A method for configuring an array of pem electrolytic cells based on cost minimization

Abstract

This invention belongs to the field of renewable energy conversion technology and discloses a method for configuring a PEM electrolyzer array based on minimizing cost. The method includes: S1: establishing a photovoltaic model and an electrolyzer model; S2: setting the initial photovoltaic array configuration scale and inputting local meteorological data; S3: calculating hydrogen production and levelized cost of hydrogen; S4: optimizing the calculation to determine the optimal photovoltaic array configuration scale with the goal of minimizing cost. This reduces the DC-AC-DC conversion process, thereby reducing energy transmission losses and improving the efficiency of the hydrogen production system; and by configuring based on minimizing hydrogen cost, it lowers the hydrogen production cost of the PV-PEM direct coupling system.

Description

Technical Field

[0001] This invention belongs to the field of renewable energy conversion technology, and in particular relates to an array configuration method for PEM electrolyzers based on minimizing costs. Background Technology

[0002] Traditional photovoltaic power generation coupled with electrolyzers often employs a power transmission method that converts direct current (DC) to alternating current (AC) and then back to DC. The primary aim is to ensure stable operation of the electrolyzer, thereby reducing hydrogen production costs and making the produced green hydrogen industrially affordable. However, this coupling method involves multiple energy conversions, increasing energy losses during transmission and reducing the overall energy efficiency of the hydrogen production system. It also increases the system's complexity and investment costs. Direct coupling of the hydrogen production system eliminates components such as DC-DC converters, reducing system complexity, investment, and energy efficiency.

[0003] Existing technologies disclose a method for optimizing the structural parameters of an electrolyzer in a photovoltaic (PV) direct-coupled hydrogen production system, as well as a PV direct-coupled water electrolysis device and method. However, existing solutions all focus on optimizing technical indicators such as increasing hydrogen production, reducing energy transfer losses, and improving energy utilization efficiency, with insufficient research on the economic aspects of the hydrogen production system. To achieve direct coupling between PV power generation and the PEM electrolyzer, configuring the PV array to reduce hydrogen production costs becomes a crucial task.

[0004] Traditional optimization methods involve continuously adjusting the series and parallel connections of photovoltaic arrays based on sunlight conditions, aiming to maximize the efficiency of the hydrogen production system and minimize energy transmission losses. However, this approach prioritizes efficiency while neglecting economic factors, resulting in some photovoltaic modules not being operational during hydrogen production and contributing to persistently high hydrogen production costs. Summary of the Invention

[0005] The purpose of this invention is to provide an array configuration method for PEM electrolyzers based on the lowest cost, so as to solve the problem of poor economic performance of direct coupling of photovoltaic power generation and PEM electrolyzers for hydrogen production mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: An array configuration method for PEM electrolyzers based on cost minimization, the method comprising the following steps: S1: Establish photovoltaic and electrolytic cell models; S2: Set the initial photovoltaic array configuration scale and input local meteorological data; S3: Calculate hydrogen production and levelized cost of hydrogen; S4: Determine the optimal photovoltaic array configuration size with the goal of minimizing costs.

[0007] Furthermore, in S1, the photovoltaic model is established as follows: The photovoltaic model of a single photovoltaic module is expressed as follows: , , in, , This indicates the current and voltage of the photovoltaic module. Indicates the reverse saturation current of the diode. Represents photocurrent, Indicates series resistance. Indicates the parameters for fitting the reference curve. Indicates the short-circuit current coefficient. , Indicates solar irradiance and reference solar irradiance. , Indicates panel temperature and reference temperature. , These represent the diode's reverse saturation reference current and short-circuit current, respectively. Indicates the band gap of Si. Indicates the number of batteries. This indicates that the solar irradiance G = 1000 W / m 2 And the reference conditions at temperature T=25℃.

[0008] Furthermore, in S1, the electrolytic cell model is established as follows: The electrolytic cell model is expressed as: in, This indicates the voltage required for the electrolytic cell to operate normally. This indicates the open-circuit voltage of the electrolytic cell. This represents the activation overpotential of the electrolytic cell, and this represents the ohmic overpotential of the electrolytic cell.

