2025, Vol. 42 
2. School of Chemical Science, University of Chinese Academy of Sciences, Beijing 100049, China
2. 中国科学院大学化学科学学院, 北京 100049
Renewable energy sources, such as solar and wind, are expected to become essential to the future energy supply under the dual-carbon target. However, their intermittent and fluctuating nature dictates that renewable energy generation requires energy storage systems to ensure a stable power supply. Large-scale energy storage technologies developed include pumped storage, flywheel, compressed air, superconductivity, and electrochemical energy storage[1-5]. Among them, electrochemical energy storage converts renewable energy into chemical energy storage, compared with pumped water and compressed air. It is not limited to the geographical environment and has a broad development prospect. As a long-duration energy storage technology, vanadium redox flow battery (VRFB) is considered one of the most promising technologies for large-scale energy storage due to its good safety, flexible design and long service life.
Redox flow batteries are distinguished from solid-state batteries by their typical characteristic of storing energy in electrolytes. Electrodes do not participate in the electrochemical reaction but are merely the place where the reaction is going. Thus, the power of the redox flow battery is determined by the cell or stack, and the capacity is determined by the concentration and volume of the electrolyte, which makes the design of the redox flow battery flexible. VRFB is easy to recover from capacity decay because the positive and negative active pairs are of the same substance, and its working principle is shown in Fig. 1. The tank is the container for positive and negative electrolytes, and the pump conveys the electrolyte through the tank to the electrode, where a redox reaction occurs on the electrode surface. The ionic membrane conducts hydrogen ions in the electrolyte, thus forming a closed-loop current system. The main electrochemical reactions on the electrode are as follows:
Positive reaction
| $ \begin{gathered} \mathrm{VO}^{2+}+\mathrm{H}_2 \mathrm{O} \underset{\text { Discharge }}{\stackrel{\text { Charge }}{\rightleftharpoons}} \mathrm{VO}_2^{+}+2 \mathrm{H}^{+}+\mathrm{e}^{-}, \\ \mathrm{E}_0^{+}=1.0 \mathrm{~V} ~~\text { vs. SHE. } \end{gathered} $ | (1) |
Negative reaction
| $ \begin{gathered} \mathrm{V}^{3+}+\mathrm{e}^{-} \underset{\text { Discharge }}{\stackrel{\text { Charge }}{\rightleftharpoons}} \mathrm{V}^{2+}, \\ \mathrm{E}_0^{-}=-0.26 \mathrm{~V} \quad \text { vs. SHE. } \end{gathered} $ | (2) |
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Fig. 1 Schematic diagram of the operating principle of VRFB |
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With the continuous development of redox flow battery, modeling techniques have been widely used in design and development in recent years due to the short research cycle, low cost, the convenience of variable coupling research, etc. The models of VRFB can be classified into various types, and different scale types of models are suitable for different application areas, mainly including aggregate models, micro-dimensional models, and molecular scale models [6-13]. Although numerical simulation can provide design and optimization ideas for batteries or stacks, it exhibits low integration with the operation process, poor coupling, and limited practical application of simulation results. This paper intends to combine models and data with digital twin (DT). It suggests applying digital models to developing and researching redox flow battery modules or systems. Creating a mapping relationship between virtual equipment (VE) and physical entity (PE) achieves more efficient and more thoughtful decision-making and management. For battery stacks, the combination of modeling and artificial intelligence (AI) holds promise as a design tool to improve battery efficiency, especially as VRFB operational data continues to accumulate. For the system, VRFBs have many components, making their management and monitoring more challenging than other energy storage systems. The application of DTs can facilitate integrating power systems with VRFBs, improve fault prediction and data management, and accelerate industrialization.
1 Overview and applications of DTs 1.1 DefinitionAs DTs have been studied and deepened in various fields, the understanding and definitions of different researchers have become increasingly diverse. The concept of DTs was first proposed by Professors Grieves and Vickers[14] at University of Michigan in 2002 for product lifecycle management. It was initially referred to as the “mirrored space model” and later named the “digital twin”. In a report released by National Aeronautics and Space Administration in 2010[15], it was mentioned that “DT is a multidisciplinary, multi-physical quantity, multi-scale, and multi probability simulation process that fully utilizes physical models, sensor updates, and historical operational data to complete mapping in virtual space, reflecting the full lifecycle process of corresponding physical equipment.” Zhang[16] summarized the definition of DTs from engineering and academic perspectives, digital model of physical object. It can evolve in real-time by receiving data from the physical object, thus maintaining consistency with the physical object throughout its lifecycle. Based on the DTs analysis, prediction, diagnosis and training can be performed, then the simulation results are fed back to the physical object, thus helping to make decisions about the physical object.
