MPPT (Maximum Power Point Tracking) method of laser wireless energy transmission system based on improved starfish optimization algorithm

Abstract

The invention provides a laser wireless energy transmission system MPPT (Maximum Power Point Tracking) method based on an improved starfish optimization algorithm, which is characterized in that the improved starfish intelligent optimization algorithm is given based on an implicit laser wireless energy transmission multivariable coupling action mechanism and expanded data, and a maximum power value point in the system is searched. Firstly, a starfish algorithm implementation step is established, then a multi-stage heuristic intelligent optimization algorithm framework of initialization, exploration and development is established, and starfish energy is dynamically updated by using a predation and regeneration mechanism. Secondly, introducing a Cauchy distribution function to expand a search range, improving adaptability by a random contraction exponential function, and improving diversity of an initial population by spatial pyramid matching to improve an original starfish optimization algorithm; according to the method, the maximum power point of the laser wireless energy transmission system can be obtained through an implicit multivariable coupling mechanism.

Description

TECHNICAL FIELD

[0001] The application relates to a laser wireless energy transmission system MPPT method based on an improved starfish optimization algorithm and belongs to the field of laser wireless energy transmission. BACKGROUND

[0002] As a new long-distance energy transmission method, laser wireless energy transmission technology has shown broad application prospects in the fields of unmanned aerial vehicles, space exploration and remote sensor power supply in recent years. The technology transmits energy from the transmitting end to the photovoltaic cell array at the receiving end through a laser beam, overcoming the distance limitation of traditional wire transmission and the efficiency decay problem of electromagnetic coupling technology. However, the output characteristics of the laser energy transmission system are affected by factors such as light intensity, temperature change and load fluctuation, showing complex multi-peak nonlinear characteristics, which leads to the fact that the traditional maximum power point tracking method is easy to fall into local optimization, significantly reducing the energy conversion efficiency of the system.

[0003] To solve the MPPT optimization problem under the condition of multiple peaks, intelligent optimization algorithms are introduced into this field. In recent years, scholars have improved different intelligent optimization algorithms by fusing methods such as chaotic initialization, adaptive step size and hybrid strategy, which has significantly improved the optimization performance of the algorithm in complex environments. Applying the improved starfish optimization algorithm to the maximum power point tracking problem of the laser wireless energy transmission system is expected to overcome the limitations of traditional perturbation and observation method, conduct increment method and other methods under dynamic light conditions, and provide a new solution for the efficient and stable operation of laser wireless energy transmission. SUMMARY

[0004] In view of the above technical deficiencies, the purpose of the present application is to provide a laser wireless energy transmission system MPPT method based on an improved starfish optimization algorithm, so that the laser wireless energy transmission system can quickly track to the maximum power point, and to a certain extent, improve the conversion rate of laser energy.

[0005] The present application is implemented according to the following technical solutions:

[0006] First aspect: the present application provides a laser wireless energy transmission system MPPT method based on an improved starfish optimization algorithm, which specifically comprises the following steps:

[0007] Initialization stage. Input algorithm parameters and problem information, then randomly generate a population within the design variable boundary, and evaluate the fitness value. After the initialization stage is completed, the algorithm enters the main loop;

[0008] In the main loop, the running probability of the exploration stage and the development stage is the same, which depends on the random number between (0, 1) in the algorithm and the comparison between the algorithm parameters G p and 0.5, where G p is 0.5;

[0009] Exploration phase. In this phase, a hybrid search mode is employed, both five-dimensional and one-dimensional search modes are used simultaneously. Two different update strategies are designed for different dimensions. After obtaining the updated position, the boundary of the design variable is checked;

[0010] Development phase. The predation and regeneration phases are established. The parallel bidirectional search mode is used, and the distance between the global solution and other sea stars is calculated. Then the algorithm updates the position of each sea star using the predation behavior. After that, when i = N, the regeneration phase is entered, and the position is updated again;

[0011] Termination phase. After the above phase is finished, the fitness value will be evaluated. According to the obtained fitness value, the current best solution of all sea stars is obtained iteratively, and then the above phase is repeated to update the position of the sea star, and the best solution is updated at the same time in each iteration. When the maximum iteration number criterion is met, the main loop is stopped and the final global solution is output.

