The cost model is divided into two modules: Battery Cell Design and Cost Calculation. The first module is responsible for designing batteries in the three standard geometries, following user-defined performance requirements; the second module calculates the costs of the necessary materials and manufacturing costs. Our cost model is implemented in MATLAB
® (Version R2021a), and it facilitates automated and expedited cost estimations compared to traditional, spreadsheet-based models like BatPaC [
7].
Figure 2 illustrates the model framework: the user provides battery performance and composition parameters, which are used to design compliant battery cells. Subsequently, using process-specific and facility-wide parameters, the production time for a single battery cell is calculated based on its geometry and design. This enables the calculation of the required machines and facility size, ultimately resulting in the production cost estimation for each designed cell.
2.1. Battery Cell Design
The Battery Cell Design module prompts users to input the following information: (i) the desired cell energy in Wh, denoted as
; (ii) the cathode thickness in micrometers,
; (iii) the chosen cathode and anode materials; (iv) the cell dimensions in millimeters. Initially, the module calculates the mass of active material in the cathode using Equation (
1), which relates the energy stored in a cell with the product of the cathode mass, the specific capacity of the cathode, and the cathode’s average discharge voltage.
where
is the mass of positive active material;
and
are the specific capacity and average discharge tension of the positive active material—both these values are known and available in the literature. Variables in the model are denoted as
, where
X represents a physical property and
y indicates the associated component, as described in
Table 1 and
Table 2.
Next, the module computes the total mass of the cathode by considering the mixing percentages of the cathode components, including the binder and carbon black:
Since electrodes are usually described by their active material and the mixing percentage of other components, the density of the cathode is given by a weighted average of the individual components (Equation (
3)). The porosity is also considered in the calculation.
Finally, the density is used to determine the total volume and area of the cathode, as in Equation (
4). The volume of the cathode is the ratio between the corresponding mass and density, while the area is given by the ratio between the calculated cathode volume and the user-defined cathode thickness.
where Equations (
1)–(
4) are valid for all cell geometries, but the following steps in the cell design are different for stacking and winding type cells. Once the total area and volume of the necessary cathode material are known, the Battery Cell Design module calculates how to incorporate it into the battery geometry.
Pouch and prismatic cells are modeled as stacked cell layers, while cylindrical cells are winded (
Figure 3). Through the user (iv), the length and height of the cell frame are defined; the missing dimension, the width, is calculated by the Battery Cell Design module. The area of each bi-layer is calculated from the user-defined cell frame dimensions, and the battery cell will have as many bi-layers are necessary to reach the total cathode area and volume, determined in Equation (
4). The anode coating in a layer is modeled to be slightly larger than the cathode to guarantee full overlap between the positive and negative active materials: there is an excess length of two mm on each side of the anode (Equation (
5)). The internal area of pouch and prismatic cells are calculated differently. The thickness of the seam in pouch cells is substituted by the thickness of the cell can and cell top in prismatic cells.
Subsequently, the number of bi-cell layers is calculated by Equation (
6). Our model only allows integer layer numbers, taking the next smallest integer (ceil) in case of a fractional result, and adjusting the cell parameters according to the added cathode material. Once the cathode parameters are determined, the relevant anode dimensions are calculated with a linear system (Equation (
7)), analogous to Equations (
1)–(
4). The addition of the N:P term dictates a higher ratio of anode–cathode, guaranteeing the minimum battery performance standards are determined by the positive active material.
For the stacking of bi-cell electrode layers, the thickness of one layer is given by:
which, multiplied by the total number of layers, results in the internal width of the battery cell. The width of the current collectors is divided by two to account for the electrode coating in both sides of the collector.
Cylindrical cells, on the other hand, are modeled as the winding of a long, bi-cell, electrode layer; the user input (iv) is the cell height; the missing dimension, the diameter, is calculated by the Battery Cell Design module. Initially, the electrode lengths are determined from the total cathode area and the internal height of the cell with a system of Equation (
9); the two mm anode excess is considered.
Subsequently, the other anode parameters are determined in an analogous manner to stack-type cells through Equation (
7). To calculate the resulting diameter, we consider the electrodes to be coiled into an Archimedean spiral, with
(Equation (
10)) as the distance between loops.
The Battery Cell Design module outputs the complete battery dimensions. For pouch and prismatic cells, the width is calculated based on the user-input length and height. For cylindrical cells, the diameter is calculated based on the user-input height. Additionally, the module calculates all necessary materials to meet the specified performance parameters.
2.2. Cost Calculation
We estimate the production costs of the designed lithium-ion cells using a process-based cost modeling (PBCM), considering industry-standard manufacturing processes for cylindrical, pouch, and prismatic cell formats. The PBCM approach is widely recognized and utilized across various industries to estimate costs in a production chain. Berckmans et al. [
16] adopted this methodology to compare the costs of NMC- and silicon-based batteries. Other studies have developed PBCMs focused on specific cell formats: Ciez and Whitacre [
12] exclusively analyzed cylindrical cells, while Duffner et al. [
17] studied the production of pouch cells.
The production steps considered in our PBCM is outlined in
Figure 4. The processes from mixing to vacuum drying constitute the electrode manufacturing stage; they are followed by cell-assembly processes, which are different for pouch and prismatic cells, marked with the number one, and for cylindrical cells, marked with number two. The manufacturing cost is calculated summing the labor, energy, equipment, maintenance, building, and overhead costs of each process. The total production cost is the sum of materials and manufacturing cost.
Table 3 shows the facility-wide parameters adopted to calculate the costs. Similar to the cell parameter user inputs, these could be altered to represent different scenarios.
