Energy storage capacity configuration method of wind-hydrogen mixing system considering dynamic efficiency and heat balance of electrolytic cell

Abstract

The invention discloses a wind-hydrogen mixing system energy storage capacity configuration method considering dynamic efficiency and heat balance of an electrolytic cell. Integrating an electrolytic cell dynamic efficiency model, a heat balance link model, a storage battery operation model, a fuel cell operation model, a hydrogen storage tank energy balance model, a wind power output power model and a capacity configuration objective function, and establishing a wind-hydrogen hybrid system energy storage capacity configuration model considering the electrolytic cell dynamic efficiency and heat balance; and solving the energy storage capacity configuration model of the wind-hydrogen hybrid system by using a distributed robust method to obtain a capacity configuration scheme. According to the method, through the synergistic effect of dynamic efficiency modeling and a heat balance system, the total cost of the system is reduced compared with that of a traditional method. The redundant capacity of the electrolytic cell and the fuel cell is reduced, and the capacity of the hydrogen storage tank is reasonably configured, so that the optimal balance between the investment cost and the operation risk is realized on the premise of guaranteeing the reliability of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system capacity optimization configuration, and in particular to a wind-hydrogen hybrid system energy storage capacity configuration method considering dynamic efficiency and thermal balance of electrolytic cell. BACKGROUND

[0002] With the acceleration of global energy transformation, wind power, as an important part of clean and renewable energy, its installed capacity continues to grow. However, the intermittency and volatility of wind power output increase the difficulty of grid acceptance, and efficient energy storage systems are needed to achieve power smoothing and energy regulation. Hydrogen energy storage has become one of the core technologies for building wind-hydrogen hybrid systems due to its large capacity storage, long period regulation and multi-energy coupling characteristics. Currently, the energy storage capacity configuration of wind-hydrogen hybrid system faces three major technical challenges: (1) Limitations of electrolytic cell dynamic characteristics modeling: In the traditional design of wind-hydrogen hybrid system, the electrolytic cell is often simplified as a constant efficiency energy conversion device, ignoring the nonlinear characteristics of its operating efficiency changing with current density. In fact, the Faraday efficiency of proton exchange membrane electrolytic cell and the operating voltage are significantly affected by current density, showing a typical polarization curve rule. If this dynamic characteristic is ignored, the energy storage capacity configuration will deviate greatly from the actual demand, resulting in waste of system investment cost or insufficient hydrogen energy output.

[0003] (2) Efficiency decay and safety hazards caused by lack of thermal management: About 30%-50% of the energy in the electrolysis process is released in the form of heat energy. The traditional system does not have a heat balance mechanism, which causes the operating temperature of the equipment to deviate from the rated range, exacerbating membrane electrode wear and hydrogen diffusion loss. Specifically, fluctuations in the operating temperature of the electrolytic cell affect the ion conductivity of the proton exchange membrane, and also cause hydrogen and oxygen to permeate across the membrane, which not only reduces hydrogen production efficiency, but also may cause overheating risk of the equipment. In addition, the direct discharge of unrecycled waste heat also leads to low energy utilization rate.

[0004] (3) Lack of robustness in dealing with wind power uncertainty: Existing capacity configuration methods mostly use deterministic optimization or traditional stochastic programming, which are difficult to deal with extreme fluctuation scenarios of wind power output. For example, the stochastic optimization method based on probability distribution assumption needs to rely on a large amount of historical data, but sudden changes in wind speed in actual operation may cause the model to fail. When the power tracking accuracy requirement of the grid on the wind-hydrogen hybrid system is improved, the lack of robust optimization scheme will lead to excessive conservative energy storage capacity configuration or system instability. SUMMARY

[0005] To solve the above technical problems, the present application provides a wind-hydrogen hybrid system energy storage capacity configuration method considering dynamic efficiency and thermal balance of electrolytic cell, which realizes: 1) Refined electrolyzer modeling: By characterizing the nonlinear relationship between Faraday efficiency and current density, the energy conversion characteristics of the electrolyzer in the millisecond-level dynamic response are accurately represented, solving the error problem of the traditional constant efficiency model; 2) Thermal balance synergistic optimization: Construct a waste heat recovery and temperature control model, and realize closed-loop temperature control of electrolyzer and fuel cell through heat storage tank and heat exchanger to reduce efficiency decay and hydrogen loss; 3) Wasserstein distance uncertainty handling: Construct a wind power uncertainty set based on Wasserstein distance, incorporate extreme scenarios into the optimization framework, and avoid excessive redundancy in capacity configuration while ensuring system reliability.

