Optimization method of copper-clad aluminum busbar for reducing weight and conductive loss of photovoltaic module

Abstract

The application discloses a copper-clad aluminum busbar optimization method for reducing weight and conductive loss of a photovoltaic module, and relates to the technical field of photovoltaic busbar design, and comprises the following steps: according to electrical and geometric parameters of the photovoltaic module, a modified differential evolution algorithm is used to perform collaborative optimization on material size combination and structural configuration of the busbar. In the mutation operation, an adaptive mutation probability control of a simulated annealing strategy is introduced, and a dynamic crossover rate adjustment of a historical population entropy value is fused in the crossover operation. The aluminum core width, height and copper layer thickness of the top surface and the bottom surface are synchronously output in each iteration. Through calculation of unit length mass, direct current resistance and current carrying capacity, iterative optimization is performed under a current carrying safety margin, and joint optimization of weight and conductive loss is realized. The method improves global search and convergence precision of the algorithm, realizes collaborative matching of multiple parameters, reduces the weight of the busbar and reduces the conductive loss.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic busbar design technology, specifically an optimized method for copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules. Background Technology

[0002] Traditional copper-clad aluminum busbars often employ empirical design or single-parameter optimization methods, designing by fixing the copper layer thickness and aluminum core size, adjusting only cross-sectional parameters or material ratios, without achieving simultaneous optimization of multiple structural parameters. When conventional differential evolution algorithms are applied to busbar design, mutation probabilities and crossover rates are set at fixed values, and these parameters remain unchanged during population iteration.

[0003] Fixed algorithm parameters are prone to premature convergence and insufficient search accuracy, making it difficult to balance the algorithm's global search and local exploitation capabilities. Step-by-step optimization of the busbar aluminum core geometry and copper layer thickness leads to coupling relationships between parameters that cannot be matched in a coordinated manner. There is a conflict between weight reduction and conduction loss suppression, making it difficult to achieve joint optimality under current carrying capacity constraints.

[0004] An adaptive mutation and dynamic crossover adjustment mechanism needs to be introduced into the differential evolution algorithm. At the same time, the aluminum core width, aluminum core height, top copper layer thickness, and bottom copper layer thickness should be optimized in parallel to achieve iterative optimization of the joint objective of weight and conductivity loss. Summary of the Invention

[0005] This invention aims to solve at least one of the technical problems existing in the prior art; To this end, the present invention proposes an optimization method for copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules, including: The electrical and geometric parameters of the photovoltaic module are provided. Based on the electrical and geometric parameters, an improved differential evolution algorithm is used to perform parallel and collaborative optimization of the material size combination and structural configuration of the busbar. The improved differential evolution algorithm introduces an adaptive mutation probability control mechanism based on simulated annealing strategy in the mutation operation and integrates a dynamic crossover rate adjustment strategy based on historical population entropy value in the crossover operation. In each iteration, the improved differential evolution algorithm simultaneously outputs the optimized busbar cross-sectional geometric parameters and copper layer thickness parameters. The busbar cross-sectional geometric parameters include the width and height of the aluminum core, and the copper layer thickness parameters include the top copper layer thickness and the bottom copper layer thickness. Based on the optimized geometric parameters of the busbar cross section and the copper layer thickness parameters, the mass per unit length, DC resistance, and current carrying capacity of the copper-clad aluminum busbar are calculated. Using the mass per unit length, DC resistance, and current carrying capacity, and under the condition of satisfying the preset current carrying safety margin, the geometric parameters of the busbar cross section and the copper layer thickness parameters are iteratively adjusted until the joint optimization objective of global weight and conductivity loss is met, thus generating the final copper-clad aluminum busbar design specifications.

[0006] Furthermore, the provision of electrical and geometric parameters for the photovoltaic module includes: The electrical and geometric parameters include the number of solar cells, the size of the solar cells, the spacing between the solar cells, the operating current range, the maximum system voltage, and the ambient temperature range. Extract the total number of series-connected solar cells from the photovoltaic module design specification document, and use that as the number of solar cells. Extract the length and width data of a single solar cell as the cell size; Extract the gap distance between adjacent solar cells in the module layout, and use it as the solar cell spacing; The maximum power point current, open-circuit voltage, and maximum operating current under expected operating conditions of the photovoltaic module are extracted from the module technical specifications and together constitute the operating current range. The maximum system voltage is defined as the highest voltage to ground or the maximum terminal voltage after series connection that the component can withstand in the system application. The highest and lowest ambient temperatures in the climate data of the region where the photovoltaic modules are expected to be deployed are extracted as the ambient temperature range.

[0007] Furthermore, based on the aforementioned electrical and geometric parameters, an improved differential evolution algorithm is used to perform parallel and collaborative optimization of the material size combination and structural configuration of the busbar, including: Construct a solution space for optimizing decision variables, wherein the decision variables include the width of the aluminum core, the height of the aluminum core, the thickness of the top copper layer, and the thickness of the bottom copper layer; The constraints of the decision variables are set, including the lower limit of the manufacturing process of the aluminum core width and height, the lower limit and upper limit of the copper layer thickness of the plating process, and the maximum allowable width of the busbar determined by the spacing between the battery cells. An optimization objective function is defined, which is the weighted sum of the mass per unit length and the Joule heat loss power generated by the DC resistance at the upper limit of the operating current range; The initial population of the decision variables is input into the improved differential evolution algorithm, which performs iterative search within the solution space defined by the constraints. In each iteration, a calculation sub-process is invoked to calculate the corresponding optimization objective function value based on the decision variable values ​​decoded by the current individual. The calculation sub-process simultaneously calculates the mass per unit length, DC resistance, and current carrying capacity. The improved differential evolution algorithm drives the population evolution based on the optimized objective function value until the preset maximum number of iterations or the objective function convergence threshold is reached, and outputs the optimal individual. The optimal individual encodes the optimized busbar cross-sectional geometric parameters and copper layer thickness parameters.

