A power distribution network scenario probability reactive power optimization method considering wind and light correlation

Abstract

This disclosure provides a probabilistic reactive power optimization method for distribution network scenarios considering wind and solar correlation, belonging to the field of power generation technology. Specifically, it includes: constructing a stochastic model of wind and solar output; introducing Spearman rank correlation coefficient to quantify the spatial correlation between wind and solar; generating initial independent samples using Latin hypercube sampling, and performing rank reorganization through Cholesky decomposition and sorting to generate an initial set of wind and solar joint output scenarios satisfying a preset correlation; using K-means clustering based on Euclidean distance to reduce scenarios, extracting typical scenarios and determining probabilities based on the original sample size; constructing an optimization model based on typical scenarios and their probabilities, with the objective of minimizing the expected values ​​of active power loss and voltage deviation under multiple scenarios; and using a hybrid intelligent algorithm combining genetics and particle swarm optimization to solve the problem, obtaining a reactive power optimization scheduling strategy to reduce network losses and voltage deviation. This disclosed solution improves optimization efficiency, accuracy, and adaptability.

Description

Technical Field

[0001] This disclosure relates to the field of power generation technology, and in particular to a probabilistic reactive power optimization method for distribution network scenarios that takes into account the correlation between wind and solar power. Background Technology

[0002] Currently, most existing studies tend to assume that the power output of distributed generation (DG) in different geographical locations or of different types is independent of each other. In reality, driven by the same meteorological system in the same region, there is a natural physical connection between wind speed and solar radiation intensity, exhibiting significant correlation and complementarity. For example, under specific climatic conditions, strong sunlight during the day is often accompanied by lower wind speeds, while wind speeds may be higher at night or on cloudy or rainy days. This "wind-solar complementarity" characteristic is of great significance for fluctuations in system power output.

[0003] If the interdependence between wind and solar power output is ignored in reactive power optimization modeling and treated as an independent random variable, the generated probabilistic power flow scenario will deviate from the actual operating conditions, thereby causing improper configuration of reactive power regulation resources or the risk of node voltage exceeding limits.

[0004] It is evident that there is an urgent need for a probabilistic reactive power optimization method for distribution network scenarios that takes into account wind and solar correlation, which offers high efficiency, accuracy, and adaptability. Summary of the Invention

[0005] In view of this, the present disclosure provides a probabilistic reactive power optimization method for distribution network scenarios that takes into account wind and solar correlation, which at least partially solves the problems of poor optimization efficiency, accuracy and adaptability in the prior art.

[0006] This disclosure provides a probabilistic reactive power optimization method for distribution network scenarios that takes into account wind and solar correlation, including: Step 1: Construct stochastic models for the output of wind turbine generators and photovoltaic generators. Wind speed is modeled using a two-parameter Weibull distribution and converted into active power output of the wind turbine. Solar intensity is modeled using a Beta distribution and converted into active power output of the photovoltaic generator. Step 2: Introduce the Spearman rank correlation coefficient to quantify the spatial correlation characteristics between the output of wind turbine generators and photovoltaic generators; Step 3: Based on the active power output of wind turbines and photovoltaic power, an initial independent sample matrix of wind and solar power and load is generated by Latin hypercube sampling. Then, according to the Spearman rank correlation coefficient, the initial independent sample matrix is ​​reorganized by Cholesky decomposition and sorting method to generate an initial set of wind and solar power joint output that meets the preset correlation constraints. Step 4: Use the K-means clustering algorithm based on Euclidean distance to reduce the initial scene set of wind and solar power output, extract multiple typical scenes, and determine the probability of occurrence of each typical scene based on the number of original samples clustered in each typical scene. Step 5: Based on typical scenarios and their occurrence probabilities, construct a reactive power optimization model with the comprehensive optimization objectives of minimizing the expected value of system active power loss and the expected value of node voltage deviation under multiple scenarios, and set constraints, including power flow equation constraints, node voltage constraints, reactive power compensation equipment output constraints, and distributed power source reactive power output constraints. Step 6: A hybrid intelligent optimization algorithm combining genetic algorithm and particle swarm optimization algorithm is used to solve the reactive power optimization model to obtain the reactive power optimization scheduling strategy of the distribution network, so as to reduce system network loss and reduce voltage deviation.

[0007] According to a specific implementation of this disclosure, the process of constructing the stochastic output model of the wind turbine generator specifically includes: Based on the power characteristic curve of the wind turbine, the wind speed is divided into three intervals: cut-in wind speed, rated wind speed, and cut-out wind speed, which correspond to the full-load operation, partial output, and shutdown states of the wind turbine, respectively. Among them, the relationship between the active power output of the wind turbine and the wind speed in the partial output interval is represented by a piecewise linear function.