[0006] The technical solution adopted in this invention is as follows: A method for configuring the energy storage capacity of a wind-hydrogen hybrid system, considering the dynamic efficiency and thermal balance of the electrolyzer, includes: Step 1: Based on the topological characteristics of the wind-hydrogen hybrid system, establish the framework of the wind-hydrogen hybrid system; Based on the dynamic operating mechanism and electrochemical characteristics of the electrolyzer, a dynamic efficiency model of the electrolyzer is constructed. Based on the operating characteristics of the wind-hydrogen hybrid system, a thermal equilibrium model is constructed; Based on the operating characteristics of lead-acid batteries, a battery operation model is constructed; Based on the operating characteristics of proton exchange membrane fuel cells, a fuel cell operating model is constructed; An energy balance model for hydrogen storage tanks is constructed using the total energy stored in the hydrogen storage tanks as the key parameter. Based on the actual power output characteristics of wind power, a wind power output power model is constructed; Using energy storage capacity as the optimization variable, a capacity configuration objective function is constructed to minimize system investment costs.

[0007] Step 2: Based on the wind-hydrogen hybrid system framework, integrate the dynamic efficiency model of the electrolyzer, the thermal balance model, the battery operation model, the fuel cell operation model, the hydrogen storage tank energy balance model, the wind power output power model, and the capacity configuration objective function to establish a wind-hydrogen hybrid system energy storage capacity configuration model that considers the dynamic efficiency and thermal balance of the electrolyzer.

[0008] Step 3: Solve the energy storage capacity configuration model of the wind-hydrogen hybrid system using the split-Brow bar method to obtain the capacity configuration scheme.

[0009] In step 1, a framework for a wind-hydrogen hybrid system is established. For example... Figure 1 As shown, the wind-hydrogen hybrid system takes the wind farm as its core and achieves dynamic energy balance through multi-energy coupling of electricity, hydrogen, and heat.

[0010] The wind-hydrogen hybrid system consists of a wind farm, an electrochemical energy storage unit (battery), a hydrogen energy storage section, and a thermal balance section. The wind power dispatch system allocates electrical energy according to the wind power output status. When there is surplus, the electrical energy is stored in the battery on the one hand, and drives the electrolyzer to decompose water into hydrogen and store it in the hydrogen storage tank on the other hand. At the same time, the waste heat generated in the electrolysis process is recovered to the heat storage tank through the heat storage heat exchanger. When wind power is insufficient, the hydrogen storage tank releases hydrogen to power the fuel cell, and the battery discharges simultaneously to supplement the grid demand. Meanwhile, the thermal storage tank regulates the distribution of heat energy through a thermal circulation system to meet the heat load requirements. Through the coordinated storage and dynamic scheduling of electricity, hydrogen, and heat, this system not only effectively mitigates the volatility of wind power but also improves energy utilization.

[0011] In step 1, a dynamic efficiency model is constructed based on the dynamic operating mechanism and electrochemical characteristics of the proton exchange membrane electrolyzer. The proton exchange membrane electrolyzer achieves real-time control of hydrogen production rate by actively adjusting the operating current and rapidly mitigating fluctuations in renewable energy power generation based on its millisecond-level dynamic response characteristics. Its operating characteristics follow typical polarization curve patterns, and the functional relationship between operating voltage and current density can be characterized as follows: (1); In formula (1): for t The operating voltage of the electrolytic cell at all times; t For the running interval; The voltage is the reversible voltage; T is the operating temperature; R and F are the ideal gas constant and Faraday constant, respectively. and These are the partial pressures of hydrogen and oxygen, respectively. The activity of H2O; Internal equivalent ohmic resistance; and These are the charge transfer coefficients of the anode and cathode, respectively; and These are the exchange current densities at the anode and cathode, respectively. denoted as current density.

[0012] Under ideal conditions, the Faraday efficiency is 1. However, actual electrolyzers exhibit permeability, meaning that hydrogen and oxygen diffuse during mass transfer. This does not conform to the actual operating characteristics of an electrolyzer. Faraday efficiency It can be described by membrane flux density and hydrogen production density, and its functional expression is as follows: (2); In formula (2): , These represent the hydrogen and oxygen permeability in the diffusion mechanism, respectively. Hydrogen permeability caused by pressure difference; , These represent the partial pressures of hydrogen at the cathode and oxygen at the anode in the catalyst layer, respectively. d The thickness is denoted as .

[0013] Considering the input, output, and energy conversion relationships of the electrolyzer, the operating efficiency of the electrolyzer is as follows: (3); In formula (3): for t The operating efficiency of the electrolytic cell at all times; The high calorific value of hydrogen under standard conditions; express t Hydrogen production at any given time; Output power of the electrolytic cell In summary, the operating efficiency of an electrolytic cell changes dynamically with the input power of the electrolytic cell. Figure 3 The figure shows the relationship between the operating efficiency, Faraday efficiency and power of an electrolyzer with a maximum capacity of 100MW.

