An optimal design method for a photovoltaic energy storage and charging system

Abstract

This invention provides an optimal design method for a photovoltaic-energy storage-charging system, belonging to the field of new energy power generation and energy storage technology. This invention introduces an improved NSGA-II optimization algorithm for optimizing the capacity design of the photovoltaic and energy storage system. By accurately calculating the annual revenue and payback period under different scales, it seeks the optimal combination of photovoltaic and energy storage capacities, and combines manual calculation methods for cross-validation to ensure the reliability of the results. Furthermore, this invention improves key aspects of the traditional NSGA-II algorithm, such as initialization of the population, non-dominated sorting, crowding calculation, crossover, and mutation operations, resulting in significant improvements in efficiency and accuracy. By optimizing the scale of photovoltaic and energy storage construction, this invention maximizes annual revenue while minimizing the payback period, significantly improving the system's economic benefits, shortening the investment payback period, and increasing annual returns.

Description

Technical Field

[0001] This invention relates to the field of new energy power generation and energy storage technology, specifically to an optimal design method for a photovoltaic-storage-charging system. Background Technology

[0002] With the transformation of the energy structure and the promotion of a low-carbon economy, photovoltaic (PV) power generation and energy storage technologies are gradually becoming important components of the power industry. PV power generation systems have advantages such as being green, environmentally friendly, and pollution-free, but they are affected by the timing of sunlight and weather conditions, leading to significant fluctuations in power generation. Energy storage systems, on the other hand, store electrical energy through batteries to meet peak electricity demand and improve system stability. However, the construction costs of both PV and energy storage systems are high, especially the investment in energy storage systems, resulting in a long payback period for the overall project. Therefore, how to achieve the optimal configuration of PV and energy storage systems through scientific design has become a key issue in improving system economics and reducing the payback period.

[0003] Currently, traditional photovoltaic (PV) and energy storage system designs mostly focus on selecting the system capacity scale; however, this approach does not fully consider the optimal matching of PV and energy storage system capacities. If the power generation capacity of the PV system and the storage capacity of the energy storage system are not properly matched, a series of adverse consequences will occur. On the one hand, some electrical energy cannot be fully utilized, resulting in resource waste; on the other hand, insufficient energy storage capacity will make it difficult to cope with peak demand. These problems will directly affect the system's profitability, lengthen the payback period, and reduce the project's return on investment.

[0004] Therefore, optimizing the design under different photovoltaic and energy storage capacities to minimize payback time and maximize annual returns has become a difficult point and challenge in the current design of photovoltaic-storage-charging systems. Summary of the Invention

[0005] To address the problems existing in current technologies, this invention provides an optimal design method for photovoltaic-energy storage-charging systems. This invention introduces an improved NSGA-II optimization algorithm to optimize the capacity design of the photovoltaic and energy storage systems. By accurately calculating the annual returns and payback periods under different scales, the optimal combination of photovoltaic and energy storage capacities is sought. This method can optimize the scale construction of the photovoltaic and energy storage systems to maximize annual returns while minimizing the payback period, significantly improving the economic efficiency of the system, shortening the investment payback period, and increasing annual returns.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0007] This invention provides an optimal design method for a photovoltaic energy storage and charging system, comprising the following steps:

[0008] Step S1: Collect relevant data on photovoltaic power generation and energy storage systems in a certain region, and define the scale range of photovoltaic and energy storage systems;

[0009] Step S2: Set the payback period and annual return as the objective functions, use the NSGA-II algorithm for multi-objective iterative optimization, and output the optimal configuration scheme of photovoltaic and energy storage system capacity;

[0010] Step S3: Based on the collected relevant data and the scale range of photovoltaic and energy storage systems, calculate the annual revenue and payback period for different scale ranges, and plot the curves based on the calculation results;

[0011] Step S4: Compare the results of manual calculation in Step S3 with the results of automatic output by the NSGA-II algorithm in Step S2, adjust the output of the NSGA-II algorithm, and output the optimal configuration scheme for the photovoltaic and energy storage system capacity.

[0012] Preferably, step S2, setting the payback period and annual return as objective functions, uses the NSGA-II algorithm for multi-objective iterative optimization to output the optimal configuration scheme of photovoltaic and energy storage system capacity, specifically includes the following steps:

[0013] Step S21: Initialize the population and generate an initial population of individuals that is a combination of photovoltaic capacity and energy storage capacity;

[0014] Step S22: Using the initial population as the parent population, calculate the objective function value of each individual in the parent population according to the set objective function, and perform non-dominated sorting of the individuals in the parent population according to the objective function value, dividing the parent population into multiple non-dominated levels.

[0015] Step S23: Calculate the crowding distance for each individual in the non-dominant tier and sort them;

[0016] Step S24: Based on the non-dominance level and crowding distance results, select superior parent individuals from the parent population for crossover and mutation operations to generate new individuals to form the offspring population.

[0017] Step S25: Merge the parent population with the offspring population, recalculate the non-dominated ordering and crowding distance, and select superior individuals to form a new parent population;

[0018] Step S26: If the preset number of iterations is reached or the termination condition is met, output the optimal solution. The output optimal solution is the optimal configuration of the photovoltaic and energy storage system capacity; otherwise, return to step S24 to continue iterating.

[0019] Preferably, in step S21, an adaptive sampling initialization strategy is used to initialize the population. Specifically, during the initial population generation process, based on a random generation of the initial population within the set scale range of the photovoltaic and energy storage system, historical operating data and prediction results are introduced, and the population is initialized using a dynamically adjusted perturbation factor. The calculation formula for generating the initial population is:

[0020]

[0021] in, This is the initial generation of photovoltaic capacity population; This represents the initial generation of energy storage capacity population; P PV,min and P PV,max The minimum and maximum values ​​are the preset range for the scale of the photovoltaic system; E storage,min and E storage,max ε represents the minimum and maximum values ​​within the preset range of energy storage system size. init This is a disturbance factor that is dynamically adjusted based on historical operating data and forecast results;

[0022] Disturbance factor ε init The calculation formula is:

[0023]

[0024] Where, σ data The standard deviation of historical data represents the volatility of the data; μ data is the mean of historical data; k1 is the adjustment coefficient, k1 = 0.1-0.2.

[0025] Preferably, in the non-dominated sorting process of step S22, a dynamically adjusted target weight w is introduced. k The weights of each objective are dynamically adjusted according to the current stage of the optimization process to optimize the objective function mapping. The calculation formula is as follows:

[0026]

[0027] Among them, Fitnesss i The overall objective function for output; w k The target weights are automatically adjusted based on the current optimization progress to balance the relationship between the two objectives; f k (i) represents the k-th objective function of the i-th generation individual; M represents the number of objective functions.

[0028] Preferably, in step S23, a congestion distance calculation method based on environmental constraints is adopted. Specifically, this method incorporates an environmental constraint ratio C into the traditional congestion distance calculation. env Improved congestion distance d i The calculation formula is:

[0029]

[0030] Where, d i Let f be the crowding distance for the i-th generation individual; the first term of the formula is the traditional crowding distance calculation, f k,i+1 f represents the target value of the (i+1)th generation neighboring individuals under the k-th target; k,i-1 f represents the target value of the (i-1)th generation neighboring individuals under the k-th target; k,max and f k,min These represent the maximum and minimum values ​​of neighboring individuals under the k-th objective, respectively; M is the number of objective functions; the second term is the proportion of environmental constraints introduced, C. env C env,i Let C be the environmental constraint value satisfied by the current solution of the i-th generation. env,max α represents the maximum permissible environmental constraint value; α is the weighting coefficient.