[0012] In a second aspect, the present application provides a laser wireless energy transmission system MPPT method based on an improved sea star optimization algorithm, and the specific method implementation principle comprises:

[0013] Algorithm initialization phase:

[0014] In the initialization phase of the algorithm, the position of the sea star is randomly generated between the boundary of the design variable, which can be represented as a matrix:

[0015]

[0016] Wherein, X is a matrix that saves the position of the sea star with the size of N×D, N is the population size, and D is the dimension of the design variable. In the initialization phase, the position of each sea star is evaluated as:

[0017] X ij =l j +r(u j -l j ),i=1,2,...,N,j=1,2,...,D

[0018] Wherein, X ij represents the jth dimension position of the ith sea star, r represents a random number between (0, 1), u j and l j are the upper and lower bounds of the jth dimension design variable respectively. After generating the initialized position matrix, the fitness value of all sea stars is obtained by evaluating from the objective function, which is stored in the form of a vector:

[0019]

[0020] where F is a matrix of size N x 1 that stores and updates the obtained fitness values.

[0021] Exploration phase of the algorithm:

[0022] The exploration phase simulates the exploration behavior of a sea star, simulating the search ability of the five arms of the sea star, in which the eyes are embedded at the end of the arms. In the exploration phase of the algorithm, a new search mode is given, which combines the five-dimensional search mode of D>5 and the one-dimensional search mode of D≤5 for different optimization problems. The dimension threshold is determined by the five arms (or eyes) of the sea star.

[0023] If the dimension of the optimization problem is greater than 5 (i.e. D>5), the search space of the task is large, so the sea star needs to move all the arms to explore the surrounding environment. In addition, the arms of the sea star also need to obtain the optimal position between the search agents guiding the movement. Therefore, the mathematical model of this phase is established:

[0024]

[0025] where, and represent the obtained position and the current position of the sea star, respectively. represents the current optimal position with dimension p, and p is a randomly selected five-dimensional dimension in dimension D. α1 and θ are calculated as follows:

[0026]

[0027] where T represents the current iteration process, T max represents the maximum number of iterations. The sine and cosine terms represent the left or right movement of the arms of the sea star, approaching the food with the same probability. In the exploration phase, α1 is randomly generated for each candidate and the updated position in the iteration, while θ changes with the iteration, θ∈[0, π / 2], the two parameters are used to measure the influence of the distance between the optimal position in the selected updated dimension and the current position. For the case of D>5 optimization problem, the five-dimensional search mode in the formula is used to update the position information of the five dimensions, to ensure the search ability of the algorithm and improve the search efficiency. After that, when the updated position exceeds the boundary of the design variable, the arm will tend to stay at the previous position rather than move to the updated position. The above process can be described as:

[0028]

[0029] where p represents the updated dimension, l b,p and u b,p represent the boundary of the design variable, respectively.

[0030] If the dimension of the optimization problem is not greater than 5 (D≤5), the exploration phase will only use the single-dimensional search pattern to update the position. In this case, the sea star only has one arm moving, searching for the food source using the position information of other sea stars. The updated position can be determined as:

[0031]

[0032] where, and are the p-dimensional positions of two randomly selected sea stars, Ai and A2 are two random numbers between (-1, 1), and p is a randomly selected number in D-dimensional space. t is the energy of the sea star, and the calculation formula is:

[0033]

[0034] where θ is calculated by the formula. Similar to the above update rule, if the position obtained by the sea star exceeds the boundary, the sea star will tend to stay at the previous position rather than move to the updated position.

[0035] Algorithm development phase:

[0036] The algorithm considers the predation and update behavior in the development phase to search for global solutions, so two update strategies are designed in this phase. To model the predation phase of the sea star, the algorithm uses a parallel bidirectional search strategy that requires the use of information from other sea stars and the current best position of the population. First, calculate the five distances between the best position and other sea stars, then randomly select two distances to confirm the update of each sea star's position using the parallel bidirectional search strategy. The distance can be calculated as:

[0037]

[0038] where r1 and r2 are random numbers between (0, 1), and d m1 and d m2 are randomly selected in d m . The predation behavior of the sea star is shown in the figure. Based on the parallel bidirectional search strategy, in the same iteration, the candidate vector of the sea star better guides the solution to move, while the other candidate vector moves backward. Therefore, the candidate has the same ability to overcome local optima.

