A method and system for analyzing flexibility and identifying bottlenecks of a renewable energy hydrogen production system under uncertainty

Abstract

The present application provides a kind of flexibility analysis and bottleneck identification method and system of renewable energy hydrogen production system under uncertainty condition, and flexibility analysis method is used as the renewable energy output of supply side as uncertain variable, and the energy, mass conservation constraint and equipment operation condition constraint of system are combined to construct flexibility analysis model, the flexibility analysis model can be given for each equipment configuration capacity, judge whether the energy, mass conservation constraint and operation condition constraint of system can be met by adjusting the scheduling plan of system under the fluctuation of renewable energy output of supply side, and the flexibility factor of system under the fluctuation is calculated, to quantify the ability of system to maintain supply and demand balance, resist parameter fluctuation.For renewable energy hydrogen production system with insufficient flexibility, the bottleneck equipment that limits the stability of system is identified by the bottleneck identification method as the basis for further modification of renewable energy hydrogen production system.

Description

Technical Field

[0001] This invention relates to the field of hydrogen production by electrolysis using renewable energy sources such as wind and solar power, and specifically to a method and system for flexibility analysis and bottleneck identification of renewable energy hydrogen production systems under uncertain conditions. Background Technology

[0002] In the design and optimization of traditional hydrogen production systems, it is often assumed that the system's operating parameters remain constant (Journal of Chemical Engineering of Chinese Universities, 2017, 31(01):161-169) to optimize the system's design and scheduling scheme. However, in renewable energy hydrogen production systems, renewable energy sources such as wind and solar power fluctuate with weather conditions, and the fluctuations are frequent and exhibit obvious random distribution characteristics. When the output of renewable energy deviates from the design expectations, the system design scheme obtained by assuming constant operating parameters may have the potential for operational failure in actual operation. Therefore, in scenarios where the output of renewable energy on the system supply side fluctuates, it is essential to develop a new system design method and production stability assessment tool for renewable energy hydrogen production systems.

[0003] Extensive research has been conducted on how to reduce the impact of renewable energy output fluctuations on system operational stability. In the system design phase, improving the prediction accuracy of uncertain variables is often used to enhance system stability. Although the prediction accuracy of random variables has gradually improved with increased computing power and capabilities (as seen in research on dynamic scheduling methods for integrated energy systems considering uncertainty), errors between predicted and actual values ​​are unavoidable (Journal of Physics: Conference Series, 2019, 1343(1):012103). When prediction errors occur, the system design optimization results cannot accurately reflect whether the system can operate normally. Currently, there is a lack of methods to determine whether a renewable energy hydrogen production system can maintain normal operation under uncertain scenarios for a given system design scheme.

[0004] During the system's operational phase, real-time adjustments to the system's scheduling plan can mitigate the adverse effects of uncertainties on the system's supply-demand balance. The system can restore supply-demand balance by adjusting renewable energy curtailment rates, electrolyzer operating power, and the input and output power of energy and hydrogen storage units. However, the ability of adjusting the scheduling plan to maintain system operational stability is limited. In scenarios with drastic fluctuations in uncertainties, relying solely on scheduling plan adjustments cannot guarantee normal system operation at every moment. Currently, there is a lack of assessment tools to quantify the stability maintenance capability of a given system and methods to calculate the range of uncertainties that a system can mitigate solely by adjusting its own scheduling plan.

[0005] When adjusting the scheduling plan alone cannot meet the supply and demand balance of the system, the system design is often modified by adding backup equipment or setting a certain redundancy for the capacity of each device. However, if each device is equipped with backup equipment or the redundant capacity is increased, the system's economy will be reduced (IEEE Transactions on Smart Grid, 2016, 7(6):2943-2952). Since the working principles and performance of each device are different, their ability to resist the adverse effects of fluctuations in uncertain variables on the stability of system operation is also different. Therefore, it is necessary to identify the bottleneck device that has the greatest impact on system stability, and determine the modification plan by increasing the capacity of the bottleneck device. This can improve the system's economy while ensuring the safe operation of the system. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a method and system for flexibility analysis and bottleneck identification of renewable energy hydrogen production systems under uncertain conditions. For renewable energy hydrogen production systems, this invention comprehensively considers the impact of fluctuations in renewable energy output on the normal operation of the system. Through flexibility analysis, it provides a quantitative tool for assessing the stable production capacity of renewable energy hydrogen production systems. Through bottleneck identification, it identifies bottleneck equipment that limits the improvement of system flexibility, providing guidance for upgrading and transforming systems to improve their ability to absorb supply-side fluctuations.

[0007] This invention is achieved through the following technical solution:

[0008] A method for flexibility analysis of renewable energy hydrogen production systems under uncertainty conditions includes:

[0009] S1, obtain the configuration capacity of supply-side equipment, electrolyzers, batteries and hydrogen storage tanks in the renewable energy hydrogen production system;

[0010] S2, input the configuration capacity of supply-side equipment, electrolyzers, batteries and hydrogen storage tanks into the flexibility analysis model; the flexibility analysis model includes supply-side renewable energy output fluctuation range constraints, supply-side energy balance constraints, demand-side hydrogen demand balance constraints, electrolyzer operating condition constraints, battery operating condition constraints and hydrogen storage tank operating condition constraints.

