simulation. For the smallest cell size considered (18650), a quad core (Intel Xeon E5-1620) workstation requires about 10 h to simulate a current cycle of 3600 s. Larger cells with more FE-elements need proportionally more time. By using the meta-model-based thermal simulation, a conventional notebook (Intel Core i5) requires only 3 s for the same cycle, regardless of the cell size. Exporting the meta-models to Matlab-Functions leads to the fact that the SUMO-toolbox is not required for evaluation. Apart from the time saving, this is a big advantage, since no software is needed in addition to Matlab. VIII. SCENARIOS AND OPTIMIZATION RESULTS Due to the rapid calculation, a full-factorial examination of all cell sizes is possible for the optimization. For all 25 cell sizes, Tmax and Tdiff are determined for a given current cycle. Interpolation is carried out between the grid points. Given the upper limits for Tmax and Tdiff, the cell with the largest capacity (CN) is to be found. Three different driving scenarios and two different restriction combinations are investigated. In all cases, the aforementioned air cooling is applied. At the maximum load, the cells are discharged with 3 C for 1200 s. The highway/acceleration scenario is the same as explained above during validation. The city cycle is a mixture of acceleration (max. 1 C), constant slow speed and recuperation phases (max. 0.5 C) with a total duration of 4900 s. Optimized cell sizes can be found in Table 4. TABLE 4 THERMALLY OPTIMIZED CELL SIZE FOR DIFFERENT SCENARIOS
25
24.99
24.98 -3
-2.1
-2.5
Tmax = 35 °C Tdiff = 5 °C -2
-1.5 C-Rate
-1
-0.5
0
Fig. 7 2-dimensional section (at Tavg,start = 25.0°C) of the Tavg meta-model
Max. Load
Highway/ Acceleration
City cycle
R = 14.6 mm L = 150.0 mm CN = 18.83 Ah
R = 15.0 mm L = 150.0 mm CN = 19.92 Ah
R = 15.0 mm L = 150.0 mm CN = 19.92 Ah
Tmax = 34.96 °C Tdiff = 3.46 °C
Tmax = 24.31 °C Tdiff = 2.37 °C
Tmax = 21.14 °C Tdiff = 0.27 °C
Tmax= 30 °C Tdiff= 2 °C
R = 9.7 mm L = 150.0 mm CN = 7.94 Ah
R = 13.7 mm L = 149.6 mm CN = 16.46 Ah
R = 15.0 mm L = 150.0 mm CN = 19.92 Ah
Tmax = 29.96 °C Tdiff = 1.39 °C
Tmax = 23.88 °C Tdiff = 2.00 °C
Tmax = 21.14 °C Tdiff = 0.27 °C
Considering the maximum load scenario, the results are displayed in graphics. Fig. 8a) shows the maximum temperatures reached as a function of the cell size. The maximum temperature difference is plotted in Fig. 8b). IX.
DISCUSSION
A. Optimization results It can be seen, that a maximum allowed temperature of 35 °C and a temperature difference of 5 °C does not lead to smaller cell sizes. Every dimension can fulfill the restrictions in all three cycles. By reducing the maximum temperature to 30 °C and a temperature difference of 2 °C, the radius of the optimum cell is smaller than the boundary radius of 15 mm. The cell length is not affected. It is likely to assume that the relatively high axial heat conducting value and the assumption, that the whole lateral surface, independent of the cell length, is cooled, is the reason for this result. B. Meta-model based simulation To derive a meta-model from an existing FE-model of a cylindrical battery cell took more than 300 h on a modern
With a proper design of experiment (DOE) the calculation effort could be significantly reduced, because with the right subset of well-selected design points, the number of simulations can be minimized. Furthermore, so far the temperature difference is not considered when building the meta-model for the average temperature. New findings have shown that the meta-model based simulation of larger battery cells has a larger error in the average temperature, which can be reduced by considering the temperature difference also in the average temperature model. Moreover it can be found, that it is necessary to increase the bit length of Ansys Output values. Especially at low currents, when the temperature difference between Tstart and Tend is small, the meta-model result of the temperature difference of one time step could be zero, if not accurate enough. This could lead to a stagnant temperature course, whereas the simulation model’s temperature slightly changes. These errors accumulate over time. The usage of this method has its limitations. Based on the type of model, it is sometimes hard to derive meta-models with accuracy high enough (ε < 0.01) for transient metamodel based simulations. Reasons can be an erratic model behavior or the wrong choice of input values or missing input values, respectively.