[0008] According to a specific implementation of this disclosure, the expression for the Spearman rank correlation coefficient is as follows:

[0009] in, and Let X and Y represent the ranks of each observation in variables X and Y, respectively. Describing covariance, It represents the standard deviation.

[0010] According to a specific implementation of this disclosure, the step of reorganizing the rank of the initial independent sample matrix using the Cholesky decomposition and sorting method includes: The initial sample matrix generated by Latin hypercube sampling is subjected to Cholesky decomposition to obtain a lower triangular matrix. This matrix is ​​then transformed with the Cholesky decomposition result of the target Spearman rank correlation coefficient matrix. The elements in the initial independent sample matrix are sorted and reorganized so that the rank correlation coefficient matrix of the reorganized sample matrix approximates the preset Spearman rank correlation coefficient matrix.

[0011] According to a specific implementation of this disclosure, the step of using a K-means clustering algorithm based on Euclidean distance to reduce the initial scene set for combined wind and solar power output includes: Step 4.1: Normalize each feature dimension in the initial scene matrix; Step 4.2: Randomly select K scenes as initial cluster centers; Step 4.3: Calculate the Euclidean distance between each of the remaining scenes and each cluster center, and assign each scene to the nearest cluster. Step 4.4: Calculate the mean of all scenes within each cluster and update the cluster centers; Step 4.5: Repeat steps 4.3 and 4.4 until the cluster centers converge. The final cluster centers are then used as the typical scenario.

[0012] According to a specific implementation of this disclosure, the expression for the probability of occurrence is:

[0013] in, To belong to the The number of original sample points in each cluster. This represents the total number of samples.

[0014] According to a specific implementation of this disclosure, the expression corresponding to the comprehensive optimization objective is:

[0015] in, For a moment, For the first The probability of each scenario occurring For the system in the first The active power loss of the system in this scenario and These are the weighting coefficients. Let be the voltage deviation of the system in the k-th scenario.

[0016] According to a specific implementation of the present disclosure, the constraints further include: constraints on the number of parallel capacitor banks switched on and off, constraints on the reactive power output of the static var generator (SVG), constraints on the reactive power output of the wind turbine, and constraints on the reactive power output of the photovoltaic unit.

[0017] According to a specific implementation of this disclosure, the hybrid intelligent optimization algorithm that combines genetic algorithm and particle swarm optimization specifically includes: A genetic algorithm is used for global search, and the population is updated through crossover and mutation operations. Periodically extract elite subgroups from the current genetic algorithm population, and use particle swarm optimization algorithm to perform local fine search on the elite subgroups; The elite individuals optimized by the particle swarm optimization algorithm are replaced back into the original population to form a new generation of population. The velocity and position update formulas of the particle swarm optimization algorithm are as follows:

[0018]

[0019] in, For particle i, the individual optimality is determined. This is the current optimal solution for the elite subgroup.

[0020] According to a specific implementation of this disclosure, the reactive power optimization scheduling strategy includes: the reactive power output of wind turbines, the reactive power output of photovoltaic units, the number of parallel capacitor banks switched on and off, and the reactive power output of static var generators (SVG).

[0021] The probabilistic reactive power optimization scheme for distribution network scenarios considering wind-solar correlation in this embodiment includes: Step 1, constructing a stochastic model of the output of wind turbine generators and photovoltaic generators, wherein wind speed is modeled using a two-parameter Weibull distribution and converted into active power output of wind turbines, and solar intensity is modeled using a Beta distribution and converted into active power output of photovoltaic generators; Step 2, introducing the Spearman rank correlation coefficient to quantify the spatial correlation characteristics between the output of wind turbine generators and photovoltaic generators; Step 3, based on the active power output of wind turbines and photovoltaic generators, generating an initial independent sample matrix of wind, solar and load using Latin hypercube sampling, and reorganizing the initial independent sample matrix according to the Spearman rank correlation coefficient using the Cholesky decomposition and sorting method to generate a wind-solar joint output that satisfies preset correlation constraints. Step 4: Using the K-means clustering algorithm based on Euclidean distance, the initial set of wind and solar combined power output scenarios is reduced to extract multiple typical scenarios, and the probability of occurrence is determined based on the number of original samples in each typical scenario cluster. Step 5: Based on the typical scenarios and their probability of occurrence, a reactive power optimization model is constructed with the comprehensive optimization objectives of minimizing the expected value of system active power loss and the expected value of node voltage deviation under multiple scenarios, and constraints are set, including power flow equation constraints, node voltage constraints, reactive power compensation equipment output constraints, and distributed power source reactive power output constraints. Step 6: A hybrid intelligent optimization algorithm combining genetic algorithm and particle swarm optimization algorithm is used to solve the reactive power optimization model to obtain the reactive power optimization scheduling strategy of the distribution network, so as to reduce system network loss and reduce voltage deviation.