[0031] Preferably, in step S24, when performing the mutation operation on the selected parent individuals, an adaptive mutation operator based on local convergence is introduced. The mutation operation automatically adjusts the mutation probability according to the local dissimilarity of the population, and the mutation probability P... mut The calculation formula is:

[0032]

[0033] Among them, P mut Let λ be the mutation probability. conv P is the convergence speed parameter. min_mut Δf is the lower bound of the mutation probability. local Δf is a measure of local dissimilarity, representing the local distribution of solutions in the current population. local The calculation formula is:

[0034]

[0035] Among them, f neighbor f is the fitness value of the solutions in the neighborhood surrounding the current solution; current f is the fitness value of the current solution. max f is the maximum fitness value of the solutions in the neighborhood surrounding the current solution; min It is the minimum fitness value of the solutions in the neighborhood surrounding the current solution.

[0036] Preferably, in step S24, when performing the crossover operation on the selected parent individuals, a directional crossover operator based on the changing trend of the objective function is introduced. The crossover operation dynamically adjusts the crossover point position according to the gradient information of the objective function, and the calculation formula is as follows:

[0037]

[0038] in, The sub-solution after the crossover operation; P parent1 and P parent2 There are two parent solutions; α is the cross coefficient, which is dynamically adjusted according to the changing trend of the objective function. The formula for calculating the cross coefficient α is:

[0039]

[0040] Among them, f parent1 and f parent2 is the objective function value of the two parent individuals, and ∈ is a small constant to prevent the denominator from being zero.

[0041] Preferably, during the iterative process of the NSGA-II algorithm in step S26, the convergence weight w is dynamically adjusted. c and diversity weight w d This enables dynamic control of convergence and diversity at different iteration stages of the algorithm, expressed by the following formula:

[0042] S next =arg max(w c ·C convergence +w d ·f diversity )

[0043] Among them, S next C is the selected population for the next generation. convergence The formula used to measure the deviation of the entire population from the current optimal solution is:

[0044]

[0045] Among them, f i f is the target value for the i-th generation individual; best The target value of the current optimal solution; N is the population generation number; f diversity f represents the distribution of solutions in the population, and measures the uniformity of the distribution by the difference between adjacent solutions. diversity The calculation formula is:

[0046]

[0047] w c This is the convergence weight, which gradually increases with the number of iterations; w d The diversity weight gradually decreases as the number of iterations increases, and the calculation formula is as follows:

[0048]

[0049] w d =1-w c

[0050] Where gen is the number of iterations of the NSGA-II algorithm, and max_gen is the maximum number of iterations of the NSGA-II algorithm.

[0051] Preferably, in step S3, calculating the annual return and payback period for different scale ranges includes the following steps:

[0052] Step S31: Based on the set scale range of the photovoltaic system, gradually increase the photovoltaic capacity settings in fixed increments to obtain multiple photovoltaic capacity settings;

[0053] Step S32: Based on the set scale range of the energy storage system, gradually increase the energy storage capacity by a fixed step size to obtain multiple energy storage capacity settings; set multiple energy storage consumption methods for each energy storage capacity, including full consumption, peak consumption, and partial consumption;

[0054] Step S33: Combine multiple photovoltaic capacity settings with multiple energy storage capacity settings to obtain all photovoltaic capacity and energy storage capacity combination schemes. Under each photovoltaic capacity and energy storage capacity combination scheme, calculate the annual income and payback period according to different energy storage consumption methods.

[0055] Step S34: Based on the calculation results of the scheme, plot the relationship curves between energy storage capacity and annual income, and between energy storage capacity and payback period.

[0056] Preferably, when evaluating the optimal photovoltaic and energy storage system capacity configuration scheme output by the method, a time-based annual revenue calculation model based on dynamic market electricity prices and load forecasting is adopted. By combining dynamic electricity prices and load demand, the annual revenue is calculated in a time-based manner. The calculation formula of the annual revenue objective function is defined as follows:

[0057]

[0058] Among them, R annual (P PV E storage ) represents the annual return; P PV For photovoltaic power generation capacity; E storage Energy storage and discharge capacity; E storage (t) represents the energy storage discharge amount during time period t; p market (t) represents the dynamic market electricity price at time t; η PV η is the efficiency factor for photovoltaic power generation. storage C is the efficiency factor of the energy storage system. PV C is the cost of photovoltaic construction. storage The cost of building the energy storage system is represented by T, which represents the number of time periods.

[0059] Compared with the prior art, the beneficial effects of the present invention are:

[0060] 1. This invention introduces an improved NSGA-II algorithm, aiming to minimize payback period and maximize annual return. It optimizes the capacity design of photovoltaic (PV) and energy storage systems by precisely calculating annual return and payback period under different scales, seeking the optimal combination of PV and energy storage capacity. Cross-validation is performed using manually calculated strategies to ensure the reliability of the results. This method can optimize the scale construction of PV and energy storage systems, maximizing annual return while minimizing payback period, significantly improving system economic efficiency, shortening the investment payback period, and increasing annual return.

[0061] Through the above innovations, this invention comprehensively improves the scientific rigor, applicability, and economic value of photovoltaic and energy storage system optimization, from initializing the population, optimizing the objective function, handling environmental constraints, to verification methods.

[0062] 2. This invention systematically improves upon the traditional NSGA-II algorithm, addressing key aspects from population initialization, non-dominated sorting, crowding calculation, to crossover and mutation operations. The optimized algorithm achieves significant improvements in efficiency and accuracy, as detailed below:

[0063] 1) Efficient Population Initialization Strategy: This invention proposes an adaptive sampling-based population initialization strategy that combines historical data and prediction results, significantly improving the initial quality of the population. By reducing redundant computational problems caused by random initialization, this strategy enables the algorithm to enter the optimal solution search region more quickly. Compared with traditional random initialization methods, this method is more targeted and more efficient, providing a solid foundation for the efficient operation of the optimization algorithm.

[0064] 2) Dynamically weighted non-dominated sorting and objective function mapping: In non-dominated sorting, this invention innovatively introduces a dynamic objective weight adjustment mechanism. This mechanism flexibly adjusts the priority of maximizing profit and minimizing payback time according to the stage of the optimization process, thereby achieving adaptive optimization. Through this mechanism, the algorithm can focus on key objectives at different stages, improving the flexibility and accuracy of multi-objective optimization and effectively solving the limitations caused by fixed weights in traditional methods.

[0065] 3) Improved Congestion Distance Based on Environmental Constraints: Addressing environmental conditions such as power supply limitations and grid capacity constraints in practical engineering projects, this invention introduces an environmental adaptability factor into the congestion distance calculation, giving higher priority to solutions that meet the constraints during the optimization process. This improvement not only enhances the practical feasibility of the optimized solution but also ensures that the results better align with actual engineering needs, providing more valuable guidance for the configuration of photovoltaics and energy storage.

[0066] 4) Adaptive Mutation Operator: This invention designs an adaptive mutation operator based on local convergence. By dynamically adjusting the mutation probability and mutation magnitude, the algorithm can escape the trap of local optima. Simultaneously, this operator achieves a balance between global search and refined local search, effectively improving the algorithm's exploration capability and convergence in complex solution spaces.