[0014] Based on the working principle of the electrolyzer and the relationship between hydrogen production and operating current, the power consumption of the electrolyzer is... and hydrogen production As shown below: (4); (5); In formula (5): Indicates the conversion factor; This represents the number of electrolytic cells connected in series. Represented as t Faraday efficiency at any moment This indicates the operating current of the electrolytic cell; (6); In formula (6): Indicates the effective reaction area.

[0015] In step 1, a thermal balance model is constructed based on the operating characteristics of the wind-hydrogen hybrid system; The heat balance stage plays a crucial role in hydrogen energy storage, balancing the heat energy demands of various system components. This system recovers waste heat, transferring excess heat generated in the hydrogen storage stage to other heat load units for utilization. Based on this working mechanism, the heat balance stage model can be expressed as: (7); In equation (7): , They are respectively Moment, present The thermal energy stored in the thermal storage tank at any given time, expressed in kW·h; , They are respectively t The heat power consumed by the system at any given time and the heat power provided to the heating load, in kW; For the efficiency of the thermal storage heat exchanger; This indicates the heat generation capacity of the electrolytic cell; This indicates the heat output power of the fuel cell; The heat power consumed by the system It consists of the heat dissipation power of the electrolytic cell and the heat dissipation power of the fuel cell, as shown in equation (8): (8); In equation (8): , , They are respectively t The operating temperature of the electrolytic cell and the ambient temperature at all times, in K; , These are the heat dissipation coefficients per unit capacity of the electrolyzer and the fuel cell, respectively. , These are the installed capacities of electrolyzers and fuel cells, respectively, in kW; Simultaneously, the system operation should also meet thermal balance and electrical power balance constraints. The system's thermal balance can be modeled using the heat and power exchange between the electrolyzer, fuel cell, and heat storage tank, i.e.: (9); In equation (9): for t The heat exchange power between the thermal storage heat exchanger and the thermal storage tank at any given time, expressed in kW; This indicates the heat power consumed by the system.

[0016] In step 1, when modeling and analyzing lead-acid batteries, a simplified model is often used, which is expressed as follows: (10); In formula (10): , Residual batteries t The charging and discharging power during a given period; The maximum power of a single charge and discharge cycle of the battery; , For storage batteries The charging and discharging flag parameters for each time period are all binary variables; , These are the charge and discharge efficiencies of the battery, respectively. for tThe output power of the battery during a given period; , They are respectively t Time period and t- The amount of electricity stored in the battery during period 1; , These are the upper and lower limits of the battery's energy storage capacity, respectively. This represents the battery energy storage capacity during time period t. This refers to the configured capacity of the battery.

[0017] In step 1, a basic model is often used to study the operating characteristics of proton exchange membrane fuel cells, which is expressed as follows: (11); In equation (11): , They are respectively t The power generation and heat generation of a proton exchange membrane fuel cell at any given time are expressed in kW. for t The hydrogen consumption rate of a proton exchange membrane fuel cell at any given time, expressed in mol / h. The efficiency of a proton exchange membrane fuel cell; This indicates the high calorific value of hydrogen.

[0018] In step 1, the total energy stored in the hydrogen storage tank is used as the key parameter to construct an energy balance model for the hydrogen storage tank: During water electrolysis, the hydrogen storage system is responsible for collecting and storing the generated hydrogen in a hydrogen storage tank; while in the power generation stage, the hydrogen storage system will transport the stored hydrogen and externally introduced oxygen to the fuel cell to drive the power generation reaction. (12); In equation (12): for t Internal input power of the hydrogen storage tank during a given period; , They are respectively t -1 moment, current time t The total energy stored in the hydrogen storage tank at any given time, expressed in kW·h; For time intervals; Represented as t The operating efficiency of the electrolytic cell at all times.

[0019] In step 1, a wind power output model is constructed based on the actual power output characteristics of wind power. The wind farm output power model is established as follows: (13); In equation (13): The installed capacity of the wind farm is expressed in kW. To obtain based on wind speed t Power coefficient at time; for t The actual output power of the wind farm at any given time, expressed in kW.

[0020] The reliable grid-connected power of wind farms participating in grid dispatch is: (14); In equation (14): , They are respectively t The reliable grid-connected power and day-ahead predicted output power of the wind farm at any given time, in kW; δ This is the availability factor for wind power.

[0021] The output power balance constraint of the wind-hydrogen hybrid system can be expressed as: (15); In equation (15): t The actual output power of the wind farm at any given time, in kW; In step 1, based on the existing installed capacity of wind farms, the capacity of electrolyzers, fuel cells, hydrogen storage tanks and batteries are used as optimization variables. In the worst case caused by the uncertainty of wind farm power, the system investment cost is minimized while meeting the tracking deviation requirements of the grid dispatch curve. (16); In equation (16): The system investment cost is expressed in dollars. This refers to the capacity of the hydrogen storage tank, expressed in kWh. , These are the unit power investment factors for electrolyzers and fuel cells, respectively, in $ / kW; , These are the unit capacity investment coefficients for hydrogen storage tanks and batteries, respectively, in $ / kWh.

