A method for optimizing control of a vanadium flow battery based on gradient descent method
By constructing a multi-field coupled model for a vanadium redox flow battery using the gradient descent method and dynamically adjusting the electrolyte flow rate, the efficiency optimization problem of flow control in a vanadium redox flow battery was solved, resulting in improved system efficiency and enhanced dynamic response capability throughout the entire life cycle, and extended battery life.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SINOMA INT ENG
- Filing Date
- 2025-07-30
- Publication Date
- 2026-07-14
Smart Images
Figure CN122393343A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electrochemical energy storage technology, and in particular to an efficiency optimization and control method for all-vanadium redox flow batteries based on gradient descent. Background Technology
[0002] Currently, vanadium redox flow batteries (VRFB) are an important direction for large-scale energy storage technology. Their efficiency is significantly affected by the electrolyte flow rate: low flow rate will aggravate concentration polarization and reduce the reaction rate; high flow rate will lead to a surge in pump power loss. The balance between the two is the core of efficiency optimization.
[0003] Existing technologies mostly employ the equal-interval division method, dividing the state of charge (SOC) range into equal parts, fixing a single flow rate for each segment, and selecting the flow rate with the lowest power in each interval as the optimal value through simulation. However, this method relies on preset discrete flow rate points, and the optimal flow rate may exist within the interval rather than at the endpoints, resulting in insufficient accuracy; moreover, fixed intervals cannot dynamically respond to changes in battery state. In the high SOC region, high flow rates can easily lead to a sharp increase in pump losses, while in the low SOC region, low flow rates can easily exacerbate concentration polarization, making it difficult to achieve optimal efficiency throughout the entire cycle and restricting the engineering application of VRFB. Summary of the Invention
[0004] The purpose of this invention is to provide an efficiency optimization control method for vanadium redox flow batteries based on the gradient descent method. To optimize the efficiency of vanadium redox flow batteries, a gradient descent method is adopted as the efficiency optimization control strategy. By dynamically adjusting the electrolyte flow rate parameter, the dominant polarization type and energy loss characteristics of different SOC ranges are matched, and the influence of flow rate on the efficiency of vanadium redox flow batteries under varying temperature conditions is analyzed.
[0005] To achieve the above objectives, this invention provides a method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent, comprising the following steps:
[0006] S1. Construct a multi-field coupling model of the all-vanadium redox flow battery that takes into account the bypass current. The multi-field coupling model is used to characterize the relationship between electrochemistry, hydrodynamics, bypass current, temperature and circuit loss in the all-vanadium redox flow battery system.
[0007] S2. Based on the multi-field coupling model, with electrolyte flow rate as the optimization parameter, define an objective function for the electrolyte flow rate. The objective function is related to the power of the vanadium redox flow battery system.
[0008] S3. The objective function in step S2 is iteratively optimized using the gradient descent method to update the electrolyte flow rate until the preset termination condition is met, thus obtaining the optimal electrolyte flow rate.
[0009] S4. Based on the optimal electrolyte flow rate obtained in step S3, the efficiency of the all-vanadium redox flow battery system is controlled.
[0010] Preferably, in step S1, the multi-field coupling model of the all-vanadium redox flow battery that takes into account the bypass current includes an electrochemical model, a hydrodynamic model, a bypass current model, a temperature model, and an equivalent circuit loss model.
[0011] The electrochemical model calculates the core voltage of the fuel cell stack using the Nernst equation, as shown in the following formula:
[0012]
[0013] Among them, U 0 Here, is the standard electrode potential, R is the universal gas constant, T is the temperature, z is the number of electrons transferred, and F is the Faraday constant. [V 2+ ]、[VO 2+ ]、[V 3+ [These represent the concentrations of vanadium ions in various valence states;]
[0014] The core voltage is coupled as an input parameter to the equivalent circuit loss model.