[0022] The beneficial effects of this disclosure are as follows: The scheme of this disclosure accurately quantifies the spatial correlation characteristics between wind and solar power by introducing the Spearman rank correlation coefficient, and constructs a random variable sampling model that reflects the correlation of multi-source power output by combining Latin hypercube sampling and Cholesky decomposition and sorting techniques. K-means clustering algorithm is used to reduce the number of scenarios, achieving refined extraction of typical operating conditions while preserving probabilistic statistical characteristics. The reduced set of typical scenarios is then substituted into the SGA algorithm optimization framework for optimization, realizing multi-condition collaborative reactive power optimization decision-making considering the wind-solar complementary characteristics. Compared to the independent distribution model, it can more accurately characterize system operating risks, taking into account operating economy while reducing the risk of voltage exceeding limits under extreme operating conditions. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A flowchart illustrating a probabilistic reactive power optimization method for a power distribution network scenario that takes into account wind and solar correlation, provided in an embodiment of this disclosure; Figure 2 This is a schematic diagram of Latin hypercube sampling provided in an embodiment of the present disclosure; Figure 3 This is a schematic diagram illustrating a specific process for Latin hypercube sampling, provided in an embodiment of the present disclosure. Figure 4 This is a schematic diagram of the Cholesky decomposition and sorting method provided in an embodiment of the present disclosure; Figure 5 This is a schematic diagram of a K-means clustering algorithm provided in an embodiment of the present disclosure. Detailed Implementation

[0025] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0026] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0027] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0028] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The illustrations only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0029] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0030] This disclosure provides a probabilistic reactive power optimization method for distribution network scenarios that takes into account wind and solar correlation. The method can be applied to the probabilistic reactive power optimization process of distribution network scenarios in power scenarios.

[0031] See Figure 1 This is a flowchart illustrating a probabilistic reactive power optimization method for a distribution network scenario that takes into account wind and solar correlation, provided by an embodiment of this disclosure. Figure 1 As shown, the method mainly includes the following steps: Step 1: Construct stochastic models for the output of wind turbine generators and photovoltaic generators. Wind speed is modeled using a two-parameter Weibull distribution and converted into active power output of the wind turbine. Solar intensity is modeled using a Beta distribution and converted into active power output of the photovoltaic generator. In practice, the process of constructing the stochastic model for wind turbine output includes: A wind turbine generator mainly consists of a wind turbine, a speed-increasing gearbox, a generator, a power electronic converter, and a control system. Its working principle is as follows: airflow drives the wind turbine to rotate, converting wind energy into mechanical energy; the gearbox then increases the rotational speed, driving the generator to operate, ultimately converting the mechanical energy into electrical energy. As a clean and renewable energy source, wind power has advantages such as low energy consumption, no pollution, and sustainable utilization, and has great application potential in power systems.

[0032] Natural wind speed exhibits characteristics of continuous random variation. The two-parameter Weibull distribution, due to its simple form and excellent fitting effect, is often used to describe the probability distribution of actual wind speed. Its distribution function F(V) is: (1) In the formula, and These are the scale and shape parameters of the Weibull distribution, used to control the shape of the Weibull distribution curve. Scale parameter Reflects the average wind speed of a wind farm; This indicates the peak value of the distribution curve. The wind speed at the given wind farm is expressed in m / s.

[0033] Its probability density function f(V) can be obtained as follows: (2) and The least squares method can be used to identify the wind speed based on historical data of actual wind speed measured on site.

[0034] The Weibull distribution model described above can effectively characterize the stochastic characteristics of wind speed, but its direct application to power grid optimization control still faces challenges: the continuous probability distribution of actual wind speed is difficult to directly embed into the discretized decision-making framework of the power system. The core advantage of the scenario analysis method lies in the construction of probabilistic scenario sets, transforming uncertainties that are difficult to accurately characterize in real-world systems into discretized probabilistic events, effectively simplifying the modeling and solution process of complex systems. Therefore, the scenario analysis method can be used to transform the continuous probability distribution of wind speed into an operable set of discrete scenarios.

