Machine learning-enabled performance prediction and optimization for iron–chromium redox flow batteries†

Yingchun Niu‡ , Ali Heydari‡ , Wei Qiu , Chao Guo , Yinping Liu , Chunming Xu , Tianhang Zhou * and Quan Xu *
State Key Laboratory of Heavy Oil Processing; China University of Petroleum (Beijing), Beijing 102249, China. E-mail: zhouth@cup.edu.cn; xuquan@cup.edu.cn

First published on 8th February 2024

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1. Introduction

Renewable energy sources like hydropower, wind, and solar energy have gained significant attention due to the growing concern over energy shortages and environmental issues.^1,2 It is projected that by 2050, renewable energy will become the primary source of energy with an average annual growth rate of 3.6%. Within this renewable mix, solar and wind energies are expected to contribute around 70% of the total output.³ However, one major challenge with these renewable sources is their inherent volatility and intermittency. This makes their practical applications difficult without a reliable way to store excess electricity generated during peak production periods. Electrical energy storage plays a crucial role in improving grid-connection flexibility for renewables, enhancing power grid reliability, maximizing the utilization of renewable resources, extending the infrastructure lifespan, and improving the power quality.⁴ Batteries serve as an effective solution by storing electrical energy from renewables in chemical form and converting it back into usable electricity when needed. Therefore, battery technology can greatly accelerate the adoption and integration of renewable energies into our existing grids. Redox flow batteries (RFBs) offer several advantages that make them particularly attractive for large-scale storage applications. One key advantage is their ability to independently design capacity or energy requirements within a wide range – from 100 kW up to 100 MW for power and from 100 kW h up to 100 MW h for energy. RFBs also possess inherent safety features along with easy expandability options at moderate costs while providing flexible operation capabilities.^5,6 The basic components of RFBs include electrodes (cathode/anode), bipolar plates, membranes/ion exchange membranes or porous separators, as well as two external tanks used for holding electrolyte solutions.⁷ These electrolytes on both sides are pumped into porous electrodes where they undergo electrochemical redox reactions at the electrode surfaces while being separated by membranes/separators to prevent mixing between the anode and cathode sides.^4,8 When evaluating RFBs, common performance indicators include energy efficiency (EE), capacity decay rate, current density, and coulombic efficiency (CE).⁹ These indicators are crucial for understanding battery performance and long-term operational stability.

The iron–chromium redox flow battery (ICRFB) is recognized as the first true redox flow battery.^10,11 It utilizes abundant and low-cost redox-active materials such as ferrous chloride (FeCl₂) and chromium chloride (CrCl₃), making it a cost-effective energy storage system.¹² ICRFBs are highly scalable due to their unique design that separates the energy storage capacity from power output, have a long cycle life compared to many other battery technologies, possess relatively high energy densities among flow battery systems, offer enhanced safety features and have quick response times. Researchers have made significant efforts to enhance the efficiency and optimize the performance of ICRFBs. For example, studies have been conducted by Wang et al. on various electrolyte compositions containing FeCl₂, CrCl₃, and HCl with different molar masses to understand their electrochemical performance.¹³ They concluded that with the increase of the concentration of Fe/Cr in the electrolyte, the redox reaction peak current increases. The effect of chelation has also been explored by Waters et al. using Fe diethylenetriaminepentaacetic acid (FeDTPA) and Cr 1,3-diaminopropanetetraacetic acid (CrPDTA) as additives in a KBi electrolyte.¹⁴ Investigations into indium chloride (InCl₃) addition to improve battery performance have been conducted by Wang and co-workers as well.¹⁵ The results showed that In³⁺ effectively inhibits the HER and accelerates the kinetics of Fe²⁺/Fe³⁺ and Cr³⁺/Cr²⁺ to a certain extent. Membrane thickness has also been studied, with researchers finding that commercial Nafion membranes of certain thicknesses are more suitable for high current density operation in ICRFBs.^16,17 Zhang and co-workers further researched the electrochemical properties of PGF and CF with added BiCl₃ catalyst.¹⁸ Additionally, studies by Li et al. have focused on improving the electrocatalytic performance of graphite felt electrodes through treatments such as boric acid thermal etching to enhance hydrophilicity.¹⁹ After H₃BO₃ thermal etching, the hydrophilicity of the graphite felt was obviously enhanced.