In conclusion, the different interpretations of DTs are summarised. DT is the combination of actual operational data, simulation models and machine learning technology that can simulate the actual operational state in almost real-time. Through the virtual-real interaction, the virtual mapping and operating state of the whole life cycle of the system is realized. It requires the incorporation of AI techniques, but differs from AI itself in that it is primarily based on the mapping of PE and is widely applied in domains such as industry and cities. In addition, the United States and Germany have proposed cyber-physical system[17] as the core support technology of advanced manufacturing industry. The goal of cyber-physical system is to realize the interactive fusion of the physical and information worlds. Through big data analysis, AI and other new-generation information technology in the virtual world simulation analysis and prediction, to drive the operation of the physical world with optimal results. DT also better explains cyber-physical system.
1.2 DT model architectureThe core of DT is model and data. To make it can be applied in more fields on the ground, the technical team of Beihang University developed the DTs model from the initial 3-dimensional(3D) structure to a 5-dimensional (5D) structural model[18] (Fig. 2), including PE, VE, services system (Ss), digital twin data (DD) and connection (CN)[19].
| $ \mathrm{M}_{\mathrm{DT}}=(\mathrm{PE}, \mathrm{VE}, \mathrm{Ss}, \mathrm{DD}, \mathrm{CN}) . $ | (3) |
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Fig. 2 DT 5D model[18] |
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The DT 5D model can be integrated and fused with the Internet of Things (IoT), big data and AI to meet the needs of information-physical system integration, data fusion, and virtual-real bi-directional connectivity and interaction. MDT in Eq.(3) is a generic reference architecture, CN denotes the connection between components.
1.2.1 PEPE exists objectively and is the basis for the composition of the DT 5D model, accurate analysis and maintenance of PE is a prerequisite for the establishment of MDT. Generally, PE consists of the various functional subsystems and sensory devices. Subsystems perform the predefined tasks during operation and sensors collect the states of the subsystems and working conditions. Malfunctioning of any part may cause the PE to fail. The functional subsystem generally consists of a control system, a power system, and an actuation system, and completes the task through inter-system collaboration. Various types of sensors are deployed on the PE to enable real-time monitoring of data and operational status.
1.2.2 VEVE is the digital counterpart of PE, which is the key to DT composition. Its integration includes 4 core models: geometry model (Gv), physics model (Pv), behavior model (Bv), and rule model (Rv)[20-21]. Gv describes the geometric 3D model such as size, shape, assembly relationship, which is closer to PE in terms of details and visual level. Pv builds upon Gv by incorporating physical attributes including stress, fatigue, deformation, which is portrayed from the perspective of dynamic mathematical model. Bv describes the real-time responses and behaviors generated by the external environment and disturbances, and the internal operation mechanism of the PE in different time scales with different granularity and spatial scales, which are under the joint effect of the internal operation mechanism. Rv models the rules of operation of PE, based on empirical knowledge and guidelines. These rules evolve with self-learning to equip the model with evaluation, optimization, prediction and review functions. The assembly and integration of the above 4 types of models lead to the creation of complete VE corresponding to PE.
| $ \mathrm{V E}=(\mathrm{G}_{\mathrm{v}}, \mathrm{P}_{\mathrm{v}}, \mathrm{B}_{\mathrm{v}}, \mathrm{R}_{\mathrm{v}}) . $ | (4) |
Ss serve all kinds of data, models, algorithms and simulation results in the DT process. It is oriented towards PE and VE to achieve high calibration fidelity, DD to provide data management and processing services, and CN to connect services such as data acquisition services, access perception services, and data transmission[22]. Provide integrated assessment, control, optimization, and other information systems for intelligent system operation, precise control, and reliable operation and maintenance services.