[0008] Furthermore, the calculation sub-process simultaneously calculates the mass per unit length, DC resistance, and current carrying capacity, including: Based on the width, height, top copper layer thickness, bottom copper layer thickness, aluminum density, and copper density of the aluminum core decoded by the current individual, the mass of the aluminum core portion and the mass of the copper layer portion on the cross-section of the copper-clad aluminum busbar are calculated, and the mass per unit length is obtained by summing them. Based on the geometric parameters decoded from the current individual, and combined with the resistivity of aluminum and copper at the upper limit of the ambient temperature range, the DC resistance is calculated using a parallel model of composite conductor resistances. The current-carrying capacity is calculated by back-calculating based on the DC resistance, the preset maximum allowable temperature rise, the heat dissipation coefficient of the busbar surface, and the perimeter of the busbar cross-section, using the thermal balance equation.

[0009] Furthermore, the calculation of the DC resistance using the parallel model of composite conductor resistance includes: Calculate the cross-sectional area of ​​the aluminum core based on its width and height; Calculate the cross-sectional area of ​​the top copper layer and the cross-sectional area of ​​the bottom copper layer based on the width, height, top copper layer thickness, and bottom copper layer thickness of the aluminum core. Find the volume resistivity of aluminum at the upper limit of the ambient temperature range, and the volume resistivity of copper at the upper limit of the ambient temperature range; Assuming the current is ideally distributed between the aluminum core and the copper layer according to the conductivity ratio, calculate the resistance of the aluminum core branch, the resistance of the top copper layer branch, and the resistance of the bottom copper layer branch respectively. The resistance of the aluminum core branch, the resistance of the top copper layer branch, and the resistance of the bottom copper layer branch are calculated in parallel to obtain the DC resistance per unit length.

[0010] Furthermore, the improved differential evolution algorithm introduces an adaptive mutation probability control mechanism based on simulated annealing in the mutation operation, and integrates a dynamic crossover rate adjustment strategy based on historical population entropy in the crossover operation, including: Initialize the algorithm parameters, which include population size, initial mutation factor, initial crossover probability, initial temperature of simulated annealing, and cooling rate. During the mutation phase of each iteration, the fitness variance of the current population is calculated, and the initial mutation factor is scaled according to the current temperature of the simulated annealing to obtain the adaptive mutation probability of the current iteration cycle. The scaling factor is positively correlated with the fitness variance and the current temperature. The adaptive mutation probability control is used to perform differential mutation operations on the target individual to generate experimental individuals; During the crossover phase, the entropy distribution of gene loci in the previous generation population is calculated. For dimensions where the gene locus entropy is lower than a preset threshold, the crossover rate corresponding to that dimension is increased. For dimensions where the gene locus entropy is higher than the preset threshold, the crossover rate corresponding to that dimension is decreased, thus forming a dynamic crossover rate vector. The dynamic crossover rate vector is used to control gene exchange between experimental individuals and target individuals in various dimensions to generate new candidate individuals; Calculate the fitness value of the new candidate individual and compare it with the target individual, then update the population according to a greedy selection strategy; After each iteration, the current temperature of the simulated annealing is reduced according to the cooling rate, and the current optimal individual and its corresponding busbar cross-sectional geometry parameters and copper layer thickness parameters are saved.

[0011] Furthermore, the step of iteratively adjusting the geometric parameters of the busbar cross-section and the copper layer thickness parameters, using the unit length mass, DC resistance, and current carrying capacity, under the condition of satisfying a preset current carrying safety margin, until the joint optimization objective of global weight and conductivity loss is met, includes: The preset current-carrying safety margin condition is set such that the calculated current-carrying capacity of the optimized busbar must be greater than the upper limit of the operating current range multiplied by the safety factor. In each iteration of the improved differential evolution algorithm, it is determined whether the current carrying capacity of the current individual meets the preset current carrying safety margin condition. If the current individual does not meet the preset current carrying safety margin condition, a very large penalty function value is applied to the individual that does not meet the condition, which greatly reduces the probability of it being selected to enter the next generation population. If the current individual meets the preset current-carrying safety margin condition, then the weighted sum of the unit length mass and Joule heat loss power is used as its fitness value for normal evaluation. The joint optimization objective of global weight and conductivity loss is defined as minimizing the fitness value while satisfying all constraints and the preset current-carrying safety margin.

[0012] Furthermore, the generation of the final copper-clad aluminum busbar design specifications includes: After the improved differential evolution algorithm terminates the iteration, the final optimal individual is decoded to obtain a set of optimal values ​​for the busbar cross-sectional geometric parameters and copper layer thickness parameters. Based on the width and height of the aluminum core, the cross-sectional shape of the aluminum core is determined to be rectangular, and the dimensions and tolerance ranges of the width and height are given. Based on the thickness of the top copper layer and the thickness of the bottom copper layer, the copper layer is determined to be a uniform plating layer, and the set values ​​of the thickness of the top and bottom copper layers and the thickness uniformity requirements are given. Based on the electrical and geometric parameters of the photovoltaic module, the total length of the busbar required for a single photovoltaic module is calculated; Based on the mass per unit length and the total length, calculate the overall mass of the busbar section of a single photovoltaic module; The output includes a specification document containing the dimensions of the aluminum core, the set value of the copper layer thickness, the total length, the overall mass, and the calculated DC resistance and current carrying capacity.

[0013] Furthermore, the method also includes a step of verifying the thermomechanical reliability based on the design specifications of the copper-clad aluminum busbar: A simplified three-dimensional finite element model of a photovoltaic module was established, including the copper-clad aluminum busbar, cell interconnection ribbon, cells, and encapsulation materials. In the three-dimensional finite element model, the material properties, geometric dimensions, and interface bonding state of the aluminum core and copper layer are set according to the design specifications of the copper-clad aluminum busbar. A thermal cycling load conforming to the ambient temperature range is applied to the three-dimensional finite element model. The upper and lower limits of the temperature, the heating and cooling rates, and the number of cycles of the thermal cycling load are set according to the photovoltaic module reliability test standard. Solve the three-dimensional finite element model to extract the stress-strain response at the interconnection weld between the copper-clad aluminum busbar and the battery cell during thermal cycling; The stress-strain response is analyzed to identify the location of the maximum equivalent stress and its stress value, assess whether there is a risk of delamination at the interface between the copper layer and the aluminum core, and whether the fatigue life at the busbar and the cell solder joint meets the preset cycle number requirements.