[0067] 5) Directional Crossover Strategy: This invention proposes a directional crossover strategy based on the gradient information of the objective function. By analyzing the directionality of the parent solution, the position of the crossover point is dynamically adjusted, effectively avoiding the quality degradation of the child solution caused by traditional random crossover operations. This strategy improves the overall quality and search efficiency of the child solution, enhancing the algorithm's performance in multi-objective optimization.

[0068] 6) A dynamic selection strategy to enhance convergence and maintain diversity: To ensure both convergence and diversity during the optimization process, this invention employs a dynamic selection strategy that combines population diversity distribution characteristics to dynamically balance the quality and diversity of solutions. This method effectively avoids premature convergence, enabling the algorithm to explore more potential optimal solution regions while maintaining the diversity of optimized solutions.

[0069] 3. Objective Function Optimization and Evaluation Model under Dynamic Market Environment: This invention introduces an objective function model based on dynamic market electricity prices and load forecasting. Through a precise time-based revenue calculation method, it comprehensively evaluates the economic benefits of photovoltaic and energy storage systems. Compared with traditional static evaluation methods, this model more realistically reflects the dynamic changes in the market environment, making the optimization results more valuable for practical applications.

[0070] 4. High-precision manual algorithm comparison and verification: In the verification phase, this invention combines manual calculations with three absorption methods (full absorption, peak absorption, and partial absorption) to analyze the matching patterns of photovoltaics and energy storage, and plots the relationship between energy storage capacity and annual revenue, and between energy storage capacity and payback period. Comparing the discrete data points calculated manually with the continuous results of the optimized algorithm further verifies the scientific validity and reliability of the optimized algorithm, while also demonstrating the significant advantages of this invention in terms of efficiency and accuracy. Attached Figure Description

[0071] Figure 1 This is a basic flowchart of an optimal design method for a photovoltaic energy storage and charging system according to an embodiment of the present invention;

[0072] Figure 2 This is a detailed flowchart of an optimal design method for an optical energy storage and charging system according to an embodiment of the present invention;

[0073] Figure 3 The above are the photovoltaic and original energy storage configuration absorption curves for embodiments of the present invention without using the improved NSGA-II optimization algorithm;

[0074] Figure 4 The above are the photovoltaic and primary energy storage configuration absorption curves using the improved NSGA-II optimization algorithm in an embodiment of the present invention. Detailed Implementation

[0075] The following will refer to the appendices in the embodiments of the present invention. Figure 1 - Appendix Figure 4 The technical solutions in the embodiments of the present invention are clearly and completely described herein. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0076] Example 1

[0077] Combination Figure 1 As shown in the figure, this embodiment provides an optimal design method for a photovoltaic energy storage and charging system, including the following steps:

[0078] Step S1: Collect relevant data on photovoltaic power generation and energy storage systems in a certain region, and define the scale range of photovoltaic and energy storage systems;

[0079] Step S2: Set the payback period and annual return as the objective functions, use the NSGA-II algorithm for multi-objective iterative optimization, and output the optimal configuration scheme of photovoltaic and energy storage system capacity;

[0080] Step S3: Based on the collected relevant data and the scale range of photovoltaic and energy storage systems, calculate the annual revenue and payback period for different scale ranges, and plot the curves based on the calculation results;

[0081] Step S4: Compare the results of manual calculation in Step S3 with the results of automatic output by the NSGA-II algorithm in Step S2, adjust the output results of the NSGA-II algorithm, and finally output the optimal configuration scheme for the photovoltaic and energy storage system capacity.

[0082] This invention introduces an improved NSGA-II multi-objective optimization algorithm for the optimized design of photovoltaic (PV) and energy storage system capacity. By accurately calculating the annual revenue and payback period under different scales, it seeks the optimal combination of PV and energy storage capacity, and cross-validates the results with manually calculated strategies to ensure reliability. This method can optimize the scale construction of PV and energy storage systems to maximize annual revenue while minimizing payback time, significantly improving the system's economic efficiency, shortening the investment payback period, and increasing annual returns. This provides a theoretical basis and practical guidance for the widespread application of future PV-energy storage-charging systems. This optimization process not only improves the sustainability of the power system but also reduces dependence on traditional energy sources, promoting the green transformation of the energy structure.

[0083] Example 2

[0084] Combination Figure 1 As shown in the figure, this embodiment provides an optimal design method for a photovoltaic energy storage and charging system, including the following steps:

[0085] Step S1: Collect relevant data on photovoltaic power generation and energy storage systems in a certain region, and define the scale range of photovoltaic and energy storage systems;

[0086] Step S2: Set the payback period and annual return as the objective functions, use the NSGA-II algorithm for multi-objective iterative optimization, and output the optimal configuration scheme of photovoltaic and energy storage system capacity;

[0087] Step S3: Based on the collected relevant data and the scale range of photovoltaic and energy storage systems, calculate the annual revenue and payback period for different scale ranges, and plot the curves based on the calculation results;

[0088] Step S4: Compare the results of manual calculation in Step S3 with the results of automatic output by the NSGA-II algorithm in Step S2, adjust the output results of the NSGA-II algorithm, and finally output the optimal configuration scheme for the photovoltaic and energy storage system capacity.

[0089] In this embodiment, for step S1, relevant data on photovoltaic power generation and energy storage systems are collected, and the scale range of the photovoltaic and energy storage systems is set. Taking an industrial park as an example, the specific implementation process involves collecting data including: the park's actual electricity consumption curve, the minimum and maximum photovoltaic scale allowed during the park's design, the designed scale of the photovoltaic system, the historical power generation curve of the photovoltaic system, the construction cost of the photovoltaic system, and the construction cost of the energy storage system. This type of data forms the basis for subsequent optimization calculations.

[0090] The construction scale range of photovoltaic and energy storage systems is defined. Taking an industrial park with completed photovoltaic and energy storage systems as an example, the construction scope of photovoltaic and energy storage systems is defined according to the actual conditions of the park: the size of a single photovoltaic panel is 1134mm×2382mm, the power is 550Wp, the capacity range of photovoltaic construction is 3-5MW, and the capacity range of energy storage construction is 1000-8000kWh. The initial population is used for subsequent optimization calculations.

[0091] In this embodiment, for step S2, the payback period and annual return are set as the objective functions of the NSGA-II algorithm. The optimization objective of the NSGA-II algorithm is set as minimizing the payback period and maximizing the annual return. The calculation method for the objective functions of payback period and annual return is specifically defined. The specific calculation of payback period and annual return is based on data related to photovoltaic power generation and energy storage systems, utilizing the photovoltaic power generation and energy storage demand curves, and calculating the payback period and annual return through the set objective functions.

[0092] The payback period calculation fully considers the construction costs of the photovoltaic system and the energy storage system, as well as the photovoltaic power generation, energy storage capacity, and operating revenue. The payback period is the ratio of investment cost to the system's annual revenue, and the formula for calculating the payback period is:

[0093]

[0094] The calculation of annual return fully considers the system's return on investment and operating costs, encompassing factors such as the power generation, storage capacity, and electricity price of the photovoltaic and energy storage systems. First, the total return over a 20-year period is calculated. Then, the total return is divided by the number of years, 20, and the result is the annual return. The formula for calculating annual return is:

[0095] Total revenue over 20 years = (20 × (revenue from photovoltaic power generation + revenue from energy storage power generation) - photovoltaic construction cost - energy storage construction cost)

[0096]

[0097] Other engineering costs have been included in the construction costs of photovoltaic and energy storage projects.