1.2.4 DD and CNDD is the driver of the DT, which includes PE data, VE data, Ss data, and domain knowledge data consisting of expert knowledge, industry standards, and rule constraints. In addition, the fusion data obtained by preprocessing, correlation, and fusion of the above 4 types of data is also included. The continuous updating and optimization of real-time data make DTs response system more comprehensive and accurate[23]. CN is a two-by-two connection of the above 4 components to enable efficient data transfer, thus enabling real-time iterative interactions to ensure consistency.
1.3 DTs applicationsThe first and foremost task of DT on-ground application is to create a DT model of the application object. In the early days, it was mainly used in the military industry, aerospace, and aviation, such as National Aeronautics and Space Administration carried out vehicle health control based on DTs[21]. The National Research Council of Canada reviewed and assessed the airframe DT framework developed by the United States Air Force[24]. The final assessment showed that the United States Air Force airframe DT framework can be adapted to support the Air Force fleets managed using individual aircraft tracking-based programs. Testing the developed cases, as shown in Fig. 3, proved the validity and reliability. The airframe DT framework improved the crack size distribution prediction accuracy by collecting information and updating the model.
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Fig. 3 Example of Bayesian updating on crack size distribution[24] |
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Due to the features of virtual-reality integration and real-time interaction, iterative operation and optimization, and full-process driving, DTs have been applied to all stages of the product lifecycle, including product design[25-28], manufacturing[29-32], operation and maintenance, and service[33-36]. Currently, the scenarios involved in DTs encompass 11 fields, including military, electric power, automotive, medical and marine[37-41]. Against the background of cutting-edge technologies such as big data, IoT and AI, industries are rapidly stepping into a new era of information and intelligence, which has extensively promoted the intelligent application of DTs. However, there are some problems in the actual application, such as the lack of systematic technical support and application guidelines for the digital modeling part, and the lack of theoretical techniques for information data fusion, interaction, and collaboration. Therefore, the application of DTs has a broad prospect while awaiting breakthroughs, especially in model construction.
2 DTs in batteriesThe application of DT technology to VRFB systems is not created out of thin air, and it has helped many aspects of battery development and management. It has already been used with significant effect on lithium-ion power batteries and energy storage batteries. Li et al.[42], for battery storage systems, transmitted battery-related data to the battery management system (BMS) cloud through IoT and used particle swarm optimization (PSO) to estimate the online charging health status of the batteries in the study. Figure 4 shows the final measured and estimated results, where the battery’s capacity fades with mean absolute error of 0.74% and the battery’s power fades with mean absolute error of 1.70%. The function of the VRFBs, which also requires a BMS, is mainly to monitor and control the battery appropriately. However, as the number and complexity of batteries increase, computation and data storage are limited, the prediction and optimization functions based on historical data are complex. Predicting battery health or more is possible with the help of a cloud management system.
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Fig. 4 Validation results of the PSO-based state of health (SOH) estimation algorithm[42] |
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Merkle et al.[43-44] have created a DT for lithium-ion batteries that allows real-time monitoring of the state of charge and SOH of the battery and estimation of internal battery resistance. The resulting DTs can provide digital visualization services to all parties involved in the lifecycle. Therefore, DTs as a systematic service benefit stakeholders, such as developers, equipment suppliers and system integrators. Zhang et al.[45] developed a DT for the real-time electric vehicle charging algorithm and charging pile arrangement. The battery DT is used for real-time monitoring of battery charging status and health and real-time estimation of battery internal resistance. Qu et al.[46] proposed a DT model that evaluates batteries’ performance mainly by accurately simulating the battery discharging process. Figure 5 shows capacity estimation results, and experimental data show the method to be accurate and robust. By incorporating a long short-term memory algorithm, the DTs improve the capacity measurement and battery performance assessment of lithium-ion batteries. For VRFBs, the prediction of non-measurable parameters and battery performance assessment are equally possible.
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Fig. 5 Capacity estimation results for cell[46] |
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In addition, Chun et al.[47] proposed a neural network-based method for real-time estimation of battery model parameters. By applying the measured parameter values to a lithium-ion battery’s DT model, the battery’s state of charge and SOH can be estimated. Wang et al.[48] provide a review of DTs in intelligent BMS, but mainly for lithium-ion power batteries. It outlines current research approaches and challenges in modeling, state estimation, lifetime prediction, battery safety and control. In addition, solutions for digital modeling, real-time state estimation, charging power, thermal management and dynamic balancing control in innovative BMS are presented based on DTs. Figure 6 shows the DT architecture of BMS.
