A power distribution network dynamic optimization reconstruction method considering wind and light uncertainty

Abstract

This invention discloses a dynamic optimization and reconfiguration method for distribution networks considering the uncertainties of wind and solar power, comprising the following steps: Step 1: Characterizing the correlation between wind and solar power output using a Copula function, generating an initial set of correlated scenarios using Monte Carlo sampling, and selecting typical scenarios using a two-stage scenario reduction method; Step 2: Constructing source-load equivalent load curves, using dynamic time warping distance as a similarity measure, dividing the all-day equivalent load curves into time periods using a time-constrained k-medoids clustering algorithm, and determining the optimal number of segments using a loss function curve method; Step 3: Constructing a multi-objective function with system operating cost and voltage deviation as objectives, and using the analytic hierarchy process (AHP) for weight normalization to form a comprehensive optimization objective; Step 4: Solving the reconfiguration model using an improved snow ablation optimization algorithm to obtain the optimal network reconfiguration topology for each time period, and performing dynamic reconfiguration of the distribution network based on this topology.

Description

Technical Field

[0001] This invention relates to the field of industrial model building technology, and in particular to a dynamic optimization and reconfiguration method for power distribution networks that takes into account the uncertainties of wind and solar power. Background Technology

[0002] Dynamic reconfiguration of distribution networks is an important means to improve the economic efficiency and power supply quality of the system. It can enhance system reliability and economic benefits by optimizing the network structure through reasonable adjustments to switch configurations. However, with the large-scale integration of distributed power sources with uncertain output, such as wind and solar power, into the distribution network, how to accurately model and efficiently solve the dynamic reconfiguration problem has become a current technical challenge.

[0003] In modeling uncertainties in wind and solar power, existing methods typically employ parameter estimation-based approaches that predefine specific distributions or use simple scene generation methods. This approach, to some extent, ignores the inherent characteristics of wind and solar power output, causing the results obtained from the parameter distribution model to deviate significantly from the actual data distribution. Furthermore, it overlooks the strong correlation between wind and solar power output within the same region. Consequently, the generated scene sets fail to accurately reflect the characteristics of wind and solar power output, and the resulting reconstruction schemes lack robustness.

[0004] In terms of distribution network time period segmentation, existing dynamic reconfiguration studies mostly use Euclidean distance-based clustering algorithms (such as K-means and fuzzy C-means) to segment load or source-load curves. While this can effectively segment time periods, it fails to fully consider the temporal sequence of loads. Furthermore, Euclidean distance can only measure the differences in numerical magnitude of curves and cannot effectively capture their temporal similarity in dynamic characteristics such as shape and trend of change. This may lead to the inability to obtain optimal time period segmentation results.

[0005] In solving reconfiguration models, dynamic reconfiguration of distribution networks often employs traditional intelligent optimization algorithms (such as particle swarm optimization and genetic algorithms). However, these algorithms generally suffer from problems such as strong dependence on initial solutions, susceptibility to getting trapped in local optima, and difficulty in balancing convergence speed and accuracy when dealing with such complex problems, making it difficult to meet the requirements of practical engineering.

[0006] Existing methods often neglect the spatiotemporal correlation of wind and solar power output, resulting in generated scenarios that fail to accurately reflect actual joint fluctuation characteristics and thus insufficient robustness of reconfiguration schemes. Therefore, a dynamic optimization reconfiguration method for distribution networks that considers the uncertainties of wind and solar power is proposed. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by proposing a dynamic optimization and reconfiguration method for power distribution networks that considers the uncertainties of wind and solar power.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A dynamic optimization and reconfiguration method for distribution networks that considers the uncertainties of wind and solar power includes the following steps: Step 1: Generation of wind and solar uncertainty scenarios. Based on historical wind and solar power output data, the marginal probability distribution of wind power and solar power output is established by kernel density estimation. The spatiotemporal correlation between wind and solar power output is characterized by the Copula function. An initial scenario set containing the correlation is generated by Monte Carlo sampling, and a two-stage scenario reduction method is used to select typical scenarios. Step 2: Time period division based on DTW and time-constrained k-medoids clustering. The dynamic time warping distance is used as the similarity measure of the source-load curve. The time-constrained k-medoids clustering algorithm is combined to divide the daily operation curve into time periods. The optimal number of segments is determined by the loss function curve inflection point method. Step 3: Establish a multi-objective reconfiguration model for the distribution network. Construct a multi-objective function with system operating cost and voltage deviation as objectives, and use the analytic hierarchy process (AHP) to normalize the weights to form a comprehensive optimization objective. Step 4: Solve the improved snow ablation optimization algorithm. The improved snow ablation optimization algorithm is used to solve the multi-objective reconfiguration model to obtain the optimal switch combination scheme corresponding to each time period after division. Based on this, the optimal network topology structure for each time period is constructed to realize the dynamic reconfiguration of the distribution network.