We estimated the costs of each production step by contacting manufacturers and from proprietary studies conducted at the Chair of Production Engineering of E-Mobility Components at RWTH Aachen University. The estimates are included in
Table 4. For the cell-assembly processes, the rates refer to the production of cylindrical cells with a capacity of
Wh, and for the stack-type cells, they refer to cells with a capacity of 170 Wh. In the cost model, the process rates are adjusted for the cell capacity according to Equation (
11).
where
and
are the processing time per cell in seconds and the cell capacity in Wh of the reference cell.
and
represent the same properties but for the designed cell. We adopted a scaling factor of
, which represents the cost advantages of producing larger cells. Lastly, the electrode precursor prices, such as lithium, were determined from U.S. Geological Survey [
18], converted to EUR. The price of all precursors was considered in the total electrode price. For example, NMC622 is composed of nickel, manganese, and cobalt, aside from lithium. The relative weight of each component contributes to the total price of NMC622 in our model.
The Cost Calculation module uses facility-wide and process-specific parameters from
Table 3 and
Table 4, along with battery cell designs from the previous module, to determine the average processing time for a single cell at each manufacturing stage. From this, the cost model calculates the total process time—considering the yearly production of the modeled facility—identifies the required number of machines, and estimates the necessary factory space and resource usage for each manufacturing stage.
2.2.1. Electrode Manufacturing
Electrode production (first line in
Figure 4, and first section in
Table 4) involves mixing active materials, carbon black, solvent, binder, and additives in proportions determined by the electrode configuration. The resulting slurry is coated onto copper (anode) and aluminum (cathode) foils using slot dies or doctor blades. Coating parameters like thickness, speed, and width are crucial for economic efficiency. The solvent in the slurry must be removed by letting the electrodes dry, often using a float dryer [
19]. The subsequent calendering compresses the coated foil to adjust porosity and enhance adhesion. This process is very efficient in terms of costs and has little potential for improvement since it is already mature [
20]. At this point, the electrodes are slit into smaller coils, and undergo vacuum drying to remove residual moisture and solvent in an oven for 12 h to 30 h at low temperatures of 60 °C to 150 °C [
21].
2.2.2. Cell Assembly
The cell assembly steps differ depending on the cell geometry. For cylindrical cells, after the final drying, in the electrode manufacturing stage, electrode coils are sorted in the following order: anode–separator–cathode–separator. These layers are wound into a cylindrical shape and packed into the cell housing. Cell tabs are welded to contact terminals before sealing. The cell container is, then, filled with electrolyte and sealed a final time. Afterwards, the cells undergo formation, which includes the initial charging and discharging under defined conditions to create the solid electrolyte inter-phase (SEI) [
22]. Before being tested and classified, the cells age for up to three weeks while their open-circuit voltage is monitored.
Pouch and prismatic cells have added production steps. Each electrode layer is separated from the electrode coils. The individual sheets are then stacked (anode and cathode alternating with separator sheets in between) into a defined order and stack size. Similar to cylindrical cells, the stacked layers are packed into a solid housing or flexible pouch foil, and filled with electrolyte. Pouch cells are submitted to an optional roll pressing stage to ensure optimum distribution and absorption of the electrolyte. Subsequently, the cells undergo formation and degassing for pouch cells, whereby gas is removed from the pouch. Like cylindrical cells, stacking-type cells are aged before being tested.
2.3. Battery Parameters
The model developed in this paper allows for the design and cost calculation of battery cells of any arbitrary size, composition, and energy capacity. We have selected a set of cell dimensions for each geometry (
Table 5), against which the model will be tested. The dimensions are market standards and serve as the industry benchmark. The Battery Cell Design module calculates the undetermined dimensions—the diameter for cylindrical cells and the width for pouch and prismatic cells.
Our selection adopts the widely recognized 18650 cells as the foundational benchmark for the cost assessment of cylindrical cells. Pouch and prismatic cells are less standardized, but their dimensions were selected similarly to cylindrical cells. We based our selection on Link et al. [
2], which identified trends in cell dimensions. The cell capacities were also determined from known market values.
The electrodes in lithium-ion cells can be made from various materials and a multitude of combinations. However, the fundamental technological differences lie in the cathode materials used; anode materials are generally standard. The choice of different cell chemistries depends significantly on the application of the battery. Variations can be observed in aspects such as energy density, lifespan, performance, safety, or costs [
23]. The most relevant cell chemistries for cathodes include lithium iron phosphate oxide (LFP), lithium manganese oxide (LMO), nickel cobalt aluminum oxide (NCA), and nickel manganese cobalt oxide (NMC).
LFP-based cathodes, with their lower volumetric energy density, are anticipated to be used in buses, trucks, and stationary energy storage systems in the future. Although they exhibit faster self-discharge and lower energy density compared to other types of cathodes, they offer enhanced safety [
24]. LMO cathodes are among the more affordable options, as, like LFP, they contain neither nickel nor cobalt. However, their lower capacity often necessitates blending with NMC cathodes. The proportion of LMO in cathodes may decrease in the future as manufacturers strive to extend the range of EVs, a goal often unmet by LMO’s limited capacity alone [
25]. NCA cathodes, although considerably more expensive, offer higher capacity, energy density, and longevity [
26]. However, their thermal instability presents certain safety risks [
27]. Due to these disadvantages, NCA-based cathodes are losing relevance [
27,
28]. The most commonly used type of cathode is the NMC cathode, which is available in various compositions such as NMC-111, NMC-442, NMC-523, NMC-622, and NMC-811; the trailing numbers indicate the ratio of nickel, manganese, and cobalt [
29]. For the analysis of battery production, we compare the main battery cell chemistries: NMC532, NMC 622, NMC 811, NCA, LFP, and LMO.