[0011] The constraint on the fluctuation range of renewable energy output on the supply side is expressed as follows:

[0012]

[0013] In the formula, The uncertainty multiplier for renewable energy output on the supply side; Δθ S The fluctuation range of renewable energy output on the supply side; δ is the flexibility factor;

[0014] The supply-side energy balance constraint includes uncertainty multipliers.

[0015] S3. With the optimization objective of maximizing the flexibility factor, solve the flexibility analysis model to obtain the flexibility factor, and determine the flexibility of the renewable energy hydrogen production system based on the flexibility factor.

[0016] Preferably, the supply-side energy balance constraint includes power supply and demand balance constraint and supply-side equipment capacity constraint;

[0017] Electricity supply and demand balance constraint: The output of renewable energy on the supply side is equal to the sum of the power supplied to the electrolyzer, the power supplied to the battery, and the power of abandoned electricity.

[0018] Supply-side equipment capacity constraint: The output of renewable energy on the supply side equals the rated capacity of the supply-side equipment plus the capacity factor and the aforementioned uncertainty multiplier. The product of.

[0019] Preferably, the demand-side hydrogen demand balance constraint is specifically as follows:

[0020] The demand-side hydrogen demand is equal to the sum of the flow rate of hydrogen supplied from the electrolyzer to the demand side and the flow rate of hydrogen supplied from the hydrogen storage tank to the demand side.

[0021] Preferably, the electrolyzer operating condition constraints include electro-hydrogen conversion balance, electrolyzer capacity constraints, and electrolyzer working state constraints;

[0022] Electro-hydrogen conversion balance: The power consumption of the electrolyzer is equal to the sum of the power generated by the supply side to the electrolyzer and the power generated by the battery to the electrolyzer; the hydrogen production capacity of the electrolyzer is equal to the sum of the flow rate of hydrogen supplied from the electrolyzer to the demand side and the flow rate of hydrogen supplied from the electrolyzer to the hydrogen storage tank.

[0023] Electrolytic cell capacity constraints and electrolytic cell operating status constraints: upper and lower limits of the electrolytic cell's power consumption.

[0024] Preferably, the battery operating condition constraints include battery energy balance constraints, battery capacity constraints, battery operating state constraints, and battery initial and final state identical constraints.

[0025] Battery energy balance: The battery charge after time interval k is equal to the battery charge after time interval k-1 plus the battery charge during time interval k minus the battery discharge during time interval k.

[0026] Battery capacity constraints: Upper and lower limits of battery state of charge;

[0027] Battery operating state constraint: The battery cannot be in a charging or discharging state at the same time.

[0028] Preferably, the operating condition constraints of the hydrogen storage tank include hydrogen storage tank mass balance constraints, hydrogen storage tank capacity constraints, hydrogen storage tank working state constraints, and hydrogen storage tank initial and final state identical constraints; specifically:

[0029] Hydrogen storage tank mass balance constraint: After time interval k, the amount of gas stored in the hydrogen storage tank is equal to the amount of hydrogen stored in the hydrogen storage tank after time interval k-1 plus the amount of gas added during time interval k minus the amount of gas released during time interval k.

[0030] Hydrogen storage tank capacity constraints: Upper and lower limits on the amount of hydrogen that can be stored in the hydrogen storage tank;

[0031] Operating constraints of hydrogen storage tanks: Hydrogen storage tanks cannot be in a filling or venting state at the same time.

[0032] Preferably, the method for obtaining the configuration capacity of the supply-side equipment, electrolyzer, battery, and hydrogen storage tank in the renewable energy hydrogen production system is as follows:

[0033] S1. Construct a design optimization model for a renewable energy hydrogen production system. The design optimization model for a renewable energy hydrogen production system includes total system cost constraints, supply-side energy balance constraints, demand-side hydrogen demand balance constraints, electrolyzer operating condition constraints, battery operating condition constraints, and hydrogen storage tank operating condition constraints.

[0034] S2 obtains the renewable energy output and hydrogen demand on the supply side, as well as the operating and economic parameters of the electrolyzer, battery, and hydrogen storage tank. It then inputs these parameters into the renewable energy hydrogen production system design optimization model. With the goal of minimizing the total system cost, it solves for the configuration capacity of the supply-side equipment, electrolyzer, battery, and hydrogen storage tank.

[0035] A system for implementing the aforementioned flexibility analysis method for a renewable energy hydrogen production system under uncertainty conditions includes: a parameter acquisition module, a flexibility analysis module, and a solution module;

[0036] The parameter acquisition module is used to acquire the configuration capacity of the supply-side equipment, electrolyzer, battery and hydrogen storage tank in the renewable energy hydrogen production system.

[0037] The flexibility analysis module includes a flexibility analysis model, which is used to input the configuration capacity of supply-side equipment, electrolyzers, batteries and hydrogen storage tanks into the flexibility analysis model, and solve the flexibility analysis model with the optimization objective of maximizing the flexibility factor to obtain the flexibility factor. The flexibility of the renewable energy hydrogen production system is then determined based on the flexibility factor.

[0038] A bottleneck identification method for renewable energy hydrogen production systems under uncertainty conditions includes:

[0039] The flexibility analysis model is transformed into a bottleneck identification model using the Lagrange multiplier method.

[0040] The fluctuation range of renewable energy output on the supply side is obtained and input into the bottleneck identification model. The model is then solved with the minimum flexibility factor as the optimization objective to identify the bottleneck equipment in the renewable energy hydrogen production system.