The performance of an iron–chromium redox flow battery (ICRFB) stack is influenced by factors such as materials, architecture, and operational conditions. Achieving optimal performance requires significant effort and time through experimental optimization of these components. To expedite the research and development (R&D) process and facilitate commercialization, it is crucial to explore innovative methods for accurately predicting the performance of ICRFB stacks and overall systems. Currently, R&D efforts in ICRFB technology rely on a combination of simulation, design, and experimentation to develop efficient stack configurations with suitable materials. However, this conventional approach can be resource-intensive and costly. Furthermore, it can be challenging to precisely determine how different factors impact system performance and cost. To address these challenges specific to ICRFBs, researchers are actively exploring novel techniques that enable accurate prediction of stack performance without relying solely on extensive experimentation. These methods involve computational modeling approaches that simulate various scenarios while optimizing materials selection and stack designs. By employing predictive models tailored for ICRFBs, researchers aim to streamline the R&D process while gaining valuable insights into how different factors influence the system performance and associated costs. This approach holds great potential for accelerating advancements in ICRFB technology towards successful commercialization.

In recent years, machine learning (ML) techniques have emerged as powerful tools for accelerating various aspects of material development,²⁰ chemical synthesis planning,²¹ catalyst activity tuning,²² and system optimization.²³ These ML approaches have demonstrated their ability to efficiently predict and optimize the performance of different battery types.^24,25 Despite these advancements in other fields, there has been limited research focusing on applying ML techniques for prediction and optimization specifically in iron–chromium redox flow battery (ICRFB) systems. The prediction of battery efficiency remains challenging due to limited databases and the inherent bias in feature selection. Recently, a promising approach called active learning has emerged as an alternative method for designing and optimizing systems in various domains. Active learning, a subfield of machine learning, involves the iterative selection of unseen data points by surrogate models to improve the predictive capability of these models. This iterative process involves using the previous model, trained based on the observed results, to guide the selection of the next set of experiments. As a result, the gathered data points are utilized iteratively to update and improve the model. Active learning holds great potential for reducing computational costs associated with battery design, while also incorporating and guiding experimental data and procedures.

This article aims at using a data-driven, active-learning model to accurately predict and optimize the performance of ICRFB systems. We use active ML to rapidly design battery characteristics and operation characteristics to improve the performance of ICRFB systems (Fig. 1). The surrogate mode can be used as a guide to evaluate the most and least effective factors in the design and evaluation of ICRFBs. Post hoc analysis of the data and ML models reveals important relationships between specific battery characteristics and battery performance, providing mechanistic insight into how different features can affect the energy efficiency, coulombic efficiency, and capacity of ICRFBs. Overall, this framework will automate and accelerate the optimization of ICRFBs for the transition from laboratory scale development to industrial scale deployment.

2. Data collection and analysis

The dataset for the iron–chromium redox flow battery (ICRFB) was compiled by extracting 303 data points from all the literature sources available on ICRFB optimization. Each data point was accompanied by recorded parametric settings in the datasheet. The dataset consists of eleven input variables and three output variables, namely coulombic efficiency, voltage efficiency, and capacity. To ensure accuracy in our study, we utilized precise numerical values mentioned in the literature for continuous variables. For discrete variables, specific code numbers were assigned to represent different categories using LabelEncoder. It is important to note that due to the relatively low number of published works on ICRFBs compared to other popular types of redox flow batteries and incomplete reporting of experimental conditions across all literature sources, the number of features available in our dataset is limited. The flow rate and current density values in the collected dataset ranged from 12.5 mL min⁻¹ to 200 mL min⁻¹ and from 40 mA cm⁻¹ to 320 mA cm⁻¹ respectively. As for electrodes considered in our analysis, we focused on commonly used ones such as carbon felt (represented as CF) and graphene felt (GF), all with or without thermal treatment denoted with T such as TCF/TGF respectively. In our compiled dataset, the membranes studied included ion exchange membrane (IEM), Nafion212 (N212), Nafion115 (N115), and Nafion117 (N117). Additionally, two electrolyte additives were considered: Bi³⁺ (bismuth) and In³⁺ (indium). Finally, the size range for electrodes spanned between 4 cm² and 50 cm². The electrolyte concentration varied from 0.5 to 1.5 molar concentration. Finally, the datasets are collected for different cycle numbers each with 5 steps. This comprehensive dataset provides a valuable foundation for our study, enabling us to explore and analyze the relationships between different parameters and the performance of ICRFB systems. Note that temperature is not included in the features due to the fact that almost all the investigated manuscripts evaluated the battery performance at a temperature of 65 °C. Therefore, temperature was not considered as a feature within this research. The full list of input features is given in Table 1.

