Method and equipment for predicting external characteristics of flow battery

Abstract

The invention discloses a flow battery external characteristic prediction method and equipment. The method comprises the following steps: constructing an equivalent circuit model and a thermal model of an all-vanadium flow battery; calculating equivalent circuit parameters of the equivalent circuit model according to the initial electrolyte temperature and the initial vanadium ion concentration of each valence state; calculating battery output voltage and electric power at the current moment according to the equivalent circuit parameters and the charging and discharging current; inputting the environment temperature and the electric power at the current moment and the pump power of the circulating pump into a thermal model, and solving the temperature of the galvanic pile electrolyte at the next moment; inputting the stack electrolyte temperature at the next moment into the dynamic differential equation of the vanadium ion concentration to obtain the vanadium ion concentration at the next moment; the electrolyte temperature and the vanadium ion concentration at the next moment are fed back to the equivalent circuit model, loop iteration is conducted till the battery charging and discharging process reaches a steady state, and the output voltage and the stack electrolyte temperature of the flow battery at each moment in the charging and discharging process are obtained. The computing resources are reduced, and the prediction accuracy is improved.

Description

Technical Field

[0001] This application relates to the field of energy storage technology, and in particular to a method and device for predicting the external characteristics of flow batteries. Background Technology

[0002] Vanadium redox flow batteries (VFBs), as advanced electrochemical energy storage batteries, are considered an ideal choice for supporting renewable energy grid integration, improving grid stability, and promoting the development of energy storage technologies due to their high energy conversion efficiency, long cycle life, good safety, and environmental friendliness. The external characteristics of VFBs mainly consist of their electrical and thermal characteristics during operation, including battery voltage, power, and temperature. In actual operation, the dynamic temperature changes caused by the thermal effects during charging and discharging directly affect the battery's external characteristics. Researching the voltage and temperature characteristics of VFBs has significant engineering value for optimizing battery management, extending battery life, and ensuring safe operation.

[0003] Currently, modeling research on the external characteristics of VFBs mainly falls into two categories: equivalent circuit models and thermal models. Current equivalent circuit models are mostly based on the isothermal assumption, failing to fully consider the impact of dynamic temperature fluctuations during charging and discharging on the model parameters within the circuit. Current thermal models provide guidance for formulating thermal management strategies for VFB charging and discharging processes; however, these models often treat temperature as an independent variable, failing to establish a coupling relationship with voltage and other isoelectric characteristics, thus leading to insufficient accuracy in predicting external characteristic parameters. Summary of the Invention

[0004] To address the aforementioned issues, this application proposes a method for predicting the external characteristics of flow batteries, including:

[0005] An equivalent circuit model and a thermal model of a vanadium redox flow battery are constructed. The equivalent circuit model includes at least a circuit network consisting of open-circuit voltage, ohmic internal resistance, activation polarization overpotential element, concentration polarization overpotential element, and self-discharge branch. The self-discharge current is calculated based on the vanadium ion concentration difference between the positive and negative electrodes. The thermal model includes at least a heat transfer differential equation describing the temperature change of the electrolyte in the stack, pipelines, and storage tank.

[0006] Based on the initial electrolyte temperature and the initial concentrations of vanadium ions in each valence state, the equivalent circuit parameters of the equivalent circuit model are calculated. The equivalent circuit parameters include self-discharge current, open-circuit voltage, activation polarization overpotential, and concentration polarization overpotential.

[0007] Calculate the battery output voltage and power at the current moment based on the equivalent circuit parameters and the charging and discharging current.

[0008] Input the current ambient temperature, electrical power, and circulating pump power into the thermal model to solve for the next moment's stack electrolyte temperature;

[0009] The next moment's electrolyte temperature is input into the dynamic differential equation for vanadium ion concentration to obtain the vanadium ion concentration at the next moment.

[0010] The electrolyte temperature and vanadium ion concentration at the next moment are fed back to the equivalent circuit model, and the process is iterated until the battery charging and discharging process reaches a steady state, thus obtaining the output voltage and stack electrolyte temperature of the flow battery at each moment during the charging and discharging process.

[0011] In one example, when the equivalent circuit parameter is the open-circuit voltage, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including:

[0012]

[0013] Among them, U oc U is the open-circuit voltage. o Let T be the standard electromotive force of the fuel cell stack at equilibrium, R be the ideal gas constant, F be the Faraday constant, N be the number of individual cells in the stack, X2, X3, X4, and X5 be the concentrations of vanadium ions in different valence states, and T be the standard electromotive force of the fuel cell stack at equilibrium. s is the temperature of the battery stack electrolyte, and k is the influence coefficient of the self-discharge reaction on the open-circuit voltage. It represents the influence of self-discharge on the open-circuit voltage during the charging and discharging process. The influence coefficient is negatively correlated with the self-discharge current.

[0014] In one example, when the equivalent circuit parameter is the activation polarization overpotential, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including:

[0015]

[0016] Where, η a The activation polarization overpotential is given by R, where R is the ideal gas constant, F is the Faraday constant, N is the number of cells in the stack, and A is the number of cells in the stack. e The surface area of ​​the electrode. The positive electrode reaction rate constant is... T is the rate constant of the negative electrode reaction. s It is the temperature of the electrolyte in the fuel cell stack.

[0017] In one example, when the equivalent circuit parameter is the concentration polarization overpotential, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including:

[0018]

[0019] Where, η cLet l be the concentration polarization overpotential, l be the diffusion layer thickness, R be the ideal gas constant, F be the Faraday constant, N be the number of cells in the fuel cell stack, and A be the concentration polarization overpotential. e I is the surface area of ​​the electrode. c For the charging and discharging current, D f2 D f3 D f4 D f5 T represents the diffusion coefficient of vanadium ions of different valence states between the electrode surface region and the solution. s It is the temperature of the electrolyte in the fuel cell stack.

[0020] In one example, when the equivalent circuit parameter is the self-discharge current, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including:

[0021]

[0022] Where N is the number of cells in the stack, F is the Faraday constant, X2, X3, X4, and X5 are the concentrations of vanadium ions in different valence states, and V is the volume of the electrolyte at the positive or negative electrode.