[0009] The method also includes verification using an improved IEEE node system in a simulation environment, setting multiple load ratios and wind-solar distributed power supply access locations, and using the typical scenario with the highest probability after scenario reduction as the wind-solar power output input data for multi-scheme comparative analysis.

[0010] The reconfiguration scheme obtained by the method includes time-segmented switching state combinations, which significantly reduces system network losses and voltage deviations while reducing the number of switching operations, thereby improving the economic efficiency and power supply quality of the distribution network.

[0011] The above further includes: Furthermore, an initial scene set containing relevance is generated, specifically including: Modeling the marginal distribution of wind and solar power output based on kernel density estimation: Collect historical power output data of wind farms and photovoltaic power plants, and construct the marginal probability distribution of power output for wind power and photovoltaic power respectively. Assume that the historical sample data of wind power or photovoltaic power output is an independent and identically distributed sequence. The probability density at any power output value is calculated by Gaussian kernel function and bandwidth parameter, thereby obtaining the marginal distribution function of wind power and photovoltaic power output that conforms to the actual data distribution characteristics. Modeling the spatiotemporal correlation of wind and solar power output based on Copula function: Based on obtaining the edge distribution of wind power and solar power output, the Copula function is introduced to characterize the spatiotemporal correlation between the two. The Frank-Copula function is selected to connect the edge distribution of wind power and solar power output through the Frank-Copula function to construct the joint distribution function of wind power and solar power output. Initial scene set generation based on Monte Carlo sampling: Based on the joint distribution model, a large number of wind and solar power scene sets are generated using the Monte Carlo sampling method.

[0012] Furthermore, the two-stage scene reduction in step one includes: The K-means clustering algorithm is used to divide the initial scene set into K clusters, each containing scenes with similar output characteristics; For each cluster, the scene is further reduced using the synchronous back-substitution reduction method: calculate the Euclidean distance between scenes within the cluster, iteratively delete the scene that minimizes the probability-weighted distance, and transfer its probability to the other closest scene, until only one typical scene is retained in each cluster; Obtain K typical landscape-solar combined power output scenarios and their corresponding probability values.

[0013] Furthermore, the time-constrained k-medoids clustering process in step two includes: The dynamic time warping distance is used as a measure of similarity between time periods: for any two time periods, the optimal alignment path is found by dynamic programming, and the dynamic time warping distance is calculated. The smaller the distance, the more similar the two time periods are in terms of load change trends. A temporal constraint is introduced during the clustering process to ensure that the partitioned time periods are arranged consecutively on the time axis. The specific steps are as follows:

[0014] Initialize cluster centers: Randomly select k time periods from 24 time periods as initial cluster centers, and arrange them in chronological order to obtain a time-series cluster center set; Time period allocation: For each time period, calculate the dynamic time-normalized distance between it and the two adjacent cluster centers, and assign it to the cluster with smaller distance. At the same time, calculate the local similarity of the time period and the total similarity index of the current division. Update cluster centers: Within each cluster, select the time period that minimizes the sum of dynamic time regularization distances between all time periods within the cluster as the new cluster center; Iterative convergence: Repeatedly allocate time periods and update cluster centers until the cluster centers no longer change, and record the total similarity index under the current k value.

[0015] Furthermore, the specific steps to determine the optimal number of segments are as follows: For different k values, the time-constrained k-medoids clustering process is executed respectively, the total similarity index corresponding to each k value is calculated, and the fitting relationship curve between k value and similarity index is plotted. The optimal number of segments can be determined by identifying the inflection point of the curve, i.e., the point where the slope changes most significantly. If the k corresponding to the inflection point is an integer, then it is used directly; otherwise, the slope change rate of adjacent segments is compared, and the segment with the larger change rate is taken as the optimal value.

[0016] Furthermore, the multi-objective function in step three includes the system operating cost objective and the system voltage offset objective; The system operating cost target includes network loss costs and switching operation costs; The system voltage offset target is expressed as the degree of deviation between the voltage of each node and the rated voltage; The two objectives are weighted and summed using weighting coefficients to form a comprehensive optimization objective function.

