Photovoltaic model unknown parameter estimation method based on improved differential evolution algorithm

Abstract

The invention provides a photovoltaic model unknown parameter estimation method based on an improved differential evolution algorithm, and relates to the technical field of photovoltaic model parameter estimation. The invention provides a photovoltaic model unknown parameter estimation method based on an improved differential evolution algorithm, which comprises the following steps: distributing an identity tag for each individual to record a variation strategy and a control parameter used in the generation process of the individual, and updating the control parameter by using the identity tag; based on a control parameter uniform updating mechanism, the problem that parameters are difficult to uniformly update in an integrated environment is solved, so that the accuracy of estimating unknown parameters of a photovoltaic model by an algorithm is improved. In combination with a new parameter adaptive updating scheme, the integrated variation strategy can dynamically match appropriate control parameters in the whole search process without user intervention, so that each variation strategy is allowed to fully utilize the advantages thereof, the problem that the parameters are difficult to update uniformly in an integrated environment is solved, and the search efficiency is improved. Therefore, the precision of estimating the unknown parameters of the photovoltaic model is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic model parameter estimation, and in particular to a photovoltaic model unknown parameter estimation method based on an improved differential evolution algorithm. Background Art

[0002] The depletion of non-renewable energy sources such as oil and natural gas, as well as the atmospheric pollution caused by fossil fuels, are attracting increasing attention. People are eager to find a clean, renewable energy source to replace these. Among various renewable energy sources, solar energy generated by photovoltaic systems is gaining increasing attention due to its low operation and maintenance costs, high power density, and inexhaustible nature and advantages. The demand for solar photovoltaics as a source of electricity is growing exponentially. However, the shortcomings of current photovoltaic power generation systems, such as low power generation efficiency and instability, pose significant challenges to ongoing research and application. Therefore, establishing an accurate photovoltaic cell model to simulate and optimize photovoltaic cells to achieve higher conversion efficiency and more stable operation has become the key to current research.

[0003] Generally speaking, mainstream photovoltaic models include single-diode models, dual-diode models, triple-diode models, and photovoltaic module models. Determining the parameters of a photovoltaic model to maximize its performance under specific conditions is a key challenge in photovoltaic model research. The number of unknown parameters in a photovoltaic model increases with the number of diodes in the model branches. Furthermore, the parameter estimation problem in photovoltaic models is highly nonlinear and multimodal, posing significant challenges to existing solution methods. Numerous methods have been proposed to address this issue, which can be broadly categorized into two main categories: mathematical analysis and metaheuristic algorithms. The main idea of ​​mathematical analysis is to use a series of mathematical equations and transformations to solve for the unknown parameters. However, this method is highly dependent on specific curve data points. If the data points are not selected appropriately, significant errors can occur. Therefore, the reliability of mathematical analysis is a major concern. In contrast, the drawbacks of mathematical analysis, such as sensitivity to input and a strong dependence on the mathematical properties of the optimization problem, are not present in metaheuristic algorithms. Consequently, an increasing number of metaheuristic algorithms are being used to extract unknown parameters from photovoltaic models.

[0004] Differential evolution and its variants, as metaheuristic algorithms, have been widely used for parameter extraction in photovoltaic models due to their ease of implementation, limited control parameters, and powerful global exploration capabilities. However, none of the currently proposed differential evolution algorithms address the difficulty of uniformly setting control parameters for different mutation strategies in an integrated environment. This prompted us to investigate a novel differential evolution variant that addresses this issue by leveraging information about mutation strategies and control parameters. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing technologies and provide a method for estimating the unknown parameters of a photovoltaic model based on an improved differential evolution algorithm. By assigning an identity tag to each individual to record the mutation strategy and control parameters used in its generation process, and using the identity tag to update the control parameters, the problem of difficulty in uniformly updating parameters in an integrated environment is solved, thereby improving the accuracy of the algorithm in estimating the unknown parameters of the photovoltaic model.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] The present invention provides a method for estimating unknown parameters of a photovoltaic model based on an improved differential evolution algorithm, comprising the following steps:

[0008] Step 1: Establish an output current model of the photovoltaic model and set the parameters to be estimated;

[0009] Step 2: Initialize the individuals and control parameters in the population based on the parameters to be estimated;

