Alternating-current and direct-current micro-grid hybrid energy storage system capacity optimization configuration method based on improved black-wing algorithm

Abstract

The invention discloses an alternating current and direct current micro-grid hybrid energy storage system capacity optimization configuration method based on an improved black-wing algorithm. The method comprises the following steps: S1, constructing an alternating current and direct current micro-grid hybrid energy storage system capacity optimization configuration model; s2, setting parameters of a Heiwen optimization algorithm, generating a position vector of an initial population by utilizing Logistic chaotic mapping, and mapping each individual into a capacity configuration scheme of the hybrid energy storage system; s3, calculating a fitness value of each individual in the population, determining a current global optimal individual, executing an attack behavior for each individual in the population based on a nonlinear balance factor, and updating an individual position; s4, carrying out migration behaviors on non-optimal individuals in the population, updating positions through interaction with other individuals, and completing a round of basic iteration; and S5, executing a mirror surface reverse learning strategy based on random scaling on the current population to generate a mirror image population, and reserving better individuals to enter the next generation by adopting a survival mechanism according to the fitness value.

Description

Technical Field

[0001] This invention relates to a capacity optimization configuration method for AC / DC microgrid hybrid energy storage systems based on an improved Blackwing Kite algorithm, belonging to the field of microgrid technology. Background Technology

[0002] Microgrids, with their advantages of integration and on-site production and distribution, have become a highly efficient way to supply renewable energy, receiving strong promotion and policy support from countries around the world. By flexibly deploying wind turbines and photovoltaic power generation devices, microgrids can fully capture wind and solar energy within a local area, coordinating power output with load demand. However, the fluctuations and intermittent nature of wind speed and sunlight can cause periodic fluctuations in power generation, leading to voltage fluctuations, frequency drift, and other problems, thus weakening the power supply stability and power quality of the microgrid. Therefore, energy storage devices and intelligent dispatch algorithms are widely used in microgrids to improve their ability to adjust to fluctuations in renewable energy and ensure reliable operation under various operating conditions. In hybrid energy storage systems, lithium batteries are responsible for large-capacity, long-term energy accumulation, while supercapacitors, with their high power density, provide a rapid response to instantaneous load fluctuations. Their performance is superior to single energy storage systems, and they are gradually becoming dominant in microgrids.

[0003] The optimal configuration of hybrid energy storage system capacity revolves around two core dimensions: economic rationality and technical feasibility. In actual configuration, these objectives are not isolated but require synergistic balance through multi-objective optimization algorithms. For example, finding the optimal solution between "minimizing overall cost" and "maximizing fluctuation mitigation effect" is crucial to avoid insufficient energy storage capacity and unstable power supply due to simply pursuing low cost, or wasteful equipment investment due to excessive pursuit of stability. Most existing optimization algorithms primarily aim to minimize the operating cost of wind-solar-energy storage microgrids under load power shortage constraints, and have achieved some improvements in cost control and system performance optimization. However, these algorithms fail to fully consider the inherent volatility of renewable energy (wind and solar) and do not incorporate power fluctuation penalty costs into the objective function. As a result, the constructed energy storage models still exhibit insufficient smoothing ability in managing wind and solar energy fluctuations, making it difficult to balance operating costs and fluctuation mitigation requirements.

[0004] In addition, the inherent limitations and applicability of optimization algorithms are a major challenge in optimizing the capacity of hybrid energy storage systems. Many researchers have developed heuristic optimization search algorithms such as genetic algorithms, particle swarm optimization, gray wolf optimization, and cat swarm optimization.

[0005] For example, Chinese invention application CN201510767823.1 discloses an optimal configuration method for hybrid energy storage in isolated microgrids. This method comprehensively considers the unbalanced power supply load and the total load in the microgrid, and also takes into account the impact of intermittent energy sources and load fluctuations over time on the hybrid energy storage capacity configuration. It establishes an optimal configuration for hybrid energy storage capacity in isolated microgrids and uses a genetic algorithm to solve the optimal configuration model for hybrid energy storage capacity in isolated microgrids under different decomposition forms of the unbalanced power supply load. The method selects the optimal hybrid energy storage configuration scheme that best suits the actual situation of isolated microgrids, better meeting the planning requirements for hybrid energy storage configuration in actual isolated microgrids. This helps improve the utilization rate and service life of hybrid energy storage capacity configuration in isolated microgrids, enhances operational economy, and reduces the overall utilization cost of isolated microgrid systems. It can be widely applied to the capacity optimization configuration of hybrid energy storage in microgrids.

[0006] However, shortcomings such as insufficient initial population distribution rationality, high parameter sensitivity, insufficient stability in high-dimensional problems, slow convergence speed and low convergence accuracy, and susceptibility to local optima remain problems that optimization search strategies need to address. Numerous optimization algorithm improvement strategies, such as integrating particle swarm optimization with gray wolf optimization and incorporating chaotic graphs into improved genetic algorithms, are only applicable to battery capacity optimization models or economic models of wind-solar-storage DC microgrids, and cannot be fully applied to the capacity optimization configuration problem of AC / DC microgrid hybrid energy storage systems. Therefore, developing novel optimization search algorithms with rapid convergence to optimality, avoiding local minima during the search process, and applicable to AC / DC microgrid hybrid energy storage systems remains a key problem that needs to be solved. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings and deficiencies of the existing technology and to provide a capacity optimization configuration method for AC / DC microgrid hybrid energy storage systems based on the improved Blackwing Kite algorithm.

[0008] The capacity optimization configuration method for AC / DC microgrid hybrid energy storage systems based on the improved Black-winged Kite algorithm includes the following steps: S1. Construct a capacity optimization configuration model for a hybrid energy storage system for AC / DC microgrids; S2. Set the optimization algorithm parameters for the Black-winged Kite, use Logistic chaotic mapping to generate the position vector of the initial population, and map each individual to the capacity configuration scheme of the hybrid energy storage system. S3. Calculate the fitness value of each individual in the population, determine the current global best individual, and for each individual in the population, perform attack behavior based on the nonlinear balance factor to update the individual's position. S4. Perform migration behavior on non-optimal individuals in the population, update their positions through interaction with other individuals, and complete one round of basic iteration; S5. Execute a mirror back learning strategy based on random scaling on the current population to generate a mirror population, and use a survival-of-the-fittest mechanism based on fitness values ​​to retain better individuals for the next generation. S6. Determine whether the preset maximum number of iterations has been reached. If yes, output the hybrid energy storage system capacity configuration scheme corresponding to the global optimal solution; otherwise, return to S3 to continue iterating.

[0009] By constructing a hybrid energy storage capacity optimization model for AC / DC microgrids that incorporates power fluctuation penalty costs, the capacity configuration can simultaneously reflect the impact of wind and solar power fluctuations on system operation under economic constraints, thus improving the model's adaptability to real-world operating scenarios. Employing Logistic chaotic mapping to generate the initial population makes the distribution of candidate solutions more uniform in the search space, fundamentally addressing the early convergence limitation problem caused by insufficient initial diversity in traditional algorithms. Utilizing a nonlinear balance factor to adjust the search intensity of attack behavior allows for a smooth transition from global exploration to local development during iteration, improving the stability and convergence efficiency of the search process. Introducing migration behavior in the basic iterations allows non-optimal individuals to obtain more flexible search paths based on fitness differences, further enhancing the algorithm's ability to avoid getting trapped in local optima. Furthermore, using a mirror-backward learning strategy based on random scaling expands the spatial distribution of candidate solutions during iteration, improving the search process's coverage of different regions and making the optimization process more dynamic and global. Through the synergistic effect of the above strategies, a capacity combination scheme that better meets the operational requirements can be obtained in the complex problem of hybrid energy storage capacity configuration of AC / DC microgrids. This improves the grid stability and energy storage system utilization efficiency under renewable energy fluctuations, thereby effectively improving the shortcomings of traditional algorithms such as slow convergence, low accuracy, and easy getting trapped in local optima.