[0017] Furthermore, the improved snow ablation optimization algorithm in step four is based on the original snow ablation optimization algorithm with the following improved solution steps: Population initialization: The initial population is generated using the Tent chaotic map. By utilizing the ergodicity and randomness of the Tent map, the initial snow particles are evenly distributed in the solution space to increase the diversity of the initial population. Population partitioning and iterative updates: The population is divided into a first subpopulation focused on global exploration and a second subpopulation focused on local development, and iterative optimization begins; Position update in the first subgroup exploration phase: In the global exploration phase of the algorithm, the Levy flight strategy is introduced to replace the Brownian motion in the original algorithm. The Levy flight walking mechanism, which alternates between long and short steps, guides the snow particles in the first subgroup to perform large-scale jumps and local fine searches in the solution space, so as to enhance the algorithm's global search capability and the ability to escape local optima. Position update in the second subgroup development stage: In the local development stage of the algorithm, an adaptive weight strategy is introduced to construct a weight factor that decreases nonlinearly with the number of iterations. The weight factor is used to dynamically adjust the influence of the current optimal solution on the position update of snow particles in the second subgroup. In the later stage of iteration, a fine search is performed near the optimal solution with a smaller step size to enhance the local fine mining capability of the algorithm. Fusion differential evolution strategy: After each iteration completes the position update of the exploration and development phases, a differential evolution strategy is executed on the current population to improve population diversity and convergence stability.

[0018] Furthermore, the differential evolution strategy specifically includes: Mutation operation: A non-linear periodic adaptive mutation factor is used to replace the fixed mutation factor in the differential evolution algorithm. The mutation length is dynamically adjusted according to the current iteration number to balance the global search in the early stage of the algorithm with the local convergence in the later stage, and to generate mutated individuals. Crossover operation: Crossing mutant individuals with target individuals to generate experimental individuals, thereby increasing population diversity; Selection operation: A greedy selection strategy is adopted, comparing the fitness values ​​of experimental individuals and target individuals, and retaining the better ones to enter the next generation of the population.

[0019] The present invention has the following beneficial effects: In this invention, wind and solar power output is no longer simply treated as constant values ​​or random variables conforming to an ideal distribution. Instead, a combination of kernel density estimation and Copula function is used. This accurately characterizes the true probabilistic features of wind and solar power output and their spatiotemporal correlation within the same region. Through two-stage scenario reduction, the most representative typical scenarios are retained, enabling subsequent reconfiguration schemes to effectively address the volatility and correlation of wind and solar power output in reality. This significantly enhances the robustness and adaptability of the reconfiguration schemes and avoids the risk of reconfiguration scheme failure due to ignoring correlation. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the steps of a dynamic optimization and reconfiguration method for a distribution network that considers the uncertainties of wind and solar power, as proposed in this invention. Figure 2 This is the probability density histogram of wind power output in this invention; Figure 3 This is the photovoltaic power output probability density histogram in this invention; Figure 4 This is the original scene set of wind power output in this invention; Figure 5 This is the scenario of reduced wind power output in this invention; Figure 6 This is the original set of photovoltaic power output scenarios in this invention; Figure 7 This is the scenario of reduced photovoltaic output in this invention; Figure 8 This refers to the unreconstructed voltage distribution in this invention; Figure 9 This refers to the single reconfigured voltage distribution in this invention; Figure 10 This refers to the full-time reconfigured voltage distribution in this invention; Figure 11 This refers to the time-segmented reconstructed voltage distribution in this invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please see Figures 1-11 As shown, this invention is a dynamic optimization and reconfiguration method for distribution networks that considers the uncertainties of wind and solar power, comprising the following steps: Step 1: Generation of wind and solar uncertainty scenarios. Based on historical wind and solar power output data, the marginal probability distribution of wind and solar power output is established by kernel density estimation. The Copula function is used to construct a wind and solar power joint output probability model to characterize the spatiotemporal correlation of wind and solar power output. Monte Carlo sampling is used to generate an initial scenario set containing correlations, and a two-stage scenario reduction method is used to select typical scenarios. Step 2: Time period division based on DTW and time-constrained k-medoids clustering. The dynamic time warping DTW distance is used as the similarity measure of the source-load equivalent load curve. The time-constrained k-medoids clustering algorithm is combined to divide the all-day equivalent load curve into time periods, and the optimal number of segments is determined by the loss function curve method. Step 3: Establish a multi-objective reconfiguration model for the distribution network. Construct a multi-objective function with system operating cost and voltage deviation as objectives, and use the analytic hierarchy process (AHP) to normalize the weights to form a comprehensive optimization objective function. At the same time, set constraints that satisfy the dynamic reconfiguration of the distribution network. Step 4: Solve the improved snow ablation optimization algorithm. The improved snow ablation optimization algorithm is used to solve the reconstruction model, obtaining the optimal network reconstruction topology for each time period. Based on this topology, dynamic reconstruction of the distribution network is performed. The improved snow ablation optimization algorithm is based on the original snow ablation optimization algorithm with the following improvements: Tent chaotic mapping is used for population initialization to increase the diversity of the initial population; a Lévy flight strategy is introduced in the exploration phase to replace the original Brownian motion, enhancing the algorithm's global search capability and ability to escape local optima; an adaptive weight strategy is introduced in the development phase to enhance the algorithm's later local fine-tuning capability, and a differential evolution strategy is integrated to improve population diversity and convergence stability. That is, after each iteration completes the position update in the exploration and development phases, the mutation, crossover, and selection operations of the differential evolution algorithm are performed on the current population. The mutation operation uses a non-linear periodic adaptive mutation factor instead of a fixed mutation factor to dynamically adjust the search range, further improving population diversity and algorithm convergence accuracy.