[0098] Combination Figure 2 As shown, in this embodiment, for step S3, the annual return and payback period for different scales are manually calculated, and curves are plotted based on the calculation results. The manual calculation of the annual return and payback period for different scales includes the following steps:

[0099] Step S31: Based on the set scale range of the photovoltaic system, gradually increase the photovoltaic capacity settings in fixed increments to obtain multiple photovoltaic capacity settings.

[0100] Step S32: Based on the set scale range of the energy storage system, multiple energy storage capacity settings are obtained by gradually increasing the capacity in fixed increments. To comprehensively evaluate the impact of the energy storage system on the photovoltaic power generation system, multiple energy storage absorption methods are set for each energy storage capacity, including full absorption, peak absorption, and partial absorption, which can cover various possible situations in practical applications for different energy storage scales. Three energy storage absorption methods are set for each energy storage capacity, specifically:

[0101] Full absorption: All electricity in the service area will be absorbed through photovoltaic and energy storage systems until off-peak electricity prices are implemented.

[0102] Peak absorption: All electricity in the service area is absorbed through photovoltaic and energy storage systems until the normal electricity price is reached, that is, electricity is absorbed first during peak electricity price periods.

[0103] Partial absorption: In this mode, the photovoltaic system charges the energy storage device, which in turn provides power during peak electricity demand periods until the energy storage device is fully discharged.

[0104] Step S33: Combine multiple photovoltaic capacity settings with multiple energy storage capacity settings to obtain all photovoltaic capacity and energy storage capacity combination schemes. Under each photovoltaic capacity and energy storage capacity combination scheme, calculate the annual income and payback period according to different energy storage consumption methods.

[0105] Step S34: Based on the calculation results of the proposed schemes, plot the relationship between energy storage capacity and annual revenue, and between energy storage capacity and payback period. In the implementation process, first plot the results of all these schemes, then use Newton's difference method and least squares method to process the data, ultimately plotting a continuous relationship curve. The obtained relationship curve reveals the impact of changes in the scale of photovoltaic and energy storage on the system's economics, and provides decision-makers with an intuitive and scientific basis for optimizing the configuration of photovoltaic and energy storage systems.

[0106] For example, the set photovoltaic (PV) capacity range is 3-5MW with increments of 0.5MW, and the set energy storage capacity range is 1000-8000kWh with increments of 1000kWh. Starting with 3.5MW, the PV capacity is gradually increased in 0.5MW increments until it reaches 5MW, resulting in 5 different PV capacity settings. Similarly, starting with 1000kWh, the energy storage capacity is gradually increased in 1000kWh increments until it reaches 8000kWh, resulting in 8 different energy storage capacity settings. These 5 PV and 8 energy storage capacity settings are then paired to create 40 possible combinations. The annual return and payback period are calculated for each combination and each nanometer of the system. Based on the results of all these combinations, points are plotted to create a trend curve, and finally, the optimal point is determined based on the plotted curve.

[0107] For step S4, verify and compare the results of manual calculation with the output of the NSGA-II algorithm, compare and analyze the payback time and annual income under different scales, assist decision-makers in making the best choice, adjust the results to a reasonable state, and finally output the optimal configuration scheme of photovoltaic and energy storage system capacity.

[0108] In the verification phase, the manually calculated discrete data points are compared with the continuous optimization curve results of the optimization algorithm to ensure the scientific validity and reliability of the algorithm. This also demonstrates the significant advantages of this invention in terms of efficiency and accuracy. During the comparison, if some manually calculated discrete points match the algorithm's optimization results, it indicates that the algorithm can effectively solve for the optimal configuration and possesses high accuracy. To further verify the algorithm's effectiveness, the algorithm results are also verified based on the manually calculated results to ensure that the optimization results are reasonable, reliable, and have practical application value.

[0109] In this embodiment, to accurately evaluate the performance of photovoltaic and energy storage systems, this invention proposes a time-based annual revenue calculation model based on dynamic market electricity prices and load forecasting. This model evaluates the optimal photovoltaic and energy storage system capacity configuration scheme output by the method. This model overcomes the limitations of traditional simple annual revenue calculations by combining dynamic electricity prices and load demand, employing a precise time-based approach to calculate annual revenue, thus making the system's revenue more dynamic and accurate, and thus closer to real-world application scenarios. The formula for calculating the objective function annual revenue is defined as follows:

[0110]

[0111] Among them, R annual (P PV E storage ) represents the annual income (yuan / year); P PV Photovoltaic power generation capacity (MW); E storage Energy storage and discharge capacity; E storage (t) represents the energy storage discharge amount (kWh) during time period t; p market (t) represents the dynamic market electricity price (yuan / kWh) at time t; η PV η is the efficiency factor for photovoltaic power generation. storage C is the efficiency factor of the energy storage system. PV C represents the construction cost of photovoltaic power generation (in yuan). storage The cost of the energy storage system is RMB; T represents the number of time periods.

[0112] This model has the following significant features: 1. First, it considers dynamic market electricity prices: Unlike traditional static pricing models, this invention introduces a dynamic market electricity price model, taking into account peak and off-peak electricity prices at different times. Through this variable, the objective function can comprehensively reflect the impact of electricity price fluctuations on the revenue of photovoltaic and energy storage systems, thus more realistically assessing economic benefits. 2. Second, it considers the synergistic effect of energy storage and photovoltaics: The power generation of the photovoltaic system and the discharge of the energy storage system complement each other at different times, improving the utilization efficiency of power generation capacity and meeting load demand. 3. This model also comprehensively considers photovoltaic power generation efficiency, thus more accurately reflecting the actual operating performance of the system. 4. Finally, it considers construction cost constraints: The model explicitly deducts the construction costs of photovoltaics and energy storage, ensuring that the optimization results, while pursuing maximum economic benefits, also meet the actual constraints of investment costs. Through this time-based dynamic electricity price model, the algorithm can dynamically adjust the configuration scheme of photovoltaics and energy storage according to future electricity price fluctuations, thereby maximizing the economic benefits of the system.

[0113] This invention, by combining dynamic electricity pricing and load forecasting, overcomes the limitations of traditional static assessments, providing a more realistic reflection of system benefits. The introduction of time-based revenue calculations and multi-dimensional parameter comprehensive evaluation ensures that the optimization results accurately match actual operating conditions. Compared to traditional static assessment methods, this model more realistically reflects the dynamic changes in the market environment, making the optimization results more practically valuable. Furthermore, this model is applicable to the assessment and design of various photovoltaic and energy storage scales, providing strong support for developing scientific and reasonable system construction plans and significantly improving the practicality and reliability of the optimization process.