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The data processing and ML modeling for this study were conducted using Python 3.7, utilizing popular packages such as NumPy, pandas, and sklearn. Initially, the dataset was collected from previous literature. After defining the features and output variables, the dataset was split into train and test subsets. Next, hyperparameters were tested and corrected. To handle the multidimensional nature of the dataset, four different models, namely linear regression, random forest, extra trees regressor and gradient boosting were utilized to select the most accurate model based on the prediction accuracy. Machine learning (ML) is a broad concept that relies on statistical models and data analysis. Upon providing the computer with a rule discovery algorithm and sufficient relevant data, it can uncover previously unknown connections between input and output variables, a process commonly referred to as “training.” Once trained, the model can be utilized to forecast the extent of correlation between various input features and target output variables. After ensuring the accuracy of our models, the gradient boosting model was selected as the most accurate model to calculate the efficiency parameters for each unique combination of features.

3. Results and discussion

3.1. Performance of ML models

In this study, a performance prediction model for redox flow batteries was developed using an operating parameter-based approach, specifically focusing on the operating current density. The analysis revealed a linear correlation between the operating current density and output parameters, particularly voltage efficiency (as shown in Fig. S1a and b†). When applying a regression for building the prediction models, it is crucial to select appropriate features. Given the higher linear correlation observed between the operating current density and efficiency parameters compared to other features, the operating current density was identified as the main feature. Other input parameters that were deemed to significantly influence the battery performance were included as auxiliary features. To ensure transparency and clarity, all features used in each model are already listed in Table 1 of this manuscript.

To assess the accuracy of our model, we divided the dataset into a training set comprising 75% of the data and a test set containing the remaining 25%. This division allowed us to evaluate how well our model predicted various performance metrics. The evaluation results are presented in Table 2. The coefficient of determination (R²), mean absolute error (MAE) and mean squared error (MSE) for different models were calculated for the test sets as shown in Table 2. These results demonstrate that our ML methodology yields accurate predictions for key performance metrics of ICRFB systems across the datasets. The comparatively higher accuracy values of the gradient boosting model indicate that our model captures and analyzes relationships between system characteristics and performance outcomes more effectively than other models.

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Thus, gradient boosting is chosen as the best model for further predictions and optimizations. Fig. 2a illustrates the distribution of collected experimental datasets from the literature resources. The residual plots for gradient boosting model predictions are given in Fig. 2b–d and the training and testing of the models are done based on the same data points. We evaluate the performance of the models based on their coefficient of determination (R²), mean absolute error (MAE) and mean squared error (MSE). The test scores for voltage efficiency, coulombic efficiency and capacity show high accuracy, as indicated in Fig. 2b–d and Table 2. It is also worth noting that the predictions for coulombic efficiency, although satisfying, have lower accuracy in all four utilized models compared to the prediction accuracies for voltage efficiency and capacity.

3.2. Transferability of the selected model

To examine the transferability of our ML model in predicting battery efficiency, we conducted a systematic analysis. We built several models with different efficiency ranges and evaluated their performance outside the training data range. In order to optimize each model's performance, we adjusted the associated hyperparameters.