[0023] In one example, calculating the battery output voltage and power at the current moment based on equivalent circuit parameters and charging / discharging current specifically includes:

[0024] The expression for the output voltage of a flow battery during the charging and discharging process is as follows:

[0025] U b =U oc +η a +η c +I c R s

[0026] Among them, U b For the output voltage, U oc η is the open-circuit voltage. a To activate the polarization overpotential, η c For concentration polarization overpotential, I c R is the charging and discharging current. s The internal resistance is ohmic;

[0027] The expression for the electrical power of a flow battery is as follows:

[0028]

[0029] In one example, the expression for the thermal model is as follows:

[0030]

[0031] Wherein, the state vector t = [T S ,Tp ,T t ] T u = [P e ,T air ,P p ] T ;

[0032] The matrix of B1 is as follows:

[0033]

[0034] The matrix of B2 is as follows:

[0035]

[0036] The matrix of G is as follows:

[0037]

[0038] Among them, C p V is the specific heat of the electrolyte in the fuel cell stack, ρ is the density of the electrolyte in the fuel cell stack, and V is the specific heat of the electrolyte in the fuel cell stack. s V is the volume of electrolyte in the fuel cell stack. t V is the volume of electrolyte in the storage tank. s T is the volume of electrolyte in the fuel cell stack. p T represents the temperature of the electrolyte in the pipeline. s It is the temperature of the battery stack electrolyte, T. t T represents the temperature of the electrolyte in the storage tank. air For ambient temperature, S S S is the surface area of ​​the electrolyte-containing portion of the battery stack. t S is the surface area of ​​the storage tank. P H is the surface area of ​​the pipe. S H is the heat transfer coefficient of the electrolyte in the fuel cell stack. P H is the heat transfer coefficient of the electrolyte in the pipe. t P is the heat transfer coefficient of the electrolyte in the storage tank. e It is electrical power, P p q represents the pump power, and q represents the flow rate of the electrolyte in the fuel cell stack.

[0039] In one example, the dynamic differential equation for vanadium ion concentration is expressed as follows:

[0040]

[0041] Where d is the thickness of the ion-exchange membrane, V is the volume of the positive or negative electrode electrolyte, k2, k3, k4, and k5 are the diffusion coefficients of vanadium ions in different valence states affected by the electrolyte temperature of the fuel cell stack, S is the area of ​​the ion-exchange membrane, and α i and β i These are the coefficient matrix and vector related to the reaction, I. cThis represents the charging and discharging current. X i This refers to the concentration of vanadium ions in various valence states.

[0042] In one example, the method further includes:

[0043] Compare the predicted temperature value with the preset safety threshold;

[0044] When the predicted temperature exceeds the preset safety threshold, a control command is generated to adjust the operating status of the cooling system or the speed of the electrolyte circulation pump.

[0045] On the other hand, embodiments of this application provide a flow battery external characteristic prediction device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a flow battery external characteristic prediction method as described above.

[0046] The above-described technical solutions adopted in the embodiments of this application can achieve the following beneficial effects:

[0047] To address the issue of insufficient accuracy in predicting voltage and temperature external characteristic parameters in traditional equivalent circuit models due to neglecting the electrothermal coupling effect, this paper considers the electrothermal interaction process of VFB during charging and discharging in peak shaving and valley filling, emergency power supply, etc. By coupling the dynamic process of stack output power and electrolyte temperature rise in real time, an electrothermal coupling dynamic interaction model is constructed to dynamically characterize the voltage and temperature external characteristic parameters, aiming to improve simulation accuracy and provide ideas for electrothermal synergistic optimization control of energy storage systems. Attached Figure Description

[0048] To more clearly illustrate the technical solution of this application, some embodiments of this application will be described in detail below with reference to the accompanying drawings, in which:

[0049] Figure 1 This application provides a schematic diagram of an all-vanadium redox flow battery structure;

[0050] Figure 2 A flowchart illustrating a method for predicting the external characteristics of a flow battery, provided in an embodiment of this application;

[0051] Figure 3 A schematic diagram of a VFB electrothermal interaction process provided in an embodiment of this application;

[0052] Figure 4 A schematic diagram of an equivalent circuit model provided in an embodiment of this application;

[0053] Figure 5A schematic diagram illustrating the calculation process of a VFB electrothermal coupling model provided in an embodiment of this application;

[0054] Figure 6 A comparison diagram of charge / discharge experiment and model output voltage changes provided in an embodiment of this application;

[0055] Figure 7 A simulation curve of electrolyte temperature change in a fuel cell stack, pipeline, and storage tank provided for embodiments of this application;

[0056] Figure 8 A temperature comparison graph between a charge / discharge experiment and a model under a 150A constant current charge / discharge condition is provided for an embodiment of this application.

[0057] Figure 9 A temperature comparison graph between a charge / discharge experiment and a model under a 200A constant current charge / discharge condition is provided for an embodiment of this application.

[0058] Figure 10 A temperature comparison graph between a charge / discharge experiment and a model under a 250A constant current charge / discharge condition is provided for an embodiment of this application.

[0059] Figure 11 This is a schematic diagram of the structure of a flow battery external characteristic prediction device provided in an embodiment of this application. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] Some embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0062] Figure 1 This is a schematic diagram of an all-vanadium redox flow battery structure provided in this application.

[0063] exist Figure 1 In a flow battery system, three basic components are integrated: a pair of reservoirs storing two different electrolytes, a battery stack responsible for generating electricity, and a hydraulic subsystem responsible for the flow of electrolyte between these components. The electrolyte is stored inside the reservoirs and the battery stack and circulates within the battery driven by a circulation pump. The battery is capable of converting electrical energy into chemical energy during charging and discharging.

[0064] Based on the above structure Figure 2This is a flowchart illustrating a method for predicting the external characteristics of a flow battery, as provided in an embodiment of this application. This process can be executed by a computing device in the relevant field, and certain input parameters or intermediate results in the process can be manually adjusted to help improve accuracy.

[0065] The analysis method involved in the embodiments of this application can be implemented by a terminal device or a server, and this application does not impose any special limitations on it. For ease of understanding and description, the following embodiments are all described in detail using a server as an example.

[0066] It should be noted that the server can be a single device or a system composed of multiple devices, i.e., a distributed server. This application does not make any specific limitations on this.

[0067] Figure 2 The process includes the following steps:

[0068] S201: Construct the equivalent circuit model and thermal model of the all-vanadium redox flow battery; the equivalent circuit model includes a circuit network consisting of open-circuit voltage, ohmic internal resistance, activation polarization overpotential element, concentration polarization overpotential element, and self-discharge branch; the thermal model includes heat transfer differential equations to describe the temperature changes of the electrolyte in the stack, pipelines, and storage tank.

[0069] In this example, the electrothermal coupling of the VFB is a bidirectional dynamic interaction between the battery's electrical and thermal behaviors during charging and discharging. Figure 1 As shown in the diagram, the structure and working principle of the VFB reveal that during charging, the vanadium ion oxidation reaction (VO2) at the positive electrode... 2+ →VO2 + The reaction at the negative electrode is endothermic, while the reduction reaction at the negative electrode (V) is endothermic. 3+ →V 2+ The exothermic reaction, combined with the thermal effects of the current flowing through the internal resistance, results in the system being primarily powered by ohmic heat. Conversely, during discharge, the reaction proceeds in the reverse direction, and the thermal effect reverses accordingly, but ohmic heat accumulation still occurs. Additional heat generated by fluid friction and mechanical losses during electrolyte circulation further exacerbates the temperature rise. Increased temperature reduces electrolyte viscosity and enhances ion mobility, thus affecting the equivalent circuit parameters of the VFB system during charge and discharge.