[0114] Example 3

[0115] Combination Figure 1 As shown in the figure, this embodiment provides an optimal design method for a photovoltaic energy storage and charging system, including the following steps:

[0116] Step S1: Collect relevant data on photovoltaic power generation and energy storage systems in a certain region, and define the scale range of photovoltaic and energy storage systems;

[0117] Step S2: Set the payback period and annual return as the objective functions, use the NSGA-II algorithm for multi-objective iterative optimization, and output the optimal configuration scheme of photovoltaic and energy storage system capacity;

[0118] Step S3: Based on the collected relevant data and the scale range of photovoltaic and energy storage systems, calculate the annual revenue and payback period for different scale ranges, and plot the curves based on the calculation results;

[0119] Step S4: Compare the results of manual calculation in Step S3 with the results of automatic output by the NSGA-II algorithm in Step S2, adjust the output results of the NSGA-II algorithm, and finally output the optimal configuration scheme for the photovoltaic and energy storage system capacity.

[0120] Combination Figure 2 As shown, in this embodiment, step S2, setting the payback period and annual return as objective functions, uses the NSGA-II algorithm for multi-objective iterative optimization to output the optimal configuration scheme of photovoltaic and energy storage system capacity, specifically includes the following steps:

[0121] Step S21: Initialize the population and generate an initial population of individuals that is a combination of photovoltaic capacity and energy storage capacity;

[0122] Step S22: Using the initial population as the parent population, calculate the objective function value of each individual in the parent population according to the set objective function, and perform non-dominated sorting of the individuals in the parent population according to the objective function value, dividing the parent population into multiple non-dominated levels.

[0123] Step S23: Calculate the crowding distance for each individual in the non-dominant tier and sort them;

[0124] Step S24: Based on the non-dominance level and crowding distance results, select superior parent individuals from the parent population for crossover and mutation operations to generate new individuals to form the offspring population.

[0125] Step S25: Merge the parent population with the offspring population, recalculate the non-dominated ordering and crowding distance, and select superior individuals to form a new parent population;

[0126] Step S26: If the preset number of iterations is reached or the termination condition is met, output the optimal solution. The output optimal solution is the optimal configuration of the photovoltaic and energy storage system capacity; otherwise, return to step S24 to continue iterating.

[0127] exist Figure 2 The right side of the diagram shows the basic workflow of the NSGA-II algorithm. The fitness function calculation is essentially the same as the objective function calculation. Fitness values ​​are used to measure the performance of individual algorithms and guide the selection process. Determining whether the objective requirements are met means outputting the most economical solution while adhering to practical requirements (e.g., non-negative economic conditions, photovoltaic energy storage results not exceeding limits, etc.).

[0128] In this embodiment, the present invention systematically improves upon the traditional NSGA-II algorithm, addressing key aspects from population initialization, non-dominated sorting, crowding calculation, to crossover and mutation operations. The optimized algorithm achieves significant improvements in efficiency and accuracy. Specific improvements are as follows:

[0129] In this embodiment, for step S21, the present invention adopts an adaptive sampling initialization strategy to initialize the population and generate an initial population combining photovoltaic capacity and energy storage capacity.

[0130] Traditional NSGA-II algorithms typically initialize the population using random generation. To improve the efficiency of population initialization and the ability to explore the solution space, this invention proposes an adaptive sampling-based initialization strategy. Specifically, during the initial population generation process, based on a random generation method within a defined scale range for photovoltaic and energy storage systems, historical operating data and prediction results are incorporated. A dynamically adjusted perturbation factor is used to initialize the population. This strategy can pre-determine potential high-efficiency regions, ensuring that the initial population distribution is more concentrated in potential optimal solution regions, thereby improving the initial quality of the population. The formula for generating the initial population is:

[0131]

[0132] in, This represents the initial generation of photovoltaic capacity population; This represents the initial generation of energy storage capacity population; PPV,min and P PV,max The minimum and maximum values ​​are the preset range for the scale of the photovoltaic system; E storage,min and E storage,max ε represents the minimum and maximum values ​​within the preset range of energy storage system size. init This is a disturbance factor that is dynamically adjusted based on historical operating data and forecast results.

[0133] Disturbance factor ε init The calculation formula is:

[0134]

[0135] Where, σ data The standard deviation of historical data represents the volatility of the data; μ data is the mean of historical data; k1 is the adjustment coefficient, k1 = 0.1-0.2.

[0136] In the specific implementation process, historical data on the industrial park and photovoltaic system in the region (such as load demand and fluctuation range of photovoltaic power generation) can provide important basis for population initialization. The historical mean and standard deviation of system power generation and demand can be used to estimate the range of disturbance factors.

[0137] The value of k1 is primarily determined by three factors: First, it is calculated using the standard deviation and mean of historical data to reflect actual data fluctuations. Second, it dynamically selects the perturbation factor based on the sensitivity of the optimization objective and the changing patterns of the objective function. Third, it calculates the perturbation amplitude based on the physical constraints of the application scenario and the upper and lower limits of the system design to ensure the effectiveness of the search space. For example, the perturbation range is estimated using the volatility (standard deviation) and average (mean) of historical data to ensure the quality of the initial population. If the data fluctuations are large, k1 is appropriately increased to expand the search space; conversely, k1 is decreased to converge to a smaller, more efficient region. When the objective function is not sensitive to the search space, k1 can be small, such as 0.1. When the objective function requires a large search range, k1 is large, such as 0.2.

[0138] The traditional NSGA-II algorithm's random initialization of the population can lead to unnecessary redundant computations and a poor initial population quality, affecting convergence speed and solution quality. This invention, however, introduces an adaptive initialization strategy that incorporates historical data, prediction results, and physical constraints to improve the quality and distribution range of the initial population. This avoids complete reliance on random population generation and directly initiates the search within potential optimal solution regions, thereby accelerating the optimization process and making population initialization more targeted and efficient.

[0139] In this embodiment, during the non-dominated ranking process in step S22, the present invention proposes a non-dominated ranking method based on dynamic adjustment of target importance, by introducing dynamically adjusted target weights w. k The objective function mapping is optimized. The relative importance of different objectives (payback time and annual return) is fully considered, and the weight of each objective is dynamically adjusted according to the current stage of the optimization process. This allows the algorithm to focus more on payback time in the early stages and prioritize annual return in later stages, thus optimizing the final solution. The calculation formula is as follows:

[0140]

[0141] Among them, Fitnesss i The overall objective function for output; w k The target weights are automatically adjusted based on the current optimization progress to balance the relationship between the two objectives; f k (i) represents the k-th objective function of the i-th individual; M represents the number of objective functions. This method can automatically switch the focus of attention for optimization tasks at different stages, thereby improving the adaptability and efficiency of the algorithm.

[0142] Applying this calculation formula to this embodiment, we define two optimization objectives: Objective 1, minimizing the payback period f1, and Objective 2, maximizing the annual return f2. The objective function mapping formula is as follows:

[0143] Firness i =w1·f1+w2·f2

[0144] Where w1 is the weight of payback period and w2 is the weight of annual return, and w1+w2=1 is set for normalization constraint.

[0145] In the early stages of optimization, global search is emphasized, with a higher weight given to maximizing annual returns (f2). In the later stages of optimization, attention is gradually increased to minimizing payback time (f1) to achieve more accurate local search and convergence. The weights w are dynamically adjusted based on the current generation t and the maximum generation T. k :

[0146]

[0147] Where w1(i) is the weight of the payback time in i iterations, and w2(i) is the weight of the annual return in i iterations. According to this formula, w1(i) gradually increases with the number of iterations, while w2(i) gradually decreases with the number of iterations.