a)
Tmax in °C
quad core workstation for 25 geometries between aforementioned geometrical boundaries. Thus, using metamodel based simulation technique only makes sense when multiple scenarios (in this case different current cycles) are to be evaluated. If a different type of cooling is to be investigated, a new meta-model set must be generated. Generating meta-models for more complex, or lager models, respectively, can take more than 2 weeks.
35 34 32 30 28 15 14
12 R in mm
10 9 65
110 130 L in mm
85
150
b)
C. Assumptions The method of extrapolating the electrical and thermal behavior based on a reference cell is an important topic to discuss. The assumption is, that a cell manufacturer can produce a multitude of cell dimensions only by cutting different lengths off the anode, cathode and separator coils. Nonetheless it is necessary to perform more tests with different cells to validate the assumption that extrapolation of [20] and moreover, extrapolation of the thermal behavior is valid.
Tdiff in °C
X. 3 2 1 15
14
12 R in mm
10 9 65
85
130 110 L in mm
Fig. 8 Results of Tmax a) and Tdiff b) at maximum load (3C, 1200 s)
150
OUTLOOK
The integration of a suitable DOE and therefore a connection between the SUMO-Toolbox and Ansys are the next logical steps. As mentioned before, at the moment, the toolbox only processes the scattered datasets that are generated beforehand with Ansys. This is no efficient way of producing meta-models with high accuracy. Moreover Kriging may not be the right choice as model builder. First tests with a polynomic model builder are promising, because fewer simulation runs were necessary to generate a metamodel with high accuracy (faster decrease of e). The present paper illustrates the newly introduced method with a cylindrical shaped lithium ion battery cell.
With meta-model based simulation models for parametric pouch and prismatic battery cells, it will be possible not only to determine the perfect cell size, but also the perfect shape depending on given boundary conditions, such as the cooling system or driving cycle, etc. Despite the original intention to speed up a timeconsuming thermal simulation, this method can be used for a multitude of similar problems. Generally speaking, this method should be suitable for every transient problem, where MOR does not meet the requirements. Therefore, it is necessary to map the dynamic behavior of a model onto a meta-model. The challenge is to identify the necessary input and output values. Furthermore, because of the low computational effort to evaluate the meta-models, it is also possible to implement them into an onboard controller. Thus, it would be possible to perform an online thermal performance prognosis for the battery in a BEV, depending on the current temperature. Hence, battery aging can be reduced, and the overall performance of the drive train can be raised, because, mostly the battery is the limiting component. XI.
CONCLUSION
It has been shown that meta-model based transient simulation can speedup transient simulations by a factor of more than 1,000, without losing too much accuracy. This enables rapid optimization of the cylindrical cell dimensions for a given current cycle. It has been shown, that a limitation of the maximum temperature of 35 °C can be fulfilled by almost every cylindrical cell geometry. A reduction of the maximum temperature to 30 °C leads to smaller cells. Moreover it is shown that the newly introduced method is already working at its early stage of development. ACKNOWLEDGMENT The research was conducted with basic research funds from the Institute of Automotive Technology. Prof. Dr.-Ing. Markus Lienkamp made an essential contribution to the conception of the research project. He reviewed the paper for relevant scientific contribution. Mr. Lienkamp gave final approval for this paper to be published and agrees to all aspects of the work. As a guarantor, he accepts responsibility for the overall integrity of the paper. REFERENCES [1]
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