[0010] Furthermore, in S1, a capacity optimization configuration model for the AC / DC microgrid hybrid energy storage system is constructed. Specifically, this includes setting the goal function as minimizing the average annual comprehensive cost of the hybrid energy storage system, where the average annual comprehensive cost includes the power fluctuation penalty cost, and setting corresponding system constraints.

[0011] The above technical solution enables the optimization model to simultaneously reflect the impact of equipment life-cycle costs and renewable energy fluctuations on system operation. This approach avoids the capacity configuration bias caused by traditional models that only focus on investment or operating costs, resulting in a more complete economic assessment of the optimization results.

[0012] Furthermore, the annual comprehensive cost of the objective function includes the weighted sum of the annual operation and maintenance cost of the equipment, the disposal cost of the energy storage equipment, the investment and construction cost of the equipment, the depreciation cost of the battery life, the depreciation cost of the supercapacitor life, and the power fluctuation penalty cost.

[0013] By incorporating power fluctuation penalty costs into the objective function through the above technical solutions, capacity configuration can quantitatively consider the adjustment pressure caused by wind and solar power fluctuations. This encourages the optimization process to automatically favor energy storage configurations with stronger mitigation capabilities. The comprehensive modeling approach described above enables a simultaneous trade-off between economic efficiency and stability factors, improving the adaptability of capacity optimization results to actual operating conditions.

[0014] Furthermore, the power fluctuation penalty cost is calculated by multiplying the power fluctuation penalty coefficient by the microgrid grid-connected power fluctuation, wherein the grid-connected power fluctuation is determined based on the real-time difference between the photovoltaic power generation, wind power generation, load power and the actual output power of the hybrid energy storage system.

[0015] The above technical solutions enable the optimization process to automatically monitor the impact of wind and solar power output changes on system stability, making energy storage capacity configuration more inclined to schemes with strong power regulation capabilities, thereby reducing the possibility of frequent power surges in microgrid operation and improving the system's operational stability under multi-source fluctuation conditions.

[0016] Furthermore, in S1, the system constraints include energy conservation constraints, energy storage device capacity constraints, energy storage device power constraints, and charge constraints; the energy conservation constraint requires that the output power of the hybrid energy storage system equals the sum of the battery power and the supercapacitor power; the energy storage device capacity constraints and power constraints respectively limit the upper and lower limits of the configuration capacity and the upper and lower limits of the charging and discharging power of the battery and the supercapacitor; the charge constraints limit that the remaining charge state of the battery and the supercapacitor during operation must be within a preset safe range.

[0017] The above technical solutions enable the optimization model to simultaneously reflect the life-cycle cost of equipment and the impact of renewable energy fluctuations on system operation. This approach avoids capacity configuration biases caused by traditional models that only focus on investment or operating costs, resulting in a more comprehensive economic assessment of the optimization results. Furthermore, incorporating power fluctuation penalty costs into the objective function allows for a quantitative consideration of the regulatory pressure generated by wind and solar power fluctuations in capacity configuration, thereby prompting the optimization process to automatically favor energy storage configurations with stronger mitigation capabilities. Through this comprehensive modeling approach, a simultaneous trade-off between economic and stability factors can be achieved, improving the adaptability of capacity optimization results to actual operating conditions.

[0018] Furthermore, in S2, generating an initial population using Logistic chaotic mapping specifically includes: generating a set of chaotic sequences distributed between 0 and 1 using the Logistic chaotic mapping equation, wherein the mapping equation controls parameters to make the system in a completely chaotic state; mapping the chaotic sequences to the range of values ​​of the decision variables of the hybrid energy storage system through linear transformation to obtain the position vector of the initial population, so as to ensure the ergodicity and diversity of the initial solution in the solution space.

[0019] The above technical solution enables the initial candidate solutions to exhibit high coverage and high dispersion across the entire search domain. This approach effectively avoids the clustering phenomenon caused by traditional random initialization, thereby improving the ergodicity and diversity of the initial population in the solution space. Improved initial distribution quality enhances the algorithm's global search capability in early iterations, allowing the optimization process to explore potential optimal solutions over a wider area, reducing the probability of the algorithm getting trapped in local optima, and providing a more representative search starting point for subsequent attack and migration behaviors, thus improving overall convergence performance and solution stability.

[0020] Furthermore, in S3, the attack behavior is performed based on the nonlinear balance factor to update the individual position. Specifically, the nonlinear balance factor adopts the form of a Logistic function and dynamically changes with the number of iterations. The nonlinear balance factor maintains a high value in the early stage of iteration to enhance global exploration capability, decreases rapidly in the middle stage of iteration to achieve a smooth transition, and maintains a low value in the later stage of iteration to enhance local development capability. When performing the attack behavior, the nonlinear balance factor is used to adjust the step size and perturbation amplitude of the individual approaching the current optimal solution.

[0021] The above technical solution enables attack behavior to exhibit differentiated search characteristics at different iteration stages. Maintaining a high nonlinear balance factor in the early stages of iteration helps expand the step size and perturbation range of candidate solutions, thereby enhancing global exploration capabilities and helping the algorithm quickly identify potential optimal solution regions in the search space. In the middle stages of iteration, the balance factor rapidly decreases, allowing the search process to gradually transition from large-scale exploration to a more targeted optimization interval, improving the continuity and stability of the search path. Maintaining a low balance factor in the later stages of iteration reduces the step size and perturbation amplitude of candidate solutions, enhancing local exploitation capabilities and helping the algorithm achieve fine-grained searching near the optimal solution. Through this dynamic adjustment method, attack behavior can maintain a more reasonable search rhythm throughout the entire iteration process, improving the overall convergence speed and accuracy of the algorithm, and reducing the probability of getting trapped in local optima due to improper step size selection.

[0022] Furthermore, in S4, the migration behavior for non-optimal individuals in the population specifically includes: for the current individual, randomly selecting another individual in the population for fitness comparison; if the fitness of the current individual is better than that of the selected individual, the current individual remains near its original position; if the fitness of the current individual is worse than that of the selected individual, the current individual combines the information of the global optimal solution and the Cauchy distribution random number to perform a position jump in order to find a new solution region.

[0023] The above technical solution introduces an adaptive global jump mechanism during the optimization process, making the movement of candidate solutions in the search space more flexible. When the fitness of the current individual is better than that of the selected individual, it is kept searching near its original position, which is beneficial for continuing to explore potential optimal solutions in the local area. When the fitness of the current individual is low, position jumps are performed by combining information from the global optimum and Cauchy distribution random numbers, allowing the individual to cross local areas over long distances and explore new solution domains. Due to the long-tail characteristic of the Cauchy distribution, this jumping method can effectively expand the search span and increase the probability of entering unexplored intervals. Through this mechanism, the possibility of the algorithm getting stuck in local optima can be significantly reduced, while maintaining population diversity and enhancing global search capabilities and the stability of the optimization process.

[0024] Furthermore, in S5, a mirror back learning strategy based on random scaling is executed on the current population, specifically including: introducing a random reflection factor, which is uniformly distributed within a preset range; calculating the position of the mirror point based on the position of the current individual, the upper and lower bounds of the search space, and the random reflection factor; the random reflection factor is used to control the degree of offset of the mirror point relative to the center of the search space, thereby realizing dynamic scaling of the search area.