[0070] More intuitively, Figure 3 This is a schematic diagram of a VFB electrothermal interaction process provided in an embodiment of this application.

[0071] exist Figure 3 middle, I c U is the charging and discharging current. b It is the output voltage, X i The concentrations of vanadium ions in various valence states (i = 2, 3, 4, 5), T airIt is the ambient air temperature, P e It is electrical power, T s It is the temperature of the electrolyte in the fuel cell stack, P p It refers to pump power.

[0072] Based on this, the electrothermal interaction of VFB is achieved through the synergistic effect of electrical power, ion concentration diffusion, pump power loss, and heat transfer: the heat source generated by the electrochemical reaction (i.e., electrical power P) e The power loss of the pump, along with the input to the heat transfer equation, affects the temperature change of the VFB system during charging and discharging.

[0073] Furthermore, changes in electrolyte temperature within the fuel cell stack affect parameters such as open-circuit voltage, concentration polarization overpotential, and polarization overpotential in the equivalent circuit. These parameters are dynamically adjusted through temperature variations. During charging and discharging, VFB power and electrolyte temperature form a closed-loop feedback loop, allowing for the fitting of the coordinated evolution of electrothermal parameters under actual operating conditions.

[0074] In this example, Figure 4 This is a schematic diagram of an equivalent circuit model provided in an embodiment of this application.

[0075] exist Figure 4 In this process, the nonlinear characteristics of circuit elements such as resistors and controlled voltage sources reflect complex electrochemical processes such as the redox reaction of vanadium ions, concentration polarization, and ohmic losses.

[0076] When VFB is charging, I c >0, direction is positive; when in discharge state, I c <0, direction is negative. U oc η is the open-circuit voltage of the battery stack. a To activate the polarization overpotential, η c R is the concentration polarization overpotential. m R is the self-discharge resistance. s For the internal resistance of ohms, C e I is the inter-electrode capacitance between the positive and negative electrode plates. z This is the self-discharge current.

[0077] Under the above equivalent circuit model, the change in vanadium ion concentration during the charging and discharging process of VFB will have a significant impact on the equivalent circuit parameters. The concentration of vanadium ions in different valence states will affect the magnitude of the open-circuit voltage and overpotential in the equivalent circuit.

[0078] Therefore, the concentration parameters of each valence state ion are corrected in real time based on the dynamic diffusion of vanadium ions during charging and discharging, and the self-discharge internal resistance, open-circuit voltage and polarization overpotential parameters in the equivalent circuit are updated iteratively.

[0079] It should be noted that in the above equivalent circuit model, the self-discharge resistance and the inter-electrode capacitance are connected in parallel, as follows:

[0080] In a VFB (Vacuum-Fiber Photovoltaic) membrane, vanadium ions of different valence states permeate through the membrane, causing self-discharge. This means that some current bypasses the external circuit and instead "leaks" directly from the positive electrode to the negative electrode internally (or, in other words, oxidized ions from the positive electrode directly undergo a chemical reaction on the negative electrode side). This is represented in the circuit by a parallel resistor R. m Connected between the positive and negative terminals (in U) oc (both ends), that is, connected in parallel with an ideal voltage source.

[0081] The fundamental reason for using a parallel resistor-capacitor combination (as an RC parallel network) in battery models is that it allows for an intuitive simulation of the complex, time-dependent electrochemical processes inside the battery from an electrical perspective.

[0082] In the above equivalent circuit model, the two overpotentials are connected in series, as follows:

[0083] Activation polarization overpotential refers to the additional potential difference caused by the activation energy of electrochemical reactions during battery charging and discharging; concentration polarization overpotential is the potential difference caused by the uneven distribution of active material concentration in the electrolyte solution; both of these overpotentials directly affect the battery output voltage, and therefore are connected in series in the circuit.

[0084] In summary, the above equivalent circuit connection methods can simulate, at the electrical level, the energy storage essence (U... oc Controlled by vanadium ion concentration), self-discharge loss (parallel R) m Ohm loss (series R) s Transient effects (parallel C) e (in parallel with the self-discharge resistor).

[0085] In this example, the heat sources of VFB during charging and discharging mainly include ohmic heat, electrochemical polarization heat, and pumping cycle heat. Ohmic heat is mainly the heat generated by the charging and discharging current flowing through the battery's ohmic internal resistance; electrochemical polarization heat is the heat generated by activation polarization and concentration polarization during the electrochemical reaction; and pumping cycle heat is mainly the mechanical losses generated during electrolyte circulation.

[0086] Pump power loss P during VFB charging and discharging process p The pump power loss is proportional to the electrolyte flow rate q in the fuel cell stack and the total pressure drop Δp in the hydraulic circuit.

[0087]

[0088] In the formula: η pump The pump efficiency is typically between 0.8 and 0.9, and this data is usually provided by the manufacturer. Combining this with the equivalent circuit established earlier, the electrical power P... eExpressed as the sum of ohmic heat and electrochemical polarization heat per unit time, the total heat Q generated by VFB during the charge / discharge time t is:

[0089]

[0090] Based on the heat transfer process of the temperature field, the temperature changes of the electrolyte in the stack, pipeline, and storage tank during the VFB charging and discharging process are obtained by taking pump power loss and electrical power as heat source terms.

[0091] S202: Calculate the equivalent circuit parameters of the equivalent circuit model based on the initial electrolyte temperature and the initial concentration of vanadium ions in each valence state; the equivalent circuit parameters include self-discharge current, open-circuit voltage, activation polarization overpotential, and concentration polarization overpotential.

[0092] This involves using the known system states (electrolyte temperature, ion concentration) to quantify the specific values ​​of each component in the equivalent circuit. This is a conversion process from physical / chemical state to circuit parameters. It links the battery's internal physical and chemical states (ion concentration, temperature) with its external electrical characteristics (parameters of the equivalent circuit).

[0093] Electrolyte temperature is an input variable for almost all critical circuit parameters. This means that once the temperature changes in subsequent iterations, the behavior (and parameters) of the entire equivalent circuit will change accordingly. This is the core of electrothermal coupling: heat affects electricity.

[0094] S203: Calculate the battery output voltage and power at the current moment based on the equivalent circuit parameters and the charging / discharging current.

[0095] After parameterizing all the complex electrochemical and physical processes involved, the results ultimately converge into two key, measurable macroscopic physical quantities: voltage and power. These two quantities serve as the link between the electrical and thermal worlds. Electric power directly drives the evolution of the thermal model, thus achieving complete electrothermal coupling.

[0096] It should be noted that the output voltage is the sum of the external performance of the equivalent circuit. Its calculation is based on Kirchhoff's voltage law, which is essentially an algebraic superposition of all voltages located at the output terminal.

[0097] S204: Input the current ambient temperature, electrical power, and circulating pump power into the thermal model to solve for the next moment's stack electrolyte temperature.