[0041] Preferably, the bottleneck identification model includes equality constraints and inequality constraints; a slack variable is defined for each inequality constraint;

[0042] The equation constraints include the balance constraints of power supply and demand, the balance constraints of electro-hydrogen conversion, the balance constraints of battery energy, the balance constraints of hydrogen storage tank mass, the constraint that the battery has the same initial and final state, and the constraint that the hydrogen storage tank has the same initial and final state.

[0043] The inequality constraints include: hydrogen demand constraints, supply-side equipment capacity constraints, electrolyzer capacity constraints, battery capacity constraints, hydrogen storage tank capacity constraints, electrolyzer operating state constraints, battery operating state constraints, and hydrogen storage tank operating state constraints.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The flexibility analysis method of this invention uses the renewable energy output on the supply side as an uncertainty variable, and constructs a flexibility analysis model by combining the system's energy and mass conservation constraints and equipment operating condition constraints. This flexibility analysis model can determine whether the system's energy and mass conservation constraints and operating condition constraints can be met by adjusting the system's scheduling plan under the condition of fluctuation in the renewable energy output on the supply side, given the configuration capacity of the supply-side equipment, electrolyzer, battery, and hydrogen storage tank. It also calculates the system's flexibility factor under the fluctuation condition to quantify the system's ability to maintain supply and demand balance and resist parameter fluctuations.

[0046] This invention also proposes a bottleneck identification method based on the Lagrange multiplier method. For renewable energy hydrogen production systems with insufficient flexibility, the bottleneck identification method of this invention identifies the bottleneck equipment that limits the stability of the system, serving as a basis for further modification of the renewable energy hydrogen production system. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the renewable energy hydrogen production system described in this invention;

[0048] Figure 2 This is a flowchart of the method described in an embodiment of the present invention;

[0049] Figure 3 Data on the output of typical daytime scenery;

[0050] Figure 4This is the system's flexibility factor under different fluctuations in supply-side output. Detailed Implementation

[0051] To further understand the present invention, the present invention will be described below with reference to embodiments. These descriptions are only for further explaining the features and advantages of the present invention and are not intended to limit the claims of the present invention.

[0052] This invention focuses on renewable energy hydrogen production systems, considering the system's ability to maintain stable production under fluctuating renewable energy output. It constructs a flexibility analysis and bottleneck identification method, including a design optimization model aiming to maximize economic efficiency, a flexibility analysis model maximizing the flexibility factor, and a bottleneck equipment identification model based on the Lagrange multiplier method. By solving these models, given the predicted renewable energy output and its fluctuation range, a design scheme for the renewable energy hydrogen production system can be obtained, along with the calculation of the flexibility factor and bottleneck equipment under uncertainty conditions. The stability of the system under arbitrary renewable energy output fluctuations is quantified, and the flexibility of the system configuration is determined, as well as the allowable parameter fluctuation range for the system to maintain normal operation under a given uncertainty scenario. This invention provides an effective method for quantitatively evaluating the ability of renewable energy hydrogen production systems to maintain stability under uncertainty conditions and offers suggestions for system modification schemes to improve system flexibility.

[0053] The method of this invention assumes the following:

[0054] 1) When analyzing the economics of renewable energy hydrogen production systems, only the costs of the main equipment, such as supply-side equipment, electrolyzers, batteries, and hydrogen storage tanks, are considered.

[0055] 2) Only the output of renewable energy fluctuates, while the operating parameters of other equipment remain unchanged.

[0056] Based on the above assumptions, and addressing the flexibility analysis and bottleneck identification issues of renewable energy hydrogen production systems under uncertainty conditions, the structure of a renewable energy hydrogen production system is as follows: Figure 1 As shown. The renewable energy hydrogen production system includes supply-side equipment, batteries, an electrolyzer, and a hydrogen storage tank; the supply-side equipment is used to convert renewable energy into electrical energy and output it to the batteries and the electrolyzer, the batteries output electrical energy to the electrolyzer, the hydrogen produced by the electrolysis of the electrolyzer is output to the hydrogen storage tank and the demand side, and the hydrogen from the hydrogen storage tank is output to the demand side; the supply-side equipment may include photovoltaic and / or wind turbines.

[0057] In this embodiment of the invention, the supply-side equipment, including photovoltaic and wind turbines, is used as an example for illustrative purposes.

[0058] The technical solution adopted in this invention is as follows: Figure 2 As shown, it includes the following three steps:

[0059] (1) Construct a design optimization model for a renewable energy hydrogen production system, input renewable energy output, hydrogen demand and relevant parameters of each device, solve the initial configuration of the renewable energy hydrogen production system, and determine the initial design scheme of the renewable energy hydrogen production system.

[0060] (2) Construct a flexibility analysis model, input the initial configuration of the renewable energy hydrogen production system and the fluctuation range of renewable energy output, calculate the flexibility factor of the renewable energy hydrogen production system with the initial configuration under different uncertainty conditions, and proceed to step (3) if the flexibility factor is less than 1.

[0061] (3) Construct a bottleneck identification model to identify bottleneck equipment that limits the flexibility of the renewable energy hydrogen production system.

[0062] If the above assumptions are not true, it will affect the calculation results of the flexibility factor and the bottleneck device identification results in this invention, but the technical solution of this invention will still be applicable. The advantages and novelty of this method will be shown through the following detailed description and related drawings.

[0063] (1) Construct a system design optimization model to determine the initial design scheme of the renewable energy hydrogen production system.