[0025] Through the above technical solution, the random reflection factor controls the offset of the mirror point relative to the center of the search space, allowing the mirror point to perform both leapfrog searches in a large area far from the current solution and fine-grained searches in a small area close to the current solution. This method offers greater flexibility compared to the fixed reflection mode, achieving a dynamic balance between global exploration and local exploitation. Furthermore, by simultaneously retaining both the original and mirror solutions and selecting the solution with better fitness, the diversity and search efficiency of the population can be further improved. These mechanisms enable the algorithm to better escape local optima when facing complex solution spaces and maintain good convergence accuracy and stability in the later stages of iteration.

[0026] Furthermore, the dynamic scaling of the search area includes an expansion mode and a contraction mode. Specifically, when the fitness of the current individual and the fitness of the mirror point satisfy a first preset relationship, the random reflection factor causes the mirror point to shift far away from the center of the interval, entering the expansion mode for coarse-grained global search; when the second preset relationship is satisfied, the random reflection factor causes the mirror point to move closer to the current solution, entering the contraction mode for fine-grained local search.

[0027] Through the above technical solution, when the first preset relationship is met, the random reflection factor causes the mirror point to shift further away from the center of the interval, thus entering an expansion mode to explore a larger area. This is beneficial for quickly escaping local regions in the early stages of the search or when trapped in local optima, enhancing global search capabilities. When the second preset relationship is met, the random reflection factor pulls the mirror point closer to the current individual, causing the search to enter a contraction mode. This allows for denser and more refined local development in potential optimal solution regions, improving solution accuracy and convergence quality. This dynamic scaling mechanism can adaptively adjust the search strategy according to the search state, maintaining a more reasonable balance between global exploration and local development, thereby improving overall solution efficiency and stability.

[0028] The beneficial effects of this invention are as follows: First, by adding a power fluctuation penalty cost to the objective function, the energy storage system enhances its ability to mitigate power fluctuations from photovoltaics and wind turbines. Second, by introducing a Logistic chaotic mapping to initialize the population, the optimization algorithm gains diverse initial solutions and better early exploration capabilities. Simultaneously, a nonlinear balance factor is added to the attack behavior, and the search intensity at different stages is controlled through the Logistic function, enhancing the flexibility of the optimization algorithm. Finally, the search space is symmetrically expanded by incorporating a mirror back-learning strategy to improve the search accuracy of the optimization algorithm in later stages. Comparative experiments show that IBKA reaches the optimal solution in the 70th iteration, with a search efficiency 50.7% higher than the BKA algorithm. It exhibits stronger convergence efficiency and global search capability. The hybrid energy storage microgrid using IBKA configuration parameters has a load loss rate and energy loss rate of 70.34% and 30.88%, respectively, which are 17.8% and 50.7% lower than the PSO algorithm, which gets trapped in a local optimum. This effectively reduces the probability of power shortages and energy waste, demonstrating superior capabilities in suppressing power fluctuations and improving grid operating efficiency and stability. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, obtaining other drawings based on these drawings without creative effort still falls within the scope of the present invention.

[0030] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a flowchart of the Improved Black-winged Kite Algorithm (IBKA); Figure 3 It is the iterative curve of the optimization function; Figure 4 This is a diagram of a wind-solar-storage AC / DC microgrid system; Figure 5 This is a typical daily power graph; Figure 6 It is an iterative curve for optimizing the overall cost of hybrid energy storage system configuration. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0032] It should be noted that all uses of "first" and "second" in the embodiments of the present invention are for the purpose of distinguishing two entities or parameters with the same name but different names. It is clear that "first" and "second" are only for the convenience of expression and should not be construed as limiting the embodiments of the present invention. Subsequent embodiments will not explain this in detail.

[0033] The directional and positional terms used in this invention, such as "up," "down," "front," "back," "left," "right," "inner," "outer," "top," "bottom," and "side," are merely for reference to the accompanying drawings. Therefore, the directional and positional terms used are for illustrating and understanding this invention, and not for limiting the scope of protection of this invention.

[0034] In the process of optimizing the capacity configuration of hybrid energy storage systems in AC / DC microgrids, the objective function does not include the power fluctuation penalty cost, and the optimization algorithm suffers from defects such as unreasonable initial population distribution, susceptibility to local optima, and slow convergence speed. This results in insufficient system resilience to renewable energy fluctuations and unsatisfactory annual comprehensive cost control. Specifically, the lack of a power fluctuation penalty cost prevents the optimization process from quantifying the impact of fluctuations on system stability, while algorithmic defects limit search efficiency and solution quality, further affecting power supply reliability and economic efficiency.

[0035] If the above problems are not addressed, the microgrid system will remain in a state of power instability for a long time. Voltage fluctuations and frequency drift may trigger protection devices, leading to local power outages. At the same time, due to unsatisfactory annual comprehensive cost control, equipment investment and operation and maintenance costs will increase, reducing the system's economic efficiency. As a result, the reliable operation and sustainable development of microgrids will be constrained, making it difficult to meet practical application needs.

[0036] In this regard, this application proposes, such as Figure 1-6 The image shows an embodiment of the capacity optimization configuration method for a hybrid energy storage system in an AC / DC microgrid based on the improved Black-winged Kite algorithm of the present invention. The capacity optimization configuration method for a hybrid energy storage system in an AC / DC microgrid based on the improved Black-winged Kite algorithm includes the following steps: S1. Construct a capacity optimization configuration model for a hybrid energy storage system for AC / DC microgrids; S2. Set the optimization algorithm parameters for the Black-winged Kite, use Logistic chaotic mapping to generate the position vector of the initial population, and map each individual to the capacity configuration scheme of the hybrid energy storage system. S3. Calculate the fitness value of each individual in the population, determine the current global best individual, and for each individual in the population, perform attack behavior based on the nonlinear balance factor to update the individual's position. S4. Perform migration behavior on non-optimal individuals in the population, update their positions through interaction with other individuals, and complete one round of basic iteration; S5. Execute a mirror back learning strategy based on random scaling on the current population to generate a mirror population, and use a survival-of-the-fittest mechanism based on fitness values ​​to retain better individuals for the next generation. S6. Determine whether the preset maximum number of iterations has been reached. If yes, output the hybrid energy storage system capacity configuration scheme corresponding to the global optimal solution; otherwise, return to S3 to continue iterating.

[0037] Among these, attack behavior based on nonlinear balance factors refers to the dynamic adjustment of individuals' search behavior towards the optimal solution. This can be achieved using exponential decay functions or linear change functions. For example, the factor value can be adjusted proportionally according to the number of iterations to control the step size and perturbation amplitude. Its main purpose is to achieve a dynamic balance between global exploration and local exploitation capabilities. Specifically, migration behavior for non-optimal individuals in the population refers to a mechanism that updates positions through inter-individual interactions. This can be achieved using random walk strategies or interpolation methods based on fitness differences. For example, positions can be randomly adjusted based on comparison results or jumps can be made using global information. Its main purpose is to enhance population diversity and avoid local optimum traps.

[0038] As a preferred implementation, the mirror back learning strategy based on random scaling refers to a method of generating mirror solutions to expand the search range. It can be implemented by using a fixed scaling ratio or dynamic scaling based on the iteration progress. For example, the mirror point position can be calculated using a constant reflection factor or a scaling factor related to the number of iterations. Its main purpose is to achieve intelligent adjustment of the granularity of the search region.

[0039] This application further proposes that, in S1, constructing a capacity optimization configuration model for a hybrid energy storage system of AC / DC microgrids specifically includes setting the minimization of the average annual comprehensive cost of the hybrid energy storage system as the objective function, wherein the average annual comprehensive cost includes the power fluctuation penalty cost, and setting corresponding system constraints.