[0148] In the early optimization stage (global search), the initial population is widely distributed, and the algorithm's objective leans towards finding the solution that maximizes profit, resulting in a larger weight w2. During non-dominated sorting, the annual profit objective f2 contributes significantly. In the later optimization stage (local convergence), as the weight w1 increases, minimizing the payback period becomes a priority. During non-dominated sorting, the contribution of the payback period objective f1 gradually increases, and the algorithm focuses on finding an equilibrium solution.

[0149] Traditional NSGA-II uses fixed weights for objective ranking, meaning the relative importance of different objective functions remains constant throughout the algorithm's execution. This prevents the algorithm from adjusting objective priorities according to different stages of the optimization process. This invention, however, introduces objective weights w... k The dynamic adjustment mechanism adjusts the weights of different objectives according to the current stage of optimization during each generation of evolution. This allows the algorithm to automatically adapt to the optimal objective function focus at different stages, thereby guiding the search process more accurately, optimizing the multi-objective optimization process, and making the algorithm more efficient at different optimization stages.

[0150] In this embodiment, for the congestion distance calculation in step S23, this invention proposes a congestion distance calculation method based on environmental constraints. This method, based on traditional congestion calculation, adds the influence of environmental constraints on individual fitness, giving higher priority to solutions with higher environmental fitness and ensuring that the optimization results are closer to actual needs. Specifically, this method incorporates an environmental constraint ratio C into the congestion distance calculation. env Improved congestion distance d i The calculation formula is:

[0151]

[0152] Where, d i Let f be the crowding distance for the i-th generation individual; the first term of the formula is the traditional crowding distance calculation, f k,i+1 f represents the target value of the (i+1)th generation neighboring individuals under the k-th target; k,i-1 f represents the target value of the (i-1)th generation neighboring individuals under the k-th target; k,max and f k,min , respectively, represent the maximum and minimum values ​​of the neighboring individuals under the k-th objective; M is the number of objective functions;

[0153] The second item is the proportion of environmental constraints introduced, C. env The crowding distance is adjusted based on the degree to which individuals meet environmental constraints. env,i Let C be the environmental constraint value satisfied by the current solution of the i-th generation. env,maxα represents the maximum permissible environmental constraint value; α is the weighting coefficient. By considering environmental constraints, solutions that do not meet the actual application conditions can be effectively filtered out, improving the robustness of the algorithm.

[0154] In the actual implementation process, if the scale of photovoltaic and energy storage construction of a certain scheme is too large and does not meet the needs of the site, but it generates significant benefits, then the scheme will be assigned a lower weighting coefficient because it clearly does not comply with environmental restrictions, thus excluding the scheme.

[0155] Traditional methods for calculating congestion distance only consider the congestion situation of the solution in the target space, neglecting actual environmental constraints (such as power supply limitations and grid capacity). This invention introduces the influence of environmental constraints into the congestion calculation. By weighting the environmental fitness, individuals that meet the environmental constraints have higher priority in the selection process, thereby guiding the search towards feasible solution regions that better conform to actual constraints. This improves the practical feasibility of the results and makes the optimized solution more aligned with real-world application needs.

[0156] In this embodiment, in step S24, when performing a mutation operation on the selected parent individual, the present invention introduces an adaptive mutation operator based on local convergence. The mutation operation automatically adjusts the mutation probability P according to the local dissimilarity of the population. mut That is, when the population converges in a certain region, the algorithm automatically adjusts the mutation probability; when the convergence speed is slow, the mutation probability P is increased. mut This enhances the exploration capability and reduces the mutation probability as the solution gradually converges within a local region. This mutation probability P... mut The calculation formula is:

[0157]

[0158] Among them, P mut Let λ be the mutation probability. conv P is the convergence speed parameter. min_mut Δf is the lower bound of the mutation probability. local Δf is a measure of local dissimilarity, representing the local distribution of solutions in the current population. local The calculation formula is:

[0159]

[0160] Among them, f neighbor f is the fitness value of the solutions in the neighborhood surrounding the current solution; current f is the fitness value of the current solution. max f is the maximum fitness value of the solutions in the neighborhood of the current solution, that is, the fitness value of the solution with the best fitness (the largest fitness value) among all neighborhood solutions; minf is the minimum fitness value among the solutions in the neighborhood of the current solution, that is, the fitness value of the solution with the worst fitness (the smallest one) among all neighborhood solutions; max -f min The fitness range of the neighborhood solutions is the difference between the maximum and minimum values. This is used to standardize the difference between the current solution and the neighborhood solutions, and to avoid the calculation results being affected by the different scales of the fitness values.

[0161] Through this dynamically adjusted mutation mechanism, the algorithm can more effectively escape local optima and find the global optimum during convergence. Simultaneously, during local convergence, directed mutation is introduced based on the gradient direction of the solution to guide the algorithm by addressing the difference between the current solution and the local optimum. The directed mutation formula is as follows:

[0162] x new =x current +α·(x best -x current )+β·randn()

[0163] Where, x current The variable value for the current solution; x best α is the local optimum of the current neighborhood; α is the mutation guidance parameter, which controls the degree of directed mutation; β is the random perturbation factor, which increases the diversity of solutions; randn() is a standard normal distribution random number.

[0164] Traditional NSGA-II algorithms typically employ fixed mutation probabilities and random perturbation amplitudes in their mutation operations. This can lead to insufficient space exploration capabilities in the early stages of the algorithm, making it unable to dynamically adjust based on local convergence during the optimization process. This fixed approach can easily result in overly random mutation operations, making it difficult to effectively guide the solution towards the optimal region or causing it to get stuck in a local optimum and unable to escape.

[0165] This invention innovatively proposes an adaptive mutation strategy based on local convergence. By dynamically adjusting the mutation probability and perturbation amplitude, it achieves adaptive optimization of the mutation process. It offers the following advantages: Dynamically adapting to convergence conditions, the mutation operation adaptively adjusts the mutation probability based on local dissimilarity, ensuring efficient search at different stages; by introducing directed mutation, the algorithm can perform refined searches near local optima, making mutations more targeted and effective, while combining random perturbation enhances global search capabilities, effectively escaping local optima; balancing convergence and diversity, the adaptive adjustment of mutation probability and perturbation amplitude avoids premature convergence, maintains population diversity, ensures comprehensive exploration of the solution space, improves solution quality and global search capabilities, and enhances the algorithm's adaptability and efficiency in complex optimization problems.

[0166] Furthermore, in this embodiment, in step S24, when performing the crossover operation on the selected parent individuals, this invention proposes a directional crossover strategy based on the gradient information of the objective function. Specifically, it introduces a directional crossover operator based on the changing trend of the objective function. By analyzing the similarity and differences between the parent individuals, the crossover operation dynamically adjusts the crossover point position according to the gradient information of the objective function. The directional crossover calculation formula is:

[0167]

[0168] in, The sub-solution after the crossover operation; P parent1 and P parent2 There are two parent solutions; α is the cross coefficient, which is dynamically adjusted according to the changing trend of the objective function. The formula for calculating the cross coefficient α is:

[0169]

[0170] Among them, f parent1 and f parent2 Let be the objective function values ​​of the two parent individuals, and ∈ be a small constant to prevent the denominator from being zero. Using this formula, we can determine which parent the offspring is closer to based on the difference in the parent individuals' objective function values, thus guiding the search towards a more favorable objective function value.