[0010] Step 2.1, initialize the individuals in the population within the range of the parameter to be estimated;

[0011] Step 2.2: Divide the individuals in the population into exploration groups elr and development group eli ;

[0012] Step 2.3, initialize the control parameters, including the maximum number of fitness evaluations nfes max , variation factor, crossover factor, threshold coefficient Ω, where the variation factor includes the variation factor of the exploration group and the variation factor of the development group, and the crossover factor includes the crossover factor of the exploration group and the crossover factor of the development group;

[0013] Initialize the mutation factor of the exploration group and the mutation factor of the development group, the mutation factor of the mth individual in the exploration group Obeying the Cauchy distribution, explore the cross factor of the mth individual in the group It obeys the normal distribution, as shown in the following formula:

[0014]

[0015] Among them, randc m To explore the Cauchy distribution of the mth individual in the group, randn i is the normal distribution of the mth individual in the exploration group, x is the peak position parameter of the Cauchy distribution, γ is the scale parameter of the half width at half the maximum value of the Cauchy distribution, μ is the mean of the normal distribution, σ 2 is the variance of the normal distribution;

[0016] Initialize the development group's mutation factor and the development group's mutation factor, the development group's nth individual's mutation factor and the cross factor of the nth individual in the development group As shown in the following formula:

[0017]

[0018] Among them, ∈ is the threshold coefficient, nfes is the number of current fitness evaluations, and rand is a random number between 0 and 1;

[0019] Step 3: Establish a mutation strategy adaptive selection mechanism to generate mutation vectors by adaptively selecting mutation strategies, and generate identity tags for each individual in the population. The identity tags include the control parameters and mutation strategies used in the process of generating mutation vectors.

[0020] Step 3.1: Select multiple mutation strategies and use different mutation strategies for individuals in different groups;

[0021] We select three mutation strategies: DE / rand / 1, DE / current-to-rand / 1, and DE / current-to-best / 1. We use different mutation strategies for individuals in different groups. Specifically:

[0022] Exploration Group elr The individuals in the exploration group use mutation strategies DE / rand / 1 and DE / current-to-rand / 1 to generate the mutation vector of the mth individual in the Gth generation population. To the development group eli The individuals in the development group use mutation strategies DE / current-to-rand / 1 and DE / current-to-best / 1 to generate the G-generation mutation vector of the n-th individual in the development group

[0023] Step 3.2: Establish a mutation strategy adaptive selection mechanism to adaptively select different mutation strategies and generate mutation vectors;

[0024] The adaptive selection mechanism of mutation strategy includes:

[0025] Sort the NP individuals in the population according to their fitness, select the top p individuals, and use the mutation strategy DE / current-to-best / 1 to generate the mutation vector;

[0026] The number of individuals p is selected as shown in the following formula:

[0027]

[0028] Among them, p max、p min are the maximum and minimum values ​​of the range of the selected individual number p, round(·) is the rounding function, and nfes is the number of current fitness evaluations;

[0029] For individuals from p+1 to NP in the population, according to the random number rand, the current fitness evaluation times nfes and the random parameter Select the mutation strategy. The specific method is:

[0030] If the random number rand is greater than And the current fitness evaluation times nfes is less than Determine the random number ran and random parameters If the random number rand is less than the random parameter Then use the mutation strategy DE / rand / 1 to generate the G-generation mutation vector of the m-th individual in the exploration group Otherwise, use the mutation strategy DE / current-to-rand / 1 to generate the G-generation mutation vector of the m-th individual in the exploration group Where η is the scaling factor;

[0031] If the random number rand is less than Or the current fitness evaluation times nfes is greater than Determine the random number rand and random parameters If the random number rand is less than the random parameter Then use the mutation strategy DE / current-to-best / 1 to generate the G-generation mutation vector of the n-th individual in the development group Otherwise, use the mutation strategy DE / current-to-rand / 1 to generate the G-generation mutation vector of the n-th individual in the development group

[0032] Random parameters As shown in the following formula:

[0033]

[0034] Among them, γ is the scale parameter;

[0035] Step 3.3: Generate an identity tag for each individual in the population. The identity tag stores the control parameters and mutation strategy used in the process of generating the mutation vector.