[0035] Based on the characteristic curves of wind turbine generators, the relationship between wind speed and power can be obtained: (3) In the formula, , , These are the fan cut-in velocity, rated velocity, and cut-out velocity, respectively. This refers to the rated capacity of the wind turbine generator set; ; .

[0036] The process of constructing a stochastic model for photovoltaic unit output includes: A grid-connected photovoltaic (PV) system mainly consists of core components such as PV panel arrays, DC chopper circuits, and grid-connected inverters. Its power generation mechanism is as follows: semiconductor devices generate the photovoltaic effect under sunlight, directly converting solar energy into electrical energy. PV power generation requires no fossil fuels, is clean, environmentally friendly, and renewable, possessing extremely high engineering development and application value.

[0037] The output power of distributed photovoltaic (PV) power is easily affected by external conditions, mainly including meteorological conditions, irradiance angle, radiation intensity, and ambient temperature and humidity. Therefore, grid-connected PV power generation exhibits significant random fluctuations, and the uncertainty of its output must be fully considered when establishing relevant models. Irradiance intensity can be described using a Beta distribution within a specific time period. This paper characterizes the output characteristics of distributed PV power using a probability density function. (4) In the formula, This represents the actual light intensity. This represents the maximum light intensity. and These are the shape and scale parameters of the Beta distribution, respectively, and their average values ​​are obtained from historical observation data of solar radiation intensity. and standard deviation Perform the calculation: (5) (6) The output power of a distributed photovoltaic power generation system can be expressed as: (7) In the formula, This refers to the number of photovoltaic panels; This refers to the area of ​​a single photovoltaic panel; The photoelectric conversion efficiency coefficient; The output power of a distributed photovoltaic (PV) power generation system also follows a Beta distribution, therefore its probability density function is: (8) Step 2: Introduce the Spearman rank correlation coefficient to quantify the spatial correlation characteristics between the output of wind turbine generators and photovoltaic generators; In practical implementation, in the fields of statistics and engineering applications, there are generally two mathematical methods for quantifying the coupling characteristics of multiple random variables. One focuses on the scalar evaluation of association strength, typically represented by the Pearson correlation coefficient and the Spearman rank correlation coefficient; the other emphasizes in-depth analysis based on the underlying structure, mainly relying on multidimensional joint probability distributions and Copula connection function theory. Given that the former's mathematical analytical form is more intuitive and easier to integrate with traditional frameworks for generating random scenarios, this approach is preferred.

[0038] (1) Pearson correlation coefficient The Pearson correlation coefficient is a commonly used method to measure the degree of correlation between random variables. The Pearson correlation coefficient ρX,Y between two variables X and Y can be defined as the ratio of their covariance to their respective standard deviations, as shown in the following expression: (9) In the formula: For variables and Covariance between variables; and The standard deviations are respectively used as and express.

[0039] The formula above defines the population correlation coefficient, which is usually expressed in lowercase Greek letters. Representation. If the variables are known. and of For a set of sample data, the corresponding sample Pearson correlation coefficient It can be represented as: (10) In the formula: and They represent Variables in group sample data and The average value.

[0040] It can also be from Estimating the standard mean of the sample points yields an expression equivalent to the above formula: (11) In the formula: yes Standard scores of the sample.

[0041] (2) Spearman rank correlation coefficient Traditionally, the Pearson correlation coefficient has been widely used to quantify the degree of linear coupling between variables and has good applicability under the strict normality assumption. However, in practical engineering, random variables such as wind and solar power output often exhibit significant non-normal characteristics. In such scenarios, continuing to use the Pearson coefficient will lead to significant evaluation distortion and error. To address this limitation, this paper introduces a non-parametric metric—the Spearman rank correlation coefficient—that is not restricted by the type of marginal distribution, to characterize the dependence between non-normally distributed variables.

[0042] In simple terms, "rank" refers to the "rank" or "position number" obtained after sorting the original observation data. In practice, for two variables... and First, sort the observations in ascending order and assign rank values. and Then, the Pearson correlation coefficient formula is used to perform correlation analysis on the ranks. In other words, the Spearman correlation coefficient is actually the "Pearson correlation coefficient between the ranks of variables," which is defined as: (12) In the formula: and Representing variables respectively and The rank corresponding to each observation in the data. Describing covariance, It represents the standard deviation.

[0043] When there is no rank repetition (i.e., no duplicate values ​​in the data), the Spearman correlation coefficient formula can be simplified to: (13) In the formula: Indicates the first The rank difference of an observation between two variables This refers to the sample size observed.