[0014] Furthermore, a thermal cycling load conforming to the ambient temperature range is applied to the three-dimensional finite element model. The upper and lower temperature limits, heating and cooling rates, and number of cycles of the thermal cycling load are set according to the photovoltaic module reliability test standard, including: Obtain standardized temperature cycling curve parameters from international or industry standards for photovoltaic module thermal cycling testing. These parameters include the minimum temperature, maximum temperature, residence time at extreme temperatures, and rate of temperature change. The lowest ambient temperature in the ambient temperature range is compared with the lowest temperature in the standardized temperature cycling curve parameters, and the temperature with the smaller value obtained from the comparison is taken as the lower limit temperature for applying the thermal cycling load. The highest ambient temperature in the ambient temperature range is compared with the highest temperature in the standardized temperature cycling curve parameters, and the temperature with the larger value obtained from the comparison is taken as the upper limit temperature for applying the thermal cycling load. In the finite element analysis software, a periodic temperature field with amplitudes of the applied lower limit temperature and the applied upper limit temperature is defined, and the load step is set according to the temperature change rate. Set the total number of load steps to simulate the number of cycles required by the standard, and start the finite element solver for transient thermal-structural coupling analysis.

[0015] Compared with the prior art, the beneficial effects of the present invention are: An adaptive mutation probability control mechanism based on simulated annealing is introduced into the mutation operation of the differential evolution algorithm. The mutation probability can be adjusted in real time according to the iteration process and the current solution distribution. The algorithm maintains a large search range in the early stage of iteration and focuses on local fine-tuning search in the later stage of iteration. In the crossover operation, a dynamic crossover rate adjustment strategy based on historical population entropy is integrated. The crossover rate changes in real time according to population diversity. When population diversity decreases, the crossover strength increases, and when population diversity is sufficient, the crossover strength tends to stabilize. The stability and search accuracy of the algorithm search process are improved, and it is less likely to get trapped in local extrema during the optimization iteration process.

[0016] An improved differential evolution algorithm was employed to perform parallel and collaborative optimization of the busbar material size combination and structural configuration. In each iteration, the aluminum core width, aluminum core height, top copper layer thickness, and bottom copper layer thickness were simultaneously determined, with multiple coupling parameters updated synchronously within the same optimization framework. Based on the optimized parameters, the mass per unit length, DC resistance, and current carrying capacity were calculated. Under the constraint of current carrying safety margin, multiple objectives were synchronously iteratively adjusted. The trends of weight and conductivity loss were matched, and the constraints and synergistic characteristics between parameters were fully utilized. The busbar structural parameters and material distribution tended towards a balanced distribution of weight and conductivity loss, and the overall design results remained consistent with the multi-objective optimization objectives. Attached Figure Description

[0017] Figure 1 This is a state diagram of the copper-clad aluminum busbar optimization method for reducing the weight and conductivity loss of photovoltaic modules as described in this invention. Figure 2 A flowchart providing the electrical and geometric parameters of a photovoltaic module; Figure 3 This is a flowchart for parallel collaborative optimization of the busbar. Detailed Implementation

[0018] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] See Figure 1 This invention provides an optimized method for copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules. The specific method includes: Provided with the electrical and geometric parameters of the photovoltaic module, an improved differential evolution algorithm is used to perform parallel and collaborative optimization of the material size combination and structural configuration of the busbar. This improved differential evolution algorithm introduces an adaptive mutation probability control mechanism based on simulated annealing in the mutation operation and incorporates a dynamic crossover rate adjustment strategy based on historical population entropy in the crossover operation. In each iteration of the algorithm, the optimized busbar cross-sectional geometric parameters and copper layer thickness parameters are output simultaneously. The cross-sectional geometric parameters include the width and height of the aluminum core, and the copper layer thickness parameters include the thickness of the top and bottom copper layers. Subsequently, based on these optimized parameters, the unit length mass, DC resistance, and current carrying capacity of the copper-clad aluminum busbar are calculated. Using the calculated unit length mass, DC resistance, and current carrying capacity, under the condition of meeting the preset current carrying safety margin, the algorithm iteratively adjusts the busbar cross-sectional geometric parameters and copper layer thickness parameters until the joint optimization objective of global weight and conductivity loss is met, thereby generating the final copper-clad aluminum busbar design specifications.

[0020] In one embodiment of the present invention, see [reference] Figure 2 The required parameters include the number of solar cells, cell size, cell spacing, operating current range, maximum system voltage, and ambient temperature range. The number of solar cells is the total number of cells connected in series, extracted from the photovoltaic module's design specifications. Cell size is the length and width data of a single solar cell, extracted from the design documents. Cell spacing is the distance between adjacent cells, extracted from the module's layout diagram. The operating current range is calculated by extracting the maximum power point current, open-circuit voltage, and maximum operating current under standard test conditions from the module's technical specifications. The maximum system voltage is determined based on the highest voltage to ground or the maximum terminal voltage after series connection that the module can withstand in system application. The ambient temperature range is extracted from the highest and lowest ambient temperatures in the climate data of the region where the photovoltaic module is expected to be deployed.

[0021] In practical implementation, providing the electrical and geometric parameters of the photovoltaic (PV) module is the first step in the optimization process. The cell quantity parameter is directly extracted from the PV module's design specification document. For an exemplary 72-cell monocrystalline silicon PV module, the total number of cells connected in series can be extracted from the electrical connection diagram or parts list in the design specification document; this value is explicitly recorded as the cell quantity. Cell size parameters are also obtained from the design document. Consulting the specifications of a single solar cell in the same PV module, the cell length and width can be extracted as 156.75 mm; these two values ​​constitute the complete cell size data. The cell spacing parameter comes from the PV module's layout drawings. The distance between adjacent cells in the module layout is measured or directly read from the drawings. For example, if the measured distance between the edges of adjacent cells is 2 mm, this 2 mm value is recorded as the cell spacing.

[0022] In some embodiments, determining the operating current range requires integrating multiple data points from the module's technical specifications. The maximum power point current under standard test conditions is extracted from the photovoltaic module's technical specifications; for example, the specifications record this value as 9.72 amps. Simultaneously, the open-circuit voltage under standard test conditions is extracted from the specifications; for example, this value is recorded as 45.5 volts. Further, based on the intended application scenario of the photovoltaic module's deployment, such as a large ground-mounted power plant, the maximum operating current of the photovoltaic module under the expected operating environment is extracted from the power plant's electrical design scheme. This current value may vary depending on system configuration and irradiance conditions; for example, it may be set at 10.5 amps in the design scheme. The maximum power point current, open-circuit voltage, and maximum operating current together constitute the operating current range describing the module's electrical operating conditions.

