Microsoft Word - PRES22_0064.docx DOI: 10.3303/CET2294023 Paper Received: 01 April 2022; Revised: 15 May 2022; Accepted: 27 May 2022 Please cite this article as: Domalanta M.R.B., Castro M.T., Del Rosario J.A.D., Ocon J.D., 2022, Cost Analysis of a Sodium-ion Battery Pack for Energy and Power Applications using Combined Multi-physics and Techno-Economic Modeling, Chemical Engineering Transactions, 94, 139- 144 DOI:10.3303/CET2294023 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 94, 2022 The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš, Sandro Nižetić Copyright © 2022, AIDIC Servizi S.r.l. ISBN 978-88-95608-93-8; ISSN 2283-9216 Cost Analysis of a Sodium-ion Battery Pack for Energy and Power Applications using Combined Multi-physics and Techno-Economic Modeling Marcel Roy B. Domalantaa,c, Michael T. Castroa,c, Julie Anne D. del Rosarioa,b,c, Joey D. Ocona,b,c* aLaboratory of Electrochemical Engineering (LEE), Department of Chemical Engineering, University of the Philippines Diliman, Quezon City 1101, Philippines bEnergy Engineering Program, National Graduate School of Engineering, College of Engineering, University of the Philippines Diliman, Quezon City 1101, Philippines cNascent Energy Technologies, Quezon City, Philippines jdocon@up.edu.ph The renewable energy transition requires energy storage technologies for grid-balancing and transportation. Lithium-ion batteries have been widely adopted for these applications, but supply risks due to geopolitical tensions have motivated the search for alternative chemistries less dependent on critical raw materials. Sodium- ion batteries have garnered notable attention as promising post-lithium chemistry due to the relative abundance of sodium and its similar manufacturing process to lithium-ion batteries. This work estimated the cost of producing sodium-ion battery packs from cells optimized via multiphysics modeling for energy or power-based applications. This study replicated a multiphysics model of a pouch format sodium-ion battery from literature in COMSOL Multiphysics®. This model determined the optimal active material used in batteries under 0.1C to 10C discharge rates to maximize the energy density. The cost of battery packs produced from the optimized cells was then determined using the Battery Performance and Cost (BatPaC) model of Argonne National Laboratory, which considers material and manufacturing costs. The optimization results reveal that energy cells have thicker electrodes and lower porosities (217 μm thick 0.11 porosity anode, 237 μm thick 0.10 porosity cathode for 0.1C), which maximize the amount of active material per unit mass. Power cells have thinner electrodes and larger porosities to minimize electrical resistance (58 μm thick 0.32 porosity anode, 63 μm thick 0.31 porosity cathode for 10C), reducing energy losses at high currents. Moreover, we compared the calculated production cost for energy and power applications for sodium-ion batteries, highlighting essential parameters affecting the price. The model observed a 26.42% increase in total material cost per kWh when transitioning from energy to power cells. The model may also be refined by considering sodium-ion batteries with different cathode and anode chemistries in different formats and their applications in different use cases. 1. Introduction Lithium-ion batteries (LIBs) have been the prevalent energy storage since their commercialization in the 1990s. The high energy capacity and technological maturity of LIBs have attracted various use cases, from mobile applications to grid-scale energy storage and transportation. Although a prominent candidate in energy storage, there have been growing concerns regarding the sustainability aspect of LIB components such as lithium sources and rare transition metals used as cathode material. Non-sustainable mining practices, limited availability, and accelerating energy storage demand increases the price of LIBs and components. These challenges of LIBs engage interests in studies to pioneer post-lithium energy storage that would meet the performance of existing LIB chemistries without sacrificing economics and sustainability. One perceptible prospect is the use of sodium in place of lithium. Sodium (Na) is a low-cost and highly abundant alternative to lithium. Furthermore, several studies theorize that Na-ion behaves similar to Li-ion in its rocking chair mechanism of intercalation and deintercalation. Na-ion batteries (NIBs) have a redox potential close to existing 139 LIBs, appealing for applications where weight and volume are not of much