[0044] Step 3: Based on the active power output of wind turbines and photovoltaic power, an initial independent sample matrix of wind and solar power and load is generated by Latin hypercube sampling. Then, according to the Spearman rank correlation coefficient, the initial independent sample matrix is ​​reorganized by Cholesky decomposition and sorting method to generate an initial set of wind and solar power joint output that meets the preset correlation constraints. In practice, Latin Hypercube Sampling (LHS) is built upon stratified sampling theory and is a scene generation method with high computational cost-effectiveness. Unlike Monte Carlo simulation, which requires an extremely large number of iterations to suppress sampling variance, LHS can obtain extremely smooth and accurate probability distribution boundaries with minimal sampling cost.

[0045] Assume the number of random variables to be sampled is The sampling scale is Any random variable See the LHS sampling diagram. Figure 2 For details of the sampling process, please refer to [link / reference]. Figure 3 The final sample matrix obtained from sampling. for: (14) In the formula: For the first A scene matrix, and They are used to describe the scene respectively. The fluctuation of active and reactive power under medium load. Corresponding to the In the first scenario The wind speed of the typhoon generator. Corresponding to the In the first scenario The solar irradiance of the photovoltaic unit.

[0046] The initial sample matrix obtained through the LHS discrete stratification mechanism This method can only guarantee a uniform probability distribution of each variable in its respective dimension, but different column vectors (i.e., different random variables) still maintain statistical independence. In practical active power distribution networks, to accurately reproduce the coupling characteristics between variables such as wind and solar power output, this independence must be broken by injecting correlation constraints through rank reorganization of the elements within the initial sample matrix. Currently, mainstream correlation ranking techniques in academia cover genetic algorithm permutation based on intelligent optimization, Cholesky decomposition ranking based on matrix transformation, and Gram-Schmidt orthogonalization strategy. Given the advantages of Cholesky decomposition in reducing the computational burden of high-dimensional matrices while ensuring reconstruction accuracy, this paper selects this method for the initial matrix. Sorting is performed to ensure that the recombined multidimensional sample sequence can approximate the correlation topology of real-world wind and solar resources.

[0047] for If there are variables, and their actual correlation coefficient matrix is ​​, The process of sorting relevance using Cholesky's decomposition and sorting method is as follows: Figure 4 As shown: After the above decomposition and transformation, the random variable sample matrix The corresponding Spearman rank correlation coefficient matrix can be approximated. This generates a sample set of random variables that meets the specified correlation requirements.

[0048] Based on the cumulative distribution functions of wind speed and solar radiation, a scene generation method combining Latin hypercube sampling and Cholesky decomposition and sorting is used to construct a scene matrix that simultaneously considers the correlation between load random fluctuations and distributed power sources. .in: For the first One scenario; and These characterize the active and reactive power fluctuations of the load under this scenario, respectively. Corresponding to the In the first scenario The wind speed of the typhoon generator. Corresponding to the In the first scenario The solar irradiance of the photovoltaic (PV) units is calculated. After the scene matrix is ​​generated, the wind speed values ​​in the matrix can be converted into the active power output of the corresponding wind turbine units by combining the active power-wind speed response curves of the wind turbines. Similarly, the solar irradiance values ​​in the matrix can be converted into the active power output of the corresponding PV units by combining the output power of the distributed PV power generation system. The resulting scene matrix takes into account the randomness of load, wind turbine output, and PV unit output, while also reflecting the correlation characteristics between distributed power generation outputs. This better reflects the actual operating conditions of the distribution network and can effectively improve the calculation accuracy of reactive power optimization results.

[0049] Step 4: Use the K-means clustering algorithm based on Euclidean distance to reduce the initial scene set of wind and solar power output, extract multiple typical scenes, and determine the probability of occurrence of each typical scene based on the number of original samples clustered in each typical scene. In practice, after LHS sampling and Cholesky matrix rearrangement, the system has successfully generated an initial scene set containing joint wind and solar probabilistic features. If these massive scenes are directly nested into the iterative optimization of the intelligent algorithm, tens of thousands of repeated power flow calculations would be required. To achieve the optimal balance between the fidelity of the probabilistic features and the computational power required for solving the problem, the scenes must be reduced. Therefore, this section introduces a K-means clustering algorithm based on Euclidean distance, aiming to extract highly representative typical scene clusters from the high-dimensional discrete initial matrix.