[0015] Preferably, in the fluid dynamics model, the pump loss current The calculation formula is:
[0016]
[0017] For the total power loss, U stack This refers to the stack voltage;
[0018] Total power loss It is obtained by summing the pressure drop losses of each component, including the pipeline pressure drop ΔP. pipe and stack voltage drop ΔP stack Pipeline pressure drop ΔP pipe The expression is f is the coefficient of friction, L is the pipe length, D is the pipe diameter, D is the electrolyte density, and A is the pipe cross-sectional area.
[0019] Stack voltage drop ΔP stack The expression is ΔP stack =k×Q 2 , where k is the voltage drop coefficient of the fuel cell stack.
[0020] Preferably, in the temperature model, the dynamic differential equation for temperature change is as follows:
[0021]
[0022] Where m is the mass of the electrolyte, c p For specific heat capacity, Q in For the inflow of heat, Qout To dissipate heat, Q gen Heat is generated by the electrochemical reaction;
[0023] Temperature T affects the electrolyte viscosity μ and density ρ;
[0024] electrolyte viscosity μ0 is the reference viscosity, and E is the activation energy;
[0025] Density ρ = ρ0 × (1 - β(T - T0)), where ρ0 is the reference density, β is the volume expansion coefficient, and T0 is the reference temperature.
[0026] Preferably, in the bypass model, the bypass current I bypass The calculation is based on the equivalent resistance of the pipeline. ρ L Where is the resistivity of the electrolyte, is the length of the pipeline, and is the cross-sectional area of the pipeline;
[0027] Bypass current And input the equivalent circuit loss model.
[0028] Preferably, in step S2, the objective function is defined as follows: The expression for the power P(Q) of the all-vanadium redox flow battery system is shown below:
[0029] P(Q)=P stack (Q)+P loss (Q);
[0030] Among them, P stack (Q) represents the fuel cell power, P loss (Q) represents power loss;
[0031] The power of the fuel cell stack is P stack (Q)=I s ×N×(U ocv -I s ×R ohm -h act -h ocn );I s U is the rated charging current, N is the number of cells in a single battery pack, and U is the rated charging current. ocv For OCV voltage, R ohm For the ohmic internal resistance, h act To activate the overpotential, h con This is concentration overpotential;
[0032] Power loss is P pump For the total power loss of the pump, η pump This represents the total power loss of the pump.
[0033] Preferably, the activation overpotential h act The calculation formula is:
[0034]
[0035] Where i is the net current density flowing through the electrode, and i0 is the exchange current density;
[0036] The formula for calculating concentration overpotential is:
[0037]
[0038] Where m is the concentration correction factor, cn is the concentration of reactants in the electrolyte solution, and A ed Let be the electrode surface area, and a and b be empirical constants.
[0039] Preferably, in step S3, the objective function is iteratively optimized using the gradient descent method, including:
[0040] Initialize the state of charge (SOC) and initial electrolyte flow rate (Q0), input them into the multi-field coupling model, and calculate the initial system power (P(Q0)).
[0041] The gradient is calculated based on the central difference formula, and its expression is:
[0042]
[0043] in, The objective function is given by the current flow Q. k The gradient at point ΔQ is a small flow increment;
[0044] The expression for gradient-based flow updates is:
[0045]
[0046] Where α is the learning rate, if |Q k+1 -Q k |<ε, then Q k+1 The optimal flow rate is determined by the flow rate; otherwise, iterative calculations are performed. Here, ε is a preset threshold.
[0047] Preferably, in step S4, after obtaining the optimal electrolyte flow rate Q... ref After a preset period T′, Q ref Re-execute the iterative optimization steps with the initial values, and update the formula as follows:
[0048] Q ref (t+T)=argminP(Q|SOC(t+T′));
[0049] Where t represents the current time.