[0022] In step 2, as shown by equations (2), (3), and (5), the relationship between the efficiency and power of the electrolytic cell is non-linear. To simplify the calculation, the following steps are taken: η e,t become M segment constant η e,m The corresponding power per unit value is The following piecewise linearization is used to linearize it; (17); In equation (17): This represents the operating state of the m-th segment of the electrolytic cell at time t. Indicates the number of segments; , These represent the power consumption of the m-th and m-1-th segments, respectively. Indicates the upper limit of the input power of the electrolytic cell; This indicates the output power of the electrolytic cell.

[0023] The optimization problem involved in this invention is a min-max optimization problem with uncertain variables, whose non-convex nature makes it difficult to solve analytically directly using traditional methods. This invention proposes a phased modeling strategy: First, based on the sub-Bruker optimization framework, an extreme scenario representation model of the wind power uncertainty set is constructed; This study is based on typical daily data from a 90MW wind farm during spring, summer, autumn, and winter. The selection of these seasonal typical daily data is crucial because wind power output is significantly affected by seasonal wind speed characteristics: spring brings frequent gusts, summer offers relatively stable winds, autumn provides moderate wind speeds, and winter sees low but persistent wind speeds. The seasonal data covers the wind farm's normal wind speed conditions throughout the year. Furthermore, "typical day" specifically refers to a regular day within that season where wind speed and output fluctuations conform to the wind farm's long-term operational statistical characteristics, excluding extreme winds and prolonged periods of no wind. This ensures the data reflects only the "normal fluctuations" in wind power, providing a benchmark for distinguishing extreme scenarios. Statistical analysis revealed that a certain interval occurred more than 90% of the time, corresponding to the daily wind power output range. The resulting empirical distribution lays the foundation for constructing an uncertainty set encompassing extreme scenarios based on Wasserstein distance.

[0024] Furthermore, the Wasserstein probability measure is introduced as a fuzzy set. The mathematical description is used to establish an uncertainty quantification model for the operating domain of the energy storage system: (18); In equation (18): This represents the probability distribution of the actual output power of the wind farm. Empirical distribution of wind farm output power; For all defined in Wasserstein divergence The probability distribution space below; This represents a "probability distribution distance metric" constructed based on Wasserstein divergence. ε Let be the radius of the fuzzy set.

[0025] The uncertain set given in the above equation can be transformed into a set of linear risk-opportunity constraints, as shown in equation (19): (19); In equation (19): K The total number of data samples; α Confidence level; , t , They are respectively t Time sample k The actual wind farm output power and reliable grid-connected power are expressed in kW. , γ, d These are dual variables.

[0026] Finally, the energy storage capacity configuration model for the wind-hydrogen hybrid system, considering the dynamic efficiency and thermal balance of the electrolyzer, can be expressed as: (20); This model is a mixed-integer linear programming (MILP) problem, which is solved directly by calling the CPLEX solver in the MATLAB 2023b environment.

[0027] In step 3, the energy storage capacity configuration model of the wind-hydrogen hybrid system is solved using the split-Bruker bar method to obtain the capacity configuration scheme.

[0028] First, the solution basis and uncertainty quantification object of the split-bar method are determined: based on the wind power output model (Equations 13 and 14) constructed in step 1, and based on the historical operation data of the wind farm, the empirical distribution of wind power is statistically obtained. This distribution provides a benchmark for characterizing uncertainty; Secondly, a wind power uncertainty set is constructed based on the Wasserstein distance to characterize the boundaries of the uncertainty: Referring to the cost minimization requirement of the capacity configuration objective function (16) in step 1, and combining the principle of "covering extreme scenarios and avoiding overly conservative approaches", a system is constructed that includes all possible real distributions of wind power. P The uncertain set is given by the formula (21): (twenty one); In the formula, For the space of all probability distributions defined under Wasserstein divergence, For the distance metric of probability distributions constructed based on Wasserstein divergence, Let be the radius of the fuzzy set, which provides a constraint boundary for subsequent worst-case optimization.

[0029] Next, a min-max optimization framework of "minimizing cost - worst-case scenario constraint" is constructed, incorporating the overall system constraints. Based on the "energy storage capacity configuration model of wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer" established in step 2, the outer objective is to minimize the system investment cost determined in step 1, while the inner objective is to find the true distribution in the uncertainty set U that makes the system constraints the tightest. This ensures that the optimized capacity configuration can still meet the requirements of grid dispatch curve tracking and electrolyzer rated temperature maintenance under extreme wind power fluctuations.