[0064] Given renewable energy output, hydrogen demand, operating parameters of major components in the system, and economic parameters, a mathematical programming model is established with the objective of minimizing the system's annualized total investment and operating costs to determine the economically optimal initial system configuration. Data on renewable energy generation, power generation between devices, and hydrogen flow rates are collected. Constraints in the model are constructed based on the physical relationships between the collected data. The optimization model can be designed in the following three steps:

[0065] 1) Determine the optimization objective

[0066] The objective is to minimize the annualized total system cost, which includes both equipment purchase cost and operation and maintenance cost. The equipment purchase cost is the product of the equipment's rated capacity and its unit price. The operation and maintenance cost is the equipment purchase cost multiplied by a fixed coefficient. The objective function of the optimization model can be expressed as:

[0067] C total =C inv +C om (1)

[0068]

[0069]

[0070] In the formula, C totalC represents the total system cost. inv C represents the total cost of equipment purchase. om Total cost of equipment operation and maintenance; The price per unit capacity of each piece of equipment; The rated capacity of each device, This represents the operation and maintenance cost coefficient. α is the set of equipment, including photovoltaics, wind turbines, electrolyzers, batteries, and hydrogen storage tanks; CRF α The annual investment factor for each piece of equipment.

[0071] 2) Determine the constraints

[0072] To achieve the aforementioned optimization objectives, an optimization model is designed to simulate the operational status of a renewable energy hydrogen production system over a given period of time, subject to constraints. The model divides this period into K time intervals, using the power generation, hydrogen flow rate, and equipment start-up / shutdown status within each interval as variables to be optimized. Renewable energy power generation data and hydrogen demand from typical cycles (days, months, or years) are used as input parameters. For any time interval k, the specific mathematical description of the constraints is as follows:

[0073] ① Supply-side energy balance constraints. For any time interval k, the output of renewable energy (supply side) Power generated by photovoltaics And fan output The output is supplied to the battery and electrolytic cell; excess electricity is discarded, as shown below:

[0074]

[0075]

[0076] In the formula, and These are the power supplies for the electrolyzer and the battery, respectively. This refers to the amount of abandoned electricity.

[0077] For any time interval k, the output of photovoltaic and wind turbines can be expressed as the product of rated capacity and capacity factor:

[0078]

[0079]

[0080] In the formula, This refers to the rated capacity of the photovoltaic system. It is the photovoltaic capacity factor; This refers to the rated capacity of the fan; It is the wind turbine capacity factor.

[0081] ② Demand-side hydrogen demand balance constraints. The system's hydrogen demand is mainly provided by hydrogen storage tanks and electrolyzers. For any time interval k, the hydrogen demand can be expressed as:

[0082]

[0083] In the formula, This refers to the demand for hydrogen. and These represent the flow rates of hydrogen supplied to the demand side from the electrolyzer and hydrogen storage tank, respectively.

[0084] ③ Electrolyzer Operating Condition Constraints. The operating conditions of the electrolyzer consist of two parts: energy conservation and hydrogen mass conservation. For any time interval k, the electrolyzer's power consumption equals the sum of the power generated by the supply side and the battery. The electrolyzer's hydrogen production is proportional to its power consumption. The hydrogen produced by the electrolyzer is supplied to the system's demand side and the hydrogen storage tank. The electrolyzer's operating constraints can be expressed as:

[0085]

[0086]

[0087]

[0088] In the formula, This refers to the electrical power consumption of the electrolytic cell; and These represent the power generation from the supply side and the battery to the electrolyzer, respectively; η ELE For electrolytic cell efficiency; η is the hydrogen production rate of the electrolyzer; e The electro-hydrogen conversion rate of the electrolyzer is denoted as .

[0089] For any time interval k, the upper and lower limits of the power consumption of the electrolytic cell can be expressed as:

[0090]

[0091]

[0092]

[0093] In the formula, τ is a large positive number; For a binary variable representing the start-up and shutdown state of an electrolytic cell, when At that time, the electrolytic cell is in working condition. At that time, the electrolytic cell is in the off state; and These represent the minimum and maximum operating states of the electrolytic cell, respectively. This is the rated power of the electrolytic cell.

[0094] ④ Battery operating condition constraints. For any time interval k, the battery's charge comes from the power supplied to it from the power supply side. The battery's discharge into the electrolyzer can be expressed as:

[0095]

[0096]

[0097] In the formula, and These are the charging and discharging power of the battery, respectively. and These refer to the battery charging and discharging efficiency, respectively.

[0098] The battery charge after time interval k is equal to the battery charge after time interval k-1 plus the charge generated during time interval k, minus the discharge generated during time interval k. This can be expressed as:

[0099]

[0100] In the formula, Let N be the battery charge after time interval k; N is the duration of each time interval.

[0101] The upper and lower limits of the battery's state of charge can be expressed as:

[0102]

[0103]

[0104] In the formula, and These represent the minimum and maximum states of charge of the battery, respectively. This refers to the battery's rated capacity.

[0105] Within any time interval k, to ensure the safety of battery operation, the battery cannot be in a charging or discharging state simultaneously. This constraint can be expressed as:

[0106]

[0107]

[0108]

[0109] In the formula, and These are binary variables representing the battery's charging and discharging states, respectively; when At this time, the battery is in a charging state; when At this time, the battery is in a discharging state; τ is a large positive number.