[0036] Step 4: Perform a crossover operation on each individual in the population to generate an experimental vector;

[0037] Perform a crossover operation on each individual in the population to generate an experimental vector As shown in the following formula:

[0038]

[0039] in, is the i-th individual in the G-th generation The target vector of the jth dimension, is the i-th individual in the G-th generation The mutation vector of the jth dimension, j rand is a randomly generated dimension index;

[0040] Step 5: Establish an identity tag recognition mechanism to identify the identity tag of each individual in the population and perform a selection operation to generate the next generation of population. When the maximum number of fitness evaluations is reached, the estimated values ​​of the unknown parameters of the photovoltaic model are obtained;

[0041] Step 5.1: Use the principal component analysis method to reduce the dimensionality of the experimental vectors of all individuals in the exploration group and the development group to obtain the reduced dimensionality data;

[0042] Step 5.2: Initialize the historical archives of the exploration and development groups based on the reduced-dimensional data.

[0043] The successful history archive of the initialization exploration group is:

[0044]

[0045] in, is the variation factor of the 1st...Mth individuals in the exploration group, is the crossover factor of the 1st...Mth individuals in the exploration group, where M is the total number of individuals in the exploration group;

[0046] The successful history archive of the initialization development group is:

[0047]

[0048] in, is the variation factor of the 1st...Nth individuals in the development group, is the crossover factor of the 1st...Nth individuals in the development group, where N is the total number of individuals in the development group;

[0049] Step 5.3: Select two crossover individuals from each of the exploration and development groups of the reduced-dimensionality data as two populations. Perform a Wilcoxon rank sum test on the two populations to determine the differences between the two populations generated using different strategy combinations and control parameters. Update the success history archive based on the results of the test.

[0050] Select one crossover individual from each of the exploration and development groups after dimensionality reduction as two populations. Perform a Wilcoxon rank sum test on the two populations, setting the null hypothesis as: there is no significant difference between the two populations. If the null hypothesis is rejected, add the control parameters of the two populations to the historical archives of the corresponding groups based on their identity labels, and update the historical archives of the exploration and development groups.

[0051] Step 5.4: Update the control parameters of the exploration group and the development group;

[0052] Update the variation factor of the mth individual in the exploration group and the cross factor of the mth individual in the exploration group The updated variation factor of the mth individual in the exploration group and the cross factor of the mth individual in the exploration group for:

[0053]

[0054] Among them, r m The historical archive index of the exploration group for the mth individual's variation factor;

[0055] Update the mutation factor of the nth individual in the development group and the cross factor of the nth individual in the development group The updated variation factor of the nth individual in the development group and the cross factor of the nth individual in the development group for:

[0056]

[0057] Among them, r n The development group historical archive index of the variation factor of the nth individual;

[0058] Step 5.5: Perform selection based on the generated experimental vector to generate the next generation of target vectors to achieve the maximum number of fitness evaluations nfes max Finally, the optimal individual in the generated next generation target vector is used as the estimated value of the unknown parameters of the PV model.

[0059] The beneficial effects of adopting the above-mentioned technical solution are as follows: The present invention proposes a method for estimating unknown parameters of photovoltaic models based on an improved differential evolution algorithm. Based on a unified update mechanism for control parameters, this method solves the problem of difficulty in uniformly updating parameters in an integrated environment, thereby improving the accuracy of the algorithm in estimating unknown parameters of photovoltaic models. Combined with a new parameter adaptive update scheme, the integrated mutation strategy can dynamically match appropriate control parameters throughout the search process without user intervention, allowing each mutation strategy to fully utilize its advantages. The method for estimating unknown parameters of photovoltaic models based on an improved differential evolution algorithm proposed in the present invention does not significantly increase the time complexity of the differential evolution algorithm, maintaining the simplicity of the differential evolution algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 A structural diagram of a single diode model provided in an embodiment of the present invention;

[0061] Figure 2 A flow chart of a method for estimating unknown parameters of a photovoltaic model based on an improved differential evolution algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0063] A photovoltaic model unknown parameter estimation method based on an improved differential evolution algorithm in this embodiment includes the following steps:

[0064] Step 1: Establish an output current model of the photovoltaic model and set the parameters to be estimated;

[0065] In this embodiment, a single diode model is taken as an example. The basic structure of the single diode model is as follows: Figure 1 As shown, according to Kirchhoff's current law, the output current I of the single diode model is obtained L , as shown in the following formula:

[0066] I L =I ph -I d -I sh

[0067] Among them, I ph is the photocurrent, I d is the forward current flowing through the diode, I sh is the current flowing through the parallel resistor, as shown in the following formula:

[0068]

[0069] Among them, I sdis the reverse saturation current of the diode, q=1.60217646×10 19 C is the electron charge, V L is the output voltage of the diode, R s is the resistance of the series resistor, R sh is the resistance of the parallel resistor, k=1.3806503×10 -23 J / K is the Boltzmann constant, a is the quality factor of the diode, and T is the operating temperature of the photovoltaic cell;

[0070] The output current model of the single diode model is established as shown in the following formula:

[0071]

[0072] Setting I ph , I sd 、R S 、R sh , a is the parameter to be estimated;

[0073] The flow chart of the photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm provided in this embodiment is as follows: Figure 2 As shown;

[0074] Step 2: Initialize the individuals and control parameters in the population based on the parameters to be estimated;

[0075] Step 2.1: Initialize the individuals in the population within the range of the parameter to be estimated. The i-th individual in the initial population As shown in the following formula:

[0076]

[0077] Among them, NP is the population size, D is the i-th individual in the initial population Dimensions, is the i-th individual in the initial population The lower bound of the value of the j-th dimension, is the i-th individual in the initial population The upper bound of the value of the j-th dimension, rand is a random number between 0 and 1;

[0078] Step 2.2: Divide the individuals in the population into exploration groups elr and development group eli ;

[0079] Step 2.3, initialize the control parameters, including the maximum number of fitness evaluations nfes max, variation factor, crossover factor and threshold coefficient Ω, where the variation factor includes the variation factor of the exploration group and the variation factor of the development group, and the crossover factor includes the crossover factor of the exploration group and the crossover factor of the development group;

[0080] Initialize the mutation factor of the exploration group and the mutation factor of the development group, the mutation factor of the mth individual in the exploration group Obeying the Cauchy distribution, explore the cross factor of the mth individual in the group It obeys the normal distribution, as shown in the following formula:

[0081]

[0082] Among them, randc m To explore the Cauchy distribution of the mth individual in the group, randn i is the normal distribution of the mth individual in the exploration group, x is the peak position parameter of the Cauchy distribution, γ is the scale parameter of the half width at half the maximum value of the Cauchy distribution, μ is the mean of the normal distribution, σ 2 is the variance of the normal distribution;

[0083] In this embodiment, x=0.5, γ=0.1, μ=0.7, σ 2 =0.1.

[0084] Initialize the development group's mutation factor and the development group's mutation factor, the development group's nth individual's mutation factor and the cross factor of the nth individual in the development group As shown in the following formula:

[0085]

[0086] Among them, ∈ is the threshold coefficient, nfes is the number of current fitness evaluations, and rand is a random number between 0 and 1;

[0087] Step 3: Establish a mutation strategy adaptive selection mechanism to generate mutation vectors by adaptively selecting mutation strategies, and generate identity tags for each individual in the population. The identity tags include the control parameters and mutation strategies used in the process of generating mutation vectors.

[0088] Step 3.1: Select multiple mutation strategies and use different mutation strategies for individuals in different groups;

[0089] We select three mutation strategies: DE / rand / 1, DE / current-to-rand / 1, and DE / current-to-best / 1. We use different mutation strategies for individuals in different groups. Specifically:

[0090] Exploration Group elrThe individuals in the exploration group use mutation strategies DE / rand / 1 and DE / current-to-rand / 1 to generate the mutation vector of the mth individual in the Gth generation population. To the development group eli The individuals in the development group use mutation strategies DE / current-to-rand / 1 and DE / current-to-best / 1 to generate the G-generation mutation vector of the n-th individual in the development group

[0091] Generate the mth individual in the Gth generation population of the exploration group according to the mutation strategy DE / rand / 1 The mutation vector As shown in the following formula:

[0092]

[0093] Among them, r1, r2, r3 are all randomly selected individual numbers, r1≠r2≠r3≠m, They are the r1, r2, and r3 individuals of the G generation respectively;

[0094] Generate the mth individual of the Gth generation population of the exploration group according to the mutation strategy DE / current-to-rand / 1 The mutation vector As shown in the following formula:

[0095]