[0171] Traditional crossover operations typically rely on fixed crossover point selection and random probabilities, which can lead to unclear directionality of solutions and significant randomness in the quality of offspring solutions, making it difficult to effectively approach the target region. The directional crossover operation proposed in this invention dynamically adjusts the crossover point position by introducing gradient information from the objective function. This gives the crossover operation not only the diversity of global search but also the directionality to approach the optimal solution region, thereby significantly improving the quality of offspring solutions and the convergence speed of the algorithm. It has the following advantages: Directional guidance: Dynamically adjusting the crossover point position through the gradient information of the objective function guides the offspring solution towards the optimal solution region, avoiding the instability caused by randomness; Improved search efficiency: The crossover operation is more precise, accelerating the convergence of the algorithm, reducing the probability of invalid search, and effectively avoiding the problem of invalid offspring generation caused by traditional random crossover; Improved offspring quality: Directional crossover can achieve a balance between global exploration and local optimization, ensuring that the generated offspring solutions have higher fitness.

[0172] In this embodiment, during the iterative process of the NSGA-II algorithm in step S26, to ensure the convergence and diversity of the algorithm during the optimization process, this invention proposes a convergence and diversity balancing strategy based on dynamic weight adjustment. This strategy can dynamically adjust the emphasis on convergence and diversity at different stages of optimization, thereby accelerating convergence towards the optimal solution while maintaining the diversity of the solution set. Specifically, this strategy introduces a dynamically adjusted convergence weight w. c and diversity weight w d This enables dynamic control of convergence and diversity at different iteration stages. The specific calculation formula is as follows:

[0173] S next =argmax(w c ·C convergence +w d ·f diversity )

[0174] Among them, S next The selected population for the next generation; C convergence It is used to measure the deviation of the entire population from the current optimal solution. It is calculated by averaging the distances between each individual in the population and the current optimal solution. The specific calculation formula is as follows:

[0175]

[0176] Among them, f i f is the target value for the i-th generation individual; best The target value of the current optimal solution; N is the population generation number; f diversity This represents the distribution of solutions in the population. The solutions are sorted by their objective value, and the uniformity of the distribution is measured by the difference between adjacent solutions. diversity The calculation formula is:

[0177]

[0178] w c This is the convergence weight, which gradually increases with the number of iterations; w d The diversity weight gradually decreases as the number of iterations increases, and the calculation formula is as follows:

[0179]

[0180] w d =1-w c

[0181] Where gen is the number of iterations of the NSGA-II algorithm, and max_gen is the maximum number of iterations of the NSGA-II algorithm.

[0182] The core challenge of the NSGA-II algorithm lies in simultaneously ensuring rapid convergence of solutions and maintaining population diversity. The dynamic weight adjustment logic of this invention runs through the entire algorithm optimization process, by adjusting the convergence weight w. c and diversity weight w d The dynamic adjustment achieves a phased balance of the optimization objective. In the initial stage (with fewer iterations), the initial population distribution is relatively random, making diversity maintenance particularly important. Therefore, weights are assigned to favor diversity maintenance (w). d >w c To broaden the search range and avoid premature convergence, the algorithm gradually transitions to the convergence phase in the intermediate stage as the number of algebras increases, by balancing w. c and w d The weights are adjusted to balance diversity exploration and convergence optimization. In the later stages (when the number of iterations approaches the maximum number of iterations), the population gradually converges to the vicinity of the optimal solution, at which point the weights gradually shift towards convergence enhancement (w). c >w d This is to accelerate the algorithm's approach to the optimal solution, thereby improving the overall optimization efficiency.

[0183] Traditional methods often fail to find a dynamic balance between convergence and diversity when dealing with multi-objective optimization problems, easily leading to premature convergence or uneven solution distribution. This invention introduces a dynamic weight adjustment mechanism, emphasizing diversity to expand the search space in the early stages and convergence acceleration in the later stages, ensuring high search performance at all stages. Its main advantages include: Adaptability: It can dynamically adjust weights according to the evolutionary stage, automatically balancing convergence and diversity; High-efficiency convergence: In the later stages, it quickly converges to the optimal solution, reducing computation time; Prevention of premature convergence: Through the diversity maintenance mechanism, it avoids the algorithm getting trapped in local optima; High practicality: It is applicable to complex multi-objective optimization problems in photovoltaic and energy storage systems, ensuring the quality and uniform distribution of solutions.

[0184] The following example compares the effects of using the improved NSGA-II algorithm before and after implementation: Before using the improved NSGA-II algorithm, the park had a 4.42MW photovoltaic system and a 1.25MW / 2.5MWh energy storage system. The total investment cost of this system was 14,640,000 yuan, with an annual return of 3,102,500 yuan, a payback period of 4.718 years, and a profit of 47,410,000 yuan over 20 years. Using the improved NSGA-II algorithm, it was found that with a 4.42MW photovoltaic system, configuring a 2.4MW / 4.8MWh energy storage system maximizes the benefits. The total investment cost of this system was 15,985,284 yuan, with an annual return of 3,774,881.1 yuan, a payback period of 4.234 years, and a profit of 59,512,338 yuan over 20 years. The payback period was shortened by 10%, and the total profit over 20 years increased by 25%. Furthermore, the grid integration curve is more reasonable; the original grid integration curve was as follows: Figure 3 As shown, after meeting the electricity demand of the industrial park, the surplus electricity generated by the photovoltaic system is used to charge the energy storage system. However, due to the small capacity of the energy storage system, some of the surplus electricity cannot be effectively stored, resulting in a waste of electrical resources. The energy storage system is completely discharged around 6 PM. After improvement and optimization, the surplus electricity of the photovoltaic system can be fully stored by the energy storage system and used to support the system until the end of the peak electricity price period, thereby maximizing the utilization of electrical resources and obtaining higher economic benefits. The improved power consumption curve is shown below. Figure 4 As shown.

[0185] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. An optimal design method for a photovoltaic energy storage and charging system, characterized in that, Includes the following steps: Step S1: Collect relevant data on photovoltaic power generation and energy storage systems in a certain region, and define the scale range of photovoltaic and energy storage systems; Step S2: Set the payback period and annual return as the objective functions, use the NSGA-II algorithm for multi-objective iterative optimization, and output the optimal configuration scheme of photovoltaic and energy storage system capacity; Step S2: Set the payback period and annual return as the objective functions, and use the NSGA-II algorithm for multi-objective iterative optimization to output the optimal configuration scheme of photovoltaic and energy storage system capacity. This specifically includes the following steps: Step S21: Initialize the population and generate an initial population of individuals that is a combination of photovoltaic capacity and energy storage capacity; Step S22: Using the initial population as the parent population, calculate the objective function value of each individual in the parent population according to the set objective function, and perform non-dominated sorting of the individuals in the parent population according to the objective function value, dividing the parent population into multiple non-dominated levels. Step S23: Calculate the crowding distance for each individual in the non-dominant tier and sort them; Step S24: Based on the non-dominance level and crowding distance results, select superior parent individuals from the parent population for crossover and mutation operations to generate new individuals to form the offspring population. Step S25: Merge the parent population with the offspring population, recalculate the non-dominated ordering and crowding distance, and select superior individuals to form a new parent population; Step S26: If the preset number of iterations has been reached or the termination condition is met, output the optimal solution. The output optimal solution is the optimal configuration of the photovoltaic and energy storage system capacity; otherwise, return to step S24 to continue iterating. During the iterative process of the NSGA-II algorithm in step S26, the convergence weight w is dynamically adjusted. c and diversity weight w d This enables dynamic control of convergence and diversity at different iteration stages of the algorithm, expressed by the following formula: S next =arg max(w c ·C convergence +w d ·f diversity ) Among them, S next C is the selected population for the next generation. convergence The formula used to measure the deviation of the entire population from the current optimal solution is: Among them, f i f is the target value for the i-th generation individual; best The target value of the current optimal solution; N is the population generation number; f diversity f represents the distribution of solutions in the population, and measures the uniformity of the distribution by the difference between adjacent solutions. diversity The calculation formula is: w c This is the convergence weight, which gradually increases with the number of iterations; w d The diversity weight gradually decreases as the number of iterations increases, and the calculation formula is as follows: In d =1-in c Where gen is the number of iterations of the NSGA-II algorithm, and max_gen is the maximum number of iterations of the NSGA-II algorithm; Step S3: Based on the collected relevant data and the scale range of photovoltaic and energy storage systems, calculate the annual revenue and payback period for different scale ranges, and plot the curves based on the calculation results; Step S4: Compare the results of manual calculation in Step S3 with the results of automatic output by the NSGA-II algorithm in Step S2, adjust the output of the NSGA-II algorithm, and output the optimal configuration scheme for the photovoltaic and energy storage system capacity.