[0023] The method also includes verification using an improved IEEE node system in a simulation environment, setting multiple load ratios and wind-solar distributed power supply access locations, and using the typical scenario with the highest probability after scenario reduction as wind-solar input data to conduct multi-scheme comparative analysis.

[0024] The reconfiguration scheme obtained by the method includes time-segmented switching state combinations, which significantly reduces system network losses and voltage deviations while reducing the number of switching operations, thereby improving the economic efficiency and power supply quality of the distribution network.

[0025] In one embodiment, generating an initial scene set containing correlations specifically includes: Modeling the marginal distribution of wind and solar power output based on kernel density estimation: Collect historical power output data of wind farms and photovoltaic power plants, and construct the marginal probability distribution of power output for wind power and photovoltaic power respectively. Assume that the historical sample data of wind power or photovoltaic power output is an independent and identically distributed sequence. The probability density at any power output value is calculated by Gaussian kernel function and bandwidth parameter, thereby obtaining the marginal distribution function of wind power and photovoltaic power output that conforms to the actual data distribution characteristics. It should be noted that the specific analysis process for modeling the edge distribution of wind and solar power output based on kernel density estimation is as follows: The nonparametric kernel density estimation (KDE) method is employed to directly perform nonparametric estimation based on actual historical data of wind and solar power, yielding a probability density function that conforms to the historical data distribution. Let the random variable X represent wind and solar power output, and n independent and identically distributed samples are extracted from the historical power output data, denoted as... Then, at any point x, the estimated value of its probability density function is... , Where n is the number of samples, and h>0 is the window width. K () represents the Gaussian kernel function. This paper selects data samples from wind power stations and photovoltaic power stations in a certain European region from 11:00 to 12:00 throughout the year, establishes a probability model through KDE, and uses the traditional Weibull and Bata parameter estimation methods to fit the actual output of wind power stations and photovoltaic power stations.

[0026] Spatiotemporal correlation modeling of wind and solar power output based on Copula function: Based on the edge distribution of wind power and solar power output, the Copula function is introduced to characterize the spatiotemporal correlation between the two. Frank-Copula is selected as the connection function to connect the edge distribution of wind power and solar power output through the Copula function, and a joint distribution function of wind power and solar power output is constructed. Specifically: The expression for Copula is: Where n is the number of variables; For the marginal distribution function of a single variable, This represents the Copula join function. This represents the joint distribution function of n variables; Initial scene set generation based on Monte Carlo sampling: Based on the joint distribution model, a large number of wind and solar power combined output scenes are generated using the Monte Carlo sampling method.

[0027] It should be noted that the specific analysis process for generating the initial scene set based on Monte Carlo sampling is as follows: Generate uniformly distributed random numbers in the interval [0,1]. Based on the selected Frank-Copula function, N sets of n uniformly distributed random variables with correlation are obtained through its conditional distribution; Based on the generated random variables, the inverse function of the marginal distribution function of wind power and photovoltaic power output is used to convert the correlated random variables into actual wind power and photovoltaic power output values, ensuring that the generated power output values ​​retain both the marginal distribution characteristics and reflect the spatiotemporal correlation between wind and solar power. The generated wind and solar power output values ​​are combined to form a scenario set containing N initial wind-solar combined scenarios. This scenario set fully reflects the uncertainty and correlation characteristics of wind and solar power output.