[0110] After the last time interval, the battery's stored capacity must be the same as before the first time interval, expressed as:

[0111]

[0112] In the formula, and These represent the battery's stored capacity before and after operation begins.

[0113] ⑤ Operating constraints of the hydrogen storage tank. The hydrogen in the storage tank comes from the electrolyzer, and the hydrogen released from the storage tank supplies the demand side of the system, as shown below:

[0114]

[0115]

[0116] In the formula, and These are the filling and venting flow rates of the hydrogen storage tank, respectively.

[0117] After time interval k, the amount of hydrogen stored in the storage tank is equal to the amount of hydrogen stored in the storage tank after time interval k-1 plus the amount of gas added during time interval k, minus the amount of gas released during time interval k, expressed as:

[0118]

[0119] In the formula, denoted as , where is the amount of hydrogen stored in the hydrogen storage tank after time interval k; N represents the duration of each time interval.

[0120] The upper and lower limits of hydrogen storage capacity in a hydrogen storage tank can be expressed as:

[0121]

[0122]

[0123] In the formula, and These represent the minimum and maximum gas storage states of the hydrogen storage tank, respectively. This refers to the rated capacity of the hydrogen storage tank.

[0124] Similar to batteries, within any time interval k, the hydrogen storage tank cannot be in a charged or degaussed state simultaneously. This constraint can be expressed as:

[0125]

[0126]

[0127]

[0128] In the formula, and These are binary variables representing the charging and venting states of the hydrogen storage tank, respectively. When At that time, the hydrogen storage tank was in a purging state; when At this time, the hydrogen storage tank is in a venting state; τ is a large positive number.

[0129] After the last time interval, the hydrogen storage capacity of the hydrogen storage tank must be the same as the hydrogen storage capacity before the first time interval, expressed as:

[0130]

[0131] In the formula, and These represent the hydrogen storage capacity before and after the initial operation of the hydrogen storage tank.

[0132] 3) Calculate the initial configuration

[0133] The design optimization model is a mixed-integer linear programming (MIP) model. Considering the above optimization objectives and constraints, mathematical programming model calculation software (such as GAMS) can be used to solve the MIP model using a solver (such as CPLEX) to obtain the economically optimal capacity configuration of photovoltaic, wind turbine, electrolyzer, battery, and hydrogen storage tank to meet the hydrogen demand requirements. The model can also obtain results such as system power generation, hydrogen flow rate, battery energy storage status, and hydrogen storage capacity in the hydrogen storage tank for any given time interval. These results are used as the initial system design scheme, and a flexibility analysis is performed on this scheme.

[0134] (2) Construct a flexibility analysis model and calculate the flexibility factor of renewable energy hydrogen production system under different uncertainty conditions.

[0135] By collecting photovoltaic and wind turbine power generation data and comparing it with the output data of wind turbines and photovoltaics used in the system design, the deviation between the actual supply-side output data and the theoretical value of renewable energy during operation can be obtained, i.e., the fluctuation range of supply-side output. The purpose of the flexibility analysis model is, given the configured capacity of photovoltaic, wind turbines, electrolyzers, batteries, and hydrogen storage tanks, to determine whether the system's energy, mass conservation constraints, and operating condition constraints can be met by adjusting the system's scheduling plan when renewable energy output fluctuates on the supply side. It also calculates the system's flexibility factor under such fluctuation conditions to quantify the system's ability to maintain supply-demand balance and resist parameter fluctuations. This can be achieved in the following three steps:

[0136] 1) Determine the optimization objective

[0137] The flexibility factor δ is defined as the maximum degree of fluctuation of uncertain variables that a system can withstand while maintaining equilibrium. When δ ≥ 1, the system has sufficient flexibility, and the system can maintain stability by changing the scheduling plan. When δ < 1, the system's flexibility can only partially meet the expected changes in uncertain variables, meaning it lacks sufficient flexibility, and the system cannot operate normally when uncertain variables fluctuate. Therefore, the objective function of the flexibility analysis model is to maximize the flexibility factor.

[0138] maxδ(33)

[0139] 2) Constraints on the fluctuation range of uncertain variables

[0140] For a given fluctuation range in renewable energy output on the supply side, the uncertainty multiplier of supply-side output can be expressed as:

[0141]

[0142] In the formula, The uncertainty multiplier for supply-side output; Δθ S The fluctuation range of supply-side output.

[0143] 3) Constraints

[0144] In the flexibility analysis model, the results obtained from the design optimization model are used as the initial system configuration. Replace equation (4) - equation (32) use Replace equation (4) - equation (32) Other constraints are consistent with equations (4) to (32).

[0145] 4) Calculate the flexibility factor

[0146] The flexibility analysis model is a mixed-integer linear programming (MIP) model. Considering the aforementioned optimization objectives and constraints, mathematical programming software (such as GAMS) can be used to solve the MIP using a solver (such as CPLEX) to obtain the flexibility factor of the renewable energy hydrogen production system under given initial configuration and supply-side fluctuations. The result of the flexibility factor can serve as an indicator of the stability of the renewable energy hydrogen production system and a basis for determining whether the system needs modification. A larger flexibility factor indicates a stronger ability of the renewable energy hydrogen production system to maintain stable operation under fluctuations in renewable energy output on the supply side; if the flexibility factor is less than 1, the renewable energy hydrogen production system lacks flexibility and cannot maintain normal operation under parameter fluctuations, requiring modification.