[0030] Then, the non-convex min-max problem is transformed into a solvable linear constraint, thus achieving model convexity. Using duality theory, the uncertainty set constraint shown in equation (18) is transformed into a set of linear risk-opportunity constraints, as shown in equation (19). This transformation converts the original non-convex optimization problem into a mixed-integer linear programming (MILP) problem, which is the final form of the model in step 2 (Equation 20), making it compatible with commercial solvers.

[0031] Finally, the solver is called to solve the MILP model and output the capacity configuration scheme. In the MATLAB 2023b environment, the CPLEX solver is called, and the electrolyzer dynamic efficiency model (1) to (6), the thermal balance model (7) to (9), the battery operation model (10), the fuel cell operation model (11), the hydrogen storage tank energy balance model (12), and the above linear constraints constructed in step 1 are used as inputs to solve for the optimal planned capacity of the electrolyzer, fuel cell, hydrogen storage tank, and battery.

[0032] This invention provides a method for configuring the energy storage capacity of a wind-hydrogen hybrid system that considers the dynamic efficiency and thermal balance of the electrolyzer. The technical advantages are as follows: 1) By establishing a dynamic efficiency model for electrolyzers, the Faraday efficiency loss under low-power conditions (such as efficiency decay caused by increased hydrogen permeability) can be accurately characterized, effectively avoiding the overestimation of equipment efficiency by traditional fixed efficiency models. Simulation results show that dynamic efficiency modeling can reduce the planned capacity of electrolyzers by 15% to 32%, significantly reducing redundant investment.

[0033] 2) The thermal balance system maintains the rated temperature of the equipment through waste heat recovery, reducing hydrogen loss due to heat dissipation during operation. At the same time, its thermal inertia effect requires the hydrogen storage tank to reserve capacity to cope with heat load fluctuations in extreme scenarios, which means that the planned capacity of the hydrogen storage tank needs to be increased by about 3 times, thereby improving the system robustness while reducing operating costs.

[0034] 3) The synergistic effect of dynamic efficiency modeling and thermal balance system reduces the total system cost by about 30% compared to traditional methods. By reducing the redundant capacity of the electrolyzer and fuel cell and rationally configuring the hydrogen storage tank capacity, the optimal balance between investment cost and operational risk is achieved while ensuring system reliability. Attached Figure Description

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of a wind-hydrogen mixing system.

[0036] Figure 2 The figures show the dynamic efficiency and Faraday efficiency curves of the electrolyzer.

[0037] Figure 3 This is a typical daily wind power output diagram.

[0038] Figure 4 A comparison chart of electrolytic cell output under different cases.

[0039] Figure 5 This is a comparison chart of fuel cell output under different case studies.

[0040] Figure 6 A comparison of the energy of hydrogen storage tanks in different cases.

[0041] Figure 7 This is the heat load data curve.

[0042] Figure 8 The results are for the heat generation operation of the fuel cell.

[0043] Figure 9 The results are for the heat generation operation of the electrolytic cell. Detailed Implementation

[0044] This invention presents an optimization method for hydrogen energy storage in a multi-energy coupling system in a low-carbon industrial park, considering the variable operating efficiency characteristics of electrolyzers. First, a refined electrolyzer model is established to dynamically characterize the nonlinear characteristics of its Faraday efficiency as a function of current density. Second, a thermal balance model is introduced to recover waste heat and maintain the rated temperature of the equipment, thereby reducing efficiency decay and hydrogen loss. Next, a mixed-integer linear programming model is constructed with the partial Bruker bar optimization method to handle the uncertainty of wind power generation, aiming to minimize capacity configuration costs. Finally, comparative analysis shows that considering the synergistic optimization of dynamic efficiency and thermal balance can significantly reduce system capacity requirements and total costs, verifying its effectiveness in improving economic efficiency and robustness. Overall, this invention provides a new model for energy storage capacity configuration in wind-hydrogen hybrid systems, considering the dynamic efficiency and thermal balance of electrolyzers, and effectively addresses the uncertainties of wind power generation by combining the partial Bruker bar optimization method, offering a new perspective on system energy storage capacity configuration and balancing the reaction temperature of electrochemical devices.

[0045] Example: This invention constructs a computational example based on actual data from a 90MW wind farm to verify the proposed energy storage capacity configuration method. The parameters of each component of the system are shown in Table 1. Data from typical days in spring, summer, autumn, and winter of the actual wind farm are selected as the predicted power of the wind farm; detailed data can be found in [reference needed]. Figure 2 As shown.

[0046] Table 1 System Parameters

[0047] To investigate the impact of accurate modeling of the electrolytic cell's dynamic efficiency and thermal balance system operating characteristics on the long-term operation of the system, this invention sets up the following four schemes for comparative analysis.