[0039] In addition, during the predation process, due to its slow movement, the sea star is easily attacked by other predators. If there is a predator capturing the sea star, the sea star may be cut off and lose an arm to escape capture. Therefore, the regeneration phase of the algorithm is only implemented in the last sea star in the population i=N. Since the regeneration phase takes several months, during which the sea star moves very slowly. Therefore, the update rule is modeled in the regeneration phase, and the position is updated by:

[0040]

[0041] where T is the current iteration process, T max represents the maximum number of iterations, N is the population size. If the obtained position information is outside the boundary of the design variable, the position information can be set as:

[0042]

[0043] In a third aspect, the application provides a laser wireless energy transmission system MPPT method based on an improved starfish optimization algorithm, and the specific improvements include:

[0044] Spatial pyramid matching (SPM) chaotic mapping:

[0045] This method improves the uniformity of population distribution in space, thereby making up for the shortcomings of random initialization. The mathematical expression is as follows:

[0046]

[0047] Improved energy linearly decreasing regulation mechanism:

[0048] By introducing a random contraction exponential function in the exploration process, the robustness and adaptability of the algorithm are enhanced, and the energy expression is:

[0049]

[0050] Cauchy distribution function:

[0051] The Cauchy distribution function is used to improve the diversity level of the population, expand the search range, and enhance the global search ability of the algorithm. Applying the standard Cauchy distribution function to the solution of the global optimal solution can effectively improve the optimization performance of the algorithm in the MPPT system. The global optimal solution based on the standard Cauchy distribution function is represented as:

[0052] BRIEF DESCRIPTION OF DRAWINGS

[0053] The accompanying drawings, which are part of this application, serve to further understand the application, and the illustrative embodiments of the application and their descriptions are used to explain the application, but do not constitute an improper limitation on the application. Obviously, the drawings described below are only some embodiments, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0054] In the drawings:

[0055] Figure 1 is a system flowchart of the application;

[0056] Figure 2 is a schematic diagram of the algorithm exploration phase of the present application;

[0057] Figure 3 is a schematic diagram of the algorithm predation behavior of the present application.

[0058] Figure 4 is a schematic diagram of the algorithm regeneration behavior of the present application;

[0059] Figure 5 is a schematic diagram of the algorithm pseudocode flow of the present application.

[0060] It should be noted that these drawings and written descriptions are not intended to limit the scope of the inventive concept in any way, but to illustrate the inventive concept to those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments will be described clearly and completely below in conjunction with the drawings of the embodiments of the present application. The following embodiments are used to illustrate the present application, but not to limit the scope of the present application. The present application will be further described below in conjunction with the drawings.

[0062] As shown in Figure 1 , the present disclosure provides an improved star optimization algorithm-based MPPT method for a laser wireless energy transmission system, comprising the following steps:

[0063] Initialization phase. Input algorithm parameters and problem information, then randomly generate a population within the design variable boundary, and evaluate the fitness value. After the initialization phase is completed, the algorithm enters the main loop;

[0064] In the main loop, the running probability of the exploration phase and the development phase is the same, which depends on the comparison between a random number between (0, 1) and an algorithm parameter G p , wherein G p is 0.5;

[0065] Exploration phase. In this phase, a hybrid search mode is used, and five-dimensional and one-dimensional search modes are used at the same time. Two different update strategies are designed for different dimensions. After the updated position is obtained, the boundary of the design variable is checked;

[0066] Development phase. The predation and regeneration phases are established. A parallel bidirectional search mode is used, and the distance between the global solution and other starfish is calculated. Then the algorithm updates the position of each starfish using the predation behavior. After that, when i = N, enter the regeneration phase, and the position is updated again;

[0067] Termination phase. After the above phase, the fitness values will be evaluated. According to the obtained fitness values, the current best solution of all starfish is iteratively obtained, and then the above phase is repeated to update the positions of starfish, and the best solution is updated at the same time in each iteration. When the maximum iteration number criterion is met, the main loop is stopped and the final global solution is output.

[0068] Further, a laser wireless energy transmission system MPPT method embodiment based on an improved starfish optimization algorithm is implemented as follows:

[0069] Algorithm initialization phase:

[0070] In the initialization phase of the algorithm, the positions of starfish are randomly generated between the boundaries of design variables, which can be represented as a matrix:

[0071]

[0072] Where X is a matrix that saves the positions of starfish with a size of NxD, N is the population size, and D is the dimension of design variables. In the initialization phase, the position of each starfish is evaluated as:

[0073] X ij =l j +r(u j -l j ),i=1,2,...,N,j=1,2,...,D

[0074] Where X ij represents the jth dimension position of the ith starfish, r represents a random number between (0, 1), u j and l j are the upper and lower bounds of the jth dimension design variable, respectively. After generating the initialized position matrix, the fitness values of all starfish are obtained by evaluating from the objective function, which is stored in the form of a vector:

[0075]

[0076] Where F is a matrix that stores and updates the obtained fitness values, with a size of Nxl.