[0050] In addressing the problem of landscape scene reduction, the K-means algorithm based on a target partitioning strategy demonstrates significant applicability. This algorithm relies on a specific difference metric (typically Euclidean distance) to cluster initially disorganized scene points. Its inherent optimization principle is to compress the gaps between samples within similar clusters while widening the boundaries between heterogeneous clusters. Finally, the convergence centroids of each cluster are extracted as the most representative typical operational profile. This process replaces a large number of basic samples with a few high-quality centroids, effectively reducing the order of the random variable dimension, thereby significantly improving the solution response speed of the global optimization model while preserving the probabilistic characteristics of the scene.

[0051] To illustrate the basic principles of the K-means clustering algorithm, we will consider clusters containing... A set of samples It has been defined as follows: (15) In the formula: It is A dimensional vector is used to describe the first dimension. The samples contained There are 10 distinct attributes. Therefore, the initial cluster centers for clustering are defined as: (16) In the formula: It is the sample number Each cluster has a center point. All contain There are several different attributes. Similarity measurement methods use the distance between sample points to classify them. This paper selects Euclidean distance as the similarity measurement method for the K-means algorithm. The calculation formula is as follows: (17) In the formula: for dimensional vector and The Euclidean distance; ; .

[0052] In selecting the clustering similarity criterion, this paper establishes Euclidean distance as the core metric for measuring the differences in multidimensional scenes. This metric not only possesses intuitive spatial distance resolution capabilities but also exhibits excellent clustering convergence adaptability when dealing with low-dimensional feature spaces. It is worth noting that, to eliminate weight bias caused by differences in the dimensions and numerical boundaries of different distributed power sources, the feature dimensions of the initial scene matrix must be normalized before importing the Euclidean distance evaluation. Based on the above theoretical setting, the specific iterative calculation process for wind and solar scene reduction using the K-means algorithm is as follows: (1) Randomly select from the initial scene set A scenario, set it as The initial cluster centers of each cluster.

[0053] (2) Calculate the distance between each scene and the center of each cluster. Usually, Euclidean distance is used, and the scenes are assigned to the nearest cluster.

[0054] (3) After the cluster division is completed, the mean of all scenarios in each category is calculated to update the cluster center of each category.

[0055] (4) Repeat steps (2) and (3) until the updated cluster centers are consistent with the original centers, or the Euclidean distance between them is less than the set threshold, and then terminate the iteration. The final cluster centers are the typical scenarios after reduction. The ratio of the number of scenarios in each category to the initial total number of scenarios is the probability of occurrence of the corresponding typical scenario.

[0056] The process of reducing scenic views based on K-means clustering algorithm is as follows: Figure 5 As shown: Step 5: Based on typical scenarios and their occurrence probabilities, construct a reactive power optimization model with the comprehensive optimization objectives of minimizing the expected value of system active power loss and the expected value of node voltage deviation under multiple scenarios, and set constraints, including power flow equation constraints, node voltage constraints, reactive power compensation equipment output constraints, and distributed power source reactive power output constraints. In practice, the construction process of the adaptive multi-objective reactive power optimization model is as follows: 1) Adaptive dynamic weight objective function By modeling the correlation between wind speed and light intensity and performing K-means cluster analysis, the standard joint distribution characteristics of wind and light intensity were obtained. A typical scenario. To balance the economy and security of distribution network operation with a high proportion of distributed power sources, a mathematical model was constructed with the comprehensive optimization objective of minimizing the expected values ​​of active power loss and voltage deviation under multiple scenarios.

[0057] The comprehensive objective function expression for multiple scenarios is as follows: (18) In the formula: For a specific moment; For the first The probability of each scenario occurring; For the system in the first Active power loss of the system in this scenario; and These are the weighting coefficients; For the first Voltage deviation of the system under various scenarios.

[0058] Constraints (1) Power flow equation constraint (19) (2) Voltage constraint (20) (3) Capacitor bank input constraints (twenty one) (4) SVG reactive power output constraint (twenty two) (5) Reactive power output constraints of wind turbine units (twenty three) (6) Reactive power output constraint of photovoltaic unit (twenty four) In the formula: For nodes The active power of the power supply; For nodes The active power of the load; For nodes The reactive power of the power source; For nodes The reactive power output of the electrical container group; For nodes The number of capacitor banks connected is an integer variable; For nodes The reactive power output of the SVG compensation device; For nodes Reactive power at the load, For nodes The reactive power output of the wind turbine unit; For nodes The reactive power output of the photovoltaic unit.

[0059] Step 6: A hybrid intelligent optimization algorithm combining genetic algorithm and particle swarm optimization algorithm is used to solve the reactive power optimization model to obtain the reactive power optimization scheduling strategy of the distribution network, so as to reduce system network loss and reduce voltage deviation.