2. The optimal design method for a photovoltaic energy storage and charging system according to claim 1, characterized in that, In step S21, an adaptive sampling initialization strategy is used to initialize the population. Specifically, during the initial population generation process, based on a random initial population generation method within the set scale range of the photovoltaic and energy storage system, historical operating data and prediction results are introduced, and a dynamically adjusted perturbation factor is used to initialize the population. The calculation formula for generating the initial population is: in, This is the initial generation of photovoltaic capacity population; This represents the initial generation of energy storage capacity population; P PV,min and P PV,max The minimum and maximum values ​​are the preset range for the scale of the photovoltaic system; E storage,min and E storage,max ε represents the minimum and maximum values ​​within the preset range of energy storage system size. init This is a disturbance factor that is dynamically adjusted based on historical operating data and forecast results; Disturbance factor ε init The calculation formula is: Where, σ data The standard deviation of historical data represents the volatility of the data; μ data is the mean of historical data; k1 is the adjustment coefficient, k1∈[0.1,0.2].

3. The optimal design method for a photovoltaic energy storage and charging system according to claim 1, characterized in that, In the non-dominated ranking process of step S22, a dynamically adjusted target weight w is introduced. k The weights of each objective are dynamically adjusted according to the current stage of the optimization process to optimize the objective function mapping. The calculation formula is as follows: Among them, Fitnesss i The overall objective function for output; w k The target weights are automatically adjusted based on the current optimization progress to balance the relationship between the two objectives; f k (i) represents the k-th objective function of the i-th generation individual; M represents the number of objective functions.

4. The optimal design method for a photovoltaic energy storage and charging system according to claim 1, characterized in that, In step S23, a congestion distance calculation method based on environmental constraints is adopted. Specifically, this method incorporates an environmental constraint ratio C into the traditional congestion distance calculation. env Improved congestion distance d i The calculation formula is: Where, d i Let f be the crowding distance of the i-th generation individual; the first term of the formula is the traditional crowding distance calculation, where f k,i+1 f represents the target value of the (i+1)th generation neighboring individuals under the k-th target; k,i-1 f represents the target value of the (i-1)th generation neighboring individuals under the k-th target; k,max and f k,min These represent the maximum and minimum values ​​of neighboring individuals under the k-th objective, respectively; M is the number of objective functions; the second term is the proportion of environmental constraints introduced, C. env , where C env,i Let C be the environmental constraint value satisfied by the current solution of the i-th generation. env,max α represents the maximum permissible environmental constraint value; α is the weighting coefficient.

5. The optimal design method for a photovoltaic energy storage and charging system according to claim 1, characterized in that, In step S24, when performing the mutation operation on the selected parent individuals, an adaptive mutation operator based on local convergence is introduced. The mutation operation automatically adjusts the mutation probability according to the local dissimilarity of the population, and the mutation probability P... mut The calculation formula is: Among them, P mut Let λ be the mutation probability. conv P is the convergence speed parameter. min_mut Δf is the lower bound of the mutation probability. local Δf is a measure of local dissimilarity, representing the local distribution of solutions in the current population. local The calculation formula is: Among them, f neighbor f is the fitness value of the solutions in the neighborhood surrounding the current solution; current f is the fitness value of the current solution. max f is the maximum fitness value of the solutions in the neighborhood surrounding the current solution; min It is the minimum fitness value of the solutions in the neighborhood surrounding the current solution.

6. The optimal design method for a photovoltaic energy storage and charging system according to claim 1 or 5, characterized in that, In step S24, when performing the crossover operation on the selected parent individuals, a directional crossover operator based on the changing trend of the objective function is introduced. The crossover operation dynamically adjusts the crossover point position according to the gradient information of the objective function. The calculation formula is as follows: in, The sub-solution after the crossover operation; P parent1 and P parent2 There are two parent solutions; α is the cross coefficient, which is dynamically adjusted according to the changing trend of the objective function. The formula for calculating the cross coefficient α is: Among them, f parent1 and f parent2 is the objective function value of the two parent individuals, and ∈ is a small constant to prevent the denominator from being zero.

7. The optimal design method for a photovoltaic energy storage and charging system according to claim 1, characterized in that, Step S3 involves calculating the annual return and payback period for different scale ranges, including the following steps: Step S31: Based on the set scale range of the photovoltaic system, gradually increase the photovoltaic capacity settings in fixed increments to obtain multiple photovoltaic capacity settings; Step S32: Based on the set scale range of the energy storage system, gradually increase the energy storage capacity by a fixed step size to obtain multiple energy storage capacity settings; set multiple energy storage consumption methods for each energy storage capacity, including full consumption, peak consumption, and partial consumption; Step S33: Combine multiple photovoltaic capacity settings with multiple energy storage capacity settings to obtain all photovoltaic capacity and energy storage capacity combination schemes. Under each photovoltaic capacity and energy storage capacity combination scheme, calculate the annual income and payback period according to different energy storage consumption methods. Step S34: Based on the calculation results of the scheme, plot the relationship curves between energy storage capacity and annual income, and between energy storage capacity and payback period.

8. The optimal design method for a photovoltaic energy storage and charging system according to claim 1, characterized in that, When evaluating the optimal photovoltaic and energy storage system capacity configuration scheme output by the method, a time-based annual revenue calculation model based on dynamic market electricity prices and load forecasting is adopted. By combining dynamic electricity prices and load demand, the annual revenue is calculated in a time-based manner. The formula for calculating the annual revenue objective function is defined as follows: Among them, R annual (P PV E storage ) represents the annual return; P PV For photovoltaic power generation capacity; E storage Energy storage and discharge capacity; E storage (t) represents the energy storage discharge amount during time period t; p market (t) represents the dynamic market electricity price at time t; η PV η is the efficiency factor for photovoltaic power generation. storage C is the efficiency factor of the energy storage system. PV C is the cost of photovoltaic construction. storage The cost of building the energy storage system is represented by T, which represents the number of time periods.

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