[0077] Algorithm exploration phase:

[0078] In a specific embodiment, Figure 2 The implementation principle of the algorithm exploration phase is given. The exploration phase simulates the exploration behavior of starfish, simulating the search ability of the five arms of starfish, with the eyes embedded at the end of the arm. In the exploration phase of the algorithm, a new search mode is given, which combines the five-dimensional search mode of D>5 and the one-dimensional search mode of D≤5 for different optimization problems. The dimension threshold is determined by the five arms (or eyes) of starfish.

[0079] If the dimension of the optimization problem is greater than 5 (i.e., D > 5), the search space of this task is large, so the sea star needs to move all its arms to explore the surrounding environment. In addition, the arms of the sea star also need to obtain the optimal position between the search agents guiding the movement. Therefore, the mathematical model of this stage is established:

[0080]

[0081] where, and represent the obtained position and the current position of the sea star, respectively. represents the current optimal position with dimension p, and p is a randomly selected five-dimensional dimension in D. and are calculated as follows:

[0082]

[0083] where, T represents the current iteration process, and T max represents the maximum number of iterations. The sine and cosine terms represent the left or right movement of the arms of the sea star, approaching the food with the same probability. In the exploration stage, each candidate generates a random while the iteration updates the position, and changes with the iteration, and the two parameters are used to measure the influence of the distance between the optimal position and the current position in the selected update dimension. For the case of optimization problem D > 5, the five-dimensional search mode in the formula is used to update the position information of five dimensions to ensure the search ability of the algorithm and improve the search efficiency. After that, when the updated position exceeds the boundary of the design variable, the arm will tend to stay at the previous position rather than move to the updated position. The above process can be described as:

[0084]

[0085] where, p represents the updated dimension, and l b,p and u b,p represent the boundaries of the design variable, respectively.

[0086] If the dimension of the optimization problem is not greater than 5 (D ≤ 5), the exploration stage will only use a single-dimensional search mode to update the position. In this case, the sea star only has one arm moving, using the position information of other sea stars to search for food sources. The updated position can be determined as:

[0087]

[0088] where, and are the p-dimensional positions of two randomly selected sea stars, and and are two random numbers between (-1, 1), and p is a randomly selected number in D. E tis the energy of the starfish, and the formula is:

[0089]

[0090] where θ is calculated by the formula. Similar to the update rule described above, if the position acquired by the starfish is outside the boundary, the starfish will tend to stay at the previous position rather than move to the updated position.

[0091] Algorithm development phase:

[0092] The algorithm considers predation and update behavior to search for global solutions in the development phase, so two update strategies are designed in this phase. To model the predation phase of the starfish, the algorithm uses a parallel bidirectional search strategy that requires the use of information from other starfish and the current best position of the population. First, calculate the five distances between the best position and other starfish, then randomly select two distances to confirm the update of each starfish's position using the parallel bidirectional search strategy. The distance can be calculated as:

[0093]

[0094] where r1 and r2 are random numbers between 0 and 1, d m1 and d m2 are randomly selected in d m . In a specific embodiment, Figure 3 The implementation principle of the algorithm exploration phase is given. Based on the parallel bidirectional search strategy, in the same iteration, the candidate vectors of the starfish better guide the movement of the solution, while the other candidate vectors move backward. Therefore, the candidates have the same ability to overcome local optima.

[0095] In addition, during the predation process, due to its slow movement, the starfish is easily attacked by other predators. If there is a predator that captures the starfish, the starfish may be cut off and lose an arm to escape capture. In a specific embodiment, Figure 4 The implementation principle of the algorithm exploration phase is given. Therefore, the regeneration phase of the algorithm is only implemented in the last starfish in the population i = N. Since the regeneration phase takes several months, during which the starfish moves very slowly. Therefore, the update rule is modeled in the regeneration phase, and the position is updated by:

[0096]

[0097] where T is the current iteration process, T max represents the maximum number of iterations, and N is the population size. If the acquired position information is outside the boundary of the design variable, the position information can be set to:

[0098]

[0099] In one specific embodiment, a spatial pyramid matching (SPM) chaotic mapping is used instead of random initialization. This method improves the uniformity of population distribution in space, thereby compensating for the shortcomings of random initialization. Its mathematical expression is as follows:

[0100]

[0101] In one specific embodiment, an improved linearly decreasing energy adjustment mechanism is presented. By introducing a stochastic shrinkage exponential function during the exploration process, the robustness and adaptability of the algorithm are enhanced. Its energy expression is as follows:

[0102]

[0103] In one specific embodiment, the Cauchy distribution function is introduced to improve the diversity level of the population, expand the search range, and enhance the global search capability of the algorithm.