[0098] Electrical power represents the heat generated by the battery during charging and discharging due to effects such as ohmic internal resistance and electrochemical polarization. Whether charging or discharging, the vast majority of this power is ultimately dissipated as heat within the system. Pump power is the power consumed by the pump driving the electrolyte circulation. During operation, the pump converts some electrical energy into heat energy due to mechanical friction and fluid viscous resistance, directly heating the circulating electrolyte.

[0099] Ambient temperature is the temperature of the air surrounding the battery, and its role in the thermal model is as a thermal boundary condition. It is the reference temperature for heat exchange between the system and the outside environment. According to Newton's law of cooling, the temperature difference between the system and the environment is the driving force for heat loss, and the ambient temperature serves as the anchor point for the entire system temperature; the model uses it to calculate the heat dissipation rate.

[0100] The thermal model is a dynamic, multi-node heat transfer model, which is the key mechanism for realizing the influence of electrical behavior on thermal behavior. Through this step, the electrical operating state of the battery is converted into its influence on the temperature field in real time, thereby realizing the dynamic coupling between electricity and heat.

[0101] S205: Input the next moment's stack electrolyte temperature into the dynamic differential equation of vanadium ion concentration to obtain the vanadium ion concentration at the next moment.

[0102] Traditional uncoupled models assume constant temperature and a constant diffusion coefficient, with ion concentration changes determined solely by current. Electrothermal coupled models, on the other hand, dynamically update the diffusion coefficient due to dynamic temperature changes, which in turn dynamically adjusts the rate of change in ion concentration.

[0103] This is precisely the feedback mechanism that enables thermal behavior to influence the internal chemical state, and in turn, the electrical behavior. Through this step, temperature changes can dynamically adjust the lowest-level chemical parameters (ion concentration) in the model, thereby achieving a truly physical-mechanically based, tightly coupled electro-thermal relationship.

[0104] S206: Feed back the electrolyte temperature and vanadium ion concentration at the next moment to the equivalent circuit model, and iterate cyclically until the battery charging and discharging process reaches a steady state, thereby obtaining the output voltage and stack electrolyte temperature of the flow battery at each moment during the charging and discharging process.

[0105] It should be noted that, in the context of simulation, steady state usually refers to the end of the preset charging and discharging process.

[0106] Based on this, the model achieves real-time updates of parameter changes during charging and discharging, enabling it to dynamically respond to changes in the battery's own state. Since the model calculates the output voltage and stack temperature at each time step, two complete data curves corresponding to the time axis are obtained at the end of the cycle. These two curves represent the battery's predicted external characteristics.

[0107] Through the aforementioned closed loop, the model successfully simulates the complex dynamic processes of the electrical, thermal, and chemical domains of a real-world vanadium redox flow battery during operation, thereby achieving a high-precision dynamic characterization of the battery's external properties.

[0108] It should be noted that, although the embodiments in this application are based on... Figure 2 Steps S201 to S206 will be described sequentially, but this does not mean that steps S201 to S206 must be performed in a strict order. The reason this embodiment follows this order is... Figure 1 The order in which steps S201 to S206 are described is provided to facilitate understanding of the technical solutions of the embodiments of this application by those skilled in the art. In other words, in the embodiments of this application, the order of steps S201 to S206 can be appropriately adjusted according to actual needs.

[0109] Currently, the equivalent circuit models of vanadium redox flow batteries mostly focus on simplified descriptions of core electrochemical parameters. For example, some models only consider open-circuit voltage and ohmic internal resistance, ignoring the significant influence of activation polarization overpotential and concentration polarization overpotential on output voltage, or failing to include the self-discharge branch, leading to deviations in the simulation of energy loss. Even if some models integrate polarization elements, they often use static parameter descriptions, failing to reflect the dynamic changes of parameters with vanadium ion concentration and electrolyte temperature during charging and discharging, resulting in insufficient prediction accuracy of output voltage and power.

[0110] In terms of thermal characteristic simulation, existing thermal models generally have limitations: On the one hand, most models only model the temperature change of the electrolyte inside the stack, ignoring the heat exchange between the electrolyte and the environment during pipeline transportation and the cumulative temperature effect of the electrolyte in the storage tank. This results in temperature predictions failing to cover the entire electrolyte circulation process and deviating from the actual operating scenario. On the other hand, electrochemical models and thermal models are often designed separately, failing to establish a dynamic coupling mechanism between temperature and vanadium ion concentration, electrochemical parameters (such as polarization overpotential and open-circuit voltage). In fact, electrolyte temperature directly affects the diffusion rate and reactivity of vanadium ions, thereby changing the equivalent circuit parameters. Furthermore, the Joule heat and polarization heat generated during the electrochemical process will have a reciprocal effect on the electrolyte temperature. This one-way simulation method leads to significant errors in the prediction of both temperature and electrochemical characteristics.

[0111] Furthermore, during the charging and discharging process of vanadium redox flow batteries, the vanadium ion concentration changes dynamically with the reaction process and is strongly coupled with the electrolyte temperature. Existing models lack a quantitative description of this coupling relationship, making it difficult to optimize equivalent circuit parameters through dynamically updated vanadium ion concentration and temperature data feedback. This results in low accuracy of dynamic response simulation during cyclic charging and discharging, failing to provide reliable model support for real-time control of the battery system (such as cooling system adjustment and circulation pump speed optimization), thus limiting the performance and safety assurance capabilities of vanadium redox flow batteries in practical engineering applications.

[0112] pass Figure 2 The proposed method establishes a VFB electrothermal coupling model that achieves electrothermal coupling through the exchange of electrical power and temperature parameters. By using loops and real-time feedback, the parameters in the equivalent circuit model are dynamically updated during the charging and discharging process, accurately reflecting the dynamic changes of the VFB's output voltage and stack electrolyte temperature under charging and discharging operation scenarios such as battery testing and emergency power supply, thus improving the accuracy of dynamic characterization of external characteristic parameters.

[0113] Furthermore, for comprehensive models that reflect both the internal dynamic characteristics of the VFB and characterize its external equivalent characteristics, such comprehensive models have higher mechanistic depth and accuracy in characterizing external characteristics compared to single-characteristic models. However, these models are more complex, involving a large number of coupled parameters, making computation and solution relatively difficult. This application, however, does not require the aforementioned comprehensive model. Instead, it establishes a comprehensive model that integrates electrochemical and thermophysical coupling characteristics, covers the entire electrolyte cycle, and dynamically feeds back key parameters. This allows for accurate prediction of output voltage and electrolyte temperature during charging and discharging with limited computational resources.