[0096] Generate the nth individual in the Gth generation population of the development group according to the mutation strategy DE / current-to-rand / 1 The mutation vector As shown in the following formula:

[0097]

[0098] Generate the nth individual in the Gth generation population of the development group according to the mutation strategy DE / current-to-best / 1 The mutation vector As shown in the following formula:

[0099]

[0100] in, is the best individual of the G generation;

[0101] Step 3.2: Establish a mutation strategy adaptive selection mechanism to adaptively select different mutation strategies and generate mutation vectors;

[0102] The adaptive selection mechanism of mutation strategy includes:

[0103] Sort the NP individuals in the population according to their fitness, select the top p individuals, and use the mutation strategy DE / current-to-best / 1 to generate the mutation vector;

[0104] The number of individuals p is selected as shown in the following formula:

[0105]

[0106] Among them, p max 、p min are the maximum and minimum values ​​of the range of individual number p, respectively, and round(·) is the rounding function;

[0107] For individuals from p+1 to NP in the population, according to the random number rand, the current fitness evaluation times nfes and the random parameter Select the mutation strategy. The specific method is:

[0108] If the random number rand is greater than And the current fitness evaluation times nfes is less than Determine the random number rand and random parameters If the random number rand is less than the random parameter Then use the mutation strategy DE / rand / 1 to generate the G-generation mutation vector of the m-th individual in the exploration group Otherwise, use the mutation strategy DE / current-to-rand / 1 to generate the G-generation mutation vector of the m-th individual in the exploration group Where η is the scaling factor;

[0109] If the random number rand is less than Or the current fitness evaluation times nfes is greater than Determine the random number rand and random parameters If the random number rand is less than the random parameter Then use the mutation strategy DE / current-to-best / 1 to generate the G-generation mutation vector of the n-th individual in the development group Otherwise, use the mutation strategy DE / current-to-rand / 1 to generate the G-generation mutation vector of the n-th individual in the development group

[0110] Random parameters As shown in the following formula:

[0111]

[0112] Among them, γ is the scale parameter;

[0113] In this embodiment, γ is set to 0.0012, p max =0.1, p min =0.01, η=0.07;

[0114] Step 3.3: Generate an identity tag for each individual in the population. The identity tag stores the control parameters and mutation strategy used in the process of generating the mutation vector.

[0115] Step 4: Perform a crossover operation on each individual in the population to generate an experimental vector;

[0116] Perform a crossover operation on each individual in the population to generate an experimental vector As shown in the following formula:

[0117]

[0118] in, is the i-th individual in the G-th generation The target vector of the jth dimension, is the i-th individual in the G-th generation The mutation vector of the jth dimension, j rand is a randomly generated dimension index;

[0119] Step 5: Establish an identity tag recognition mechanism to identify the identity tag of each individual in the population and perform a selection operation to generate the next generation of population. When the maximum number of fitness evaluations is reached, the estimated values ​​of the unknown parameters of the photovoltaic model are obtained;

[0120] Step 5.1: Use the principal component analysis method to reduce the dimensionality of the experimental vectors of all individuals in the exploration group and the development group to obtain the reduced dimensionality data;

[0121] Step 5.1.1. Centralize the experimental vectors of all individuals in the exploration group and the development group to obtain the original experimental vector U G , as shown in the following formula:

[0122]

[0123] in, They are the 1st, 2nd, ..., nth in the Gth generation exploration group. elr The experimental vector of individuals, They are the 1st, 2nd, ..., nth in the G generation development group. eli The experimental vector of individuals, n elr and n eli are the number of individuals in the exploration group and the exploitation group, respectively;

[0124] Step 5.1.2: Calculate the original experimental vector U G The mean As shown in the following formula:

[0125]

[0126] Step 5.1.3: original experimental vector U G The mean Build the center and get the matrix after the center is built

[0127]

[0128] Where I is the identity matrix;

[0129] Step 5.1.4: Matrix after the calculation center is built The covariance matrix Σ is as follows:

[0130]

[0131] Step 5.1.5: Perform eigenvalue decomposition on the covariance matrix Σ, as shown in the following formula:

[0132] Σ=WΛM T

[0133] Among them, Λ=diag(λ1,λ2,…,λ D ) is the eigenvalue, W=[w1,w2,…,w D ] is the eigenvector corresponding to the eigenvalue, D is the number of unknown parameters in the photovoltaic model;

[0134] Step 5.1.6: Select the matrix after the center is built With the first dimension feature vector w1, we get the reduced dimension data Z G :

[0135]

[0136] Step 5.2: Initialize the historical archives of the exploration and development groups based on the reduced-dimensional data.