[0028] In one embodiment, the two-stage scenario reduction in step one includes: The K-means clustering algorithm is used to divide the initial scene set into K clusters, each containing scenes with similar output characteristics; For each cluster, the scene is further reduced using the synchronous back-substitution reduction method: calculate the Euclidean distance between scenes within the cluster, iteratively delete the scene that minimizes the probability-weighted distance, and transfer its probability to the other closest scene, until only one typical scene is retained in each cluster; Obtain K typical landscape-solar combined power output scenarios and their corresponding probability values.

[0029] It should be noted that the specific analysis process for the two-stage scenario reduction is as follows: First, K-means clustering is used to divide the original scene set S into k clusters, denoted as C1, C2, ..., Cn. k The number of scenes in each cluster are N1, N2, ..., N k For each cluster C i Then, through synchronous back-substitution elimination, the intra-cluster scenario is further reduced to a single typical scenario. The specific steps are as follows:

[0030] (1): Let S be any scenario in the cluster. m and Scene S n The probability is P m and P nScenes within a cluster have equal initial probabilities, and the distance between scenes is measured using Euclidean distance. ; (2): For intra-cluster scenario S m ∈C i Calculate its probability distance value and select E. i Minimum scene S d As a scenario to be deleted: ; (3): In C i Find with S d The nearest scene S v Delete scene S d The probability is added to the nearest scene S. v Up, and remove scenario S from the cluster. d ; (4): Repeat (2)-(3) until a typical scenario is retained within the cluster.

[0031] In one embodiment, the time-constrained k-medoids clustering process in step two includes: The dynamic time warping distance is used as a measure of similarity between time periods: for any two time periods, the optimal alignment path is found by dynamic programming, and the dynamic time warping distance is calculated. The smaller the distance, the more similar the two time periods are in terms of load change trends. A temporal constraint is introduced during the clustering process to ensure that the partitioned time periods are arranged consecutively on the time axis. The specific steps are as follows:

[0032] Initialize cluster centers: Randomly select k time periods from 24 time periods as initial cluster centers, and arrange them in chronological order to obtain a time-series cluster center set; Time period allocation: For each time period, calculate the dynamic time-normalized distance between it and the two adjacent cluster centers, and assign it to the cluster with smaller distance. At the same time, calculate the local similarity of the time period and the total similarity index of the current division. Update cluster centers: Within each cluster, select the time period that minimizes the sum of dynamic time regularization distances between all time periods within the cluster as the new cluster center; Iterative convergence: Repeatedly allocate time periods and update cluster centers until the cluster centers no longer change, and record the total similarity index under the current k value.

[0033] In one embodiment, the specific steps for determining the optimal number of segments are as follows: For different k values, the time-constrained k-medoids clustering process is executed respectively, the total similarity index corresponding to each k value is calculated, and the fitting relationship curve between k value and similarity index is plotted. The optimal number of segments can be determined by identifying the inflection point of the curve, i.e., the point where the slope changes most significantly. If the k corresponding to the inflection point is an integer, then it is used directly; otherwise, the slope change rate of adjacent segments is compared, and the segment with the larger change rate is taken as the optimal value.

[0034] It should be noted that the process of dividing the distribution network time period based on the source-load curve using DTW and time-constrained k-medoids clustering is as follows: (1): Construct the source-load equivalent load curve for the entire time period and the dataset matrix of the curve. ,in, This represents the power matrix of all nodes in the system during time period t. This represents the power of node n within time period t, where time period t is the time interval. System nodes ; (2): Randomly select k time periods from P as initial cluster centers, and arrange them in the order of the time periods to obtain the time-series center set. ; (3): For each time period t, calculate The DTW distance to two temporally adjacent cluster centers is used to assign them to clusters with smaller distances, while the similarity for that time period is also calculated. The overall similarity index of the current division , , ; (4): Within each cluster, select the time period power that minimizes the sum of DTW distances between all time periods within the cluster as the new cluster center; (5): Repeat (3) and (4) until the cluster center no longer changes, the iteration ends, and the similarity index under the K value is recorded; Similarity index S K The number of segments increases negatively with the number of time segments k. This invention uses the loss function curve method to select the optimal number of segments. Let the horizontal axis represent the number of segments k and the vertical axis represent the similarity index S. K Construct a fitting relationship curve between the number of segments and the similarity index, and determine the optimal number of segments by identifying the inflection point of the curve; If the number of segments k corresponding to the inflection point is an integer, then it is directly determined as the optimal k value. Otherwise, calculate the rate of change of the slope of adjacent segments, and determine the number of segments with the more significant slope change as the optimal k value.

[0035] In one embodiment, the multi-objective function in step three includes a system operating cost objective and a system voltage offset objective; The system operating cost target includes network loss costs and switching operation costs; The system voltage offset target is expressed as the degree of deviation between the voltage of each node and the rated voltage; The two objectives are weighted and summed using weighting coefficients to form a comprehensive optimization objective function.