[0048] Case 1: The method of the present invention is an operation method that takes into account the dynamic efficiency characteristics of the electrolyzer.

[0049] Case 2: Operating method considering system thermal balance and ignoring the dynamic efficiency characteristics of the electrolyzer.

[0050] Case 3: Considering the dynamic efficiency characteristics of the electrolyzer, the system thermal balance is ignored.

[0051] Case 4: Operating method without considering system thermal balance and electrolytic cell dynamic efficiency characteristics.

[0052] The simulation results of the four schemes are shown in Table 2.

[0053] Table 2 Capacity Configuration Results

[0054] The analysis focuses on the impact of electrolyzer dynamic efficiency modeling on system operating efficiency and capacity configuration, mainly referring to... Figure 4 , Figure 5 ,and Figure 6 This will be explained. The output comparison of the electrolyzer and fuel cell in different cases is shown below: Dynamic efficiency analysis of electrolyzers: First, as shown in Table 1, compared to Case 4, considering dynamic efficiency, the planned capacity of the electrolyzer decreased from 9.34MW to 6.32MW in Case 1, a reduction of 32.3%; although the hydrogen storage tank capacity increased, the total investment cost still decreased by approximately 6%. This difference in capacity configuration is due to the fact that the electrolyzer's dynamic efficiency model can accurately identify the efficiency variation patterns under different power conditions, thereby optimizing the hydrogen production strategy. For example... Figure 4 As shown, in Case 1, the electrolyzer operated in the low to medium power range for most of the time, significantly reducing the high-power operation period compared to Case 4. Combined with... Figure 2The efficiency curves show that the efficiency of the electrolyzer in the low-to-medium power range is higher than that in the high-power range. Therefore, Case 1 requires less power under the same hydrogen production conditions, which significantly reduces the demand for high-capacity electrolyzers.

[0055] Further from Figure 6 It is evident that the hydrogen storage tank in Case 1 exhibits more stable energy fluctuations, indicating a more continuous and stable hydrogen production process. This continuity eliminates the system's reliance on instantaneous, large-scale hydrogen production, thereby reducing the capacity requirements for the fuel cell and hydrogen storage system and enhancing overall operational flexibility and coordination.

[0056] In summary, the electrolyzer dynamic efficiency model improves the overall system operating efficiency without increasing equipment burden by more rationally allocating hydrogen production load and utilizing the nonlinear relationship between efficiency and power, and significantly reduces capacity redundancy and investment costs.

[0057] Thermal balance analysis: In the operation of a wind-hydrogen mixing system, the thermal balance mechanism plays a crucial role in maintaining the stable operating temperature of the electrochemical device, improving energy efficiency, and mitigating system fluctuations. This study compares Case 1 and Case 3 to explore the actual operating performance of the thermal balance system under various seasonal and operational conditions.

[0058] First, as shown in Table 1, in Case 1 where a heat balance mechanism is introduced, although the capacity of the hydrogen storage tank increases significantly from 8.91 MW·h in Case 3 to 31.82 MW·h, the total system investment cost remains below 10.63 M$, with the increase being far lower than the increase in hydrogen storage capacity. This indicates that the heat balance system improves system stability and efficiency without causing a significant increase in system cost; on the contrary, by reducing hydrogen loss, it is more in line with engineering practice.

[0059] like Figure 8 As shown, during the summer when wind power output is at its lowest, the thermal output of the fuel cell in Case 1 is significantly lower than that in Case 3. This is because, when wind power is insufficient, the system relies on the heat energy recovered from the heat storage tank to thermally compensate for the fuel cell, thereby reducing its additional heat generation burden. Due to the higher air temperature, the addition of thermal balance effectively controls the temperature rise of the fuel cell, avoiding overheating and improving system operational safety. In contrast, Case 3 lacks thermal balance, and the fuel cell must rely on its own heat generation to maintain system operation, resulting in heat energy waste and the risk of equipment overheating. During the autumn period when wind power resources are abundant and the ambient temperature is suitable, the thermal output of the fuel cell in Case 1 is slightly higher than that in Case 3. This is because thermal balance rationally allocates heat energy according to the current operating conditions, ensuring that both the electrolyzer and the fuel cell remain within their optimal operating temperature range.

[0060] Figure 9This further reflects the trend of heat generation changes in the electrolyzer, whose heat generation power is highly correlated with wind power output. During periods of high wind power output, the electrolyzer operates at high load for hydrogen production, resulting in a significant increase in heat generation power. However, during the autumn season when wind power output is relatively abundant, Case 1 actively intervenes to regulate the heat balance, meeting hydrogen production needs while limiting the electrolyzer's prolonged high-load operation in a high-temperature environment to prevent efficiency degradation due to excessive temperature rise.