[0114] Specifically:

[0115] The equivalent circuit model of this application integrates open-circuit voltage, ohmic internal resistance, activation polarization overpotential, concentration polarization overpotential, and self-discharge branch, comprehensively covering the key electrochemical mechanisms affecting battery output characteristics. Simultaneously, by feeding back dynamically updated vanadium ion concentration and electrolyte temperature to the equivalent circuit model, real-time dynamic correction of core parameters such as self-discharge current and polarization overpotential is achieved. This ensures that the calculated output voltage and power at each moment during charging and discharging highly match the actual battery operating state, significantly reducing prediction errors. This accurate prediction capability can directly provide data support for power scheduling and charging / discharging strategy optimization of the battery system, avoiding low operating efficiency caused by misjudgments of output characteristics.

[0116] The thermal model comprehensively describes the temperature changes of the electrolyte in the battery stack, pipelines, and storage tank using heat transfer differential equations. It covers the entire heat exchange scenario of the electrolyte circulation process (such as heat conduction between pipelines and the environment, and temperature accumulation in the storage tank). Simultaneously, the thermal model inputs include ambient temperature, battery power (sources of reaction heat and Joule heat), and circulation pump power (source of mechanical heat), fully considering the influence of multiple heat sources on temperature. This allows for accurate calculation of the battery stack electrolyte temperature at the next moment. Combined with a cyclic iteration mechanism, it can predict the temperature change trend throughout the charging and discharging process in advance, providing accurate temperature data support for subsequent safety control measures such as cooling system adjustment and circulation pump speed optimization. This effectively avoids risks such as vanadium ion reactivity decay and electrolyte stability degradation caused by excessive electrolyte temperature, ensuring the long-term safe operation of the battery system.

[0117] A closed-loop coupling mechanism was constructed for electrolyte temperature, vanadium ion concentration, and equivalent circuit parameters: temperature changes affect the vanadium ion diffusion rate and reactivity, thereby altering the equivalent circuit parameters; the heat generated during the electrochemical process reacts to the temperature, and the vanadium ion concentration is dynamically updated with the reaction progress and fed back to the equivalent circuit model. This mechanism fully replicates the interaction patterns of key parameters during the operation of a vanadium redox flow battery, effectively avoiding simulation distortion caused by the separation of the electrochemical and thermal models and static parameters. Through iterative iteration until the system reaches steady state, the output voltage and electrolyte temperature data at each moment during charging and discharging can be output, fully presenting the dynamic operating characteristics of the battery. The simulation results can be directly adapted to the engineering design requirements of large-capacity, high-power vanadium redox flow batteries (such as stack structure optimization and cooling system selection), significantly reducing the cost and cycle of actual engineering tests.

[0118] Furthermore, based on real-time dynamic parameter feedback, operating parameters such as charge / discharge current and circulating pump speed can be optimized, reducing polarization losses and thermal stress damage caused by parameter mismatch. On the other hand, by predicting long-term trends in temperature and output characteristics, maintenance strategies (such as electrolyte concentration adjustment and cooling system overhaul) can be formulated in advance to slow down the stack degradation rate. Ultimately, this achieves the comprehensive benefits of improved battery system operating efficiency and extended service life, further enhancing the competitiveness of vanadium redox flow batteries in large-scale energy storage applications.

[0119] In one example, the output voltage expression of a flow battery during the charging and discharging process is as follows:

[0120] U b =U oc +ηa+ηc+I c R s

[0121] Among them, U b For the output voltage, U oc η is the open-circuit voltage. aTo activate the polarization overpotential, η c For concentration polarization overpotential, I c R is the charging and discharging current. s It is the internal resistance of the Ohm.

[0122] It should be noted that when current flows through the internal resistance, a voltage is generated across the internal resistance. These two overpotentials can be regarded as the additional voltage that the electrochemical reaction needs to increase or decrease to overcome the resistance, and are always considered as additional losses when the battery drives the current.

[0123] Based on this, the expression for the electrical power consumed by a flow battery is as follows:

[0124]

[0125] In this example, the stack reaches equilibrium when no current flows through the VFB electrode. Let the standard electromotive force of the stack at equilibrium be U. o The Nernst equation for the open-circuit voltage during charging and discharging is as follows:

[0126]

[0127] Among them, U oc R is the open-circuit voltage, F is the ideal gas constant (J / (mol K)), N is the Faraday constant, X2, X3, X4, and X5 are the concentrations of vanadium ions in different valence states, and k is the influence coefficient of self-discharge reaction on open-circuit voltage, which represents the influence of self-discharge on open-circuit voltage during battery charging and discharging.

[0128] It should be noted that the influence coefficient and the self-discharge current are negatively correlated, with k being greater than 0 and less than 1, which means that self-discharge diverts a portion of the voltage drop. Specifically, the larger the self-discharge current, the smaller the corresponding influence coefficient and the smaller the open-circuit voltage. For example, a mapping table between the self-discharge current and the influence coefficient can be obtained based on the results of charge-discharge experiments.

[0129] In this example, the concentration gradient of vanadium ions near the electrode surface is the main driving force for the diffusion of vanadium ions in the electrolyte solution due to the concentration difference caused by the concentration gradient between vanadium ions. Self-discharge reactions also occur at the positive and negative electrodes due to the concentration gradient between vanadium ions. To facilitate the study of vanadium ion diffusion, this application assumes that: (1) the self-discharge reaction is instantaneous; (2) the electrolyte volume at the positive and negative electrodes remains constant; and (3) the total concentration of vanadium ions remains constant during charge-discharge cycles.

[0130] Based on this, and according to the fundamental principles of vanadium ion diffusion and Fick's law, the dynamic differential equations for the concentrations of vanadium ions in different valence states during charging and discharging are as follows:

[0131]

[0132] Where d is the thickness of the ion-exchange membrane, V is the volume of the positive or negative electrode electrolyte, k2, k3, k4, and k5 are the diffusion coefficients of vanadium ions in different valence states affected by the electrolyte temperature of the fuel cell stack, S is the area of ​​the ion-exchange membrane, and α i and β i These are the coefficient matrix and vector related to the reaction, I. c This represents the charging and discharging current. X i This refers to the concentration of vanadium ions in various valence states.

[0133] Furthermore, based on the above dynamic differential equations, the state equations are listed as follows:

[0134]

[0135] Where x = [X2, X3, X4, x5,] T k = [k2, k3, k4, k5] T β=[β2,β3,β4,β5,] T =[1,-1,-1,1] T .

[0136] From α i The coefficient matrix is ​​as follows:

[0137]

[0138] It should be noted that the above β = [β2, β3, β4, β5,] T =[1,-1,-1,1] T It is the coefficient during charging, and takes its opposite value during discharging. And α... i It remains unchanged.

[0139] In this example, when the battery is charging or discharging, I c ≠0, current flows through the electrodes, and VFB deviates from equilibrium. Due to factors such as internal resistance and overpotential, the battery output voltage deviates from the open-circuit voltage. In the equivalent circuit model, the ohmic internal resistance is the sum of the internal resistances of the bipolar plates, membrane, and electrolyte. The expression for the ohmic internal resistance is as follows:

[0140] R s =R b +R f +R e

[0141] Among them, R b R represents the equivalent resistance of the bipolar plate. f R represents the equivalent resistance of the membrane. e This represents the equivalent resistance of the electrolyte.