[0036] Specifically: Taking into account both reducing system operating costs and improving reliability, a multi-objective function is established, and the objective function is normalized. The expression is as follows: Where ω1 and ω2 represent the weight coefficients of each objective function. The weight values ​​are determined using the analytic hierarchy process (AHP). Considering that the overall system operating cost is slightly more important than the voltage deviation, ω1 and ω2 are calculated to be 0.75 and 0.25, respectively.

[0037] In one embodiment, the improved snow ablation optimization algorithm in step four is based on the original snow ablation optimization algorithm with the following improved solution steps: Population initialization: The initial population is generated using the Tent chaotic mapping. The randomness, regularity, and ergodicity of the Tent mapping are utilized to increase the diversity of the initial population and avoid the algorithm getting trapped in local optima. Population partitioning and iterative updates: The population is divided into a first subpopulation focused on global exploration and a second subpopulation focused on local development, and iterative optimization begins; Position update in the first subgroup exploration phase: In the global exploration phase of the algorithm, the Levy flight strategy is introduced to replace the Brownian motion in the original algorithm. The Levy flight walking mechanism, which alternates between long and short steps, guides the snow particles in the first subgroup to perform large-scale jumps and local fine searches in the solution space, so as to enhance the algorithm's global search capability and the ability to escape local optima. Position update in the second subgroup development stage: In the local development stage of the algorithm, an adaptive weight strategy is introduced to construct a weight factor that decreases nonlinearly with the number of iterations. The weight factor is used to dynamically adjust the influence of the current optimal solution on the position update of snow particles in the second subgroup. In the later stage of iteration, a fine search is performed near the optimal solution with a smaller step size to enhance the local fine development capability of the algorithm. Fusion differential evolution strategy: After each iteration completes the position update of the exploration and development phases, a differential evolution strategy is executed on the current population to improve population diversity and convergence stability.

[0038] In one embodiment, the differential evolution strategy specifically includes: Mutation operation: A non-linear periodic adaptive mutation factor is used to replace the fixed mutation factor in the differential evolution algorithm. The mutation length is dynamically adjusted according to the current iteration number to balance the global search in the early stage of the algorithm with the local convergence in the later stage, and to generate mutated individuals. Crossover operation: Crossing mutant individuals with target individuals to generate experimental individuals, thereby increasing population diversity; Selection operation: A greedy selection strategy is adopted, comparing the fitness values ​​of experimental individuals and target individuals, and retaining the better ones to enter the next generation of the population.

[0039] Specifically: Snow melting optimization algorithm: 1. Initialization Phase: In the initial phase, a batch of snow particles is randomly generated to form the initial population, and its matrix expression is as follows: Where L and U represent the upper and lower bounds of the solution space, respectively. Represents a random number within the range [0,1]. 2. In the exploration phase, the Snow Ablation Optimization (SAO) algorithm employs a dual-population mechanism, dividing the population into two subpopulations, one focused on exploration and the other on development. The number of snow particles in each subpopulation is adjusted in real-time during the iteration process. This phase simulates the random diffusion of snow or liquid water after iterating into water vapor, represented by Brownian motion. The position update formula during the exploration phase is: ; ; Among them, BM i ( t ) represents Brownian motion. X i ( t G( represents the position of the i-th individual in the t-th iteration.) t () represents the current optimal solution. This represents a random individual selected from the set. Indicates the location of the population centroid. X second ( t )and X third ( t ) represent the positions of the second and third best individuals in the current population, respectively. X c ( t The centroid of an individual whose fitness is in the top 50% is represented by , and this centroid is designated as the leader. N 1 represents the number of leaders;

[0040] 3. Development Phase: This phase simulates the tendency of snow melting into liquid water and flowing downhill, developing high-quality fitness values ​​around the current optimal solution. This behavior is represented by the day-to-day method, and the subgroup... The location update formula during the development phase is:

[0041] ; Where M is the snowmelt rate, DDF is the degree-day coefficient, and its value ranges from [0.35, 0.6]. T represents the daily average temperature. t max The maximum number of iterations, A random number within the range [-1, 1];