[0023] Optionally, the ambient temperature range is obtained based on climate data of the region where the photovoltaic modules are expected to be deployed. Historical meteorological statistics for the target installation region, such as a location in Qinghai Province, China, are queried. The highest historical ambient temperature for this region is extracted as 40 degrees Celsius, and the lowest as -30 degrees Celsius. This range of -30 to 40 degrees Celsius is defined as the ambient temperature range and used to calculate the resistivity of the material under extreme temperatures. In practice, the six parameters—number of solar cells, cell size, cell spacing, operating current range, maximum system voltage, and ambient temperature range—constitute a complete and quantifiable set of input conditions, providing clear boundaries and calculation benchmarks for subsequent optimization algorithms.

[0024] In one embodiment of the present invention, see [reference] Figure 3A solution space is constructed with aluminum core width, aluminum core height, top copper layer thickness, and bottom copper layer thickness as decision variables. Constraints are set for the decision variables, including lower limits for the manufacturing process of aluminum core width and height, lower and upper limits for the plating process of copper layer thickness, and the maximum allowable width of the busbar determined by the cell spacing. The objective function is set as the weighted sum of the mass per unit length and the Joule heat loss power generated by DC resistance at the upper limit of the operating current range. The initial population formed by encoding the decision variables is input into the improved differential evolution algorithm, which iteratively searches within the solution space limited by the constraints. In each iteration, a calculation subprocess is called, which simultaneously calculates the corresponding mass per unit length, DC resistance, current carrying capacity, and the final objective function value based on the decoded decision variable values ​​of the current individual. When calculating the mass per unit length, the masses of the aluminum core and copper layer are calculated and summed based on the aluminum core width, aluminum core height, copper layer thickness, and the densities of aluminum and copper, respectively. When calculating DC resistance, a parallel model of composite conductor resistance is used. First, the cross-sectional areas of the aluminum core, top copper layer, and bottom copper layer are calculated based on geometric parameters. Then, the volume resistivity of aluminum and copper at the upper limit of the ambient temperature range is looked up. Assuming ideal current distribution according to conductance ratio, the resistance of each branch is calculated separately. Finally, parallel calculations are performed to obtain the DC resistance per unit length. When calculating current carrying capacity, it is derived from the DC resistance, the preset maximum allowable temperature rise, the heat dissipation coefficient of the busbar surface, and the cross-sectional perimeter, based on the thermal balance equation. The improved differential evolution algorithm drives population evolution based on the objective function value until the termination condition is reached, outputting the optimal individual that encodes the optimal busbar cross-sectional geometric parameters and copper layer thickness parameters.

[0025] In practical implementation, based on the electrical and geometric parameters of photovoltaic modules, an improved differential evolution algorithm is used to perform parallel and collaborative optimization of the material size combination and structural configuration of the busbar. A four-dimensional solution space is constructed with aluminum core width, aluminum core height, top copper layer thickness, and bottom copper layer thickness as decision variables. The values ​​of these decision variables directly represent the physical dimensions of the busbar cross-section. Constraints are set for the decision variables: the lower limits for the aluminum core width and height are 1.0 mm and 0.5 mm, respectively; the lower limit for the copper layer thickness is 0.01 mm, and the upper limit is 0.1 mm; the maximum allowable width of the busbar, determined by the cell spacing, is 2 mm. The optimization objective function is set as the weighted sum of the mass per unit length and the Joule heat loss power generated by DC resistance at the upper limit of the operating current range. The weighting coefficients are assigned values ​​based on the priority of module lightweighting and electrical efficiency. The randomly generated initial population of decision variables is input into the improved differential evolution algorithm, which iteratively searches within the constraint-bound solution space.

[0026] In some embodiments, in each iteration of the improved differential evolution algorithm, an independent computational subprocess is invoked. This subprocess receives the decoded decision variable values ​​for the current individual and simultaneously calculates the corresponding mass per unit length, DC resistance, current carrying capacity, and the final optimization objective function value. Based on the decoded aluminum core width, aluminum core height, top copper layer thickness, bottom copper layer thickness, and the densities of aluminum and copper, the mass of the aluminum core portion and the copper layer portion on the cross-section of the copper-clad aluminum busbar are calculated and summed to obtain the mass per unit length. The DC resistance is calculated based on a parallel model of composite conductor resistance. The volume resistivity of aluminum and copper at the upper limit of the ambient temperature range is queried, and the resistance values ​​of the aluminum core branch, top copper layer branch, and bottom copper layer branch are calculated and then connected in parallel. The current carrying capacity is calculated based on the thermal balance equation, using the preset maximum allowable temperature rise, the heat dissipation coefficient of the busbar surface, and the perimeter of the busbar cross-section for back-calculation.

[0027] The specific calculation process for DC resistance in the calculation sub-process is as follows: The cross-sectional area of ​​the aluminum core is calculated based on its width and height. The cross-sectional areas of the top and bottom copper layers are then calculated based on the width, height, and thicknesses of the top and bottom copper layers. The volume resistivity of aluminum and copper at the upper limit of the ambient temperature range is obtained from the material handbook. Assuming an ideal current distribution between the aluminum core and copper layers according to their conductivity ratios, the resistances of the aluminum core branch, the top copper layer branch, and the bottom copper layer branch can be calculated using their respective resistivities and cross-sectional areas. The resistances of the three branches are then calculated in parallel to obtain the DC resistance per unit length. The formula for parallel calculation is:

[0028] in: This indicates the resistance of the aluminum core branch. This indicates the resistance of the top copper layer branch. This indicates the resistance of the copper layer branch on the bottom surface.

[0029] Optionally, after the computational subprocess completes the evaluation of all individuals in the current population, the improved differential evolution algorithm drives the population's evolution based on the calculated optimization objective function value. Individuals with smaller optimization objective function values ​​have higher fitness. The improved differential evolution algorithm continuously performs selection, mutation, and crossover operations until a preset maximum number of iterations is reached or the change in the objective function value over multiple generations is less than a convergence threshold, at which point the iteration process terminates. The improved differential evolution algorithm outputs the optimal individual with the highest fitness in the current population. This optimal individual encodes the specific values ​​of the busbar cross-sectional geometry parameters and copper layer thickness parameters obtained through the optimized search.