concern, such as stationary energy storage, power tools, and light-duty electric vehicles. NIBs have taken the energy storage market at an accelerating pace where various market players have given tremendous research efforts and investments to develop ground-breaking NIB technologies (Chen et al., 2018). The design of individual cells is typically performed via multiphysics modeling, which simulates the reactions and ion transport in an electrochemical system. The model can determine the distribution of continuum-scale parameters, such as concentration, potential, and temperature, in a battery (Li et al., 2015). More importantly, the model can determine the allocation of materials that optimizes the performance of a battery. For instance, Schneider et al. (2019) used a NIB multiphysics model to determine the electrode thicknesses and porosities that maximize the energy density at various C-rates. The authors investigated the environmental impact of Na- ion batteries through a life cycle assessment from the optimized material usage. Multiphysics modeling was also utilized to optimize LIBs (Hosseinzadeh et al., 2017), lead-acid, and vanadium redox flow batteries. A review of these studies can be found in (Castro et al., 2021). BatPaC is a bottom-up cost and battery pack design modeling tool developed by Argonne National Laboratory (Nelson et al., 2019). A unique advantage of BatPaC is that the battery electrochemical performance, such as power and energy metrics, can be bridged to analyze the cost to performance relationship of a battery design. The chemistry and design of the battery can be modified to compare and screen various materials and the impact of altering their properties, such as dimensions, pricing, and sizing. A study by Vaalma et al. (2018) compared the cost and performance of existing LIB technologies and exchanging materials to tailor-fit the NIB chemistry for stationary power applications. Their works concluded the price advantage of NIB technologies would overcome LIB when the supply of lithium and rare earth materials in LIB becomes an issue and the price point increases. Another study by Peters et al. (2019) examined the economic impact of a cylindrical cell geometry for LIBs and NIBs. The study notes that existing NIB technologies may have difficulty matching the price per kWh of LiNiMnCoO2-graphite (NMC) in energy density but would have a competitive economic and performance advantage against LiFePO4-graphite (LFP) for stationary applications providing enhanced safety, cycle life, and viable cost. Despite multiphysics and cost and performance modeling being powerful tools in breaking the laboratory barrier of battery chemistries to advance commercial applications, no study has been reported to merge these techniques to analyze NIBs. This study addresses the research gap by developing a multiphysics model for NIB and translating the optimized cells' relevant parameters to establish the economic comparison of manufacturing energy and power-type NIBs by providing detailed information on the cost contribution of cell components. 2. Methodology The methodology is divided into three parts, where the schematics are shown in Figure 1. First was the multiphysics modeling of the NIB varying performance of energy and power applications. Second, the generated multiphysics model's optimized parameters were translated to the cost model to demonstrate battery production economics. Lastly, the cost and performance correlation of the optimized energy and power NIBs were investigated. Figure 1: Schematic representation of methodology from multiphysics modeling to cost analysis and finally, cost- performance examination of NIBs. 2.1 Multiphysics modeling The NIB considered in this work utilizes a hard carbon anode, NaNi1/3Co1/3Mn1/3O2 cathode, and NaPF6 electrolyte and is described in Schneider et al. (2019). The battery is described by the pseudo-2D (P2D) model illustrated in Figure 2, which couples the 1D charge and mass transport of Na+ ions across the battery (i.e., from the anode to cathode during discharge) and the 1D diffusion of Na+ ions into the spherical electrode particles. Na+ ion transport in the electrolyte is described by Newman's concentrated solution theory, which accounts for the interactions between ions in addition to diffusion, migration, and convection effects. The porous electrodes 140 are also modeled according to Newman's porous electrode theory, which averages their solid and liquid phase properties weighted according to their volume fractions. It is worth noting that the P2D model was pioneered by Doyle, Fuller, and Newman (1994) for LIBs and has been applied in the modeling of NIBs (Chayambuka et al., 2022). The mathematical formulation of the P2D model and the input model parameters are detailed in the work of Schneider et al. (2019). This work replicates the same model in COMSOL Multiphysics®. Figure 2: Schematic diagram of the P2D model. 