[0042] Improved Snow Melting Optimization Algorithm (ISAO): 1. Initialization Improvement: The original SAO uses random initialization, which makes it difficult to guarantee a uniform distribution of initial solutions in the solution space, reducing population diversity and affecting the optimization results. This invention uses Tent mapping for population initialization. Tent mapping has the characteristics of randomness, regularity, and ergodicity, which can increase the diversity of the initial population and avoid the algorithm getting trapped in local optima. The Tent mapping expression is: ,in Take 0.499; 2. Improvement strategies in the exploration and development phase: The original SAO algorithm is prone to getting trapped in local optima and unstable optimization results when dealing with nonlinear multi-objective optimization problems. For dynamic reconfiguration of distribution networks, the exploration and development phase of SAO has been improved to enhance its performance and solve practical problems. SAO employs Brownian motion during the exploration phase, which can easily lead to local optima when dealing with complex high-dimensional problems. This paper introduces the Lévy flight strategy, utilizing its alternating long and short step sizes to traverse high-dimensional and complex solution spaces, thereby enhancing global search capabilities. The improved position update formula is as follows:

[0043] Where α is the step size scaling factor, levy(β) represents the path following a Lévy distribution, and β is 1.5. μ and ν are random numbers following a normal distribution.

[0044] To address the issue of insufficient local mining capability caused by the randomness of Brownian motion during the development phase of SAO, an adaptive weighting strategy is introduced. This strategy constructs a weight factor that decreases non-linearly with the number of iterations. The adaptive weights are used to update the position, thereby enhancing the algorithm's local mining capability. The adaptive weights and the improved position update formulas are as follows:

[0045] ; ; Fusion Improvement Differential Evolution Strategy: The position updates during the exploration and development phases depend on the current optimal position and centroid position of the population, which leads to a rapid decline in population diversity in the later stages of iteration and a tendency to fall into local optima. This paper integrates SAO with the Differential Evolution (DE) strategy, and through mutation, crossover and selection operations, it can effectively expand the search range and improve population diversity. Mutation Operation: The mutation factor F is a key parameter controlling the DE algorithm. Traditional methods set it to a fixed value, which is difficult to adapt to the search requirements at different stages of the optimization process. Therefore, a nonlinear periodic adaptive operator is introduced. This replaces the original fixed mutation factor, allowing the search range to be dynamically adjusted as the iteration progresses. , , ,in, The initial mutation factor is typically taken between [0.5, 1], for adaptive... Let G be a periodic function, where G is the maximum number of iterations and k is the current number of iterations. ;

[0046] Crossover operation: After mutation, the crossover operation generates experimental individuals by comparing the target individual and the mutated individual in binary form and using the specified crossover probability. ,in, It is the crossover probability factor, which is set to 0.8 in this paper; Representing dimension, yes Random numbers in the data; Selection Operation: A greedy selection strategy is employed, involving a competitive evaluation between experimental and target individuals. Superior individuals are retained for the next generation. Through rigorous fitness comparison, the population is ensured to continuously acquire better individuals in iterations, represented as: .

[0047] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic optimization and reconfiguration method for distribution networks considering the uncertainties of wind and solar power, characterized in that, Includes the following steps: Step 1: Generation of wind and solar uncertainty scenarios. Based on historical wind and solar power output data, the marginal probability distribution of wind and solar power output is established by kernel density estimation. The Copula function is used to construct a wind and solar power joint output probability model to characterize the spatiotemporal correlation of wind and solar power output. Monte Carlo sampling is used to generate an initial scenario set containing correlations, and a two-stage scenario reduction method is used to select typical scenarios. Step 2: Time period division based on DTW and time-constrained k-medoids clustering. The dynamic time warping DTW distance is used as the similarity measure of the source-load equivalent load curve. The time-constrained k-medoids clustering algorithm is combined to divide the all-day equivalent load curve into time periods, and the optimal number of segments is determined by the loss function curve method. Step 3: Establish a multi-objective reconfiguration model for the distribution network. Construct a multi-objective function with system operating cost and voltage deviation as objectives, and use the analytic hierarchy process (AHP) to normalize the weights to form a comprehensive optimization objective function. At the same time, set constraints that satisfy the dynamic reconfiguration of the distribution network. Step 4: Solve the improved snow ablation optimization algorithm. Use the improved snow ablation optimization algorithm to solve the multi-objective reconfiguration model, obtain the optimal network reconfiguration topology for each time period, and perform dynamic reconfiguration of the distribution network based on the topology.