[0030] In one embodiment of the present invention, at the start of the algorithm, parameters such as population size, initial mutation factor, initial crossover probability, initial simulated annealing temperature, and cooling rate need to be initialized. During the mutation phase of each iteration, the variance of the fitness values ​​of all individuals in the current population is calculated, and the initial mutation factor is scaled according to the current temperature of the simulated annealing strategy. The scaling factor is positively correlated with the fitness variance and the current temperature, thereby obtaining the adaptive mutation probability for the current iteration cycle. This probability is used to control the differential mutation operation on the target individual to generate test individuals. During the crossover phase, the entropy distribution of the previous generation population at each gene locus (i.e., each decision variable dimension) is calculated. For dimensions with entropy values ​​below a preset threshold, the corresponding crossover rate is increased; for dimensions with entropy values ​​above the preset threshold, the corresponding crossover rate is decreased, thus forming a dynamic crossover rate vector. This dynamic crossover rate vector is used to control gene exchange between test individuals and target individuals at various dimensions, thereby generating new candidate individuals. The fitness value of the new candidate individuals is calculated and compared with that of the target individual, and the population is updated according to a greedy selection strategy. After each iteration, the current temperature of the simulated annealing is reduced according to the set cooling rate, and the current optimal individual and its corresponding busbar cross-sectional geometry parameters and copper layer thickness parameters are saved.

[0031] In its implementation, the improved differential evolution algorithm introduces an adaptive mutation probability control mechanism based on simulated annealing in the mutation operation, and integrates a dynamic crossover rate adjustment strategy based on historical population entropy in the crossover operation. The first step of the algorithm execution is to initialize the algorithm parameters, including population size, initial mutation factor, initial crossover probability, initial temperature and cooling rate of simulated annealing. Refer to Table 1; a set of specific algorithm parameters is as follows: Table 1: Parameter Table of Improved Differential Evolution Algorithm

[0032] In some embodiments, during the mutation phase of each iteration, the variance of the fitness values ​​of all individuals in the current population is calculated. The fitness values ​​are determined by the optimization objective function value output by the computation sub-process. The initial mutation factor is scaled according to the current simulated annealing temperature to obtain the adaptive mutation probability for the current iteration cycle. The scaling factor is positively correlated with the fitness variance and the current simulated annealing temperature. The scaling operation can be expressed as:

[0033] in: This represents the adaptive mutation probability of the current iteration period. Indicates the initial variation factor. This represents the variance of the current population's fitness. This represents a normalization coefficient. This indicates the current temperature of the simulated annealing. This represents the initial temperature for simulated annealing. Experimental individuals are generated by performing differential mutation operations on the target individual using the calculated adaptive mutation probability control.

[0034] In practice, during the crossover phase, the entropy distribution of each gene locus is calculated based on the previous generation population. Each gene locus corresponds to one of the four dimensions of the decision variable: aluminum core width, aluminum core height, top copper layer thickness, and bottom copper layer thickness. For dimensions where the entropy value is below a preset threshold, the crossover rate for that dimension is increased; for dimensions where the entropy value is above the preset threshold, the crossover rate is decreased, thus forming a dynamic crossover rate vector with the same dimensions as the decision variable. This dynamic crossover rate vector is used to control gene exchange between the experimental and target individuals across each dimension, generating new candidate individuals. The fitness value of the new candidate individuals is calculated and compared with that of the target individual. A greedy selection strategy is then used to determine whether to retain the target individual or update the population with the new candidate individuals.

[0035] In one embodiment of the present invention, a preset current-carrying safety margin condition is set, requiring that the calculated current-carrying capacity of the optimized busbar must be greater than the upper limit of the operating current range multiplied by a safety factor. In each iteration of the improved differential evolution algorithm, it is determined whether the current-carrying capacity of the current individual meets this condition. If not, a penalty function value with a very large value is applied to the individual, significantly worsening its fitness value and thus greatly reducing its probability of being selected for the next generation. If satisfied, the weighted sum of unit length mass and Joule heat loss power is used as its fitness value for normal evaluation. The joint optimization objective of global weight and conductivity loss is defined as minimizing the fitness value while satisfying all geometric and process constraints and the aforementioned current-carrying safety margin condition. After the algorithm terminates iteration, the final optimal individual is decoded to obtain a set of optimal busbar cross-sectional geometric parameters and copper layer thickness parameters. Based on the width and height of the aluminum core, the cross-sectional shape of the aluminum core is determined to be rectangular, and the dimensions and tolerance ranges of the width and height are given. Based on the copper layer thicknesses on the top and bottom surfaces, the copper layer is determined to be a uniform plating layer, and the thickness setting value and uniformity requirements are given. Combining the electrical and geometric parameters of the photovoltaic module, the total length of the busbar required for a single module is calculated, and the overall mass is calculated based on the mass per unit length and the total length. The final output is a specification document containing information such as aluminum core dimensions, copper layer thickness setting value, total length, overall mass, DC resistance, and current carrying capacity.

[0036] In practical implementation, the unit length mass, DC resistance, and current carrying capacity output from the calculation subprocess are used to drive an improved differential evolution algorithm to iteratively adjust the busbar cross-sectional geometry and copper layer thickness parameters, while meeting a preset current carrying safety margin. The preset current carrying safety margin requires that the calculated current carrying capacity of the optimized busbar must be greater than the upper limit of the operating current range multiplied by a safety factor. For example, if the upper limit of the operating current range is 10.5 amps and the safety factor is set to 1.2, then the current carrying capacity must be greater than 12.6 amps. The joint optimization objective of global weight and conductivity loss is defined as minimizing the fitness value while satisfying all geometric constraints, process constraints, and the preset current carrying safety margin. formula:

[0037] in: Represents the fitness value. Indicates mass per unit length. This represents the Joule heat loss power generated by the DC resistance at the upper limit of the operating current range. and These represent the weighting coefficients for mass and power loss, respectively.