[0104] By applying the standard Cauchy distribution function to the solution of the global optimum, the optimization performance of the algorithm in the MPPT system can be effectively improved. The solution of the global optimum based on the standard Cauchy distribution function is expressed as:

[0105]

[0106] Numerous specific details are set forth in the specification provided herein. However, it will be understood that the implementation of this invention...

[0107] Examples can be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0108] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features found in other embodiments but not others, combinations of features from different embodiments are also within the scope of protection of this invention and form different embodiments. For example, in the embodiments described above, those skilled in the art can use them in combination based on known technical solutions and the technical problems to be solved by this application.

[0109] The above merely describes the preferred embodiments of the present application, and is not intended to limit the present application in any form. Although the present application has been disclosed with the preferred embodiments as above, it is not intended to limit the present application, and any skilled person in the art can make some changes or modifications to the above-mentioned technical content with the above-mentioned prompt without departing from the technical solution of the present application, and any simple modification, equivalent change and modification of the above-mentioned embodiments made according to the technical essence of the present application without departing from the technical solution of the present application still belong to the scope of the present application.

Claims

1. A method for MPPT (Multi-Level Phototransfer) in a laser wireless power transfer system based on an improved starfish optimization algorithm, characterized in that, Includes the following steps: Initialization phase. Input algorithm parameters and problem information, then randomly generate a population within the design variable boundaries and evaluate fitness values. After the initialization phase, the algorithm enters the main loop; In the main loop, the probability of running the exploration and development phases is the same, depending on the random number between (0,1) and the algorithm parameter G. p The comparison between them, where G p The value is 0.5; Exploration Phase. A hybrid search approach is employed in this phase, using both five-dimensional and one-dimensional search methods simultaneously. Two different update strategies are designed for different dimensions. After obtaining the update location, the boundaries of the design variables are checked. Development phase. A predation and regeneration phase was established. A parallel bidirectional search mode was used to calculate the distance between the global solution and other starfish. The algorithm then updates the position of each starfish based on predation behavior. Afterwards, when i = N, the regeneration phase begins, and its position is updated again. Termination Phase. After the above phase, the fitness values ​​are evaluated. Based on the obtained fitness values, the current best solution for all starfish is obtained iteratively. Then, the above phase is repeated to update the starfish positions, and the best solution is updated in each iteration. When the maximum number of iterations criterion is met, the main loop stops and the final global solution is output.

2. The MPPT method for a laser wireless power transfer system based on an improved starfish optimization algorithm as described in claim 1, characterized in that, The algorithm initialization phase is as follows: During the algorithm's initialization phase, the starfish positions are randomly generated between the boundaries of the design variables, and can be represented as a matrix: Where X is a matrix storing the positions of starfish of size N×D, N is the population size, and D is the dimension of the design variables. During the initialization phase, the position of each starfish is evaluated as follows: X ij =l j +r(u j -l j ),i=1,2,...,N,j=1,2,...,D Among them, X ij Let r represent the j-th position of the i-th starfish, r represent a random number between (0,1), and u represent the position of the j-th dimension of the i-th starfish. j and l j These are the upper and lower bounds of the j-th dimension design variable, respectively. After generating the initial position matrix, the fitness values ​​of all starfish are obtained by evaluating the objective function, which is stored in vector form: Where F is a matrix of size N×1 used to store and update the obtained fitness values.