[0050] Therefore, the efficiency optimization and control method for all vanadium redox flow batteries based on the gradient descent method using the above structure, as described in this invention, has the following beneficial effects:
[0051] (1) Significantly improved flow optimization accuracy
[0052] Traditional methods are limited by discrete flow points, resulting in inherent errors in optimal flow selection. This invention achieves continuous dynamic flow adjustment through gradient descent, precisely matching the nonlinear coupling relationship of SOC polarization. This overcomes the accuracy limitations imposed by discretization.
[0053] (2) Improved system efficiency throughout the entire life cycle
[0054] Traditional methods require high flow rates to suppress concentration polarization in the high SOC region, but this leads to a sharp increase in pump power loss and a drop in efficiency of over 10%. This invention employs a dynamic balancing mechanism: rapidly increasing flow rate in the low SOC region to suppress concentration polarization; and triggering flow safety constraints in the high SOC region to avoid pump overload; thus improving the overall system efficiency throughout its lifecycle.
[0055] (3) Enhanced dynamic response capability
[0056] Traditional segmented control requires pre-setting SOC interval boundaries and cannot respond to battery state changes in real time. This invention performs gradient optimization online every 1 second and autonomously identifies polarization mechanism transition points.
[0057] The flow rate is automatically reduced when the SOC is around 0.3, in response to the shift from concentration polarization to pump loss dominance.
[0058] Fine-tune the flow rate within the SOC range of 0.65–0.82 to match the changes in diffusion impedance;
[0059] It solves the response latency problem of the fixed segmentation strategy and extends battery life by more than 15% (data verified by a semi-physical platform).
[0060] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0061] Figure 1 This is a flowchart illustrating the efficiency optimization and control method for an all-vanadium redox flow battery based on gradient descent, as described in this invention.
[0062] Figure 2 This is a schematic diagram of a system for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent, according to the present invention. Detailed Implementation
[0063] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0064] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0065] Example
[0066] like Figure 1 As shown, this invention provides a method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent, comprising the following steps:
[0067] S1. Construct a multi-field coupling model of the all-vanadium redox flow battery that takes into account the bypass current. The multi-field coupling model is used to characterize the relationship between electrochemistry, hydrodynamics, bypass current, temperature and circuit loss in the all-vanadium redox flow battery system.
[0068] This model consists of five coupled parts: an equivalent circuit loss model, a fluid dynamics model, a bypass current model, an electrochemical model, and a temperature model. The coupling principle is as follows: Figure 2 As shown
[0069] The input parameter for the electrochemical model is the actual current I flowing into the stack. s Initial concentrations C of vanadium ions in various valence states i 0 The concentrations of vanadium ions in different valence states at different times are obtained by using the mass conservation differential equation system, based on factors such as electrolyte flow rate Q and electrolyte temperature.
[0070] The electrochemical model calculates the core voltage of the fuel cell stack using the Nernst equation, as shown in the following formula:
[0071]
[0072] Among them, U 0 Here, is the standard electrode potential, R is the universal gas constant, T is the temperature, z is the number of electrons transferred, and F is the Faraday constant. [V 2+ ]、[VO 2+ ]、[V 3+ [These represent the concentrations of vanadium ions in various valence states;]
[0073] The core voltage is coupled as an input parameter to the equivalent circuit loss model.
[0074] In the fluid dynamics model, the pressure loss of the fuel cell stack is calculated by fully considering the pressure drop loss caused by the electrolyte flow in the pipeline, specifically dividing the flow rate into pipeline flow rate, fuel cell stack flow rate, and circulating pump flow rate. Then, based on fluid dynamics principles, the pressure drop loss in different components can be calculated, thereby obtaining the total power loss. Finally, the pump loss current is obtained by combining the calculation formula of pump loss current. The pump loss current is input into the equivalent circuit loss circuit model and coupled with it. Simultaneously, the model calculates electrolyte density ρ, taking temperature into account, as input to the bypass current model, facilitating the dynamic calculation of the equivalent resistance by the bypass current model.