Claims

1. A method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, characterized in that... include: Step 1: Based on the topological characteristics of the wind-hydrogen hybrid system, establish the framework of the wind-hydrogen hybrid system; Based on the dynamic operating mechanism and electrochemical characteristics of the electrolyzer, a dynamic efficiency model of the electrolyzer is constructed. Based on the operating characteristics of the wind-hydrogen hybrid system, a thermal equilibrium model is constructed. Based on the operating characteristics of lead-acid batteries, a battery operation model is constructed; Based on the operating characteristics of proton exchange membrane fuel cells, a fuel cell operating model is constructed; An energy balance model for hydrogen storage tanks is constructed using the total energy stored in the hydrogen storage tanks as the key parameter. Based on the actual power output characteristics of wind power, a wind power output power model is constructed; Using energy storage capacity as the optimization variable, a capacity configuration objective function is constructed to minimize system investment costs. Step 2: Based on the wind-hydrogen hybrid system framework, integrate the dynamic efficiency model of the electrolyzer, the thermal balance model, the battery operation model, the fuel cell operation model, the hydrogen storage tank energy balance model, the wind power output power model, and the capacity configuration objective function to establish a wind-hydrogen hybrid system energy storage capacity configuration model that considers the dynamic efficiency and thermal balance of the electrolyzer. Step 3: Solve the energy storage capacity configuration model of the wind-hydrogen hybrid system using the split-Brow bar method to obtain the capacity configuration scheme.

2. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 1, is characterized in that: In step 1, a dynamic efficiency model is constructed based on the dynamic operating mechanism and electrochemical characteristics of the proton exchange membrane electrolyzer. The functional relationship between the operating voltage and current density of a proton exchange membrane electrolyzer is characterized as follows: （1）； In formula (1): for t The operating voltage of the electrolytic cell at all times; t For the running interval; The voltage is the reversible voltage; T is the operating temperature; R and F are the ideal gas constant and Faraday constant, respectively. and These are the partial pressures of hydrogen and oxygen, respectively. The activity of H2O; Internal equivalent ohmic resistance; and These are the charge transfer coefficients of the anode and cathode, respectively; and These are the exchange current densities at the anode and cathode, respectively. Current density; Faraday efficiency It can be described by membrane flux density and hydrogen production density, and its functional expression is as follows: （2）； In formula (2): , These represent the hydrogen and oxygen permeability in the diffusion mechanism, respectively. Hydrogen permeability caused by pressure difference; , These represent the partial pressures of hydrogen at the cathode and oxygen at the anode in the catalyst layer, respectively. d For film thickness; Considering the input, output, and energy conversion relationships of the electrolyzer, the operating efficiency of the electrolyzer is as follows: （3）； In formula (3): for t The operating efficiency of the electrolytic cell at all times; The high calorific value of hydrogen under standard conditions; express t Hydrogen production at any given time; This refers to the output power of the electrolytic cell. Based on the working principle of the electrolyzer and the relationship between hydrogen production and operating current, the power consumption of the electrolyzer is... and hydrogen production As shown below: （4）； （5）； In equation (5): Indicates the conversion factor; This represents the number of electrolytic cells connected in series. Represented as t Time Faraday efficiency This indicates the operating current of the electrolytic cell; （6）； In formula (6): Indicates the effective reaction area.

3. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 2, is characterized in that: In step 1, based on the operating characteristics of the wind-hydrogen hybrid system, a thermal equilibrium model is constructed, represented as: （7）； In equation (7): , They are respectively Moment, present The thermal energy stored in the thermal storage tank at any given time, expressed in kW·h; , They are respectively t The heat power consumed by the system at any given time and the heat power provided to the heating load, in kW; For the efficiency of the thermal storage heat exchanger; This indicates the heat generation capacity of the electrolytic cell; This indicates the heat output power of the fuel cell; The heat power consumed by the system It consists of the heat dissipation power of the electrolytic cell and the heat dissipation power of the fuel cell, as shown in equation (8): （8）； In equation (8): , , They are respectively t The operating temperature of the electrolytic cell and the ambient temperature at all times, in K; , These are the heat dissipation coefficients per unit capacity of the electrolyzer and the fuel cell, respectively. , These refer to the installed capacity of electrolyzers and fuel cells, respectively. The system operation should also meet thermal balance and electrical power balance constraints. The thermal balance of the system operation can be modeled using the heat and power exchange between the electrolyzer, fuel cell, and heat storage tank, i.e.: （9）； In equation (9): for t The heat exchange power between the thermal storage heat exchanger and the thermal storage tank at any given time, expressed in kW; This indicates the heat power consumed by the system.

4. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 3, is characterized in that: In step 1, when modeling and analyzing the lead-acid battery, the model is expressed as follows: （10）； In formula (10): , Residual batteries t The charging and discharging power during a given period; The maximum power of a single charge and discharge cycle of the battery; , For storage batteries The charging and discharging flag parameters for each time period are all binary variables; , These are the charge and discharge efficiencies of the battery, respectively. for t The output power of the battery during a given period; , They are respectively t Time period and t- The amount of electricity stored in the battery during period 1; , These are the upper and lower limits of the battery's energy storage capacity, respectively. This represents the battery energy storage capacity during time period t. This refers to the configured capacity of the battery.

5. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 4, is characterized in that: To study the operating characteristics of proton exchange membrane fuel cells, the following model is used: （11）； In equation (11): , They are respectively t The power generation and heat generation of a proton exchange membrane fuel cell at any given time are expressed in kW. for t The hydrogen consumption rate of a proton exchange membrane fuel cell at any given time, expressed in mol / h. The efficiency of a proton exchange membrane fuel cell; This indicates the high calorific value of hydrogen.

6. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 5, is characterized in that: In step 1, an energy balance model for the hydrogen storage tank is constructed: During water electrolysis, the hydrogen storage system is responsible for collecting and storing the generated hydrogen in a hydrogen storage tank; while in the power generation stage, the hydrogen storage system will transport the stored hydrogen and externally introduced oxygen to the fuel cell to drive the power generation reaction. （12）； In equation (12): for t Internal input power of the hydrogen storage tank during a given period; , They are respectively t -1 moment, current time t The total energy stored in the hydrogen storage tank at any given time, expressed in kW·h; For time intervals; Represented as t The operating efficiency of the electrolytic cell at all times.

7. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 6, is characterized in that: In step 1, a wind power output model is constructed based on the actual power output characteristics of wind power. The wind farm output power model is established as follows: （13）； In equation (13): The installed capacity of the wind farm is expressed in kW. To obtain based on wind speed t Power coefficient at time; for t The actual output power of the wind farm at any given time, in kW; The reliable grid-connected power of wind farms participating in grid dispatch is: （14）； In equation (14): , They are respectively t The reliable grid-connected power and day-ahead predicted output power of the wind farm at any given time, in kW; δ This is the availability factor for wind power. The output power balance constraint of the wind-hydrogen hybrid system can be expressed as: （15）； In equation (15): t The actual output power of the wind farm at any given time, expressed in kW.

8. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 7, is characterized in that: In step 1, the capacity of the electrolyzer, fuel cell, hydrogen storage tank and battery are used as optimization variables. Under the worst case caused by the uncertainty of wind farm power, the system investment cost is minimized while meeting the grid dispatch curve tracking deviation requirements. （16）； In equation (16): The system investment cost is expressed in dollars. This refers to the capacity of the hydrogen storage tank, expressed in kWh. , These are the unit power investment factors for electrolyzers and fuel cells, respectively, in $ / kW; , These are the unit capacity investment coefficients for hydrogen storage tanks and batteries, respectively, in $ / kWh.

9. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 8, is characterized in that: In step 2, as shown by equations (2), (3), and (5), the relationship between the efficiency and power of the electrolytic cell is non-linear; to simplify the calculation, the following steps are taken: η e,t become M segment constant η e,m The corresponding power per unit value is The following piecewise linearization is used to linearize it; （17）； In equation (17): This represents the operating state of the m-th segment of the electrolytic cell at time t. Indicates the number of segments; , These represent the power consumption of the m-th and m-1-th segments, respectively. Indicates the upper limit of the input power of the electrolytic cell; This indicates the output power of the electrolytic cell.

10. The method for configuring the energy storage capacity of a wind-hydrogen hybrid system considering the dynamic efficiency and thermal balance of the electrolyzer, as described in claim 9, is characterized in that: A phased modeling strategy is proposed: First, based on the Bruker bar optimization framework, an extreme scenario representation model of the wind power uncertainty set is constructed; Introducing Wasserstein probability measure as a fuzzy set The mathematical description is used to establish an uncertainty quantification model for the operating domain of the energy storage system: （18）； In equation (18): This represents the probability distribution of the actual output power of the wind farm. Empirical distribution of wind farm output power; For all defined in Wasserstein divergence The probability distribution space below; This represents a "probability distribution distance metric" constructed based on Wasserstein divergence. ε Let be the radius of the fuzzy set; The uncertain set given in the above equation can be transformed into a set of linear risk-opportunity constraints, as shown in equation (19): （19）； In equation (19): K The total number of data samples; α Confidence level; , t , They are respectively t Time sample k The actual wind farm output power and reliable grid-connected power are expressed in kW. , γ, d As dual variables; Finally, the energy storage capacity configuration model for the wind-hydrogen hybrid system, considering the dynamic efficiency and thermal balance of the electrolyzer, is expressed as follows: （20）。

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