[0040] Therefore, this application systematically solves the problems of insufficient power fluctuation mitigation capability and unsatisfactory annual comprehensive cost control in the capacity optimization configuration of AC / DC microgrid hybrid energy storage systems due to insufficient consideration of the economic impact of power fluctuations and algorithm defects. This is achieved by incorporating the power fluctuation penalty cost into the objective function and improving the core mechanism of the Black-winged Kite algorithm, including chaotic mapping to generate the initial population, dynamic balance factor to adjust search behavior, migration behavior to enhance diversity, and mirror back learning strategy to optimize search granularity.

[0041] In some of the embodiments described above in this application, it is proposed to set the minimum annual comprehensive cost of the hybrid energy storage system as the objective function to optimize the configuration of the hybrid energy storage system in AC / DC microgrids. However, in its implementation, the specific composition of the annual comprehensive cost is not clearly defined, which may lead to the neglect of key factors such as power fluctuation penalty cost, making it impossible to effectively balance operating costs and fluctuation suppression requirements. This results in unreasonable energy storage capacity configuration and weakens the microgrid's ability to smooth out renewable energy fluctuations.

[0042] This application further proposes that, in step S1, the objective function is set to minimize the average annual comprehensive cost of the hybrid energy storage system. The average annual comprehensive cost includes the power fluctuation penalty cost. Corresponding system constraints are set, specifically including that the average annual comprehensive cost of the objective function includes the weighted sum of the annual operation and maintenance cost of the equipment, the disposal cost of the energy storage equipment, the investment and construction cost of the equipment, the depreciation cost of the battery life, the depreciation cost of the supercapacitor life, and the power fluctuation penalty cost.

[0043] Specifically, this application's solution systematically defines the components of the average annual comprehensive cost, ensuring that the optimization model comprehensively covers key cost dimensions affecting the economy and stability of hybrid energy storage systems. Setting the minimization of the average annual comprehensive cost as the objective function provides a clear economic optimization guide for algorithm iteration, directing the search process to focus on the globally optimal configuration. The inclusion of annual equipment operation and maintenance costs reflects the continuous expenditure on daily system operation and maintenance, avoiding focusing solely on initial investment while neglecting long-term maintenance burdens during optimization. Consideration of energy storage equipment disposal costs makes the total cost assessment more aligned with actual engineering scenarios, preventing the accumulation of hidden costs. Equipment investment and construction costs, as an initial investment element, prompt the optimization process to balance short-term investment with long-term benefits within budget constraints. The calculation of battery life depreciation costs addresses the capacity decay characteristics of lithium batteries, guiding the algorithm to select configurations that extend battery life. The consideration of supercapacitor life depreciation costs optimizes the balance between the instantaneous response strength and lifespan consumption of supercapacitors. The introduction of power fluctuation penalty cost quantifies the impact of renewable energy fluctuations on grid stability into economic costs. These costs are then integrated into the objective function through a weighted mechanism, forcing the optimization process to simultaneously balance cost minimization and fluctuation mitigation effects. This effectively enhances the microgrid's adaptability to the intermittency of wind and solar power.

[0044] Through the above solution, this application effectively solves the problem of incomplete annual comprehensive cost composition, ensures that the optimization model fully covers key cost dimensions, achieves an effective balance between operating costs and fluctuation suppression requirements, thereby improving the microgrid's ability to smooth renewable energy fluctuations and avoiding the problem of sacrificing power supply stability in the pursuit of economic efficiency.

[0045] In some of the embodiments described above in this application, a power fluctuation penalty cost is proposed to quantify the impact of microgrid power fluctuations on system stability. However, in its implementation, the existing optimization model does not include the power fluctuation penalty cost in the objective function, which makes it difficult for the constructed energy storage model to accurately reflect the actual impact of renewable energy fluctuations on system operation. It is difficult to effectively balance operating costs and fluctuation suppression requirements, thereby weakening the smoothing ability of the hybrid energy storage system to wind and solar energy fluctuations, making it difficult to guarantee power supply stability and power quality.

[0046] This application further proposes that the power fluctuation penalty cost is calculated by multiplying the power fluctuation penalty coefficient by the microgrid grid-connected power fluctuation, wherein the grid-connected power fluctuation is determined based on the real-time difference between the photovoltaic power generation, wind power generation, load power and the actual output power of the hybrid energy storage system.

[0047] Among them, the power fluctuation penalty cost refers to transforming the potential damage to system stability caused by microgrid power fluctuations into a quantifiable economic cost indicator. It can be achieved using linear or nonlinear functional relationships based on grid operation standards, with the aim of enabling the optimization model to directly reflect the actual economic impact of power fluctuations on system operation. The power fluctuation penalty coefficient can be understood as a quantitative parameter characterizing the degree of economic damage caused by unit power fluctuations. It can be a fixed value determined by statistical analysis of historical fault data or a variable dynamically adjusted according to grid dispatch strategies, with the aim of establishing a mapping relationship between power fluctuation and economic cost. The microgrid grid-connected power fluctuation specifically refers to the instantaneous fluctuation amplitude of the power interaction between the microgrid and the external main grid. It can be obtained by filtering the power data collected by the real-time monitoring system, with the aim of accurately capturing the power imbalance state within the microgrid. The real-time difference can be understood as the dynamic difference calculated based on synchronously collected photovoltaic power generation, wind power generation, load power and the actual output power data of the hybrid energy storage system. It can be calculated at the millisecond level using high-precision sensors in conjunction with data acquisition units, with the aim of avoiding fluctuation assessment distortion caused by data lag.

[0048] Through the above technical solution, this application can accurately convert the impact of renewable energy fluctuations on system stability into economic cost indicators, enabling the hybrid energy storage system capacity optimization configuration model to effectively take into account the power fluctuation suppression requirements while minimizing the average annual comprehensive cost, thereby improving the smoothing ability of the hybrid energy storage system to wind and solar energy fluctuations and ensuring the power supply stability and power quality of the microgrid.

[0049] In the aforementioned scheme of this application, system constraints are proposed to ensure the feasibility of the optimized configuration of the hybrid energy storage system. However, in this process, the specific content of the constraints is not specified in detail, which may lead to unrealistic configuration schemes generated by the optimization model, and thus fail to effectively guarantee the safe and stable operation of the system.

[0050] In this regard, this application further proposes that, in S1, the system constraints include energy conservation constraints, energy storage device capacity constraints, energy storage device power constraints, and charge constraints; the energy conservation constraints require that the output power of the hybrid energy storage system be equal to the sum of the battery power and the supercapacitor power; the energy storage device capacity constraints and power constraints respectively limit the upper and lower limits of the configuration capacity and the upper and lower limits of the charging and discharging power of the battery and the supercapacitor; the charge constraints limit that the remaining charge state of the battery and the supercapacitor during operation must be within a preset safe range.

[0051] Among them, energy conservation constraints refer to the basic physical constraints that ensure the energy balance of the system. These can be achieved through real-time power monitoring and feedback control mechanisms, with the aim of avoiding the generation of invalid solutions due to energy non-conservation. Energy storage device capacity constraints refer to the boundary conditions that limit the physical size and storage capacity of energy storage devices. These can be set with upper and lower limits based on the technical specifications provided by the equipment manufacturer, with the aim of preventing the configuration scheme from exceeding the actual capacity limit of the equipment. Energy storage device power constraints refer to the operational limitations that limit the charging and discharging rates of energy storage devices. These can be determined with upper and lower limits based on the rated parameters of the power converter, with the aim of avoiding the risk of overload or underload during operation. Charge constraints refer to the safe range for monitoring the remaining energy state of energy storage devices. These can be set with ranges based on the battery chemical characteristics and safe operation requirements, with the aim of preventing overcharging or over-discharging.

[0052] Through the above scheme, the hybrid energy storage system configuration scheme generated by the optimization model of this application can strictly meet the physical laws and equipment operation constraints, effectively avoid the problem of invalid solutions caused by the lack of constraints, significantly improve the feasibility of the configuration scheme and the reliability of system operation, and ensure stable power supply of the microgrid under the condition of renewable energy fluctuations.