1D mass and charge transport across the battery is coupled with 1D diffusion into the electrode particles. After building the multiphysics model, the anode thickness, porosity, and cathode porosity are determined. The battery's energy density is maximized under various C-rates: C/10, C/4, 1C, 4C, and 10C discharge until a 1.8 V cut-off voltage. Low C-rates result in optimized cells for energy, while high C-rates yield batteries designed for power. Note that the cathode thickness is adjusted. Its coulombic capacity balances the anode's, as described by Schneider et al. (2019); hence it is not optimized like an independent variable. 2.2 Cost and performance modeling The Battery Performance and Cost (BatPaC) 4.0 model was used to investigate the cost of NIBs geared towards energy and power applications (Nelson et al., 2019). The multiphysics model of NIBs allows the determination of integral parameters that impact the target application of the battery pack, whether for energy or power. These parameters were carried forward to the cost model to determine their influence on the battery expense. The optimized parameters for NIB energy and power cells used in the study are shown in Table 1. This study analyzed a 7 kW, 11.5 kWh prismatic battery pack consisting of 72 cells designed for stationary applications adapted from the works of Vaalma et al. The BatPaC model was modified to adhere to specific energy and power requirements used in this study (Vaalma et al., 2018). Since large-scale production of NIBs still lack commercial cost data, pack material costs of NIB cells were adapted from the works of Vaalma et al. (2018).The material costs for various NIB performances obtained in the model were compared with LIB chemistries such as LFP and LiNi0.33Mn0.33Co0.33O2-graphite (NMC-333). Furthermore, the cost distribution of individual cell components and the material cost pack energy price of NIBs was analyzed and compared with LIBs. Table 1: Optimized parameters from the multiphysics model translated to the BatPaC model Parameter Energy Cell Power Cell C-rate where parameters were optimized C/10 C/4 1C 4C 10C Cathode active material capacity (mAh/g) 119.00 119.00 119.00 119.00 119.00 Cathode active material density (g/cm3) 4.7500 4.7500 4.7500 4.7500 4.7500 Cathode electrolyte volume fraction 10.384 12.985 25.281 22.764 31.330 N/P ratio after formation 0.9989 0.9989 0.9989 0.9989 0.9989 Anode active material capacity (mAh/g) 329.00 329.00 329.00 329.00 329.00 Anode active material density (g/cm3) 1.7000 1.7000 1.7000 1.7000 1.7000 Anode electrolyte volume fraction 10.635 16.832 23.546 15.058 31.601 Open circuit voltage at 20% SOC (V) 2.3916 2.4093 2.3863 2.3939 2.3424 Open circuit voltage at 50% SOC (V) 2.8048 2.8184 2.774 2.6889 2.5383 LIB chemistries parameters and material costs use default BatPaC 4.0 values. 3. Results and discussion 3.1 Multiphysics modeling The optimized electrode thicknesses and porosities, and cell energy densities of energy and power cells are presented in Figure 3. It can be readily observed that energy cells have thick electrodes and low porosities, while power cells have thin electrodes and high porosities. The difference is because energy cells must have a higher coulombic content, utilizing larger and densely packed electrodes. In contrast, power cells are plagued with ohmic losses due to higher currents; hence, they need thinner electrodes and larger porosities to minimize electrical and ionic resistances. Ohmic losses in power cells also explain their lower energy density than energy 141 cells. It is worth noting that Schneider et al. (2019) and Hosseinzadeh et al. (2017) observed similar trends in electrode thicknesses and porosities during the optimization of NIBs and LIBs, respectively. Figure 3: Optimized electrode thicknesses and porosities and the resulting cell energy densities at various C- rates relative to their values at a discharge C-rate of 1. 