In our dataset, we determined the mean voltage efficiency, coulombic efficiency, and capacity. We collected training data points that were centered around these mean values. For our first case, we selected training data points that were within 5% of the mean output values, while the remaining points were used for testing. We repeated this process for six more cases, gradually expanding the range of training datasets to 10%, 20%, and 30% of the calculated mean output value. Fig. 2e–g illustrates the absolute error in the model's prediction for both the training and test datasets for the model with 30% training size. Other results are summarized in ESI Fig. S2.† We observed that all three models performed reasonably well in predicting the data points within the training range and the nearby region. However, the error in prediction increased as we moved further away from the training data range. Additionally, we found that the capacity and voltage efficiency prediction models had higher R² values compared to the coulombic efficiency prediction model, especially for smaller ranges of training data. The R² values for the coulombic efficiency prediction model became comparable to those of the voltage efficiency or capacity models when the training data size accounted for approximately 25% of the overall dataset (Fig. S3†).

3.3. Explainability of the selected model

In this section, our attention is directed towards examining the relationships between various properties of iron–chromium redox flow batteries and their output efficiencies. To achieve this, we employ the SHAP³² analysis on our GB model. The objective is to identify the most influential features that impact the battery's efficiency, as illustrated in Fig. 3a–d. For further illustrations, SHAP force plots are also provided in Fig. S4† within their corresponding mean values in Fig. S5.† Furthermore, we rank the importance of features in each efficiency model, which is depicted in Fig. S6.† Upon comparing these two figures, we notice a striking similarity among the top features identified for each output variable. However, the difference lies in the order of importance assigned to these features. Fig. 3b–d illustrates the relationship between the values of the top descriptors and the efficiency prediction of the model. The analysis is based on the SHAP (Shapley additive explanations) values, which provide insights into the contribution of each feature to the model's prediction. If higher feature values correspond to more positive SHAP values, it indicates a positive effect of the feature on the efficiency prediction. In other words, the feature is directly correlated with battery efficiency, and higher values of the feature tend to result in higher efficiency. Conversely, if higher feature values lead to more negative SHAP values, it signifies a negative effect of the feature on the efficiency prediction. This implies an inverse correlation between the feature and battery efficiency, where higher feature values are associated with lower efficiency. As we observe, the electrode type and cycle number seem to be the most common important features among all the efficiency parameters. Obviously, the cycle number is of great significance as it indicates the battery performance degradation after each cycle which is commonly known as the decay rate among the scientific community. Besides, the electrode type has a direct relationship with the reaction rate; thus, utilizing different electrodes will greatly affect the battery performance as proven by previous literature.²⁶ Furthermore, current density has a remarkable influence on voltage and coulombic efficiency. This further confirms the results of various research articles regarding the performance of iron–chromium redox flow batteries.^13,15,33 This is why the electrode size seems to have a comparatively higher impact on capacity. This relationship could be due to the fact that higher current densities can lead to increased electrochemical reactions, resulting in changes in voltage and coulombic efficiency whereas the size of the electrodes in iron–chromium redox flow batteries has a significant influence on the battery's capacity. It is also worth noting that Bi³⁺ has a moderate but notable influence on the performance of batteries due to its strong effect on battery stability as implied by researchers earlier.^26,27,29 Other features such as electrolyte and other catalyst concentration, flow rate and membrane type are considered to have less effect on battery performance. Fig. 3e and f demonstrates SHAP values for each electrode and membrane type respectively. As shown in Fig. 3f, batteries utilizing CC and TCC electrodes correspond to the highest influence on values of performance efficiency due to specific defect sites engineered by the authors applying these electrodes.²⁶ As shown in Fig. 3e, performance parameters are primarily affected by utilizing N117 and N212 membranes due to their proof to have the highest effect on decreasing and increasing battery performance respectively.¹⁶

Fig. S5† shows the factors that have a direct or inverse relationship with battery efficiency based on the SHAP values. Accordingly, an increase in electrolyte and catalyst concentration will generally result in enhancement of battery efficiency and performance. This is why an increase in current density will result in an overall decrease of all the performance variables of the battery. The effect of utilizing each electrode is also depicted in Fig. S7.† While TCC can be considered as an electrode that simultaneously enhances all the performance variables, TiN-3D GF has a negative influence on all the performance parameters, leading to less efficiency. The rest of the electrode types do not possess universal influence on battery performance and their function must be separately investigated for each performance parameter.