[0053] As one specific implementation method, the specific steps of S1 include: A. Objective function for optimal capacity configuration of energy storage system The capacity optimization configuration model for hybrid energy storage systems uses the rated capacity and rated power of supercapacitors and batteries as optimization targets, with the goal of minimizing the average annual comprehensive cost of hybrid energy storage. To enhance the energy storage system's ability to mitigate power fluctuations from photovoltaics and wind turbines, a power fluctuation penalty cost is added to the configuration target. The overall optimization objective is as follows.

[0054] (1) In the formula: To optimize the overall goal, For the annual operation and maintenance costs of the equipment, For the disposal costs of energy storage equipment, For equipment investment and construction costs, Battery life depreciation costs, The depreciation cost for supercapacitors over their lifespan. Costs are incurred to penalize power fluctuations. The specific costs are as follows: (2) In the formula: and These are the average annual operating and maintenance costs per unit capacity of batteries and supercapacitors, respectively. and These are the rated capacities of the battery and the supercapacitor, respectively.

[0055] (3) In the formula: and These are the average annual disposal costs per unit capacity of batteries and supercapacitors, respectively.

[0056] (4) (5) In the formula: and These are the initial investment costs for batteries and supercapacitors, respectively. and These refer to the lifespan of batteries and supercapacitors, respectively. and These are the rated power of the battery and the supercapacitor, respectively. and These are the initial investment costs per unit power and per unit capacity of the battery, respectively. and These are the initial investment costs per unit power and per unit capacity of the supercapacitor, respectively.

[0057] (6) In the formula: The discount rate per unit capacity of the battery. For the rated lifespan of the battery, This refers to the number of days the energy storage device is used annually.

[0058] (7) In the formula: This represents the depreciation rate per unit capacity of the supercapacitor. This refers to the rated lifespan of the supercapacitor.

[0059] (8) In the formula: This is the power fluctuation penalty coefficient. This represents the total number of iterations. Photovoltaic power generation capacity, For wind power generation capacity, For grid-connected power, For load power, four power values ​​over time Constantly changing.

[0060] B. Constraints of the optimization model The constraints for satisfying the hybrid energy storage optimization problem include the following four points: 1) Energy conservation constraints (9) In the formula: The power of the hybrid energy storage is the sum of the power of the battery and the supercapacitor.

[0061] 2) Energy storage equipment capacity constraints (10) In the formula: , , , These are the minimum and maximum limits for the rated capacity of supercapacitors and batteries, respectively.

[0062] 3) Power constraints of energy storage devices (11) In the formula: , These are the real-time output power of the supercapacitor and the battery, respectively. , These are the rated power of the supercapacitor and the battery, respectively.

[0063] 4) Charge condition constraints (12) In the formula: , , , These are the minimum and maximum limits for the charge capacity of batteries and supercapacitors, respectively.

[0064] This application further proposes that, in S2, generating an initial population using a Logistic chaotic mapping specifically includes: generating a set of chaotic sequences distributed between 0 and 1 using a Logistic chaotic mapping equation, wherein the mapping equation controls parameters to make the system in a completely chaotic state; mapping the chaotic sequences to the range of values ​​of the decision variables of the hybrid energy storage system through a linear transformation to obtain the position vector of the initial population, so as to ensure the ergodicity and diversity of the initial solution in the solution space.

[0065] Among them, the Logistic chaotic mapping equation refers to a nonlinear dynamic system that can be implemented using an iterative mathematical expression. Its purpose is to utilize the inherent randomness of the chaotic system to avoid the periodic clustering of pseudo-random numbers. The control parameter refers to the key variable that adjusts the behavior of the mapping equation. It can be implemented by dynamically adjusting the value within the chaotic threshold range. Its purpose is to accurately induce the fully chaotic state of the system to ensure the high unpredictability of the sequence. The linear transformation refers to the mathematical operation of adapting the standardized sequence to the solution space of the engineering problem. It can be implemented by using affine transformation based on the upper and lower bounds of the decision variables. Its purpose is to strictly follow the physical boundary constraints so that the initial solution is uniformly distributed within the feasible region.

[0066] Through the above technical solutions, the uniformity of the initial population distribution in the solution space is significantly improved, effectively overcoming the problem of uneven solution space coverage caused by traditional random initialization methods, and enabling the initial solution to have sufficient ergodicity and diversity. This mechanism avoids the optimization algorithm from getting stuck in local optima due to population homogeneity in the early stage of iteration, enhances the global search capability of the Blackwing Kite algorithm in high-dimensional decision space, and improves the convergence speed and solution stability, providing high-quality initial solution set support for the capacity configuration problem of AC / DC microgrid hybrid energy storage system.

[0067] This application further proposes that, in S3, the attack behavior is performed based on a nonlinear balance factor to update the individual's position, specifically including: the nonlinear balance factor adopts the form of a Logistic function and dynamically changes with the number of iterations; the nonlinear balance factor maintains a high value in the early stage of iteration to enhance global exploration capability, decreases rapidly in the middle stage of iteration to achieve a smooth transition, and maintains a low value in the later stage of iteration to enhance local development capability; when performing the attack behavior, the nonlinear balance factor is used to adjust the step size and perturbation amplitude of the individual approaching the current optimal solution.

[0068] The nonlinear balance factor is a parameter that dynamically regulates the search behavior of the algorithm. It can be implemented using nonlinear functions with smooth transition characteristics, such as the Sigmoid function or the hyperbolic tangent function. Its purpose is to adaptively coordinate the global exploration and local development capabilities according to the iteration progress. Maintaining a high value in the early stage of iteration can be understood as keeping the factor close to its upper limit in the initial stage. Its purpose is to significantly expand the search range for position updates and encourage the population to fully explore the solution space to avoid local optimum traps. The rapid decline in the middle stage of iteration to achieve a smooth transition specifically refers to the nonlinear decay trend of the factor in the middle stage. Its purpose is to accelerate the phase transition of the search strategy, reduce invalid computation during the transition period, and maintain path stability. Maintaining a low value in the later stage of iteration can be understood as the factor approaching its lower limit in the convergence stage. Its purpose is to finely adjust the search step size and focus on the in-depth mining of potential optimal regions. Adjusting the step size and perturbation amplitude refers to dynamically controlling the distance that individuals move towards the optimal solution and the intensity of random perturbations through the nonlinear balance factor. Its purpose is to make the search process respond to the changes in the iteration stage in real time and adaptively balance the search breadth and accuracy.

[0069] Through the above scheme, this application effectively solves the problem that fixed or linearly changing balance factors are difficult to adapt to the needs of the algorithm iteration stage, avoids the risk of early local convergence caused by the imbalance between global exploration and local development capabilities, significantly improves the convergence stability and solution domain accuracy of the algorithm in the high-dimensional optimization problem of AC / DC microgrid hybrid energy storage system, and ensures the reliability and economy of the capacity configuration scheme of hybrid energy storage system.

[0070] In some of the embodiments described above in this application, a nonlinear balance factor is proposed to regulate the execution process of the attack behavior. However, in its implementation, the fixed or linearly changing balance factor is difficult to adapt to the needs of different stages of algorithm iteration, resulting in an imbalance between global exploration and local development capabilities. This makes the algorithm prone to getting stuck in local optima in the early stage and the convergence speed decreases in the later stage, making it unable to effectively cope with the stability challenges in the high-dimensional optimization problem of AC / DC microgrid hybrid energy storage system.