2. The method according to claim 1, characterized in that, Generate an initial scene set containing relevance, specifically including: Modeling the marginal distribution of wind and solar power output based on kernel density estimation: Collect historical power output data of wind farms and photovoltaic power plants, and construct the marginal probability distribution of power output for wind power and photovoltaic power respectively. Assume that the historical sample data of wind power or photovoltaic power output is an independent and identically distributed sequence. The probability density at any power output value is calculated by Gaussian kernel function and bandwidth parameter, thereby obtaining the marginal distribution function of wind power and photovoltaic power output that conforms to the actual data distribution characteristics. Spatiotemporal correlation modeling of wind and solar power output based on Copula function: Based on obtaining the edge distribution of wind power and solar power output, the Copula function is introduced to characterize the spatiotemporal correlation between the two. Frank-Copula is selected as the connection function to connect the edge distribution of wind power and solar power output through the Frank-Copula function, thus constructing a joint distribution function of wind power and solar power output. Initial scene set generation based on Monte Carlo sampling: Based on the joint distribution model, a large number of wind and solar power scene sets are generated using the Monte Carlo sampling method.

3. The method according to claim 1, characterized in that, The two-stage scenario reduction in step one includes: The K-means clustering algorithm is used to divide the initial scene set into K clusters, each containing scenes with similar output characteristics; For each cluster, the scene is further reduced using the synchronous back-substitution reduction method: calculate the Euclidean distance between scenes within the cluster, iteratively delete the scene that minimizes the probability-weighted distance, and transfer its probability to the other closest scene, until only one typical scene is retained in each cluster; Obtain K typical landscape-solar combined power output scenarios and their corresponding probability values.

4. The method according to claim 1, characterized in that, The temporal constraint k-medoids clustering process in step two includes: Initialize cluster centers: Randomly select k time periods from 24 time periods as initial cluster centers, and arrange them in chronological order to obtain a time-series cluster center set; Time period allocation: For each time period, calculate the Dynamic Time Warping (DTW) distance between it and the two adjacent cluster centers before and after it, and assign it to the cluster with the smaller distance. At the same time, calculate the local similarity of the time period and the total similarity index of the current division. Update cluster centers: Within each cluster, select the time period that minimizes the sum of dynamic time regularization distances between all time periods within the cluster as the new cluster center; Iterative convergence: Repeatedly allocate time periods and update cluster centers until the cluster centers no longer change, and record the total similarity index under the current k value.

5. The method according to claim 4, characterized in that, The specific steps to determine the optimal number of segments are as follows: For different k values, the time-constrained k-medoids clustering process is executed respectively, the total similarity index corresponding to each k value is calculated, and the fitting relationship curve between k value and similarity index is plotted. By identifying the inflection points of the curve, the optimal number of segments can be determined; If the k corresponding to the inflection point is an integer, then it is used directly; otherwise, the slope change rate of adjacent segments is compared, and the segment with the larger change rate is taken as the optimal value.

6. The method according to claim 1, characterized in that, The multi-objective function in step three includes the system operating cost objective and the system voltage offset objective; The system operating cost target includes network loss costs and switching operation costs; The system voltage offset target is expressed as the degree of deviation between the voltage of each node and the rated voltage.

7. The method according to claim 1, characterized in that, The improved snow ablation optimization algorithm in step four is based on the original snow ablation optimization algorithm with the following improved solution steps: Population initialization: The initial population is generated using the Tent chaotic mapping. Population partitioning and iterative updates: The population is divided into a first subpopulation focused on global exploration and a second subpopulation focused on local development, and iterative optimization begins; Position update in the first subgroup exploration phase: In the global exploration phase of the algorithm, the Levy flight strategy is introduced to replace the Brownian motion in the original algorithm. The Levy flight walking mechanism, which alternates between long and short steps, guides the snow particles of the first subgroup to perform large-scale jumps and local fine searches in the solution space. Position update in the second subgroup development stage: In the local development stage of the algorithm, an adaptive weight strategy is introduced to construct a weight factor that decreases nonlinearly with the number of iterations. The weight factor is used to dynamically adjust the influence of the current optimal solution on the position update of snow particles in the second subgroup. In the later stage of iteration, a fine search is performed near the optimal solution with a smaller step size. Fusion differential evolution strategy: After each iteration completes the position update of the exploration and development phases, the differential evolution strategy is executed on the current population.

8. The method according to claim 7, characterized in that, The differential evolution strategy specifically includes: Mutation operation: A non-linear periodic adaptive mutation factor is used to replace the fixed mutation factor in the differential evolution algorithm. The mutation length is dynamically adjusted according to the current iteration number to balance the global search in the early stage of the algorithm with the local convergence in the later stage, and to generate mutated individuals. Crossover operation: Crossing the mutated individual with the target individual to generate experimental individuals; Selection operation: A greedy selection strategy is adopted, comparing the fitness values ​​of experimental individuals and target individuals, and retaining the better ones to enter the next generation of the population.

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