[0038] In some embodiments, in each iteration of the improved differential evolution algorithm, it is determined whether the current carrying capacity of the current individual meets a preset current carrying safety margin condition. If the current individual does not meet the preset current carrying safety margin condition, a very large penalty function value is applied to the individual that does not meet the condition. The penalty function value is set to a constant much larger than the normal fitness value, such as 1.0e10, which significantly reduces the probability of it being selected into the next generation population. If the current individual meets the preset current carrying safety margin condition, its fitness value is used as a normal evaluation using the weighted sum of mass per unit length and Joule heat loss power. Refer to Table 2, which shows the data comparison of two different individuals in one evaluation: Table 2: Comparison of Candidate Individual Evaluation Results

[0039] It is understandable that after the improved differential evolution algorithm terminates its iterations, the final optimal individual is decoded to obtain a set of optimal values ​​for the busbar cross-sectional geometry and copper layer thickness. Based on the width and height of the aluminum core, the cross-sectional shape of the aluminum core is determined to be rectangular, and the dimensions and tolerance ranges for the width and height are given. For example, the optimal value for the aluminum core width is 1.6 mm with a tolerance of ±0.1 mm, and the optimal value for the aluminum core height is 0.9 mm with a tolerance of ±0.05 mm. Based on the thickness of the top and bottom copper layers, the copper layer is determined to be a uniform plating layer, and the set values ​​for the thickness of the top and bottom copper layers and the thickness uniformity requirements are given. For example, the set value for the copper layer thickness is 0.03 mm, and the thickness uniformity requirement is ±0.005 mm.

[0040] In practical implementation, the total length of the busbar required for a single photovoltaic module is calculated by combining the electrical and geometric parameters of the photovoltaic module. The total length depends on the number of solar cells, cell size, cell spacing, and internal connection method. Based on the calculated mass per unit length and total length, the overall mass of the busbar section of a single photovoltaic module is calculated. The final output is a specification document that includes the set values ​​for the aluminum core dimensions, copper layer thickness, total length, overall mass, and calculated DC resistance and current carrying capacity. The specification document clearly records all design specifications in tabular and text formats.

[0041] In one embodiment of the present invention, a simplified three-dimensional finite element model of a photovoltaic module is established, comprising a copper-clad aluminum busbar, cell interconnection ribbons, cells, and encapsulation materials. In this three-dimensional finite element model, the material properties, geometric dimensions, and interface bonding state between the aluminum core and the copper layer are set according to the design specifications of the copper-clad aluminum busbar. A thermal cycling load conforming to the ambient temperature range is applied to the three-dimensional finite element model. The upper and lower limits of the temperature, the heating and cooling rates, and the number of cycles for this thermal cycling load are set according to the photovoltaic module reliability testing standards. Specifically, this includes: obtaining standardized temperature cycling curve parameters from relevant international or industry standards, including minimum temperature, maximum temperature, residence time at extreme temperatures, and temperature change rate; comparing the lower limit of the ambient temperature range with the standard minimum temperature, and taking the smaller value as the lower limit temperature for the thermal cycling load; comparing the upper limit of the ambient temperature range with the standard maximum temperature, and taking the larger value as the upper limit temperature; defining a periodic temperature field with amplitudes of the lower and upper limit temperatures in the finite element analysis software, and setting the load step according to the standard temperature change rate; setting the total number of load steps to simulate the number of cycles required by the standard, and starting the finite element solver for transient thermal-structural coupling analysis. After the solution is completed, the stress-strain response at the copper-clad aluminum busbar and the cell interconnection solder joint during thermal cycling is extracted. The stress-strain response was analyzed to identify the location and value of the maximum equivalent stress, assess whether there is a risk of delamination due to thermal mismatch at the interface between the copper layer and the aluminum core, and assess whether the fatigue life at the busbar and cell solder joint meets the preset cycle number requirements.

[0042] In the specific implementation, the thermomechanical reliability verification step based on the copper-clad aluminum busbar design specifications involves establishing a simplified three-dimensional finite element model of a photovoltaic module, including the copper-clad aluminum busbar, cell interconnection ribbons, cells, and encapsulation materials. The three-dimensional finite element model is constructed based on a typical photovoltaic module structure, such as a module containing 72 series-connected cells arranged in a 6x12 array. In the three-dimensional finite element model, the material properties, geometric dimensions, and interface bonding state of the aluminum core and copper layer are set according to the copper-clad aluminum busbar design specifications. The material properties of the aluminum core are set to the elastic modulus, Poisson's ratio, and coefficient of thermal expansion of aluminum alloy AA1060, while the material properties of the copper layer are set to the elastic modulus, Poisson's ratio, and coefficient of thermal expansion of copper C11000. The geometric dimensions of the aluminum core are set to a width of 1.6 mm and a height of 0.9 mm, the copper layer thickness is set to 0.03 mm, and the interface bonding state is set to bonded contact to simulate the metallurgical bonding between the copper layer and the aluminum core.

[0043] In some embodiments, a thermal cycling load conforming to the ambient temperature range is applied to the three-dimensional finite element model. The upper and lower limits of the thermal cycling load, the heating and cooling rates, and the number of cycles are set according to the photovoltaic module reliability testing standard. Standardized temperature cycling curve parameters are obtained from the international standard IEC61215 or industry standards for photovoltaic module thermal cycling testing. These parameters include a minimum temperature of -40°C, a maximum temperature of 85°C, a residence time of 10 minutes at extreme temperatures, and a temperature change rate of 100°C / hour. The minimum ambient temperature of -30°C within the ambient temperature range is compared with the minimum temperature of -40°C in the standardized temperature cycling curve parameters. The temperature of -40°C, which has the smaller value obtained from the comparison, is taken as the lower limit temperature for applying the thermal cycling load. The maximum ambient temperature of 40°C within the ambient temperature range is compared with the maximum temperature of 85°C in the standardized temperature cycling curve parameters. The temperature of 85°C, which has the larger value obtained from the comparison, is taken as the upper limit temperature for applying the thermal cycling load.

[0044] It is understandable that a periodic temperature field with amplitudes defined by the lower and upper application temperatures is used in the finite element analysis software, and the load steps are set according to the rate of temperature change. The temperature field starts at the lower application temperature of -40℃, reaches the upper application temperature of 85℃ after a heating phase, maintains this temperature for a specified time, and then returns to the lower application temperature of -40℃ after a cooling phase, thus completing a full cycle. The total number of load steps is set to simulate the number of cycles required by the standard. formula:

[0045] in: Indicates the total number of load steps. This indicates the number of iterations required by the standard. This indicates that the maximum temperature to be applied is 85°C. This indicates that the lower limit temperature for application is -40℃. This indicates a temperature change rate of 100℃ / hour. This indicates a stay of 10 minutes. This indicates the time step selected in the finite element analysis. The finite element solver is then started to perform transient thermal-structural coupling analysis. The solution process calculates the thermal stress and deformation caused by temperature changes at each load step.