[0137] Initialize the exploration group history archive as:

[0138]

[0139] in, is the variation factor of the 1st...Mth individuals in the exploration group, is the crossover factor of the 1st...Mth individuals in the exploration group, where M is the total number of individuals in the exploration group;

[0140] Initialize the development group history archive to:

[0141]

[0142] in, is the variation factor of the 1st...Nth individuals in the development group, is the crossover factor of the 1st...Nth individuals in the development group, where N is the total number of individuals in the development group;

[0143] Step 5.3: Select one crossover individual from each of the exploration and development groups after dimensionality reduction as two populations. Perform a Wilcoxon rank sum test on the two populations to determine the differences between the two populations generated using different mutation strategies and control parameters. Update the historical archives of the exploration and development groups based on the results of the test.

[0144] From the data Z after dimensionality reduction G Select one individual from each of the exploration group and development group as two populations, perform the Wilcoxon rank sum test on the two populations, and set the null hypothesis as: there is no significant difference between the two populations. If the null hypothesis is rejected, then according to the identity labels of the two populations, add the control parameters of the two populations to the historical archives of the corresponding groups and update the historical archives of the exploration group and development group. The method for updating the historical archive of the exploration group is shown in the following formula:

[0145]

[0146] in, and are the variation factor and crossover factor of the kth individual in the historical archive of the exploration group, fd k is the experimental vector of the kth individual in the exploration group history archive Fitness and the kth individual in the successful archive of the exploration group Fitness Absolute difference, ω k To update the weights, is the variation factor of the kth individual in the historical archive of the G+1th generation exploration group, is the crossover factor of the kth individual in the historical archive of the G+1th generation exploration group, is the variation factor of the kth individual in the historical archive of the Gth generation exploration group, is the crossover factor of the kth individual in the historical archive of the Gth generation exploration group;

[0147] The method for updating the development group's historical archive is the same as the method for updating the exploration group's historical archive;

[0148] In this embodiment, the initial value of k is set to 1;

[0149] Step 5.4: Update the control parameters of the exploration group and the development group;

[0150] Update the variation factor of the mth individual in the exploration group and the cross factor of the mth individual in the exploration group The updated variation factor of the mth individual in the exploration group and the cross factor of the mth individual in the exploration group for:

[0151]

[0152] Among them, r m The historical archive index of the exploration group for the mth individual's variation factor;

[0153] Update the mutation factor of the nth individual in the development group and the cross factor of the nth individual in the development group The updated variation factor of the nth individual in the development group and the cross factor of the nth individual in the development group for:

[0154]

[0155] Among them, r n The development group historical archive index of the variation factor of the nth individual;

[0156] Step 5.5: Perform selection based on the generated experimental vector to generate the next generation of target vectors to achieve the maximum number of fitness evaluations nfes max Finally, the optimal individual in the generated next generation target vector is used as the estimated value of the unknown parameters of the PV model;

[0157] Perform selection operations based on the generated experimental vectors to generate the target vector for the G+1 generation As shown in the following formula:

[0158]

[0159] Reach the maximum number of fitness evaluations nfes max Finally, the optimal individual in the generated next generation target vector is used as the estimated value of the unknown parameters of the PV model.

[0160] To verify the effectiveness of the method for estimating unknown photovoltaic model parameters provided in this example, simulations of the unknown photovoltaic model parameters were performed on a desktop PC with an Intel i5-13400 CPU @ 2.50 GHz and 16 GB of memory. Matlab R2024a was used. The maximum number of fitness evaluations, nfes_max, was set to 50,000, and each algorithm was independently run 30 times.

[0161] To fully evaluate the performance of SEDE-UP, we selected other powerful heuristic algorithms and their variants for comparative experiments. These include two recently proposed and highly competitive DE variants: DPDE and SEDE; four highly representative DE variants: SHADE, LSHADE, JADE, and RLDE; and five advanced metaheuristic algorithms: WDO, IJAYA, MLBSA, GWO, and PGJAYA. The parameters of each algorithm for the comparative experiments are shown in Table 1.