3.4. Optimization of the batteries

As previously mentioned, after consideration of model accuracies and adjustment of hyperparameters for utilized models based on Fig. S8–S10,† gradient boosting was selected to perform active learning. Active learning of battery efficiency prediction was conducted through 10 iterations using a gradient boosting predictive model. Each iteration involved exploring 30 candidate samples, consisting of voltage efficiency, coulombic efficiency, capacity, and their associated feature values. The goal of the optimization process was to maximize the performance efficiency of the batteries. To evaluate the performance of the optimizer, the focus was on identifying sequences with higher maximum performance efficiency compared to the maximum performance achieved in the previous iteration. This approach ensured a continuous improvement in the battery's efficiency throughout the active learning process. Finally, the model recommends optimum batteries with the following design: a flow rate in the range of 50 to 100 ml min⁻¹, with electrode types of CP, CF, TCC, TGF and CC using IEM, N115 and N212 membranes, when operated in current densities between 40 and 80 mA cm⁻² along with the electrode size in 25–50 cm² interval leading to excellent values of energy efficiency of around 83–86% and capacity of 1.5–1.9 A h. These findings further confirm the results shown in the SHAP plots provided in Fig. 3.

Determining the appropriate stopping criteria for an iterative process, such as active learning, is crucial in optimization algorithms. Typically, the process is terminated when the desired outcome of the target property has been achieved or when the computational budget has been exhausted.³⁴ In this study, the number of iterations was set to 10, and the desired efficiencies were successfully obtained within this limited number of iterations. Given our theoretical understanding of the problem, it is known that the maximum voltage and coulombic efficiency cannot exceed 100 percent. Therefore, the desired solution was considered to be slightly less than this maximum value. By setting a predefined number of iterations and considering the theoretical limits of the efficiency parameters, the active learning process was effectively terminated once the desired efficiencies were obtained within the specified constraints. Detailed information can be found in the ESI.† Based on the analysis of Fig. 4a, after 10 iterations, the optimum values were observed to be approximately 88% for voltage efficiency, approximately 98% for coulombic efficiency, and approximately 1.75 A h for capacity. These values indicate the desired performance levels achieved by the model after the active learning process. Notably, voltage efficiency and capacity require around 4 or 5 iterations to achieve noticeable optimization. On the other hand, coulombic efficiency demonstrates a distinct behavior, necessitating at least 8 iterations to exhibit a substantial increase that can be considered as an optimized efficiency value. This disparity in convergence rates among the efficiency parameters highlights the differing optimization requirements and sensitivities of the battery system.

In order to assess the reliability of the proposed model, TCC and SCC electrodes from the ML mode (Fig. 4b, indicated by pink and blue star symbols, respectively) were selected for validation due to accessibility in our lab. The prepared two electrodes were analyzed by XPS. As shown in Fig. 4(c) and (e), the C 1s spectrum is resolved into five peaks at 284.7, 285.3, 286.5, and 289 eV, representing graphite carbon, defect carbon, C–O, and O–CO, respectively. As shown in Fig. 4(d) and (f), the O 1s spectra of the two samples consist of three peaks attributed to CO (531.8 eV), C–OH (532.3 eV), and H–OH (533.2 eV). In order to analyze the pore size distribution of the two electrode materials, BET (Brunauer–Emmett–Teller) testing was conducted to confirm the defect structures of TCC and SCC electrodes. The adsorption/desorption isotherms of TCC and SCC electrodes shown in Fig. 4(g) are typical type IV isotherms, indicating that the surfaces of the two electrode materials have high adsorption capacity. At the same time, the BET surface area of the TCC electrode was also found to be 0.6637 m² g⁻¹, and the BET surface area of the SCC electrode was 0.7052 m² g⁻¹. Its sufficient specific surface area provides abundant reaction sites for the electrode.