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Fig. 6 DT framework for intelligent BMS[48] |
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As battery research has matured and intensified, problems and challenges have arisen. Its internal parameters are highly nonlinear and coupling and its life is associated with various factors. With the rapid development of big data, AI and the IoT, there is an opportunity to use DTs to deal with such complex systems. It is now possible to combine data, models and algorithms for battery health assessment, parameter prediction and safety control, particularly for the widely used lithium-ion batteries. For VRFBs, which are more system-coupled, adding DTs is more likely to facilitate further innovation and development.
3 VRFBs and DTs 3.1 Problems with VRFBsAs a long-duration energy storage and relatively mature redox flow battery, VRFBs boast intrinsic safety, high value retention, and unlimited capacity expansion. Its application scenarios in power systems include the following[11, 49]: 1)Power supply side[50-52]: tracking plan generation of wind and solar energy, ensuring the stability and continuity of combined output, and improving the quality of power generation from renewable energy power stations; 2)Grid side[53-55]: achieving load balancing of the grid, peak use of valley power, and enhancing the utilization of power generating equipment; 3)User side[56-57]: optimizing operation and configuration of distributed power generation, enabling the peak-valley arbitrage, and reducing the cost of power consumption.
Although VRFB has been developed significantly, some urgent problems must be solved. Firstly, the initial construction cost of VRFBs is several times that of lithium-ion batteries. It is the main factor restricting its development. In addition, the operating temperature zone of VRFB is narrow, and the suitable temperature is 10-40℃. Exceeding the upper and lower limits of the operating temperature will impair the system’s operating efficiency and service life. Finally, operation and maintenance technology is crucial for the management of the whole life cycle of the energy storage system, and the existing BMS is a system to manage and maintain each cell, with functions such as data acquisition, condition monitoring, state of charge estimation, charging and discharging control[58]. However, the primary function of BMS still focuses on monitoring and controlling the system, it is difficult to warn of the failure problems based on some force majeure factors.
3.2 DT benefits of VRFBsDT through the IoT, big data, machine learning and other technologies, with model construction as the core task, fully using sensor data and operating models to achieve digital simulation of PE in virtual space. The final actual operational state is realized through machine learning and related analysis[59]. For the problems identified in VRFB, DT can provide direct solution or optimizating pathways.
By simulating and optimizing the charging and discharging process of the energy storage battery, the DT of the VRFB improves the system’s efficiency, which is one of the most effective ways of reducing costs. It is a system optimization function of the DT, so it can be implemented in the VRFB. In addition, the heat transfer behavior of VRFB system is another essential task that affects the system’s performance. If the vanadium electrolyte is operated at conditions higher than 40℃, precipitation becomes a critical danger, causing a capacity drop or even line blockage. Thermal management of the VRFB system can be achieved by using DT technology, which in addition to monitoring the temperature, can also predict the system temperature and thus intervene in advance if there is a potential temperature change in the system. Finally, the DT is integrated with the BMS to aid the intelligent management of the VRFB system. Sensors are used for real-time data transmission and access to AI learning algorithms and visualization functions for operation and maintenance. Based on the above, risk diagnosis, fault warning and system optimization of VRFBs are achieved.
4 DT for VRFBs 4.1 5D conceptual DT for VRFBsThe development of the DT architecture for the VRFB system is strictly based on a 5D conceptual model, as shown in Fig. 7.
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Fig. 7 DT architecture of the VRFB |
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PE refers to all the objects of the VRFB energy storage system in the real world, including the power unit (stacks), the energy unit (electrolyte and tanks), the electrolyte delivery unit (pumps, lines, valves, and sensors, etc.), BMS, energy management system, and energy conversion system. The PE, according to its functions and structures, generally includes three levels: the unit PE, system PE, and system of systems PE. The essential operating equipment configured by the combination of stacks, tanks and circulation system is considered unit-level PE, the smallest unit to realize the function; system-level and system-systems-PE are stratified according to different application scenarios and control requirements. For example, the power reactor’s voltage monitoring and liquid level control are PE systems based on essential equipment. The analysis and optimization of voltage and energy efficiency requires studying the whole complex system level.