3.2 Cost and performance modeling Table 2: NIB pack material cost distribution generated from BatPaC Cost per battery pack Energy Cell Power Cell C-rate where parameters were optimized C/10 C/4 1C 4C 10C Cathode ($/pack) 291.2802 289.9448 294.3518 303.1949 320.2595 Anode ($/pack) 219.5146 218.4143 221.4064 228.1189 240.4765 Carbon and binders ($/pack) 50.75068 50.50169 51.29572 52.92181 56.04062 Cathode current collector ($/pack) 30.63340 31.34421 36.87249 36.83832 43.54778 Anode current collector ($/pack) 32.19790 32.94491 38.67315 38.62207 45.60770 Separators ($/pack) 218.0745 223.2704 263.2035 262.8592 311.6324 Electrolyte ($/pack) 82.73342 102.9603 163.7348 137.0237 234.6476 Cell hardware ($/pack) 61.32324 61.67397 63.02704 62.76461 64.97423 Module hardware ($/pack) 250.1180 250.4179 253.0477 253.9965 259.8645 Battery jacket ($/pack) 257.8318 259.0939 283.4248 263.0981 312.1787 Total cost of materials ($/pack) 1494.460 1520.570 1669.040 1639.450 1889.230 Total battery pack energy price ($/kWh) 124.5400 126.7100 139.0900 136.6200 157.4400 The results of the cost of NIB pack on energy and power cells in terms of materials and total energy cost are summarized in Table 2, and an analogous figure is shown in Figure 4a. Figure 4: Material cost distribution of NIB pack (a) varying from energy and power applications and (b) in terms of average material contribution. The NIB pack optimized for 10C operation intended for quick energy release and rapid response power applications exhibits the highest cost. The NIB pack optimized for C/10 operation intended for long-usage and long-cycling energy applications exhibits the lowest cost based on materials and energy price. A cost increase of 26% was observed comparing the C/10 energy cell and 10C power cell. The results show a general increasing total cost of material and pack energy price as the C-rate increases. This relationship denotes higher prices for NIB power cells compared to energy cells. Figure 4b illustrates the average individual cost distribution of NIB pack components. The cost distribution presents that the cathode price contributes the most to the overall 142 material cost (18.25%), followed by the battery jacket (16.75%) and the separator (15.57%). When neglecting the non-active component, such as the battery jacket, these results are analogous to Hirsh et al. Their study displayed the same cost trend for NIBs containing nickel, cobalt, or both (Hirsh et al., 2020). Despite the separator being the third most expensive component, for an energy NIB pack optimized for C/10, Table 2 exhibits that the anode cost is higher than that of the separator, indicating lesser separator materials are used for energy applications. This finding exposed a gap in current NIB studies focusing on lowering the cost of electrodes. An equally integral aspect of cost reduction is the separator which must also be prioritized and investigated. Furthermore, cost reduction on non-active material must be considered, such as the battery jacket. The energy price in terms of $/kWh was also examined for representative NIB cells and compared with commercially available LIBs shown in Figure 5a. Only the battery chemistry and respective cost of materials were substituted in the model to level the application towards 11.5 kWh stationary use cases. The model results exhibit that the NIB pack optimized for C/10 energy applications shows competitive price points against LFP and NMC-333. The NIB energy cell has a lower total material cost per energy than LFP, demonstrating a promising post-lithium alternative for energy storage in terms of economics and performance. The study of Roberts et al. emphasized how NIBs are more cost-efficient and provide higher safety and minimal maintenance than lead-acid batteries. This finding shows a promising outlook for NIBs in energy applications and would, in time, replace lead-acid batteries (Roberts and Kendrick, 2018). As NIBs are widely accepted as a drop-in technology from LIB, moving forward to NIB production would entail a more accessible entry to the market than competing energy storage technologies such as fuel cells. For a NIB pack power cell being used for stationary applications, the material cost per energy is higher than that of presented LIBs. NMC-333 and LFP are regarded to have similar power performance where this metric allows these technologies to be employed for electric vehicle (EV) applications (Ding et al., 2019). The results may indicate that using NIBs for power applications such as EVs may be more costly in the current market than existing LIB technologies. However, this study did not account for possible future market prices sensitivity. If the cost of lithium and other rare metals in the cathode material increases due to supply issues, a shift in overall costs is expected to move according to the market demand. Figure 5: Cost