[0046] In practical implementation, after solving the three-dimensional finite element model, the stress-strain response at the interconnection weld between the copper-clad aluminum busbar and the solar cell is extracted during thermal cycling. In finite element post-processing, the elements and nodes of the interconnection weld between the copper-clad aluminum busbar and the solar cell are located, and the curves showing the equivalent stress, shear stress, and principal strain at these locations throughout the entire thermal cycling process are output. The stress-strain response is analyzed to identify the location and stress value of the maximum equivalent stress, such as the stress concentration area at the interface between the copper-clad aluminum busbar and the first solar cell. The risk of delamination at the copper layer and aluminum core interface is assessed by checking the contact state and normal stress of the interface elements to determine whether separation or slippage occurs during thermal cycling. The fatigue life at the busbar and solar cell weld meets the preset cycle count requirement. This is estimated based on the extracted strain amplitude and relevant fatigue life models, and the estimated cycle count is compared with the standard required cycle count.

[0047] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. An optimization method for copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules, characterized in that, The method includes: The system provides electrical and geometric parameters of photovoltaic modules. Based on these parameters, an improved differential evolution algorithm is used to perform parallel and collaborative optimization of the material size combination and structural configuration of the busbar. The improved differential evolution algorithm introduces an adaptive mutation probability control mechanism based on simulated annealing strategy in the mutation operation and integrates a dynamic crossover rate adjustment strategy based on historical population entropy value in the crossover operation. The electrical and geometric parameters include the number of solar cells, solar cell size, solar cell spacing, operating current range, maximum system voltage, and ambient temperature range. In each iteration, the improved differential evolution algorithm simultaneously outputs the optimized busbar cross-sectional geometric parameters and copper layer thickness parameters. The busbar cross-sectional geometric parameters include the width and height of the aluminum core, and the copper layer thickness parameters include the top copper layer thickness and the bottom copper layer thickness. Based on the optimized geometric parameters of the busbar cross section and the copper layer thickness parameters, the mass per unit length, DC resistance, and current carrying capacity of the copper-clad aluminum busbar are calculated. Using the unit length mass, DC resistance and current carrying capacity, under the condition of meeting the preset current carrying safety margin, the geometric parameters of the busbar cross section and the copper layer thickness parameters are iteratively adjusted until the joint optimization target of global weight and conductivity loss is met, and the final copper-clad aluminum busbar design specifications are generated. Based on the electrical and geometric parameters, an improved differential evolution algorithm is used to perform parallel and collaborative optimization of the material size combination and structural configuration of the busbar, including: Construct a solution space for optimizing decision variables, wherein the decision variables include the width of the aluminum core, the height of the aluminum core, the thickness of the top copper layer, and the thickness of the bottom copper layer; The constraints of the decision variables are set, including the lower limit of the manufacturing process of the aluminum core width and height, the lower limit and upper limit of the copper layer thickness of the plating process, and the maximum allowable width of the busbar determined by the spacing between the battery cells. An optimization objective function is defined, which is the weighted sum of the mass per unit length and the Joule heat loss power generated by the DC resistance at the upper limit of the operating current range; The initial population of the decision variables is input into the improved differential evolution algorithm, which performs iterative search within the solution space defined by the constraints. In each iteration, a calculation sub-process is invoked to calculate the corresponding optimization objective function value based on the decision variable values ​​decoded by the current individual. The calculation sub-process simultaneously calculates the unit length mass, DC resistance, and current carrying capacity. The improved differential evolution algorithm drives the evolution of the population based on the optimized objective function value until the preset maximum number of iterations or the objective function convergence threshold is reached, and outputs the optimal individual. The optimal individual encodes the optimized busbar cross-sectional geometric parameters and copper layer thickness parameters. The improved differential evolution algorithm introduces an adaptive mutation probability control mechanism based on simulated annealing in the mutation operation, and integrates a dynamic crossover rate adjustment strategy based on historical population entropy in the crossover operation, including: Initialize the algorithm parameters, which include population size, initial mutation factor, initial crossover probability, initial temperature of simulated annealing, and cooling rate. During the mutation phase of each iteration, the fitness variance of the current population is calculated, and the initial mutation factor is scaled according to the current temperature of the simulated annealing to obtain the adaptive mutation probability of the current iteration cycle. The scaling factor is positively correlated with the fitness variance and the current temperature. The adaptive mutation probability control is used to perform differential mutation operations on the target individual to generate experimental individuals; During the crossover phase, the entropy distribution of gene loci in the previous generation population is calculated. For dimensions where the gene locus entropy is lower than a preset threshold, the crossover rate corresponding to that dimension is increased. For dimensions where the gene locus entropy is higher than the preset threshold, the crossover rate corresponding to that dimension is decreased, thus forming a dynamic crossover rate vector. The dynamic crossover rate vector is used to control gene exchange between experimental individuals and target individuals in various dimensions to generate new candidate individuals; Calculate the fitness value of the new candidate individual and compare it with the target individual, then update the population according to a greedy selection strategy; After each iteration, the current temperature of the simulated annealing is reduced according to the cooling rate, and the current optimal individual and its corresponding busbar cross-sectional geometry parameters and copper layer thickness parameters are saved.

2. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 1, characterized in that, The provision of electrical and geometric parameters for photovoltaic modules includes: Extract the total number of series-connected solar cells from the photovoltaic module design specification document, and use that as the number of solar cells. Extract the length and width data of a single solar cell as the cell size; Extract the gap distance between adjacent solar cells in the module layout, and use it as the solar cell spacing; The maximum power point current, open-circuit voltage, and maximum operating current under expected operating conditions of the photovoltaic module are extracted from the module technical specifications and together constitute the operating current range. The maximum system voltage is defined as the highest voltage to ground or the maximum terminal voltage after series connection that the component can withstand in the system application. The highest and lowest ambient temperatures in the climate data of the region where the photovoltaic modules are expected to be deployed are extracted as the ambient temperature range.

3. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 2, characterized in that, The calculation sub-process simultaneously calculates the mass per unit length, DC resistance, and current carrying capacity, including: Based on the width, height, top copper layer thickness, bottom copper layer thickness, aluminum density, and copper density of the aluminum core decoded by the current individual, the mass of the aluminum core portion and the mass of the copper layer portion on the cross-section of the copper-clad aluminum busbar are calculated, and the mass per unit length is obtained by summing them. Based on the geometric parameters decoded from the current individual, and combined with the resistivity of aluminum and copper at the upper limit of the ambient temperature range, the DC resistance is calculated using a parallel model of composite conductor resistances. The current-carrying capacity is calculated by back-calculating based on the DC resistance, the preset maximum allowable temperature rise, the heat dissipation coefficient of the busbar surface, and the perimeter of the busbar cross-section, using the thermal balance equation.

4. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 3, characterized in that, The calculation of the DC resistance using the parallel model of composite conductor resistance includes: Calculate the cross-sectional area of ​​the aluminum core based on its width and height; Calculate the cross-sectional area of ​​the top copper layer and the cross-sectional area of ​​the bottom copper layer based on the width, height, top copper layer thickness, and bottom copper layer thickness of the aluminum core. Find the volume resistivity of aluminum at the upper limit of the ambient temperature range, and the volume resistivity of copper at the upper limit of the ambient temperature range; Assuming the current is ideally distributed between the aluminum core and the copper layer according to the conductivity ratio, calculate the resistance of the aluminum core branch, the resistance of the top copper layer branch, and the resistance of the bottom copper layer branch respectively. The resistance of the aluminum core branch, the resistance of the top copper layer branch, and the resistance of the bottom copper layer branch are calculated in parallel to obtain the DC resistance per unit length.

5. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 4, characterized in that, The process involves iteratively adjusting the geometric parameters of the busbar cross-section and the copper layer thickness parameters, using the unit length mass, DC resistance, and current-carrying capacity, while meeting a preset current-carrying safety margin, until the joint optimization objective of global weight and conductivity loss is achieved. This includes: The preset current-carrying safety margin condition is set such that the calculated current-carrying capacity of the optimized busbar must be greater than the upper limit of the operating current range multiplied by the safety factor. In each iteration of the improved differential evolution algorithm, it is determined whether the current carrying capacity of the current individual meets the preset current carrying safety margin condition. If the current individual does not meet the preset current carrying safety margin condition, a very large penalty function value is applied to the individual that does not meet the condition, which greatly reduces the probability of it being selected to enter the next generation population. If the current individual meets the preset current-carrying safety margin condition, then the weighted sum of the unit length mass and Joule heat loss power is used as its fitness value for normal evaluation. The joint optimization objective of global weight and conductivity loss is defined as minimizing the fitness value while satisfying all constraints and the preset current-carrying safety margin.

6. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 5, characterized in that, The final copper-clad aluminum busbar design specifications include: After the improved differential evolution algorithm terminates the iteration, the final optimal individual is decoded to obtain a set of optimal values ​​for the busbar cross-sectional geometric parameters and copper layer thickness parameters. Based on the width and height of the aluminum core, the cross-sectional shape of the aluminum core is determined to be rectangular, and the dimensions and tolerance ranges of the width and height are given. Based on the thickness of the top copper layer and the thickness of the bottom copper layer, the copper layer is determined to be a uniform plating layer, and the set values ​​of the thickness of the top and bottom copper layers and the thickness uniformity requirements are given. Based on the electrical and geometric parameters of the photovoltaic module, the total length of the busbar required for a single photovoltaic module is calculated; Based on the mass per unit length and the total length, calculate the overall mass of the busbar section of a single photovoltaic module; The output includes a specification document containing the dimensions of the aluminum core, the set value of the copper layer thickness, the total length, the overall mass, and the calculated DC resistance and current carrying capacity.

7. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 6, characterized in that, The method also includes a step of verifying the thermomechanical reliability based on the design specifications of the copper-clad aluminum busbar: A simplified three-dimensional finite element model of a photovoltaic module was established, including the copper-clad aluminum busbar, cell interconnection ribbon, cells, and encapsulation materials. In the three-dimensional finite element model, the material properties, geometric dimensions, and interface bonding state of the aluminum core and copper layer are set according to the design specifications of the copper-clad aluminum busbar. A thermal cycling load conforming to the ambient temperature range is applied to the three-dimensional finite element model. The upper and lower limits of the temperature, the heating and cooling rates, and the number of cycles of the thermal cycling load are set according to the photovoltaic module reliability test standard. Solve the three-dimensional finite element model to extract the stress-strain response at the interconnection weld between the copper-clad aluminum busbar and the battery cell during thermal cycling; The stress-strain response is analyzed to identify the location of the maximum equivalent stress and its stress value, assess whether there is a risk of delamination at the interface between the copper layer and the aluminum core, and whether the fatigue life at the busbar and the cell solder joint meets the preset cycle number requirements.

8. The method for optimizing copper-clad aluminum busbars to reduce the weight and conductivity loss of photovoltaic modules according to claim 7, characterized in that, A thermal cycling load conforming to the ambient temperature range is applied to the three-dimensional finite element model. The upper and lower limits of the temperature, the heating and cooling rates, and the number of cycles of the thermal cycling load are set according to the photovoltaic module reliability test standard, including: Obtain standardized temperature cycling curve parameters from international or industry standards for photovoltaic module thermal cycling testing. These parameters include the minimum temperature, maximum temperature, residence time at extreme temperatures, and rate of temperature change. The lowest ambient temperature in the ambient temperature range is compared with the lowest temperature in the standardized temperature cycling curve parameters, and the temperature with the smaller value obtained from the comparison is taken as the lower limit temperature for applying the thermal cycling load. The highest ambient temperature in the ambient temperature range is compared with the highest temperature in the standardized temperature cycling curve parameters, and the temperature with the larger value obtained from the comparison is taken as the upper limit temperature for applying the thermal cycling load. In the finite element analysis software, a periodic temperature field with amplitudes of the applied lower limit temperature and the applied upper limit temperature is defined, and the load step is set according to the temperature change rate. Set the total number of load steps to simulate the number of cycles required by the standard, and start the finite element solver for transient thermal-structural coupling analysis.

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