[0147] (3) Construct a bottleneck identification model to identify bottleneck equipment that limits the improvement of the flexibility factor of renewable energy hydrogen production system.

[0148] The flexibility analysis model is transformed into a bottleneck identification model using the Lagrange multiplier method. For systems with insufficient flexibility, the bottleneck identification model can identify the bottleneck equipment under a given initial system configuration and supply-side output fluctuation. The principle is to use the complementary relaxation theorem to identify the constraints in a tightened state under these fluctuation conditions, which are the bottlenecks of the renewable energy hydrogen production system. Each piece of equipment is constrained by its rated capacity and operating state. If the constraints of a piece of equipment are in a tightened state, then that equipment is the bottleneck of the system. Since hydrogen demand constraints are essential for the stability of the renewable energy hydrogen production system, hydrogen demand constraints are not considered a bottleneck regardless of whether they are in a tightened state. The bottleneck identification model can be implemented in the following six steps:

[0149] 1) Determine the optimization objective

[0150] The Lagrange multiplier method transforms the maximization problem in the flexibility analysis model into a minimization problem, that is, taking the minimization of the flexibility factor of the renewable energy hydrogen production system as the optimization objective, expressed as:

[0151] minδ(35)

[0152] 2) Equality constraints

[0153] Equations (4) to (32) in the flexibility analysis model are organized, and the energy conservation and mass conservation equations in the model are determined as equality constraints in the bottleneck identification model. The equality constraints are:

[0154] ① Electricity supply and demand balance. Equations (4) and (5) are transformed into:

[0155]

[0156] ② Electro-hydrogen conversion equilibrium. Equations (9)-(11) are transformed into:

[0157]

[0158] ③ Battery energy balance. Equations (15) to (17) are transformed into:

[0159]

[0160] ④ Hydrogen storage tank mass balance. Equations (24)-(26) are transformed into:

[0161]

[0162] ⑤ The energy storage device remains in the same initial and final states. Equations (23) and (32) are transformed into:

[0163]

[0164]

[0165] 3) Slack variables

[0166] Organize equations (4) to (32) in the flexibility analysis model, and define a slack variable s for the capacity constraint and inequality constraint j in the model. j s j Since both variables are negative, it can be used to determine whether the inequality constraint is in a tightening state. If s j If the slack variable is 0, then the inequality constraint is in a tightened state. In the bottleneck identification model, the slack variable can be represented as:

[0167] ①Constraints on hydrogen demand

[0168]

[0169] ② Photovoltaic capacity constraints

[0170]

[0171] ③ Wind turbine capacity constraints

[0172]

[0173] ④ Electrolytic cell constraints: Electrolytic cell capacity constraint (Equation (45)) and electrolytic cell operating state constraint (Equations (46)-(47))

[0174]

[0175]

[0176]

[0177] ⑤ Battery constraints: battery capacity constraints (equations (48)-(49)) and battery operating state constraints (equations (50)-(52))

[0178]

[0179]

[0180]

[0181]

[0182]

[0183] ⑥ Constraints on the hydrogen storage tank: hydrogen storage tank capacity constraints (equations (53)-(54)) and hydrogen storage tank operating state constraints (equations (55)-(57))

[0184]

[0185]

[0186]

[0187]

[0188]

[0189] 4) Lagrange conditions

[0190] In the Lagrange multiplier method, the objective function is denoted by f, and the equality constraint is g. i The inequality constraint is h j Where i∈I, j∈J, I is the set of equality constraints, and J is the set of inequality constraints. The Lagrange conditions are:

[0191]

[0192] Substituting the Lagrange condition into the flexibility analysis model proposed in this paper, and taking the partial derivatives for each variable in the equal and inequality constraints of equations (36)-(57), the sum of the partial derivatives is 0, expressed as:

[0193]

[0194]

[0195] μ j ≥0 (61)

[0196] In the formula, x is a variable in the system, and g i For the i-th equality constraint, h j For the j-th inequality constraint, λ i μ is the Lagrange multiplier for the i-th equality constraint. j Let be the Lagrange multiplier constrained by the j-th inequality.

[0197] 5) Complementary relaxation theorem

[0198] According to the complementary relaxation theorem, the inner product of the relaxation variable and the Lagrange multiplier of each inequality constraint is 0, expressed as:

[0199] μ j s j =0 (62)

[0200] 6) Identify bottlenecks

[0201] The bottleneck identification model is a mixed-integer linear programming (MIP) model. Considering the aforementioned optimization objectives and constraints, it can be solved using mathematical programming software (such as GAMS) and a MIP solver (such as CPLEX). For situations lacking flexibility, the bottleneck identification model can obtain the slack variables for each inequality constraint under a given supply-side fluctuation range. If the slack variable is 0, the inequality constraint is in a tightened state, and the device to which the inequality constraint belongs is the bottleneck device. By increasing the capacity of the system's bottleneck devices or setting up backup equipment, the system's ability to maintain stable operation can be significantly improved.

[0202] The present invention also provides a system for implementing a flexibility analysis method for a renewable energy hydrogen production system under uncertainty conditions, comprising: a parameter acquisition module, a flexibility analysis module, and a solution module;

[0203] The parameter acquisition module is used to acquire the configuration capacity of the supply-side equipment, electrolyzer, battery and hydrogen storage tank in the renewable energy hydrogen production system;

[0204] The flexibility analysis module includes a flexibility analysis model, which is used to input the configuration capacity of supply-side equipment, electrolyzers, batteries and hydrogen storage tanks into the flexibility analysis model, and solve the flexibility analysis model with the optimization objective of maximizing the flexibility factor to obtain the flexibility factor. The flexibility of the renewable energy hydrogen production system is then determined based on the flexibility factor.