[0071] In this regard, this application further proposes that, in S4, the migration behavior for non-optimal individuals in the population specifically includes: for the current individual, randomly selecting another individual in the population for fitness comparison; if the fitness of the current individual is better than that of the selected individual, then the current individual remains near its original position; if the fitness of the current individual is worse than that of the selected individual, then the current individual combines the information of the global optimal solution and the Cauchy distribution random number to perform a position jump in order to find a new solution region.

[0072] In practical applications, the phrase "randomly selecting another individual from the population for fitness comparison for the current individual" refers to a performance-based interaction mechanism. This can be implemented using methods such as uniform random selection, roulette wheel selection, or tournament selection. The aim is to introduce dynamic diversity through random interaction, avoiding population homogenization caused by fixed-pattern migration, and ensuring that position updates are always based on real-time performance evaluation. The phrase "if the current individual's fitness is better than the selected individual, then the current individual is kept near its original position" can be understood as a protection mechanism for high-quality solutions. This can employ Gaussian perturbation, small-range random movement, or local search strategies. This is achieved to prevent the loss of high-fit individuals due to excessive perturbation during the critical convergence stage, ensuring the algorithm's ability to refine its local development capabilities. Specifically, the statement that if the fitness of the current individual is inferior to that of the selected individual, the current individual will perform a position jump by combining information from the global optimal solution and random numbers from the Cauchy distribution refers to an intelligent guidance mechanism for inferior solutions. This mechanism can use the Cauchy distribution to generate non-uniform step sizes, combined with the direction vector of the global optimal solution. The aim is to direct the updates of inferior solutions towards potentially high-quality regions, avoiding blind search, while utilizing the heavy-tailed characteristic of the Cauchy distribution to perform large-scale jumps and break through the current local traps.

[0073] Through the above scheme, this application effectively solves the problem of imbalance between exploration and exploitation in migration behavior, improves the algorithm's ability to escape local optima, accelerates the global convergence process, and achieves significant results in maintaining population diversity. This enables the capacity optimization configuration of AC / DC microgrid hybrid energy storage system to achieve an efficient balance between global exploration and local exploitation in complex high-dimensional problems.

[0074] In some of the embodiments described above in this application, a migration behavior is proposed for non-optimal individuals in the population to update their positions through interaction with other individuals. However, in its implementation, there is a lack of an effective mechanism to distinguish individual performance differences and dynamically adjust the search strategy, which leads to the migration behavior being too random or conservative, the population diversity being easily destroyed, and the population being prone to getting trapped in local optima. At the same time, the convergence efficiency is low, making it difficult to achieve a balance between global exploration and local development in complex high-dimensional optimization problems.

[0075] In this regard, this application further proposes that, in S5, a mirror back learning strategy based on random scaling is implemented for the current population, specifically including: introducing a random reflection factor, which is uniformly distributed within a preset range; calculating the position of the mirror point based on the position of the current individual, the upper and lower bounds of the search space, and the random reflection factor; the random reflection factor is used to control the degree of offset of the mirror point relative to the center of the search space, thereby realizing dynamic scaling of the search area.

[0076] The random reflection factor can be understood as a random parameter uniformly distributed within a preset range. Specifically, it can be implemented by randomly generating values ​​within a reasonable range. Its purpose is to avoid search rigidity caused by a fixed scaling factor and enhance the algorithm's adaptability to different optimization stages. Calculating the mirror point position refers to the process of determining the mirror point based on the current individual position, search space boundary information, and the random reflection factor. This can be implemented by combining linear transformation with random perturbation. Its purpose is to generate diverse candidate solutions to maintain population diversity and avoid invalid searches. The dynamic scaling of the search area can be understood as a mechanism to adjust the mirror point offset through the random reflection factor. Specifically, it can be implemented by automatically adjusting the search range size according to the iteration process. Its purpose is to balance the needs of global exploration and local development, ensuring that the algorithm has corresponding search capabilities at different stages.

[0077] Through the above scheme, this application can adaptively adjust the search area range according to the algorithm iteration state, enhance the global exploration capability in the early stage of iteration to cover a wider solution space, and strengthen the local development capability in the later stage of iteration to achieve fine convergence, effectively reducing the risk of the algorithm getting stuck in a local optimum and improving the convergence speed and optimization accuracy of the capacity optimization configuration of the hybrid energy storage system.

[0078] In some of the embodiments described above in this application, dynamic scaling of the search region is proposed to optimize the mirror back learning strategy. However, in its implementation, the fixed range of the random reflection factor cannot adaptively adjust the search granularity according to the current search state, resulting in insufficient search range when global exploration is required, making it difficult to escape the local optimum, or excessive search range when local exploration is required, thus reducing convergence efficiency.

[0079] In response, this application further proposes that the dynamic scaling of the search area includes an expansion mode and a contraction mode, specifically including: when the fitness of the current individual and the fitness of the mirror point satisfy a first preset relationship, the random reflection factor causes the mirror point to shift far away from the center of the interval, entering the expansion mode for coarse-grained global search; when the second preset relationship is satisfied, the random reflection factor causes the mirror point to move closer to the current solution, entering the contraction mode for fine-grained local search.

[0080] Among them, the expansion mode refers to the mode of expanding the search range in mirror back learning, which can be achieved by triggering a large-scale exploration based on fitness differences, with the aim of avoiding the algorithm getting stuck in local optima in the early stages; the contraction mode refers to the mode of narrowing the search range in mirror back learning, which can be achieved by achieving precise focusing based on fitness convergence, with the aim of improving convergence accuracy in the promising region; the first preset relationship refers to the condition that the fitness difference between the current individual and the mirror point is large, which can be the relationship that the fitness difference exceeds a preset threshold, with the aim of identifying states that need to be explored globally; the second preset relationship refers to the condition that the fitness difference between the current individual and the mirror point is small, which can be the relationship that the fitness difference is below a preset threshold, with the aim of identifying states that need to be explored locally; the random reflection factor refers to the random variable that controls the degree of mirror point offset, which can be evenly distributed within a preset interval, with the aim of achieving dynamic scaling of the search area.

[0081] Through the above scheme, this application realizes adaptive dynamic scaling of the search area, effectively expanding the search range to escape local optima when global exploration is needed, and accurately narrowing the search range to improve convergence efficiency when local development is needed, thereby improving the solution quality and speed of capacity optimization configuration of AC / DC microgrid hybrid energy storage system.

[0082] The core objective of this application is to minimize the annualized total cost of a microgrid system while ensuring the reliability of the optimized configuration. An improved Black-winged Kite Optimization Algorithm (IBKA) is proposed for capacity optimization of a microgrid hybrid energy storage system. Specific improvements include: adding a power fluctuation penalty cost to the objective function to improve the energy storage system's ability to mitigate power fluctuations from photovoltaics and wind turbines; introducing a Logistic chaotic mapping to initialize the population, enriching the initial solutions and enhancing the algorithm's early exploration capabilities; adding a nonlinear balance factor to the attack behavior, using a Logistic function to regulate the search intensity at different stages, thus improving the algorithm's flexibility; and integrating a mirror back-learning strategy to expand the search space and improve the algorithm's later search accuracy.

[0083] A. Black-winged Kite Algorithm The basic principle of the Black-winged Kite Optimization Algorithm (BKA) is to simulate the attack and migration behaviors of black-winged kites during hunting in nature. Attack behavior can be understood as the process of finding an optimal solution within a specific range, with the prey representing the global optimum. Migration behavior represents the algorithm's exploration of a larger area, preventing it from falling into local optima and searching for new solution regions. The basic algorithm consists of the following three steps: 1) Population initialization The Black-winged Kite algorithm follows the same population initialization operation as other optimization algorithms. First, it randomly initializes the positions of several individuals within the defined domain, with each individual representing a feasible solution. The population initialization process can be represented as: (15) In the formula: To assign an individual number to a member of the population. For the position vector of an individual, , Let these represent the lower and upper bounds of the solution to the problem, respectively. For population size, These are uniformly distributed random numbers.