[0142] In this example, activation polarization overpotential refers to the additional potential difference caused by the activation energy of the electrochemical reaction during battery charging and discharging, and is mainly related to the electrochemical reaction kinetics at the electrode and electrolyte interface. The activation polarization overpotential of the flow battery (positive and negative electrodes) is:

[0143]

[0144] Among them, A e The surface area of ​​the electrode. The positive electrode reaction rate constant is... is the negative electrode reaction rate constant.

[0145] In this example, the concentration polarization overpotential is due to the potential difference caused by the uneven distribution of the active substance concentration in the electrolyte solution. This overpotential is a direct result of the limitation on mass transfer during the electrochemical reaction. Under ideal steady-state diffusion conditions, the expression for the concentration polarization electropotential is:

[0146]

[0147] Where l is the thickness of the diffusion layer, and D fi The diffusion coefficient (i = 2, 3, 4, 5) is expressed in m³. 2 / s, this coefficient is used to characterize the diffusion of i-valent vanadium ions between the electrode surface region and the solution.

[0148] In one example, the self-discharge resistance is determined by the electrolyte conductivity and the specific fluidic framework design. Based on mass and charge conservation, the expression for the VFB self-discharge current is as follows:

[0149]

[0150] The expression for the equivalent resistance of VFB self-discharge is as follows:

[0151]

[0152] In one example, it is assumed that the electrolytes in both the battery stack and the storage tank are completely mixed and have a constant overall volume, and that the positive and negative electrodes have identical structures and characteristics. Considering the slow flow rate of the electrolyte in the storage tank and pipelines, the heat transfer process in these areas is treated as natural convection.

[0153] Since the electrolyte in the fuel cell stack mainly transfers heat with the pipes and air, and combining the laws of electrical power and energy conservation, the expression for the temperature of the fuel cell stack electrolyte during the charging and discharging process is as follows:

[0154]

[0155] Among them, C pV is the specific heat of the electrolyte, ρ is the density of the electrolyte, and V is the specific heat of the electrolyte. s T is the volume of electrolyte in the fuel cell stack. p T represents the temperature of the electrolyte in the pipeline. s It is the temperature of the battery stack electrolyte, S S H represents the surface area of ​​the electrolyte-containing portion of the battery stack. S is the heat transfer coefficient of the electrolyte in the fuel cell stack.

[0156] The electrolyte in the pipeline mainly undergoes heat transfer with the fuel cell stack, storage tank, and air. Based on the calculated pump power and thermal convection conditions, the expression for the electrolyte temperature in the pipeline is as follows:

[0157]

[0158] Among them, V p T represents the volume of electrolyte in the pipeline. p The temperature of the electrolyte in the pipeline, h P S is the heat transfer coefficient of the electrolyte in the pipeline. P This refers to the surface area of ​​the pipe.

[0159] The heat transfer process in the storage tank is mainly natural convection, occurring primarily in the ambient air and through the pipes. The expression for the electrolyte temperature in the storage tank is as follows:

[0160]

[0161] Among them, V t H represents the volume of electrolyte in the storage tank. t S is the heat transfer coefficient of the electrolyte in the storage tank. t T is the surface area of ​​the storage tank. t This refers to the temperature of the electrolyte in the storage tank.

[0162] It should be noted that because the electrolyte in a flow battery is a flowing liquid, the heat transfer process is treated as heat convection. According to the flow battery schematic, the stack, pipes, and storage tank are connected in sequence, taking into account the heat transfer between the stored electrolytes and the heat transfer with the air.

[0163] Electrolyte in the fuel cell stack: Heat transfer between the electrolyte and air in the piping and the fuel cell stack. Electrolyte in the piping: Heat transfer between the electrolyte in the fuel cell stack and the storage tank and the piping. Electrolyte in the storage tank: Heat transfer between the electrolyte in the piping and the storage tank.

[0164] In summary, the three heat transfer processes constitute the thermal model of the entire system, which can be used to solve for the real-time changes in electrolyte temperature in the fuel cell stack, pipelines, and storage tank as it is charged and discharged.

[0165] Based on this, and according to the expressions for the electrolyte in the fuel cell stack, the electrolyte in the pipeline, and the electrolyte in the storage tank, the state-space equation expression is as follows:

[0166]

[0167] Wherein, the state vector t = [T S ,T p ,T t ] T u = [P e ,T air ,P p ] T .

[0168] The matrix of B1 is as follows:

[0169]

[0170] The matrix of B2 is as follows:

[0171]

[0172] The matrix of G is as follows:

[0173]

[0174] In summary, the above equations solve for the variable t, which can be used to determine the temperature of the electrolyte in the fuel cell stack, storage tank, and pipelines.

[0175] In one example, after obtaining the predicted temperature value of the battery pack electrolyte, the predicted temperature value can be compared with a preset safety threshold. When the predicted temperature value exceeds the preset safety threshold, a control command is generated to adjust the operating status of the cooling system or the speed of the electrolyte circulation pump.

[0176] In summary, the key to control logic is proactive prediction rather than passive response. By predicting risks in advance and intervening early, the safe operation of the fuel cell stack can be ensured, the power generation efficiency can be avoided due to temperature fluctuations, and the service life of the fuel cell stack and related equipment can be extended.

[0177] More intuitively, Figure 5 This is a schematic diagram illustrating the calculation process of a VFB electrothermal coupling model provided in an embodiment of this application.

[0178] The temperature of the battery stack electrolyte is closely related to the open-circuit voltage and polarization overpotential parameters in the equivalent circuit. Consequently, the output power of the VFB is tightly coupled with the temperature of the battery stack electrolyte. By dynamically linking the power and the battery stack electrolyte parameters, the external characteristics of the VFB during operation can be dynamically simulated.

[0179] exist Figure 5In this process, the model parameters are updated in real time through iterative cycles to form a VFB electrothermal coupling model, which accurately describes the output voltage and temperature characteristics of the VFB.

[0180] The specific process is as follows:

[0181] (1) Initialization parameters: Set the initial vanadium ion concentration, electrolyte temperature, and ambient temperature.

[0182] (2) Calculate electrochemical parameters: Calculate the self-discharge current, open-circuit voltage, activation polarization overpotential, and concentration polarization overpotential in the equivalent circuit based on the vanadium ion concentration and electrolyte temperature.

[0183] (3) Calculate the output voltage and power: Calculate the VFB voltage and power based on the charging and discharging current and equivalent circuit parameters.

[0184] (4) Update electrolyte temperature: Based on the heat transfer equation of the temperature field and combined with the ambient temperature, update the electrolyte temperature of the fuel cell stack by the power loss of electric power and pump power.

[0185] (5) Feedback adjustment: The updated electrolyte temperature of the fuel cell stack is fed back to the calculation of vanadium ion concentrations of each valence state and the calculation of electrochemical parameters.