[0205] The existing renewable energy hydrogen production system operates according to equations (4)-(32). Given the renewable energy output data and the main equipment parameters of the system, the optimal configuration of the system can be optimized, and a flexibility analysis can be performed on this configuration. The flexibility analysis method and bottleneck identification method of this invention can also be used to perform flexibility analysis and bottleneck equipment identification on existing renewable energy hydrogen production systems, and to modify the renewable energy hydrogen production system based on the analysis and identification results.

[0206] To verify the feasibility of this invention and demonstrate its application, a simulation was conducted using the method proposed in this invention, based on the hydrogen demand of a local refinery and historical weather and solar power output data. The refinery's hydrogen demand is 1392 kg / h. Historical meteorological data was clustered into typical day meteorological data as design conditions, as shown in the attached figure. Figure 3 As shown. The calculation time interval in the model is set to one hour. Based on the design optimization model proposed in step (1) of the invention, the economically optimal system configuration is optimized, as shown in Appendix Table 1.

[0207] Table 1 Initial System Capacity Configuration

[0208]

[0209] The system configuration is used as the initial system configuration and substituted into the flexibility model in step (2) to calculate the system's flexibility factor under conditions of fluctuations in renewable energy output. The maximum positive and negative fluctuation amplitudes of renewable energy output are both set to 100%, with a fluctuation amplitude change step of 10%, and substituted into the flexibility analysis model. The model is solved to obtain the system's flexibility factor under different fluctuation amplitudes, as shown in the appendix. Figure 4 As shown in the figure. Calculations revealed that when the negative fluctuation range on the supply side exceeds 18.30%, the system cannot maintain stable operation, meaning it lacks sufficient flexibility. Substituting this supply-side fluctuation range into the bottleneck identification model, it was found that the bottleneck devices under this supply-side fluctuation range are photovoltaic cells, electrolyzers, and batteries. To restore the system to a stable operating state, it is recommended to prioritize expanding the capacity of these three devices or setting up backup equipment.

Claims

1. A method for flexibility analysis of a renewable energy hydrogen production system under uncertainty conditions, characterized in that, include: S1, obtain the configuration capacity of supply-side equipment, electrolyzers, batteries and hydrogen storage tanks in the renewable energy hydrogen production system; S2, input the configuration capacity of supply-side equipment, electrolyzers, batteries, and hydrogen storage tanks into the flexibility analysis model; the flexibility analysis model includes supply-side renewable energy output fluctuation constraints, supply-side energy balance constraints, demand-side hydrogen demand balance constraints, electrolyzer operating condition constraints, battery operating condition constraints, and hydrogen storage tank operating condition constraints; the flexibility analysis model is a mixed integer linear programming model; The constraint on the fluctuation range of renewable energy output on the supply side is expressed as follows: In the formula, Uncertainty multipliers for renewable energy output on the supply side; Fluctuations in the output of renewable energy on the supply side; The flexibility factor refers to the maximum degree of fluctuation of uncertain variables that the system can withstand while maintaining equilibrium; The supply-side energy balance constraints include electricity supply and demand balance constraints and supply-side equipment capacity constraints. Electricity supply and demand balance constraint: The output of renewable energy on the supply side is equal to the sum of the power supplied to the electrolyzer, the power supplied to the battery, and the power of abandoned electricity. Supply-side equipment capacity constraint: The output of renewable energy on the supply side equals the rated capacity of the supply-side equipment plus the capacity factor and the aforementioned uncertainty multiplier. The product; S3, with maximizing the flexibility factor as the optimization objective, solve the flexibility analysis model to obtain the flexibility factor, and determine the flexibility of the renewable energy hydrogen production system based on the flexibility factor; when At times, the system is flexible, maintaining stability by changing the scheduling plan; when At the same time, the system's flexibility partially meets the expected range of change of uncertain variables; when the uncertain variables fluctuate, the system cannot operate normally.

2. The method for flexibility analysis of renewable energy hydrogen production systems under uncertainty conditions according to claim 1, characterized in that, The specific demand-side hydrogen demand balance constraint is as follows: The demand-side hydrogen demand is equal to the sum of the flow rate of hydrogen supplied from the electrolyzer to the demand side and the flow rate of hydrogen supplied from the hydrogen storage tank to the demand side.

3. The method for flexibility analysis of renewable energy hydrogen production systems under uncertainty conditions according to claim 1, characterized in that, The constraints on the electrolyzer operating conditions include electro-hydrogen conversion balance, electrolyzer capacity constraints, and electrolyzer working state constraints. Electro-hydrogen conversion balance: The power consumption of the electrolyzer is equal to the sum of the power generated by the supply side to the electrolyzer and the power generated by the battery to the electrolyzer; the hydrogen production capacity of the electrolyzer is equal to the sum of the flow rate of hydrogen supplied from the electrolyzer to the demand side and the flow rate of hydrogen supplied from the electrolyzer to the hydrogen storage tank. Electrolytic cell capacity constraints and electrolytic cell operating status constraints: upper and lower limits of the electrolytic cell's power consumption.