[0084] 2) Aggressive behavior Inspired by the hunting attacks of black-winged kites, an attack strategy was designed to enhance local search capabilities. When a solution individual is close to the current optimal solution, it is considered to have entered the "attack phase." At this time, the individual will move closer to the optimal solution according to a certain step size and perform a detailed search around it. The mathematical modeling formula for the attack behavior is as follows: (13) (14) In the formula: , Indicates the first The individual in the first Current position and updated position in the dimension This is the disturbance amplitude control factor. for Random numbers between For nonlinear disturbance threshold, This represents the total number of iterations. It represents the number of iterations.

[0085] 3) Migration Black-winged kites possess long-distance flight capabilities, enabling them to migrate between multiple regions in search of new food sources. This migration is typically led by a leader. If the fitness value of the current species is lower than that of the random population, the leader will relinquish leadership and join the population. Conversely, when the leader's fitness value is higher than that of the population, it will guide the population to its destination. BKA employs a migration mechanism to mimic this behavior, promoting information exchange and long-distance searching among individuals, thus preventing the algorithm from getting trapped in local optima. Specifically, each individual randomly selects another individual for fitness comparison: if it is better than the other, it continues searching near its current trajectory; otherwise, it jumps towards the direction of the global optimum, simulating group learning behavior. The mathematical modeling formula for migration behavior is as follows: (15) (16) In the formula: This represents the fitness value of the current individual in group learning. This represents the current fitness value of the individual. Let be the fitness value of any random individual in the population. For dynamic adjustment coefficients, This represents a random number sampled from the standard Cauchy distribution.

[0086] B. Improved Black-winged Kite Optimization Algorithm 1) Population initialization method based on Logistic chaotic mapping In the Black-winged Kite Optimization Algorithm, the distribution quality of the initial population directly affects the global search capability and convergence speed. Traditional population initialization often fails to guarantee a uniform distribution of individuals throughout the decision space, leading to early iterations getting stuck in local optima or slow convergence. Therefore, combining population initialization with chaotic mapping leverages the ergodic and nonlinear characteristics of chaotic sequences to improve the algorithm's exploration efficiency while maintaining diversity.

[0087] Logistic chaotic mapping is favored for its simplicity and rich dynamic behavior. This mapping can generate a wide range of dynamic phenomena, from periodic behavior to fully chaotic states, using only a single control parameter. It can rapidly generate uniformly distributed sequences within the [0,1] interval in the early stages of iteration. Mapping Logistic chaotic sequences to the decision variable range not only ensures that initial individuals in each dimension are fully distributed across the entire search domain, but also leverages its sensitivity to initial values ​​to produce completely different distribution patterns under small perturbations, thereby further reducing the correlation between different trials. Therefore, introducing Logistic chaotic mapping for population initialization in BKA not only balances the diversity and coverage of initialization, but also provides a richer search starting point for subsequent attack and migration behaviors, laying the foundation for improving the algorithm's global convergence performance. The formula for initializing the population using Logistic chaotic mapping is: (17) In the formula: when At that time, the mapping function The output is still Interval; when At this point, the system enters a completely chaotic state, and the mapping sequence exhibits a high sensitivity to initial conditions due to its non-periodic nature. Parameters The choice of directly affects the traversal and divergence properties of the sequence.

[0088] 2) Attack behavior model based on nonlinear balance factor In the Black-winged Kite optimization algorithm, the aggressive behavior of an individual is a crucial step in the transition between exploration and exploitation. Traditional Black-winged Kite optimization algorithms use a linearly decaying balance factor to control the amplitude disturbance of individuals. While simple in form, this approach suffers from the following problems in practical applications: insufficient intensity in the early exploration phase leads to weak global search capabilities; rigid changes in the mid-stage transition hinder smooth transitions; and the algorithm is prone to getting trapped in local optima in the later exploitation phase. Overall, the search process lacks sufficient flexibility and continuity.

[0089] Therefore, a nonlinear balance factor is introduced, and the decreasing curve of the balance factor is dynamically adjusted through the Logistic function. This function, due to its inherent "S"-shaped nonlinear characteristic, can flexibly adjust the rate of change of the balance factor and reasonably allocate the search intensity at different stages. The update formula for the nonlinear balance factor is as follows: (18) In the formula: It is a nonlinear balance factor. To be evenly distributed random factors, Control the timing when the balance factor changes from a high value to a low value. To control the steepness of the descent of the balance factor, the exploration intensity at different iteration stages is adjusted by modifying parameters a and b. The improved mathematical modeling formula for the attack behavior is as follows: (19) In the formula: To distribute evenly in The angle of disturbance.

[0090] 3) Search region scaling strategy based on mirror back learning To broaden the search range of the algorithm and enhance its ability to escape local optima, mirror learning can be used. However, standard mirror learning merely utilizes simple symmetric flipping to introduce a mirror point of the original solution into the solution space. If the current solution is close to the interval boundary, simple flipping easily generates solutions with the same edges, limiting the exploration effect; if the current solution is in the center of the interval, it may still remain in a local region after flipping, failing to contribute sufficiently to diversity. Therefore, random scaling is introduced on the basis of standard mirror learning. By randomly switching modes, the mirror can be expanded to a more distant region or contracted to a closer region, thus balancing global jumps and local fine-tuning. The reflection factor of random scaling is as follows: (20) In the formula: Let be a random reflection factor, which follows the... Evenly distributed between , and These represent the fitness of the current individual and its mirror image, respectively. When When random scaling is in expansion mode, mirrored points are offset further from the center of the interval, used for coarse-grained global search; when When random scaling is used, it enters shrinking mode, bringing the mirror point closer to the current solution for fine-grained local search.

[0091] The reflectance factor is incorporated into the mirror formula. The formula is as follows: (twenty one) In the formula: and These are the upper and lower bounds of the search space, respectively; This is a mirror image point. When At that time, traditional mirror learning is resumed. At that time, the axis of symmetry automatically shifts, achieving asymmetric search.

[0092] 4) Improve the overall process of the Black-winged Kite Algorithm (IBKA). The specific implementation process of the Improved Black-winged Kite Algorithm (IBKA) is as follows: Figure 2 As shown.

[0093] Step 1: Initialize the population location and use Logistic chaotic mapping to improve the initial diversity; Step 2: Determine if the maximum number of iterations has been reached. If the condition is met, proceed to Step 3; otherwise, output the optimal solution. Step 3: Execute attack behavior based on nonlinear balance factors and update individual positions through local search; Step 4: Implement migration behavior for non-elite individuals to enhance global search capabilities; Step 5: Execute the mirror back learning strategy on the individual to generate a mirror position, retain the better solution, and return to Step 2 to determine whether the conditions are met.

[0094] Next, we will conduct specific experimental tests.

[0095] 1) Specific experimental setup To ensure the accuracy and comprehensiveness of the performance evaluation of the optimization algorithm, the following four representative test functions were selected to evaluate the performance of the Improved Black-winged Kite Optimization Algorithm (IBKA) and compared with the performance of the Black-winged Kite Optimization Algorithm (BKA) and the Particle Swarm Optimization Algorithm (PSO).

[0096] , It is a unimodal function. , These are multimodal functions, and the optimal value of all four functions is 0. These four functions can comprehensively evaluate the convergence speed, stability, and global search capability of the optimization algorithm.

[0097] The experimental parameters were set as follows: population size was set to 200, and the maximum number of iterations was 500. Each algorithm was run independently 20 times on each test function to obtain statistically significant performance metrics.