[0060] In specific implementation, the following steps are taken to solve the multi-scenario reactive power optimization model considering the correlation between wind and solar power output using the hybrid intelligent optimization algorithm SGA, which combines genetic algorithm and particle swarm optimization: Step 1: Input the basic parameters of the wind farm, including the number of wind turbines, installed capacity, wind speed distribution parameters, wind turbine power characteristic curves, SVG equipment parameters, and grid topology information.

[0061] Step 2: Based on the Weibull probability density function of wind speed and the Beta probability density function of illumination, use LHS combined with Cholesky decomposition and sorting method to construct multiple scenes, and use scene reduction based on K-means algorithm to reduce multiple scenes into n typical scenes.

[0062] Step 3: Based on the typical scenarios in Step 2, the Newton-Raphson method is used to perform power flow calculations on the distribution network containing distributed generation sources, and the node voltages, active power losses, and objective function values ​​of the system under each typical scenario are obtained.

[0063] Step 4: Based on the output of wind power and photovoltaic units, determine the reactive power regulation range of SVG and capacitor banks, and set optimization variables, including the reactive power output of wind power, photovoltaic units and SVG and the number of capacitor banks in operation.

[0064] Step 5: Set the parameters of the SGA algorithm, including population size. Genetic crossover rate Variation rate Particle swarm acceleration coefficient and Maximum number of iterations for genetics and particle swarm optimization and Encode the optimization variables, etc. ,in For the first The reactive power output of wind turbine units at all times For the first The reactive power output of photovoltaic units at all times For the first The number of capacitor banks in operation at any given time. For the first The reactive power output of the SVG at any given time is used to initialize the population.

[0065] Step 6: Generate using random initialization particles (i.e.) (A feasible solution is obtained), and the initialized solution is substituted into the power flow calculation to calculate the fitness function value. The calculation results are stored, and the global optimal solution and the individual optimal solution are recorded.

[0066] Step 7: After initialization, the algorithm enters the main iteration loop. In each iteration, the algorithm uses the synergistic effect of GA and PSO to optimize the current population. Updated to a new generation of population First, the GA stage manipulates the population through crossover and mutation to generate a temporary offspring population. This ensures that particles can fully explore the broad solution space. Subsequently, the algorithm periodically triggers a local development phase of PSO, during which the system... Randomly select a size of The elite subgroup, and the execution of [the policy / measures] against it. The second fine-grained search, in the PSO's... Second-rate During the internal iteration, each particle within the subgroup speed and location All will be updated according to the following formula: (25) (26) in, For particles The individual optimality, This represents the current optimal solution for the PSO subgroup. Before each PSO is initiated, the velocities of all particles in the subgroup are reset, allowing for a local search without historical velocities. After the next iteration, these optimized elite individuals will be replaced with... The original positions within the population will form the final new generation of species. .

[0067] Step 8: The main loop continues until the maximum number of iterations of the outer GA is reached. Determine if the maximum number of iterations has been reached. If it is, stop iterating; otherwise, return to step 7 to continue optimization.

[0068] This embodiment provides a probabilistic reactive power optimization method for distribution network scenarios considering wind-solar correlation. It accurately quantifies the spatial correlation characteristics between wind and solar power by introducing the Spearman rank correlation coefficient, and constructs a random variable sampling model reflecting the correlation of multi-source power output by combining Latin hypercube sampling and Cholesky decomposition and sorting techniques. K-means clustering is used to reduce the number of scenarios, achieving refined extraction of typical operating conditions while preserving probabilistic statistical characteristics. The reduced set of typical scenarios is then substituted into the SGA algorithm optimization framework for optimization, realizing multi-condition collaborative reactive power optimization decision-making considering the complementary characteristics of wind and solar power. Compared to independent distribution models, this method more accurately characterizes system operating risks, while also considering operational economy and reducing the risk of voltage exceeding limits under extreme conditions.

[0069] The method of this disclosure will be further explained below with reference to a specific embodiment. In order to verify the effectiveness of the aforementioned reactive power optimization model for distribution networks with distributed power sources, this chapter improves the topology based on the IEEE 33-bus system and constructs a simulation environment.