[0075] In the fluid dynamics model, pump loss current The calculation formula is:
[0076]
[0077] For the total power loss, U stack This refers to the stack voltage;
[0078] Total power loss It is obtained by summing the pressure drop losses of each component, including the pipeline pressure drop ΔP. pipe and stack voltage drop ΔP stack Pipeline pressure drop ΔP pipe The expression is f is the coefficient of friction, L is the pipe length, D is the pipe diameter, D is the electrolyte density, and A is the pipe cross-sectional area.
[0079] Stack voltage drop ΔP stack The expression is ΔP stack =k×Q 2 , where k is the voltage drop coefficient of the fuel cell stack.
[0080] In the bypass current model, the pipes are divided into main pipes and branch pipes. When the electrolyte fills the pipes, they are treated as resistors. By building the circuit and using the output bypass current as the input of the equivalent loss model, the bypass current model can be coupled into the circuit.
[0081] In the bypass model, the bypass current I bypass The calculation is based on the equivalent resistance of the pipeline. ρ L Where is the resistivity of the electrolyte, is the length of the pipeline, and is the cross-sectional area of the pipeline;
[0082] Bypass current And input the equivalent circuit loss model.
[0083] When constructing the temperature model, the concentrations of vanadium ions of various valences and the external temperature T from the electrochemical model were used. air The flow rate Q is used as an input parameter. The temperature T of the electrolyte flowing into the stack in the simulation model is calculated using the dynamic differential equation describing temperature change. stack Temperature T inside the electrolyte tank tank Temperature changes affect the viscosity and density of the electrolyte. Viscosity changes affect the ion diffusion coefficient, a key parameter of the electrochemical model, while density changes affect the equivalent resistance, a key parameter of the bypass current model. This couples the temperature model with the electrochemical model, the fluid dynamics model, and the bypass current model. Furthermore, the diffusion coefficients of vanadium ions in different valence states in fluid dynamics are calculated based on temperature.
[0084] In the temperature model, the dynamic differential equation for temperature change is shown below:
[0085]
[0086] Where m is the mass of the electrolyte, c p For specific heat capacity, Q in For the inflow of heat, Q out To dissipate heat, Q gen Heat is generated by the electrochemical reaction;
[0087] Temperature T affects the electrolyte viscosity μ and density ρ;
[0088] electrolyte viscosity μ0 is the reference viscosity, and E is the activation energy;
[0089] Density ρ = ρ0 × (1 - β(T - T0)), where ρ0 is the reference density, β is the volume expansion coefficient, and T0 is the reference temperature.
[0090] The equivalent loss circuit model can represent the relevant losses as internal resistances, such as the parasitic losses R in an energy storage system. f1 R f2 R f3 The resistance R0 of the electrode materials, electrolyte, ion exchange membrane, and current collector inside the battery; the voltage loss due to electrode reaction lag and reaction losses R1, R2, and R3 caused by changes in the concentration of active materials on the electrode surface; and the stack current I. s_i This represents the actual current flowing into the fuel cell stack; C i This represents the electrode capacitance, which is related to the vanadium ion concentration.
[0091] S2. To accurately describe the battery's operating state, relevant constraints need to be added, as shown in the table below:
[0092]
[0093] S21. Constructing the Objective Function: The charging power of the vanadium redox flow battery is provided externally, including stack power and power loss. During charging, the optimal flow rate should minimize the system power, because at this point, the external energy supply is also reduced. When using the gradient descent method for parameter optimization, the state of charge (SOC) and initial flow rate Q0 need to be initialized first and used as inputs to the multi-field coupling model. Then, the model will calculate relevant parameters, including the system power P. Thus, the objective function is constructed:
[0094] P(Q)=P stack (Q)+P loss (Q);
[0095] Where Q is the flow rate parameter, P(Q) is the system power with respect to the flow rate parameter, and P... stack (Q) represents the fuel cell power, P loss (Q) represents power loss, P stack (Q) can be derived using the following expression.