[0186] (6) Iterative cycle: Repeat steps (2)-(5) above until the VFB charging and discharging process is completed and a steady state is reached.

[0187] In one example, the model validation process is as follows:

[0188] The parameters of the VFB charge-discharge experimental platform are shown in Table 1:

[0189] Table 1

[0190] Diffusion layer thickness l / m 0.0001 <![CDATA[The volume V of the electrolyte in the stack s / L]]> 1.13 <![CDATA[The volume V of the electrolyte in the pipeline p / L]]> 2.90 <![CDATA[The volume V of the electrolyte in the liquid storage tank t / L]]> 111.7 <![CDATA[Initial temperature T of the electrolyte s / K]]> 293 <![CDATA[Total heat transfer coefficient of battery stack × area H s S s / (W·K -1 )]]> 1.78 <![CDATA[Overall heat transfer coefficient of the pipe × Area H p S p / (W·K -1 )]]> 0.7 <![CDATA[Overall heat transfer coefficient of the liquid storage tank × Area H t S t / (W·K -1 )]]> 2.07

[0191] The external characteristics of the battery are verified as follows:

[0192] (1) Output voltage

[0193] Based on the current density limitations of the selected VFB in the experiment, and considering that the 150-250A range can cover typical application scenarios of VFB such as peak shaving and valley filling, and emergency power supply [26-27], this experiment uses constant current I... c Three sets of VFB charge / discharge cycles were performed at current values ​​of 150A, 200A, and 250A. The external characteristics of the battery were investigated using a gradient current design. To ensure that the VFB does not overcharge or over-discharge during the charging and discharging process, a constant current charging was first applied to the VFB. When the VFB voltage U... b When the voltage reaches 16V, charging should be stopped immediately and the system should switch to discharging mode, discharging VFB with the same current value. When U bStop when the value is below 11V. The output voltage U is sampled every 1 second. b The value of . The output voltage U in the experimental and VFB electrothermal coupling model. b The change comparison curve is as follows Figure 6 As shown.

[0194] Depend on Figure 6 It can be seen that the output voltage values ​​of the three sets of experiments are close to those of the model, and the curve trends are the same. In the early and middle stages of charging and discharging, the model results show a high degree of agreement with the experiments. However, at the end of the charging and discharging process, the output voltage in the experiments is slightly lower than the model results. To ensure the speed of dynamic model updates, some minor factors in the VFB electrochemical reaction are ignored, therefore the charging and discharging current I... c The output voltage results for the 150A and 200A models show a high degree of agreement with the experimental results and are higher than the charge / discharge current I. c The compatibility is 250A. Furthermore, the charge / discharge time is negatively correlated with the input current, I. c The higher the value, the shorter the time it takes for VFB to complete one charge-discharge cycle. In the three sets of charge-discharge experiments, the slopes of the curves at the initial and final stages of charging and discharging were larger, reflecting that U... b The rate of change is relatively fast. As can be seen from the dynamic differential equation of vanadium ion concentration for each valence state and the expression for open-circuit voltage, the difference between vanadium ion concentration values ​​is too large at the beginning and end of the charging and discharging stages, resulting in a relatively fast rate of change of output voltage.

[0195] To quantitatively evaluate the error between the model and the experimental output, two calculation indicators, mean absolute error (MAE) and mean absolute percentage error (MAPE), are introduced to measure the error and accuracy between the model and the experimental results.

[0196] Table 2 shows the mean absolute error and mean absolute percentage error of the output voltage of the three models and experiments.

[0197] experimental group MAE / V MAPE / % 150A charge / discharge experiment 0.0489 0.35 200A charge and discharge experiment 0.0739 0.55 250A charge and discharge experiment 0.1352 0.88

[0198] As can be seen from the table, the average absolute error between the model and the experimental output voltage is less than 0.2V, and the average absolute percentage error is less than 1%. Therefore, the established VFB electro-thermal coupling model can accurately reflect the voltage output characteristics.

[0199] (2) Electrolyte temperature of the battery stack

[0200] Set the room temperature to T. air The value is 293K (20℃), with constant current charge and discharge conditions as I. c Taking 150A as an example, the electrolyte calculated by the model in Simulink at the stack temperature T s Pipeline temperature T p The electrolyte temperature in the storage tank and the storage tank temperature Tt Curves of change over time as shown Figure 7 As shown.

[0201] The results showed that regardless of whether the VFB was charging or discharging, the electrolyte temperature increased in all three processes. The temperatures were similar across all three processes, and T... s >T p >T t This is mainly attributed to: the electrolyte circulation causing the temperatures of the three components to tend towards dynamic equilibrium; the concentrated generation of ohmic heat and polarization heat in the fuel cell stack, as the core area of ​​the electrochemical reaction, resulting in the highest local temperature; and the fact that the piping system, being closer to the heat source of the fuel cell stack, has a higher electrolyte temperature rise rate than the relatively isolated storage tank.

[0202] VFB electrolyte is a highly acidic solution, which is not only highly corrosive but also easily oxidized, and is also affected by light. To protect the electrolyte, the entire battery system must be sealed to isolate it from air. In this sealed environment, traditional contact-based temperature measurement methods cannot be applied. The simulation results show that the electrolyte temperature is similar in the stack, pipes, and storage tank; therefore, this experiment used a FLIR infrared thermal imager to perform non-contact temperature measurement of the stack electrolyte temperature T. s Due to the limited accuracy of this measurement method, the data recorded in the experiment can only roughly depict the trend of temperature change. Three groups I c The temperature changes in the experiment and the model under constant current charge-discharge conditions of 150A, 200A, and 250A are as follows: Figure 8 , 9 As shown in Figure 10.

[0203] As can be seen, the experimental and model temperature output results are quite similar, both showing a monotonically increasing trend, which verifies the external temperature characteristics of the VFB electrothermal coupling model.

[0204] In summary, this study investigated the coupling relationship between the electrothermal output parameters of the VFB during charging and discharging, established a VFB electrothermal coupling model, and verified the effectiveness of the established model through constant current charging and discharging experiments. The conclusions are as follows:

[0205] The established VFB electrothermal coupling model achieves electrothermal coupling through the exchange of electrical power and temperature parameters. Through cyclic and real-time feedback, the model's parameters are dynamically updated during charge and discharge processes, accurately reflecting the dynamic changes in VFB output voltage and stack electrolyte temperature under charge and discharge operation scenarios such as battery testing and emergency power supply, thus improving the accuracy of dynamic characterization of external parameters. For the VFB output voltage, the error results between the thermoelectric coupling model and the experiment reflect the model's accuracy and precision. For the electrolyte temperature in the stack, the model and experimental temperature results are close during charge and discharge processes and both show a monotonically increasing trend.

[0206] Based on the same idea, some embodiments of this application also provide devices and non-volatile computer storage media corresponding to the above methods.