In the liquid flow battery testing system used in this study, the concentrations of iron ions, chromium ions, and acid are 1.2 M, 1.4 M, and 2.5 M, respectively. Additional 0.001 M bismuth ions will be added as a catalyst. Carbon cloth electrodes measuring 5 cm long and 2 cm wide are used as the positive and negative electrodes of the battery. Nafion 212 membrane was used as the separator between the positive and negative electrolytes. The electrolyte volume in both the positive and negative slots is maintained at 80 mL. During battery testing, the circulating flow rates of the positive and negative electrolytes were set to 20 mL min⁻¹. The performance of ICRFB was measured using a potentiostat/galvanostat. The battery operates at a current density of 140 mA cm⁻² in constant current mode. To prevent overcharging and over-discharging during the testing process, the upper and lower voltage limits are set to 1.2 V and 0.7 V, respectively. Fifty charging and discharging cycles were performed. Keeping the above conditions constant, experiments were conducted using electrodes modified with TCC and SCC, respectively. The test results are shown in Fig. 4(h) and (i). For TCC electrodes, the optimization results from the ML model are an energy efficiency of 82.69% (experiment: 82.73%) and a capacity of 1.769 A h (experiment: 1.755 A h). For SCC electrodes, the optimization results from the ML model are an energy efficiency of 83.31% (experiment: 83.15%) and a capacity of 1.785 A h (experiment: 1.776 A h). The experimental results demonstrate astonishing agreement with the predicted efficiency values which further validates the developed model to be used for efficiency prediction and optimization of iron–chromium redox flow batteries in the future. However, due to limitations in experimental equipment, we failed to test the most optimized cases explored by the active learning approach. Therefore, those cases are supposed to be tested in future research investigations.

4. Conclusions and recommendations

Optimization of the operation conditions and selection of key materials provide a powerful approach for the rational design of next-generation ICRFBs. In this study, by integrating active learning techniques with 303 data points from the existing literature, we have developed a robust design framework to efficiently discover optimized materials–operation combinations for the optimization of ICRFBs. Our work demonstrates that the interaction between innovative computational methods and empirical research can lead to optimized properties and prediction accuracy. The models we developed provide superior performance prediction for three fundamental parameters: coulombic efficiency (CE, R² = 0.9859), voltage efficiency (VE, R² = 0.9212) and capacity (R² = 0.9940). The data-driven approach also provided interpretable insights into ICRFB systems, identifying that the operation conditions (current density and cycle number) and the electrode type are the most critical descriptors affecting the voltage efficiency and coulombic efficiency while the electrode size strongly affects the capacity. In addition, the active learning protocol employed here ensures that the learning process is dynamically adjusted, driving efficient exploration of the vast design space inherent in ICRFBs. After 10 iterations, the optimum values were observed to be approximately 88% for voltage efficiency, approximately 98% for coulombic efficiency, and approximately 1.75 A h for capacity. The TCC electrode and SCC electrode are selected for the experimental validation with energy efficiency (error: ±0.15%) and capacity (error: ±0.8%) in our lab.

This work paves the way for extensive future studies in which the methodology can be extrapolated to a range of other variables. This extension could include the addition of state of charge parameters, additional electrochemical behaviors and even cost analysis to provide a more rounded view of the potential for ICRFB deployment. Furthermore, the flexibility of the framework suggests that it could be adapted to investigate other battery chemistries, different electrode and membrane configurations, or a wider range of operating conditions. The application of ML not only enhances the ability to identify complex patterns within rich datasets, but also sets the stage for molecular and structural-level simulations that could elucidate the mechanisms underlying battery stability and longevity in the future. Encouragingly, this research suggests a potential shift away from purely empirical paradigms towards one that integrates predictive modelling as a core component of battery development. A more targeted experimental compass, informed by the predictive power of ML models, could dramatically streamline the path to discovering high-performance materials, saving both time and resources in the pursuit of advanced energy storage solutions.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This manuscript is supported by the National Natural Science Foundation of China (22308376 and 22308378) and the Science Foundation of China University of Petroleum (ZX20230080, ZX20230078, 2462023XKBH005, and CNIF20230209).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3nr06578b

‡ These authors contributed equally to this work.

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