[0098] 2) Experimental test results Test results are as follows Figure 3 As shown in Table 1, for unimodal functions , The final optimization results of IBKA are 4.33e−136 and 3.30e−66, with optimization accuracy significantly higher than BKA's 1.788e−123 and 1.17e−60 and PSO's 23.8 and 45.6, demonstrating optimal global search capability; for multimodal functions , IBKA reached its optimal value after 121 and 53 iterations respectively, which is better than the 149 and 55 iterations required by BKA, and has the fastest global search capability.

[0099] Table 1 Test results of the optimization function B. Hybrid Energy Storage Capacity Optimization Configuration 1) Specific experimental setup Establish the following Figure 4 The wind-solar-storage AC / DC microgrid shown was used to test the performance of the optimization algorithm. During the test, wind turbines and photovoltaic modules generated electricity in real time based on wind speed and solar irradiance. When power generation exceeded load demand, the hybrid energy storage system stored the excess energy. When renewable energy output was insufficient, the energy storage unit released electricity to compensate for the power supply gap. An inverter converted DC to AC power, enabling the DC power from the photovoltaic and energy storage units to stably and seamlessly supply energy to the load. All components worked closely together to form a highly efficient and reliable microgrid.

[0100] Typical daily load data, photovoltaic power generation, and wind power generation in a certain area are as follows: Figure 5 As shown.

[0101] The operational reliability of a DC microgrid is evaluated using load loss rate and energy loss rate, and the expression is as follows: In the formula: , These are the load loss rate and the energy loss rate, respectively. It is the output power of renewable energy. It is the power demand of hybrid energy storage loads.

[0102] IBKA, BKA, and PSO were used to optimize the capacity configuration of hybrid energy storage in microgrids, with a maximum iteration count of 200.

[0103] 2) Experimental test results Experimental results are as follows Figure 6 As shown, the PSO algorithm got stuck in a local optimum, the BKA algorithm found the minimum configuration cost of the hybrid energy storage system after 142 iterations, while the IBKA algorithm found the optimal configuration scheme of the hybrid energy storage system in the 70th iteration, with a minimum daily cost of 627.2, and the search efficiency was improved by 50.7% compared with the BKA algorithm.

[0104] The load loss rate and energy loss rate of each optimization algorithm configuration are shown in Table 2. Compared with BKA and PSO, the hybrid energy storage microgrid using IBKA configuration parameters has a lower load loss rate and energy loss rate, effectively reducing the probability of power shortage and energy waste rate, and has a better ability to suppress power fluctuations and improve grid operation efficiency and stability.

[0105] Table 2 Operational reliability of DC microgrids The above description discloses only preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Therefore, equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

[0106] While the invention has been described with reference to several specific embodiments, it should be understood that the invention is not limited to the disclosed specific embodiments. The invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A method for optimizing the capacity configuration of a hybrid energy storage system for AC / DC microgrids based on an improved Black-winged Kite algorithm, characterized in that: Includes the following steps: S1. Construct a capacity optimization configuration model for a hybrid energy storage system for AC / DC microgrids; S2. Set the optimization algorithm parameters for the Black-winged Kite, use Logistic chaotic mapping to generate the position vector of the initial population, and map each individual to the capacity configuration scheme of the hybrid energy storage system. S3. Calculate the fitness value of each individual in the population, determine the current global best individual, and for each individual in the population, perform attack behavior based on the nonlinear balance factor to update the individual's position. S4. Perform migration behavior on non-optimal individuals in the population, update their positions through interaction with other individuals, and complete one round of basic iteration; S5. Execute a mirror back learning strategy based on random scaling on the current population to generate a mirror population, and use a survival-of-the-fittest mechanism based on fitness values ​​to retain better individuals for the next generation. S6. Determine whether the preset maximum number of iterations has been reached. If yes, output the hybrid energy storage system capacity configuration scheme corresponding to the global optimal solution; otherwise, return to S3 to continue iterating.

2. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 1, characterized in that: In step S1, a capacity optimization configuration model for the hybrid energy storage system of AC / DC microgrid is constructed. Specifically, this includes setting the goal function as minimizing the average annual comprehensive cost of the hybrid energy storage system, where the average annual comprehensive cost includes the power fluctuation penalty cost, and setting corresponding system constraints.

3. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 2, characterized in that: The annual comprehensive cost of the objective function includes the weighted sum of the annual operation and maintenance cost of the equipment, the disposal cost of the energy storage equipment, the investment and construction cost of the equipment, the depreciation cost of the battery life, the depreciation cost of the supercapacitor life, and the power fluctuation penalty cost.

4. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 2, characterized in that: The power fluctuation penalty cost is calculated by multiplying the power fluctuation penalty coefficient by the microgrid grid-connected power fluctuation, wherein the grid-connected power fluctuation is determined based on the real-time difference between the photovoltaic power generation, wind power generation, load power and the actual output power of the hybrid energy storage system.

5. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 2, characterized in that: In S1, the system constraints include energy conservation constraints, energy storage device capacity constraints, energy storage device power constraints, and charge constraints. The energy conservation constraint requires that the output power of the hybrid energy storage system be equal to the sum of the battery power and the supercapacitor power; The capacity and power constraints of the energy storage device respectively limit the upper and lower limits of the configuration capacity of the battery and the upper and lower limits of the charging and discharging power. The charge constraint requires that the remaining charge state of the battery and supercapacitor during operation must be within a preset safe range.

6. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 1, characterized in that: In step S2, the initial population is generated using the Logistic chaotic mapping, specifically including: A set of chaotic sequences distributed between 0 and 1 is generated using the Logistic chaotic mapping equation, and the mapping equation is used to make the system in a completely chaotic state by controlling parameters. The chaotic sequence is mapped to the range of values ​​of the decision variables of the hybrid energy storage system through a linear transformation to obtain the position vector of the initial population, so as to ensure the ergodicity and diversity of the initial solution in the solution space.

7. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 1, characterized in that: In step S3, the attack behavior is executed based on a nonlinear balance factor to update the individual's position, specifically including: The nonlinear balance factor adopts the form of a Logistic function and changes dynamically with the number of iterations. The nonlinear balance factor is maintained at a high value in the early stage of the iteration to enhance the global exploration capability, decreases rapidly in the middle stage of the iteration to achieve a smooth transition, and is maintained at a low value in the later stage of the iteration to enhance the local development capability. When performing an attack, the nonlinear balance factor is used to adjust the step size and perturbation magnitude of the individual as it approaches the current optimal solution.

8. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 1, characterized in that: In S4, migration behavior is performed on non-optimal individuals in the population, specifically including: For the current individual, randomly select another individual in the population for fitness comparison; If the fitness of the current individual is better than that of the selected individual, then the current individual is retained near its original position. If the fitness of the current individual is worse than that of the selected individual, the current individual combines information about the global optimal solution with Cauchy random numbers to perform a position jump in order to find a new solution region.

9. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 1, characterized in that: In step S5, a mirror back learning strategy based on random scaling is executed on the current population, specifically including: A random reflection factor is introduced, which is uniformly distributed within a preset range; The mirror point position is calculated based on the current individual's position, the upper and lower bounds of the search space, and the random reflection factor. The random reflection factor is used to control the offset of the mirror point relative to the center of the search space, thereby enabling dynamic scaling of the search area.

10. The capacity optimization configuration method for AC / DC microgrid hybrid energy storage system based on the improved Blackwing Kite algorithm as described in claim 9, characterized in that: The dynamic scaling of the search area includes expansion and contraction modes, specifically: When the fitness of the current individual and the fitness of the mirror point satisfy the first preset relationship, the random reflection factor causes the mirror point to shift far away from the center of the interval, and enters the expansion mode to perform a coarse-grained global search. When the second preset relationship is satisfied, the random reflection factor causes the mirror point to move closer to the current solution, entering a contraction mode for fine-grained local search.

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