[0009] Furthermore, the open-circuit voltage of the electrolytic cell As shown: in, This is the open-circuit voltage under standard conditions. F It is Faraday's constant. R It is the gas state constant. It is the operating temperature of the electrolytic cell. and It refers to the activities of H2 and O2. It refers to the activity of water vapor.

[0010] Furthermore, the activation overpotential of the electrolytic cell Represented as: in, This indicates the current density of the electrolytic cell. and The exchange current density of the anode and cathode is measured at a reference temperature. and are the charge transfer coefficients of the anode and cathode, respectively, and arcsinh represents the inverse hyperbolic sine function.

[0011] Furthermore, the ohmic overpotential of the electrolytic cell Represented as: in, For the component's ohmic resistor, The thickness of the proton exchange membrane. I This is the operating current of the electrolytic cell. The conductivity of the proton exchange membrane is expressed as: in This refers to the water content of the membrane.

[0012] Furthermore, in S2, the initial photovoltaic array configuration scale is set, specifically as follows: Set the initial photovoltaic array configuration scale, that is, set the number of photovoltaic modules connected in series and parallel in the initial photovoltaic array; Based on the current and voltage generated by a single photovoltaic module, the current and voltage data output by the entire initial photovoltaic array are obtained; this current and voltage data is transmitted to the electrolyzer model without loss, thereby electrolyzing water to produce hydrogen.

[0013] Furthermore, in S3, The hourly hydrogen production is expressed as: in, For Faraday efficiency, I This is the operating current of the electrolytic cell. F It is Faraday's constant; Annual hydrogen production is calculated as follows: in, This indicates the total annual hydrogen production. Indicates the amount of time in hours; The levelized cost of hydrogen is calculated as follows: in, This represents the levelized cost of hydrogen. Indicates the rate of return on capital. Indicates equipment investment cost, This indicates equipment operation and maintenance costs; capital recovery rate. Represented as Where r represents the discount rate and x represents the lifespan of the hydrogen production system.

[0014] Furthermore, S4 specifically refers to: S41, after determining the initial photovoltaic array configuration scale, input the meteorological data within a certain unit time into the photovoltaic array model to determine whether the output current and voltage data of the photovoltaic array meet the boundary conditions of the PEM electrolyzer; the boundary conditions of the PEM electrolyzer refer to the upper and lower limits of the working voltage and current of the electrolyzer. If the boundary conditions are met, calculate the amount of hydrogen produced per unit time and include it in the total annual hydrogen production. If the boundary conditions are not met, discard the meteorological data for that unit of time, input the meteorological data for the next unit of time, and repeat the above judgment process until all meteorological data for the calculation unit of time has been read; add up the hydrogen production generated in all the unit of time that meet the conditions within a year to obtain the total annual hydrogen production; the unit of time is 1 hour. Finally, the levelized cost of hydrogen corresponding to the configuration scale of this photovoltaic array is obtained; S42, with the total number of photovoltaic modules remaining unchanged, change the number of photovoltaic modules connected in series and parallel in the initial photovoltaic array configuration scale, repeat S41, and obtain multiple sets of levelized hydrogen costs corresponding to the photovoltaic array configuration scale. Select the number of photovoltaic modules connected in series and parallel with the lowest levelized hydrogen cost as the optimal photovoltaic array configuration scale.

[0015] This invention provides an array configuration method for direct coupling of photovoltaic power generation with PEM electrolyzers based on the lowest cost, and its technical advantages are as follows: (1) This invention provides an array configuration method for photovoltaic power generation directly coupled to PEM electrolyzer, which reduces the DC-AC-DC conversion process, thereby reducing energy transmission loss and improving the efficiency of hydrogen production system; (2) The array configuration method of photovoltaic power generation directly coupled PEM electrolyzer provided by the present invention is based on the minimum hydrogen cost, thereby reducing the hydrogen production cost of the PV-PEM direct coupling system. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating an array configuration method for a PEM electrolyzer based on cost minimization, provided in an embodiment of the present invention. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0018] This invention provides an array configuration method for PEM electrolyzers based on cost minimization, such as... Figure 1 As shown, the method includes: S1: Establish photovoltaic and electrolytic cell models; S2: Set the initial photovoltaic array configuration scale and input local meteorological data; S3: Calculate hydrogen production and levelized cost of hydrogen; S4: Determine the optimal photovoltaic array configuration size with the goal of minimizing costs.