[0162] Table 1 Parameters of each algorithm in the comparative experiment

[0163]

[0164] In order to further analyze the performance of SEDE-UP and the differences with other algorithms, the experimental data were statistically analyzed, as shown in Tables 2 and 3.

[0165] Table 2 Statistical comparison results of all algorithms on SDM, DDM and TDM

[0166]

[0167]

[0168] Table 3 Statistical comparison results of all algorithms on Photowatt-PWP201, STP6-120 / 36 and STM6-40 / 36

[0169]

[0170]

[0171] Tables 2 and 3 report the worst RMSE (Max), best RMSE (Min), mean RMSE (Mean), and standard deviation (Std) values ​​for the 12 algorithms across 30 independent runs. To test for differences between algorithms, a Wilcoxon rank sum test was used with a significance level of α = 0.005. The symbols >, ≈, and < indicate that the target algorithm performs better, similar, and worse, respectively, than the SEDE-UP algorithm.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A photovoltaic model unknown parameter estimation method based on an improved differential evolution algorithm, characterized by: The following steps are involved: Step 1: Establish an output current model of the photovoltaic model and set the parameters to be estimated; Step 2: Initialize the individuals and control parameters in the population based on the parameters to be estimated; Step 3: Establish a mutation strategy adaptive selection mechanism to generate mutation vectors by adaptively selecting mutation strategies, and generate identity tags for each individual in the population. The identity tags include the control parameters and mutation strategies used in the process of generating mutation vectors. Step 4: Perform a crossover operation on each individual in the population to generate an experimental vector; Step 5: Establish an identity tag recognition mechanism to identify the identity tag of each individual in the population and perform a selection operation to generate the next generation of population. When the maximum number of fitness evaluations is reached, the estimated values ​​of the unknown parameters of the photovoltaic model are obtained.

2. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 1 is characterized by: The step 2 includes: Step 2.1, initialize the individuals in the population within the range of the parameter to be estimated; Step 2.2: Divide the individuals in the population into exploration groups elr and development group eli ; Step 2.3, initialize the control parameters, including the maximum number of fitness evaluations nfes max , variation factor, crossover factor, threshold coefficient Ω, where the variation factor includes the variation factor of the exploration group and the variation factor of the development group, and the crossover factor includes the crossover factor of the exploration group and the crossover factor of the development group.

3. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 2 is characterized by: The specific method of step 2.3 is: Initialize the mutation factor of the exploration group and the mutation factor of the development group, the mutation factor of the mth individual in the exploration group Obeying the Cauchy distribution, explore the cross factor of the mth individual in the group It obeys the normal distribution, as shown in the following formula: Among them, randc m To explore the Cauchy distribution of the mth individual in the group, randn i is the normal distribution of the mth individual in the exploration group, x is the peak position parameter of the Cauchy distribution, γ is the scale parameter of the half width at half the maximum value of the Cauchy distribution, μ is the mean of the normal distribution, σ 2 is the variance of the normal distribution; Initialize the development group's mutation factor and the development group's mutation factor, the development group's nth individual's mutation factor and the cross factor of the nth individual in the development group As shown in the following formula: Among them, ∈ is the threshold coefficient, nfes is the number of current fitness evaluations, and rand is a random number between 0 and 1.

4. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 3 is characterized by: The step 3 includes: Step 3.1: Select multiple mutation strategies and use different mutation strategies for individuals in different groups; Step 3.2: Establish a mutation strategy adaptive selection mechanism to adaptively select different mutation strategies and generate mutation vectors; Step 3.3: Generate an identity tag for each individual in the population. The identity tag stores the control parameters and mutation strategy used in the process of generating the mutation vector.

5. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 4 is characterized by: The specific method of step 3.1 is: We select three mutation strategies: DE / rand / 1, DE / current-to-rand / 1, and DE / current-to-best / 1. We use different mutation strategies for individuals in different groups. Specifically: Exploration Group elr The individuals in the exploration group use mutation strategies DE / rand / 1 and DE / current-to-rand / 1 to generate the mutation vector of the mth individual in the Gth generation population. To the development group eli The individuals in the development group use mutation strategies DE / current-to-rand / 1 and DE / current-to-best / 1 to generate the G-generation mutation vector of the n-th individual in the development group 6. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 5, characterized in that: The adaptive selection mechanism of the mutation strategy described in step 3.2 includes: Sort the NP individuals in the population according to their fitness, select the top p individuals, and use the mutation strategy DE / current-to-best / 1 to generate the mutation vector; The number of individuals p is selected as shown in the following formula: Among them, p max 、p min are the maximum and minimum values ​​of the range of the selected individual number p, round(·) is the rounding function, and nfes is the number of current fitness evaluations; For individuals from p+1 to NP in the population, according to the random number rand, the current fitness evaluation times nfes and the random parameter Select the mutation strategy. The specific method is: If the random number rand is greater than And the current fitness evaluation times nfes is less than Determine the random number rand and random parameters If the random number rand is less than the random parameter Then use the mutation strategy DE / rand / 1 to generate the G-generation mutation vector of the m-th individual in the exploration group Otherwise, use the mutation strategy DE / current-to-rand / 1 to generate the G-generation mutation vector of the m-th individual in the exploration group Where η is the scaling factor; If the random number rand is less than Or the current fitness evaluation times nfes is greater than Determine the random number rand and random parameters If the random number rand is less than the random parameter Then use the mutation strategy DE / current-to-best / 1 to generate the G-generation mutation vector of the n-th individual in the development group Otherwise, use the mutation strategy DE / current-to-rand / 1 to generate the G-generation mutation vector of the n-th individual in the development group Random parameters As shown in the following formula: Among them, γ is the scale parameter.

7. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 6, characterized in that: The specific method of step 4 is: Perform a crossover operation on each individual in the population to generate an experimental vector As shown in the following formula: in, is the i-th individual in the G-th generation The target vector of the jth dimension, is the i-th individual in the G-th generation The mutation vector of the jth dimension, j rand A randomly generated dimension index.

8. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 7, characterized in that: The step 5 comprises: Step 5.1: Use the principal component analysis method to reduce the dimensionality of the experimental vectors of all individuals in the exploration group and the development group to obtain the reduced dimensionality data; Step 5.2: Initialize the historical archives of the exploration and development groups based on the reduced-dimensional data. The successful history archive of the initialization exploration group is: in, is the variation factor of the 1st...Mth individuals in the exploration group, is the crossover factor of the 1st...Mth individuals in the exploration group, where M is the total number of individuals in the exploration group; The successful history archive of the initialization development group is: in, is the variation factor of the 1st...Nth individuals in the development group, is the crossover factor of the 1st...Nth individuals in the development group, where N is the total number of individuals in the development group; Step 5.3: Select two crossover individuals from each of the exploration and development groups of the reduced-dimensionality data as two populations. Perform a Wilcoxon rank sum test on the two populations to determine the differences between the two populations generated using different strategy combinations and control parameters. Update the success history archive based on the results of the test. Step 5.4: Update the control parameters of the exploration group and the development group; Step 5.5: Perform selection based on the generated experimental vector to generate the next generation of target vectors to achieve the maximum number of fitness evaluations nfes max Finally, the optimal individual in the generated next generation target vector is used as the estimated value of the unknown parameters of the PV model.

9. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 8, characterized in that: The specific method of step 5.3 is: Select one crossed individual from each of the exploration group and development group of the dimensionality reduced data as two populations, perform the Wilcoxon rank sum test on the two populations, and set the null hypothesis as: there is no significant difference between the two populations. If the null hypothesis is rejected, then according to the identity labels of the two populations, add the control parameters of the two populations to the historical archives of the corresponding groups and update the historical archives of the exploration group and development group.

10. The photovoltaic model unknown parameter estimation method based on the improved differential evolution algorithm according to claim 9, characterized in that: The specific method of step 5.4 is: Update the variation factor of the mth individual in the exploration group and the cross factor of the mth individual in the exploration group The updated variation factor of the mth individual in the exploration group and the cross factor of the mth individual in the exploration group for: Among them, r m The historical archive index of the exploration group for the mth individual's variation factor; Update the mutation factor of the nth individual in the development group and the cross factor of the nth individual in the development group The updated variation factor of the nth individual in the development group and the cross factor of the nth individual in the development group for: Among them, r n The development group historical archive index for the variate of the nth individual.

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