3. The MPPT method for a laser wireless power transfer system based on an improved starfish optimization algorithm as described in claim 1, characterized in that, The algorithm exploration phase is as follows: The exploration phase simulates the exploratory behavior of a starfish, mimicking the search capabilities of its five arms, with eyes embedded at the ends of the arms. During this phase, a novel search pattern is introduced, combining a five-dimensional search pattern (D>5) with a one-dimensional search pattern (D≤5) for different optimization problems. The dimensionality threshold is determined by the starfish's five arms (or eyes). If the dimension of the optimization problem is greater than 5 (i.e., D>5), the search space for the task is large, so the starfish needs to move all its arms to explore the surrounding environment. Furthermore, the starfish's arms also need to determine the optimal position between search agents that guide its movement. Therefore, a mathematical model for this stage was established: in, and These represent the location where the starfish was acquired and its current location, respectively. This represents the current optimal position in dimension p, where p is one of five randomly selected dimensions from dimension D. α1 and θ are calculated as follows: a1＝(2r-1)π Where T represents the current iteration process, T max This represents the maximum number of iterations. The sine and cosine terms represent the way the starfish's arms move left or right, approaching the food with equal probability. During the exploration phase, α1 is randomly generated for each candidate and the updated position in each iteration, while θ changes with each iteration, θ∈[0,π / 2]. These two parameters measure the impact of the distance between the optimal position in the selected update dimension and the current position. For optimization problems D>5, the five-dimensional search pattern in the formula is used to update the position information in the five dimensions to ensure the algorithm's search capability and improve search efficiency. Afterward, when the updated position exceeds the boundaries of the design variables, the arms will tend to remain in the previous position rather than move to the updated position. The above process can be described as follows: in, p represents the dimension being updated, l b,p and u b,p These represent the boundaries of the design variables. If the dimension of the optimization problem is no greater than 5 (D≤5), the exploration phase will only use a one-dimensional search mode to update the position. In this case, the starfish moves only one arm, using the position information of other starfish to search for food sources. The updated position can be determined as follows: in, and These are the p-dimensional positions of two randomly selected starfish, where A1 and A2 are two random numbers between (-1, 1), and p is a number randomly selected in the D dimension. t It is the energy of the starfish, calculated using the following formula: θ is calculated using the formula. Similar to the update rule described above, if the starfish's acquired position exceeds the boundary, it will tend to remain in its previous position rather than move to the updated position.

4. The MPPT method for a laser wireless power transfer system based on an improved starfish optimization algorithm as described in claim 1, characterized in that, The algorithm development stages are as follows: The algorithm considers predation and update behaviors to search for a global solution during the development phase, therefore two update strategies are designed at this stage. To model the starfish's predation phase, the algorithm employs a parallel bidirectional search strategy, which requires utilizing information from other starfish and the current optimal position of the population. First, five distances between the optimal position and other starfish are calculated. Then, two distances are randomly selected as confirmations to update the position of each starfish, utilizing the parallel bidirectional search strategy. The distances can be calculated as follows: Where r1 and r2 are random numbers between (0,1), d m1 and d m2 It is in d m The starfish are randomly selected. The starfish's predatory behavior is shown in the figure. Based on a parallel bidirectional search strategy, in the same iteration, the starfish's candidate direction better guides the solution forward, while other candidates move backward. Therefore, the candidates have the same ability to overcome local optima. Furthermore, starfish are vulnerable to attack from other predators during predation due to their slow movement. If a predator catches a starfish, it may be severed or lose an arm to escape capture. Therefore, the regeneration phase of the algorithm is only implemented for the last starfish in the population (i=N). Since the regeneration phase takes several months, during which the starfish move very slowly, update rules are modeled for the regeneration phase, and positions are updated as follows: in, T represents the current iteration process. max This represents the maximum number of iterations, where N is the population size. If the obtained location information is outside the boundaries of the design variables, the location information can be set as:

5. The algorithm initialization stage as described in claim 2, characterized in that, Instead of random initialization, use spatial pyramid matching (SPM) chaotic mapping. This method improves the uniformity of population distribution in space, thus compensating for the shortcomings of random initialization. Its mathematical expression is as follows:

6. The algorithm exploration phase as described in claim 3, characterized in that, An improved linearly decreasing energy adjustment mechanism is presented. By introducing a stochastic shrinkage exponential function during the exploration process, the robustness and adaptability of the algorithm are enhanced. Its energy expression is as follows:

7. The algorithm development stage as described in claims 3 and 4, characterized in that, The Cauchy distribution function is introduced to improve the diversity level of the population, expand the search range, and enhance the global search capability of the algorithm. By applying the standard Cauchy distribution function to the solution of the global optimum, the optimization performance of the algorithm in the MPPT system can be effectively improved. The solution of the global optimum based on the standard Cauchy distribution function is expressed as:

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