[0019] Specifically, in S1, the photovoltaic model is established as follows: The photovoltaic model of a single photovoltaic module is expressed as follows: , , in, , This indicates the current and voltage of the photovoltaic module. Indicates the reverse saturation current of the diode. Represents photocurrent, Indicates series resistance. Indicates the parameters for fitting the reference curve. Indicates the short-circuit current coefficient. , Indicates solar irradiance and reference solar irradiance. , Indicates panel temperature and reference temperature. , These represent the diode's reverse saturation reference current and short-circuit current, respectively. Indicates the band gap of Si. Indicates the number of batteries. This indicates that the solar irradiance G = 1000 W / m 2 And the reference conditions at temperature T=25℃.

[0020] Specifically, in S1, the electrolytic cell model is established as follows: The electrolytic cell model is expressed as: in, This indicates the voltage required for the electrolytic cell to operate normally. This indicates the open-circuit voltage of the electrolytic cell. Indicates the activation overpotential of the electrolytic cell. This indicates the ohmic overpotential of the electrolytic cell.

[0021] Specifically, the open-circuit voltage of the electrolytic cell As shown: in, This is the open-circuit voltage under standard conditions. F It is Faraday's constant. R It is the gas state constant. It is the operating temperature of the electrolytic cell. and It refers to the activities of H2 and O2. It refers to the activity of water vapor.

[0022] Specifically, the activation overpotential of the electrolytic cell Represented as: in, This indicates the current density of the electrolytic cell. and The exchange current density of the anode and cathode is measured at a reference temperature. and are the charge transfer coefficients of the anode and cathode, respectively, and arcsinh represents the inverse hyperbolic sine function.

[0023] Specifically, the ohmic overpotential of the electrolytic cell Represented as: in, For the component's ohmic resistor, The thickness of the proton exchange membrane. I This is the operating current of the electrolytic cell. The conductivity of the proton exchange membrane is expressed as: in This refers to the water content of the membrane.

[0024] Specifically, in S2, the initial photovoltaic array configuration scale is set as follows: Set the initial photovoltaic array configuration scale, that is, set the number of photovoltaic modules connected in series and parallel in the initial photovoltaic array; Based on the current and voltage generated by a single photovoltaic module, the current and voltage data output by the entire initial photovoltaic array are obtained; this current and voltage data is transmitted to the electrolyzer model without loss, thereby electrolyzing water to produce hydrogen.

[0025] Specifically, in S3, The hourly hydrogen production is expressed as: in, For Faraday efficiency, I This is the operating current of the electrolytic cell. F It is Faraday's constant; Annual hydrogen production is calculated as follows: in, This indicates the total annual hydrogen production. The time unit is expressed in hours; the levelized cost of hydrogen is calculated as follows: in, This represents the levelized cost of hydrogen. Indicates the rate of return on capital. Indicates equipment investment cost, This indicates the cost of equipment operation and maintenance; Capital recovery rate Represented as Where r represents the discount rate and x represents the lifespan of the hydrogen production system.

[0026] Specifically, S4 is as follows: The algorithm requires the objective function to include the following four factors: hourly meteorological conditions for the region, boundary condition assessment of the PEM electrolyzer, leveled hydrogen cost assessment, and photovoltaic array scale optimization. The optimization calculations must be performed in the following order: Meteorological data for a random day in the region is shown in Table 1. Table 1. Meteorological data for a random day in this region. Time / h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 <![CDATA[Direct radiation / W*m -2 > 0 0 0 0 0 0 0 0 0 205 528 564 498 432 275 40 176 224 0 0 0 0 0 0 Temperature / °C -7 -7 -8 -9 -10 -11 -13 -11 -10 -9 -7 -5 -4 -3 -2 -2 0 0 -1 -2 -3 -4 -6 -6 S4 can be implemented using the following two technical approaches: The first type: (1) First, assume multiple scales of photovoltaic arrays (for example, a photovoltaic array scale consisting of 100 photovoltaic modules in series plus 1 photovoltaic module in parallel, abbreviated as 100×1; a photovoltaic array scale consisting of 200 photovoltaic modules in series plus 2 photovoltaic modules in parallel, abbreviated as 200×2; a photovoltaic array scale consisting of 300 photovoltaic modules in series plus 3 photovoltaic modules in parallel, abbreviated as 300×3). When meteorological data of a certain calculation unit in a certain place is input into the photovoltaic array model, it is necessary to determine whether the current and voltage data generated by the photovoltaic arrays corresponding to the multiple photovoltaic array scales at this time meet the boundary conditions of the PEM electrolyzer, that is, the upper and lower limits of the working voltage and current of the electrolyzer.