comparison of LIBs and representative NIBs. (a) Price of energy for full cell LIBs labeled green and NIBs labeled in maroon. (b) Battery pack material component cost distribution of LIBs and NIBs. The distribution of individual battery pack component costs of LIBs and NIBs examined are illustrated in Figure 5b. The results show an average of 13.00% decrease in cost contribution for both cathode and anode electrodes as the C-rate of application increases implying from energy application to power application. Although the cathode price increases as the use case shifts from energy to power, their cost contribution decreases, as shown in Figures 5a and Table 2. This is because thinner electrodes and larger porosities are required to lower electrical resistance for power applications. The cost contribution of the electrolyte provides the highest escalation from 5.54% for C/10 energy applications to 12.42% for 10C power applications, with an increase of 24.19% seen in Figure 4b. This finding recommends studies to heighten interest in advancing low-cost NIB electrolyte materials, notably for power applications. In contrast to LIB technologies, a general conclusion exists that NIBs have a lower cathode cost contribution than LIBs. This is mainly due to the cost of lithium and cobalt in NMC-333. Lithium alloys with aluminium at low potentials as such copper is employed as the LIB anode's current collecto which is not the case with NIBs as sodium does not alloy with aluminum at low potentials. Thus, aluminum as cathode and anode current collectors reduces the cost by substituting expensive copper. Results show that replacing the cathode and anode current collectorprovides the largest cost distribution reduction. For NMC-333 to C/10 NIB, a 40.64% cost distribution reduction was observed for cathode and 60.00% cost distribution reduction when replacing copper with aluminium as anode current collector.The combined cost and performance analysis provides insight into market viability and current use case preferential for NIBs. 143 4. Conclusions NIB technologies are receiving their comeback in interest for energy storage applications due to being a promising post-lithium alternative due to its drop-in capabilities in existing LIB plants. This study combines multiphysics modeling of NIBs for energy and power applications. It transposes the optimized parameters into a cost and performance modeling tool to investigate the impact of varying use cases on the overall cost. The multiphysics model revealed an average of 73.34% reduction in electrode thickness from energy to power cells. Energy cells tend to have thicker electrodes and lower porosities, increasing the coulombic content. In comparison, thinner electrodes and larger porosities characterize power cells to minimize ohmic losses incurred from high currents. The multiphysics model parameters were used to investigate the economics of a battery pack for stationary applications. The model demonstrates a 26.42% increase in total material cost per kWh when shifting from energy to power NIB pack. The cathode and separator provided the highest cost contribution for the active battery material. These findings suggest a research movement in engineering low-cost separators for NIBs aside from the current trend-focused solely on the electrodes. Energy cells have been found to have lower electrode cost contributions than power cells, as thinner electrodes are needed for rapid energy release in power applications. Also, NIBs designed for energy use have shown superior cost competency over existing LIB technologies being 2.59% cheaper than LFP in cost per kWh. Furthermore, cost reduction from LIB to NIB is mostly situated with the cathode price and replacing the copper current collector with aluminum. This study provides grounding on studies claiming NIBs to have a massive cost reduction with existing LIBs. Although NIBs can be a valued competitor to post-lithium chemistries, this study demonstrates that electrochemical performance must be improved to spearhead potential to market. This study provides a powerful birds-eye view of the NIB cost to performance relationship; however, it is limited to current market performance. A sensitivity analysis can be further conducted to capture future resource supply and demand outlook. Acknowledgments M.R.B.D. would like to acknowledge the Engineering Research and Development for Technology (ERDT) Graduate Scholarship. The authors would like to acknowledge the support from Nascent Energy Technologies. 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