[0096] P stack (Q)=I s ×N×(U ocv -I s ×R ohm -h act -h ocn );
[0097] In the formula, I s U is the rated charging current, N is the number of cells in a single battery pack, and U is the rated charging current. ocv For OCV voltage, R ohm For the ohmic internal resistance, h act To activate the overpotential, h con This is concentration overpotential;
[0098] Power loss is P pump For the total power loss of the pump, η pump The total power loss of the pump is 0.8, which is taken here.
[0099] overpotential h act The calculation formula is:
[0100]
[0101] Where i is the net current density flowing through the electrode, and i0 is the exchange current density;
[0102] The formula for calculating concentration overpotential is:
[0103]
[0104] Where m is the concentration correction factor, cn is the concentration of reactants in the electrolyte solution, and A ed Let be the electrode surface area, and a and b be empirical constants, usually a is taken as 1.6 and b is taken as 0.4.
[0105] S3. Initialize the state of charge (SOC) and initial electrolyte flow rate (Q0), input them into the multi-field coupling model, and calculate the initial system power P(Q0);
[0106] The gradient is calculated based on the central difference formula, and its expression is:
[0107]
[0108] in, The objective function is given by the current flow Q. k The gradient at the point is given by ΔQ, which is a small flow rate increment ranging from 0.005 to 0.02 L / min.
[0109] S4. Update the next flow Q under the condition that the constraints are met. k+1 :
[0110]
[0111] Where α is the learning rate, and its value ranges from 0.01 to 0.1.
[0112] S5. Terminate the iteration when the parameter change is less than the set threshold ε; otherwise, return to step S3. The threshold ε ranges from 0.001 to 0.1 L / min.
[0113] |Q k+1 -Q k |<ε
[0114] When the iteration terminates, record Q at this point. k+1 For optimal flow Q ref , as model input;
[0115] The update formula is as follows:
[0116] Q ref (t+T)=argminP(Q|SOC(t+T′));
[0117] Where t represents the current time.
[0118] After a preset period T′, Q is used again. ref Use this as input to initialize the model and update the latest optimal flow.
[0119] In summary, the core of this invention lies in dynamically adjusting the electrolyte flow rate parameters to match the dominant polarization type and energy loss characteristics in different SOC ranges. This strategy relies on an existing multi-field coupling model of a full vanadium redox flow battery that takes into account bypass current, and studies the impact of flow rate on the efficiency of the VRFB system under varying temperature conditions through numerical modeling and simulation analysis.
[0120] This invention achieves real-time dynamic optimization of electrolyte flow rate through gradient descent method, comprehensively surpassing traditional methods in three dimensions: accuracy, efficiency, and response speed, providing core control support for the engineering application of vanadium redox flow batteries.
[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent, characterized in that, Includes the following steps: S1. Construct a multi-field coupling model of the all-vanadium redox flow battery that takes into account the bypass current. The multi-field coupling model is used to characterize the relationship between electrochemistry, hydrodynamics, bypass current, temperature and circuit loss in the all-vanadium redox flow battery system. S2. Based on the multi-field coupling model, with electrolyte flow rate as the optimization parameter, define an objective function for the electrolyte flow rate. The objective function is related to the power of the vanadium redox flow battery system. S3. The objective function in step S2 is iteratively optimized using the gradient descent method to update the electrolyte flow rate until the preset termination condition is met, thus obtaining the optimal electrolyte flow rate. S4. Based on the optimal electrolyte flow rate obtained in step S3, the efficiency of the all-vanadium redox flow battery system is controlled.
2. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 1, characterized in that: In step S1, the multi-field coupling model of the all-vanadium redox flow battery that takes into account the bypass current includes an electrochemical model, a hydrodynamic model, a bypass current model, a temperature model, and an equivalent circuit loss model. The electrochemical model calculates the core voltage of the fuel cell stack using the Nernst equation, as shown in the following formula: Among them, U 0 Here, is the standard electrode potential, R is the universal gas constant, T is the temperature, z is the number of electrons transferred, and F is the Faraday constant. [V 2+ ]、[VO 2+ ]、[V 3+ [These represent the concentrations of vanadium ions in various valence states;] The core voltage is coupled as an input parameter to the equivalent circuit loss model.
3. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 2, characterized in that: In the fluid dynamics model, pump loss current The calculation formula is: For the total power loss, U stack This refers to the stack voltage; Total power loss It is obtained by summing the pressure drop losses of each component, including the pipeline pressure drop ΔP. pipe and stack voltage drop ΔP stack Pipeline pressure drop ΔP pipe The expression is f is the coefficient of friction, L is the pipe length, D is the pipe diameter, D is the electrolyte density, and A is the pipe cross-sectional area. Stack voltage drop ΔP stack The expression is ΔP stack =k×Q 2 , where k is the voltage drop coefficient of the fuel cell stack.
4. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 2, characterized in that: In the temperature model, the dynamic differential equation for temperature change is as follows: Where m is the mass of the electrolyte, c p For specific heat capacity, Q in For the inflow of heat, Q out To dissipate heat, Q gen Heat is generated by the electrochemical reaction; Temperature T affects the electrolyte viscosity μ and density ρ; electrolyte viscosity μ0 is the reference viscosity, and E is the activation energy; Density ρ = ρ0 × (1 - β(T - T0)), where ρ0 is the reference density, β is the volume expansion coefficient, and T0 is the reference temperature.
5. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 3, characterized in that: In the bypass model, the bypass current I bypass The calculation is based on the equivalent resistance of the pipeline. ρ L Where is the resistivity of the electrolyte, is the length of the pipeline, and is the cross-sectional area of the pipeline; Bypass current And input the equivalent circuit loss model.
6. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 1, characterized in that: In step S2, the objective function is defined as follows: The expression for the power P(Q) of the all-vanadium redox flow battery system is shown below: P(Q)=P stack (Q)+P loss (Q); Among them, P stack (Q) represents the fuel cell power, P loss (Q) represents power loss; The power of the fuel cell stack is P stack (Q)=I s ×N×(U ocv -I s ×R ohm -h act -h ocn );I s U is the rated charging current, N is the number of cells in a single battery pack, and U is the rated charging current. ocv For OCV voltage, R ohm For the ohmic internal resistance, h act To activate the overpotential, h con This is concentration overpotential; Power loss is P pump For the total power loss of the pump, η pump This represents the total power loss of the pump.
7. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 6, characterized in that: Activation overpotential h act The calculation formula is: Where i is the net current density flowing through the electrode, and i0 is the exchange current density; The formula for calculating concentration overpotential is: Where m is the concentration correction factor, cn is the concentration of reactants in the electrolyte solution, and A ed Let be the electrode surface area, and a and b be empirical constants.
8. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 1, characterized in that: In step S3, the objective function is iteratively optimized using gradient descent, including: Initialize the state of charge (SOC) and initial electrolyte flow rate (Q0), input them into the multi-field coupling model, and calculate the initial system power (P(Q0)). The gradient is calculated based on the central difference formula, and its expression is: in, The objective function is given by the current flow Q. k The gradient at point ΔQ is a small flow increment; The expression for gradient-based flow updates is: Where α is the learning rate, if |Q k+1 -Q k |<ε, then Q k+1 The optimal flow rate is determined by the flow rate; otherwise, iterative calculations are performed. Here, ε is a preset threshold.
9. The method for optimizing and controlling the efficiency of an all-vanadium redox flow battery based on gradient descent as described in claim 1, characterized in that: In step S4, the optimal electrolyte flow rate Q is obtained. ref After a preset period T′, Q ref Re-execute the iterative optimization steps with the initial values, and update the formula as follows: Q ref (t+T)=argminP(Q|SOC(t+T′)); Where t represents the current time.