[0027] If the boundary conditions are met, the hydrogen production per unit time is calculated and used to calculate the total annual hydrogen production. If the boundary conditions are not met, the meteorological data for this calculation unit time is discarded, and the meteorological data for the next calculation unit time is input. The above judgment process is repeated until all meteorological data for all calculation units time times have been read.

[0028] Generally, due to the limitations of the voltage boundary conditions of the electrolytic cell, the number of photovoltaic arrays connected in parallel is relatively easy to determine, while the number of photovoltaic arrays connected in series is the main variable.

[0029] (2) Does the levelized cost of hydrogen reach the minimum value under the scale of this photovoltaic array? After determining multiple scales of the photovoltaic array and calculating the levelized hydrogen cost at these scales, it is necessary to determine which scale has the local minimum value of the levelized hydrogen cost (for example, if the local minimum value of the levelized hydrogen cost is a 200×2 photovoltaic array scale). Based on this scale, a suitable photovoltaic array scale is reset (for example, the 100×1 photovoltaic array scale is approximated to the 200×2 photovoltaic array scale by a specific step size, and the 300×3 photovoltaic array scale is approximated to the 200×2 photovoltaic array scale by a specific step size, and in this process, the levelized hydrogen cost corresponding to each photovoltaic array scale is calculated), until the local minimum value of the levelized hydrogen cost becomes the global minimum value of the levelized hydrogen cost. At this point, the photovoltaic array scale is the optimal scale, and this scale is output.

[0030] The second type: (1) After determining the initial photovoltaic array configuration scale, meteorological data within a certain unit time is input into the photovoltaic array model to determine whether the output current and voltage data of the photovoltaic array meet the boundary conditions of the PEM electrolyzer; the boundary conditions of the PEM electrolyzer refer to the upper and lower limits of the working voltage and current of the electrolyzer. If the boundary conditions are met, calculate the amount of hydrogen produced per unit time and include it in the total annual hydrogen production. If the boundary conditions are not met, discard the meteorological data for that unit of time, input the meteorological data for the next unit of time, and repeat the above judgment process until all meteorological data for the calculation unit of time has been read; add up the hydrogen production generated in all the unit of time that meet the conditions within a year to obtain the total annual hydrogen production; the unit of time is 1 hour. Finally, the levelized cost of hydrogen corresponding to the configuration scale of this photovoltaic array is obtained; (2) Under the premise that the total number of photovoltaic modules remains unchanged, change the number of photovoltaic modules connected in series and parallel in the initial photovoltaic array configuration scale, repeat (1), and obtain multiple sets of levelized hydrogen costs corresponding to the photovoltaic array configuration scale. Select the number of photovoltaic modules connected in series and parallel with the lowest levelized hydrogen cost as the optimal photovoltaic array configuration scale.

[0031] This invention provides an array configuration method for photovoltaic power generation directly coupled to PEM electrolyzers based on minimizing costs, reducing the DC-AC-DC conversion process, thereby reducing energy transmission losses and improving the efficiency of the hydrogen production system; and by configuring based on minimizing hydrogen costs, the hydrogen production cost of the PV-PEM direct coupling system is reduced.

[0032] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for arraying PEM electrolyzers based on cost minimization, characterized in that, The method includes the following steps: S1: Establish photovoltaic and electrolytic cell models; S2: Set the initial photovoltaic array configuration scale and input local meteorological data; S3: Calculate hydrogen production and levelized cost of hydrogen; S4: Determine the optimal photovoltaic array configuration size with the goal of minimizing costs.

2. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 1, characterized in that, In S1, the photovoltaic model is established as follows: The photovoltaic model of a single photovoltaic module is expressed as follows: , , in, , This indicates the current and voltage of the photovoltaic module. Indicates the reverse saturation current of the diode. Represents photocurrent, Indicates series resistance. Indicates the parameters for fitting the reference curve. Indicates the short-circuit current coefficient. , Indicates solar irradiance and reference solar irradiance. , Indicates panel temperature and reference temperature. , These represent the diode's reverse saturation reference current and short-circuit current, respectively. Indicates the band gap of Si. Indicates the number of batteries. This indicates that the solar irradiance G = 1000 W / m 2 And the reference conditions at temperature T=25℃.

3. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 2, characterized in that, In S1, the electrolytic cell model is established as follows: The electrolytic cell model is expressed as: in, This indicates the voltage required for the electrolytic cell to operate normally. This indicates the open-circuit voltage of the electrolytic cell. Indicates the activation overpotential of the electrolytic cell. This indicates the ohmic overpotential of the electrolytic cell.

4. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 3, characterized in that, Electrolytic cell open circuit voltage It is shown as: in, This is the open-circuit voltage under standard conditions. F It is Faraday's constant. R It is the gas state constant. It is the operating temperature of the electrolytic cell. and It refers to the activities of H2 and O2. It refers to the activity of water vapor.

5. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 4, characterized in that, Electrolytic cell activation overpotential Represented as: in, This indicates the current density of the electrolytic cell. and The exchange current density of the anode and cathode is measured at a reference temperature. and are the charge transfer coefficients of the anode and cathode, respectively, and arcsinh represents the inverse hyperbolic sine function.

6. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 5, characterized in that, Ohmic overpotential of electrolytic cell Represented as: in, For the component's ohmic resistor, The thickness of the proton exchange membrane. I This is the operating current of the electrolytic cell. The conductivity of the proton exchange membrane is expressed as: in This refers to the water content of the membrane.

7. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 3, characterized in that, In S2, the initial photovoltaic array configuration scale is set as follows: Set the initial photovoltaic array configuration scale, that is, set the number of photovoltaic modules connected in series and parallel in the initial photovoltaic array; Based on the current and voltage generated by a single photovoltaic module, the current and voltage data output by the entire initial photovoltaic array are obtained; this current and voltage data is transmitted to the electrolyzer model without loss, thereby electrolyzing water to produce hydrogen.

8. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 3, characterized in that, In S3 The hourly hydrogen production is expressed as: in, For Faraday efficiency, I This is the operating current of the electrolytic cell. F It is Faraday's constant; Annual hydrogen production is calculated as follows: in, This indicates the total annual hydrogen production. Indicates the amount of time in hours; The levelized cost of hydrogen is calculated as follows: in, This represents the levelized cost of hydrogen. Indicates the rate of return on capital. Indicates equipment investment cost, This indicates the cost of equipment operation and maintenance; Capital recovery rate Represented as Where r represents the discount rate and x represents the lifespan of the hydrogen production system.

9. The array configuration method for PEM electrolyzers based on cost minimization as described in claim 8, characterized in that, S4 specifically refers to: S41, after determining the initial photovoltaic array configuration scale, input the meteorological data within a certain unit time into the photovoltaic array model to determine whether the output current and voltage data of the photovoltaic array meet the boundary conditions of the PEM electrolyzer; the boundary conditions of the PEM electrolyzer refer to the upper and lower limits of the working voltage and current of the electrolyzer. If the boundary conditions are met, calculate the hydrogen production per unit time and the total annual hydrogen production. If the boundary conditions are not met, discard the meteorological data conditions for that unit of time, input the meteorological data for the next unit of time, and repeat the above judgment process until all meteorological data for the entire calculation unit of time has been read. The unit of time is 1 hour; Finally, the levelized cost of hydrogen corresponding to the configuration scale of this photovoltaic array is obtained; S42, with the total number of photovoltaic modules remaining unchanged, change the number of photovoltaic modules connected in series and parallel in the initial photovoltaic array configuration scale, repeat S41, and obtain multiple sets of levelized hydrogen costs corresponding to the photovoltaic array configuration scale. Select the number of photovoltaic modules connected in series and parallel with the lowest levelized hydrogen cost as the optimal photovoltaic array configuration scale.

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