[0207] Figure 11 A schematic diagram of a flow battery external characteristic prediction device provided in this application embodiment includes:

[0208] At least one processor; and,

[0209] A memory communicatively connected to the at least one processor; wherein,

[0210] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform any of the above-described methods for predicting the external characteristics of a flow battery.

[0211] Some embodiments of this application provide a non-volatile computer storage medium for predicting the external characteristics of a flow battery, storing computer-executable instructions capable of executing any of the above-described methods for predicting the external characteristics of a flow battery.

[0212] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the device and medium embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the description of the method embodiments.

[0213] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the technical principles of this application should fall within the protection scope of this application.

Claims

1. A method for predicting the external characteristics of a flow battery, characterized in that, The method includes: An equivalent circuit model and a thermal model of a vanadium redox flow battery are constructed. The equivalent circuit model includes a circuit network consisting of open-circuit voltage, ohmic internal resistance, activation polarization overpotential element, concentration polarization overpotential element, and self-discharge branch. The thermal model includes heat transfer differential equations to describe the temperature changes of the electrolyte in the stack, pipelines, and storage tank. Based on the initial electrolyte temperature and the initial concentrations of vanadium ions in each valence state, the equivalent circuit parameters of the equivalent circuit model are calculated. The equivalent circuit parameters include self-discharge current, open-circuit voltage, activation polarization overpotential, and concentration polarization overpotential. Calculate the battery output voltage and power at the current moment based on the equivalent circuit parameters and the charging and discharging current. Input the current ambient temperature, electrical power, and circulating pump power into the thermal model to solve for the next moment's stack electrolyte temperature; The next moment's electrolyte temperature is input into the dynamic differential equation for vanadium ion concentration to obtain the vanadium ion concentration at the next moment. The electrolyte temperature and vanadium ion concentration at the next moment are fed back to the equivalent circuit model, and the process is iterated until the battery charging and discharging process reaches a steady state, thus obtaining the output voltage and stack electrolyte temperature of the flow battery at each moment during the charging and discharging process.

2. The method according to claim 1, characterized in that, When the equivalent circuit parameter is the open-circuit voltage, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including: Among them, U oc U is the open-circuit voltage. o Let T be the standard electromotive force of the fuel cell stack at equilibrium, R be the ideal gas constant, F be the Faraday constant, N be the number of individual cells in the stack, X2, X3, X4, and X5 be the concentrations of vanadium ions in different valence states, and T be the standard electromotive force of the fuel cell stack at equilibrium. s is the temperature of the battery stack electrolyte, and k is the influence coefficient of the self-discharge reaction on the open-circuit voltage. It represents the influence of self-discharge on the open-circuit voltage during the charging and discharging process. The influence coefficient is negatively correlated with the self-discharge current.

3. The method according to claim 1, characterized in that, When the equivalent circuit parameters are the activation polarization overpotential, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including: Where, η a The activation polarization overpotential is given by R, where R is the ideal gas constant, F is the Faraday constant, N is the number of cells in the stack, and A is the number of cells in the stack. e The surface area of ​​the electrode. The positive electrode reaction rate constant is... T is the rate constant of the negative electrode reaction. s It is the temperature of the electrolyte in the fuel cell stack.

4. The method according to claim 1, characterized in that, When the equivalent circuit parameters are concentration polarization overpotentials, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including: Where, η c Let l be the concentration polarization overpotential, l be the diffusion layer thickness, R be the ideal gas constant, F be the Faraday constant, N be the number of cells in the fuel cell stack, and A be the concentration polarization overpotential. e I is the surface area of ​​the electrode. c For the charging and discharging current, D f2 D f3 D f4 D f5 T represents the diffusion coefficient of vanadium ions of different valence states between the electrode surface region and the solution. s It is the temperature of the electrolyte in the fuel cell stack.

5. The method according to claim 1, characterized in that, When the equivalent circuit parameter is the self-discharge current, the equivalent circuit parameters of the equivalent circuit model are calculated, specifically including: Where N is the number of cells in the stack, F is the Faraday constant, X2, X3, X4, and X5 are the concentrations of vanadium ions in different valence states, and V is the volume of the electrolyte at the positive or negative electrode.

6. The method according to claims 1-5, characterized in that, The calculation of the battery output voltage and power at the current moment based on equivalent circuit parameters and charging / discharging current specifically includes: The expression for the output voltage of a flow battery during the charging and discharging process is as follows: U b =U oc +n a +n c +I c R s Among them, U b For the output voltage, U oc η is the open-circuit voltage. a To activate the polarization overpotential, η c For concentration polarization overpotential, I c R is the charging and discharging current. s The internal resistance is ohmic; The expression for the electrical power of a flow battery is as follows:

7. The method according to claim 1, characterized in that, The expression for the thermal model is as follows: Wherein, the state vector t = [T S ,T p ,T t ] T u = [P e ,T air ,P p ] T ; The matrix of B1 is as follows: The matrix of B2 is as follows: The matrix of G is as follows: Among them, C p V is the specific heat of the electrolyte in the fuel cell stack, ρ is the density of the electrolyte in the fuel cell stack, and V is the specific heat of the electrolyte in the fuel cell stack. s V is the volume of electrolyte in the fuel cell stack. t V is the volume of electrolyte in the storage tank. s T is the volume of electrolyte in the fuel cell stack. p T represents the temperature of the electrolyte in the pipeline. s It is the temperature of the battery stack electrolyte, T. t T represents the temperature of the electrolyte in the storage tank. air For ambient temperature, S S S is the surface area of ​​the electrolyte-containing portion of the battery stack. t S is the surface area of ​​the storage tank. P H is the surface area of ​​the pipe. S H is the heat transfer coefficient of the electrolyte in the fuel cell stack. P H is the heat transfer coefficient of the electrolyte in the pipe. t P is the heat transfer coefficient of the electrolyte in the storage tank. e It is electrical power, P p q represents the pump power, and q represents the flow rate of the electrolyte in the fuel cell stack.

8. The method according to claim 1, characterized in that, The expression for the dynamic differential equation of vanadium ion concentration is as follows: Where d is the thickness of the ion-exchange membrane, V is the volume of the positive or negative electrode electrolyte, k2, k3, k4, and k5 are the diffusion coefficients of vanadium ions in different valence states affected by the electrolyte temperature of the fuel cell stack, S is the area of ​​the ion-exchange membrane, and α i and β i These are the coefficient matrix and vector related to the reaction, I. c This represents the charging and discharging current. X i This refers to the concentration of vanadium ions in various valence states.

9. The method according to claim 1, characterized in that, The method further includes: Compare the predicted temperature value with the preset safety threshold; When the predicted temperature exceeds the preset safety threshold, a control command is generated to adjust the operating status of the cooling system or the speed of the electrolyte circulation pump.

10. A device for predicting the external characteristics of a flow battery, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform a flow battery external characteristic prediction method according to any one of claims 1-9.

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