4. The flexibility analysis method for a renewable energy hydrogen production system under uncertainty conditions according to claim 1, characterized in that, The battery operating condition constraints include battery energy balance constraints, battery capacity constraints, battery operating state constraints, and battery initial and final state same constraints. Battery energy balance: after a time interval k The remaining battery charge is equal to the time interval elapsed. k -1 is added to the time interval. k The amount of charge generated by the internal battery and the amount of charge generated during the time interval. k The discharge capacity of the internal battery; Battery capacity constraints: Upper and lower limits of battery state of charge; Battery operating state constraint: The battery cannot be in a charging or discharging state at the same time.

5. The method for flexibility analysis of renewable energy hydrogen production systems under uncertainty conditions according to claim 1, characterized in that, The operating conditions constraints of the hydrogen storage tank include hydrogen storage tank mass balance constraints, hydrogen storage tank capacity constraints, hydrogen storage tank working state constraints, and hydrogen storage tank initial and final state identical constraints; specifically: Hydrogen storage tank mass balance constraint: after a time interval k The gas storage capacity of the post-hydrogen storage tank is equal to the time interval between hydrogen storage tank cycles. k The hydrogen storage capacity after -1 plus the time interval k The amount of air added during the time interval is subtracted from the total air volume. k The amount of gas released inside; Hydrogen storage tank capacity constraints: Upper and lower limits on the amount of hydrogen that can be stored in the hydrogen storage tank; Operating constraints of hydrogen storage tanks: Hydrogen storage tanks cannot be in a filling or venting state at the same time.

6. The method for flexibility analysis of renewable energy hydrogen production systems under uncertainty conditions according to claim 1, characterized in that, The method for obtaining the configuration capacity of the supply-side equipment, electrolyzer, battery, and hydrogen storage tank in the renewable energy hydrogen production system is as follows: S1. Construct a design optimization model for a renewable energy hydrogen production system. The design optimization model for a renewable energy hydrogen production system includes total system cost constraints, supply-side energy balance constraints, demand-side hydrogen demand balance constraints, electrolyzer operating condition constraints, battery operating condition constraints, and hydrogen storage tank operating condition constraints. S2 obtains the renewable energy output and hydrogen demand on the supply side, as well as the operating and economic parameters of the electrolyzer, battery, and hydrogen storage tank. It then inputs these parameters into the renewable energy hydrogen production system design optimization model. With the goal of minimizing the total system cost, it solves for the configuration capacity of the supply-side equipment, electrolyzer, battery, and hydrogen storage tank.

7. A system for implementing the flexibility analysis method for a renewable energy hydrogen production system under uncertainty conditions as described in any one of claims 1-6, characterized in that, include: Parameter acquisition module, flexibility analysis module, and solution module; The parameter acquisition module is used to acquire the configuration capacity of the supply-side equipment, electrolyzer, battery and hydrogen storage tank in the renewable energy hydrogen production system. The flexibility analysis module includes a flexibility analysis model. This model takes the configuration capacity of supply-side equipment, electrolyzers, batteries, and hydrogen storage tanks as input, maximizes the flexibility factor as the optimization objective, solves the flexibility analysis model to obtain the flexibility factor, and determines the flexibility of the renewable energy hydrogen production system based on the flexibility factor. The flexibility analysis model includes constraints on the fluctuation range of renewable energy output on the supply side, energy balance constraints on the supply side, hydrogen demand balance constraints on the demand side, operating conditions constraints for the electrolyzers, operating conditions constraints for the batteries, and operating conditions constraints for the hydrogen storage tanks. The constraint on the fluctuation range of renewable energy output on the supply side is expressed as follows: In the formula, Uncertainty multipliers for renewable energy output on the supply side; Fluctuations in the output of renewable energy on the supply side; For flexibility factors; The supply-side energy balance constraints include electricity supply and demand balance constraints and supply-side equipment capacity constraints. Electricity supply and demand balance constraint: The output of renewable energy on the supply side is equal to the sum of the power supplied to the electrolyzer, the power supplied to the battery, and the power of abandoned electricity. Supply-side equipment capacity constraint: The output of renewable energy on the supply side equals the rated capacity of the supply-side equipment plus the capacity factor and the aforementioned uncertainty multiplier. The product of.

8. A bottleneck identification method for a renewable energy hydrogen production system under uncertain conditions, characterized in that, include: The flexibility analysis model described in any one of claims 1-6 is transformed into a bottleneck identification model using the Lagrange multiplier method; the bottleneck identification model includes equality constraints and inequality constraints; a slack variable is defined for each inequality constraint; The equation constraints include the balance constraints of power supply and demand, the balance constraints of electro-hydrogen conversion, the balance constraints of battery energy, the balance constraints of hydrogen storage tank mass, the constraint that the battery has the same initial and final state, and the constraint that the hydrogen storage tank has the same initial and final state. The inequality constraints include: hydrogen demand constraints, supply-side equipment capacity constraints, electrolyzer capacity constraints, battery capacity constraints, hydrogen storage tank capacity constraints, electrolyzer operating state constraints, battery operating state constraints, and hydrogen storage tank operating state constraints. The fluctuation range of renewable energy output on the supply side is obtained and input into the bottleneck identification model. The model is then solved with the minimum flexibility factor as the optimization objective to identify the bottleneck equipment in the renewable energy hydrogen production system.

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