4.1.2 VE of VRFBsOn the other hand, the VE design of the VRFB system is an all-around, full-scale digital simulation of the battery, which can reflect the actual operating state. Currently, models on VRFB energy storage systems are mainly divided into electrochemical models[6, 60-64] and equivalent circuit models[65-68], in terms of construction principles. Electrochemical models are based on the operation mechanism, which generally include the flow field, temperature field, electric field and electrochemical reactions. VRFB operation process involves the conservation of mass, momentum, charge and energy and the kinetics of electrochemical reactions. Instead of directly considering the electrochemical reactions within the battery, the equivalent circuit model simulates this electrochemical process by applying the physical effects generated by this electrochemical process to an ideal circuit element from a physical mechanism. The equivalent circuit model of the battery is established based on the relationship between its operating characteristic parameters such as current, voltage, and state of charge. Based on the VRFB energy storage system, both models can be used as carriers of VE. Ultimately, establishing the VE is further determined by the actual application requirements and the good or bad application performance.
4.1.3 Ss of VRFBsSs needs to provide different types of services for internal operation and external demand, which are “Functional Service” (F Service) to support the operation and realization of the internal functions of the DT and “Business Service” (B Service) to meet the different energy storage scenarios of other users.F Service is the functional service of VRFB’s DT, including the twin algorithm connection for PE and VE in VRFB, data storage and processing for DD, and VRFB sensing access service for CN. Ultimately, the VRFB twin system application requirements, prediction, hazard warning, fault diagnosis and VRFB optimization, etc. are realized. Specifically, such as electrolyte temperature prediction, leakage diagnosis and operation efficiency optimization. B Service is a user-oriented visual guidance and training service. For users, the application of VRFB’s DT system avoids the complexity of black-box understanding and operation, reduces the requirements for users’ professional ability and improves the convenience of use.
4.1.4 DD of VRFBsThe DD of the VRFB consists of data generated during the actual system, model construction and operation of the energy storage, and is continuously updated and iterated as the VRFB system operates in real time. It serves as a driver for the entire VRFB system and has a bidirectional delivery function. For PE data, it is collected through sensors or acquisition cards to reflect the physical elements and operational status in real time. The acquired data include voltage and current, temperature and pressure, and flow level, etc. The VE data of VRFB is the data related to the mechanism model, including the input parameters (flow field, electric field, temperature field, and electrochemical reaction related parameters), and the output parameters (validation, evaluation, and prediction and analysis parameters during the operation process) required for the modelling of the VRFB model. In addition, relevant data in the Ss, such as intelligent algorithm data, acquisition and processing data and market analysis data, are also included.
4.1.5 CN of VRFBsThe role of CN is to realize the connection and interoperability between VRFB systems. The collected data from the VRFB system is transferred to the DD, processed, and fed back to the VRFB virtual model so that the model can be corrected and optimized. At the same time, the simulation and analysis data in the model are converted into commands to control the execution of the VRFB system. In this process, intelligent algorithms are required to further process the VRFB model data for real-time updating and iteration.
4.2 Potential challengesDTs are based on a large amount of data such as voltage, current, level and temperature. It includes online, historical and tripartite data. How to effectively collect and perform fusion processing of this data and manage it for modeling and control is a problem that DTs in VRFBs may face. In addition, with the rapid development of the internet, the issue of privacy and security should also be addressed. For a highly coupled and complex system such as VRFBs, modeling becomes more difficult with a more significant scale. Collaboration between different stakeholders in the selection and combination of models, and the cross-domain updating and maintenance of models, will provide a better platform for developing VRFBs.
5 ConclusionDT technology, as a method for practicing intelligent industry, has been widely concerned by enterprises and researchers in recent years, and has been applied in more than ten fields in industry. As a promising long-duration energy storage technology, VRFB will pose higher performance and stability requirements for module development and full-process application in the future. If DT technology can be applied to VRFB, it can leverage the advantages of twin technology to promote the development of energy storage systems. In this process, it is necessary to integrate data, models, and algorithms, using visualization methods to transform the energy storage system into a real scene simulation. VRFB energy storage operation and maintenance system based on DTs can simulate actual conditions and predict possible emergencies, avoiding further losses of manpower and financial resources.
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