[0070] In this system, five switchable parallel capacitors are installed at node 24, and an SVG (Static Var Compensator) is installed at node 25. Each capacitor has a capacity of 50 kvar, and each SVG has a capacity of 300 kvar. A 0.6 MW doubly-fed wind turbine is connected to node 30, with a bus outlet voltage of 690V and a cut-in wind speed of [missing information]. The rated wind speed is 3 m / s. The cutoff wind speed is 12 m / s. 25 m / s, shape parameters and scale parameters The voltage values ​​are 2.4 and 9.5 respectively. Node 10 is connected to a 0.3MW photovoltaic (PV) unit, with the effective output period of the PV unit being from 7:00 to 19:00. To ensure the safe and stable operation of the power grid, the voltage fluctuation range of the node is limited to between 0.95 and 1.05.

[0071] To objectively and comprehensively simulate the impact of the correlation characteristics between wind and solar power output on reactive power optimization, this section selects three representative correlation coefficients. Scenario construction is performed for each value condition. Correlation coefficient. =0.5 indicates that wind and solar power outputs exhibit strong complementary characteristics (negative correlation), meaning that when wind power output is at its peak, solar power output is relatively low or vice versa. =0 means that the output of wind and solar power is independent (unrelated), and the output fluctuates randomly but does not interfere with each other; =0.5 indicates that the wind and solar power output exhibits a clear co-directional fluctuation characteristic (positive correlation), which is usually influenced by the same large-scale meteorological system in the same region.

[0072] First, based on the Weibull distribution model of wind speed and the Beta distribution model of illumination, corresponding shape and scale parameters are set. Latin hypercube sampling is used to extract 500 original sample points within each marginal distribution to ensure sufficient coverage of the probability space. Then, the Cholesky decomposition method is applied to reorder the extracted sample matrix to meet the preset correlation coefficient requirements.

[0073] Directly inputting all 500 scenarios into the reactive power optimization model would result in low computational efficiency. Therefore, this section further employs a K-means clustering algorithm based on Euclidean distance to reduce the number of scenarios in the sample. After iterative optimization, the 10 most representative typical scenarios were finally selected.

[0074] After identifying typical scenarios, it is necessary to further calculate the probability of each scenario occurring in actual operation to construct a complete set of probabilistic scenarios. Based on the clustering results, the probability of occurrence of each scenario is determined using frequency statistics: that is, counting the number of original sample points belonging to a certain cluster. and compared with the total sample size The ratio (500 in this example) is defined as the probability of this typical scenario occurring. The calculation formula is as follows: (27) This method transforms high-dimensional random fluctuation problems into discrete deterministic scenarios with specific probability weights. The specific probability distributions of typical scenarios under each correlation coefficient are then obtained.

[0075] The impact of correlation coefficient on reactive power optimization results is analyzed as follows: Based on the completion of multi-scenario construction, this section inputs the typical scenario sets and their probability distributions into the reactive power optimization model based on the SGA algorithm. Through simulation calculations on the IEEE 33-bus improved system, the profound impact of wind and solar power output correlation on the economy and security of the distribution network is analyzed.

[0076] (1) Analysis of system indicators under different correlation coefficients To analyze the mechanism by which the correlation between wind and solar power output affects the system's operating state, this section compares wind-solar hybrid power generation (FSH) with that of other systems. =-0.5), unrelated ( =0) and positive correlation ( Simulation results under three representative working conditions (=0.5).

[0077] Simulation data shows that the expected value of the system's active power loss increases significantly as the correlation coefficient increases from -0.5 to 0.5. From a physical mechanism perspective, when wind and solar power outputs are negatively correlated (complementary characteristics), the combined output of distributed generation systems exhibits a "peak shaving and valley filling" effect over time. For example, when photovoltaic output decreases due to reduced solar irradiance, the compensating effect of wind power output smooths out the overall fluctuation in line power, resulting in a more balanced current distribution in the feeders. Since line loss is proportional to the square of the current, the flattening of the current directly leads to a reduction in total loss. Conversely, under positive correlation conditions, wind and solar power outputs fluctuate in the same direction, easily generating a superimposed effect of "high current and high loss" during specific periods, thus increasing the expected value of the overall network loss.

[0078] Meanwhile, the system voltage deviation under different wind-solar correlation coefficients within a 24-hour operating cycle was compared. The results show that the voltage deviation is significantly affected by the wind-solar correlation characteristics, exhibiting a distribution pattern of "maximum positive correlation, moderate no correlation, and minimum negative correlation." As shown in the figure, under negative correlation, due to the natural complementarity of wind and solar power output in the time domain, their random fluctuations cancel each other out to some extent, smoothing out the total power injection fluctuations at the grid connection point, thus keeping the expected voltage deviation at a low level throughout the day. In contrast, the voltage deviation is most severe under positive correlation, especially during the peak renewable energy output period from 10:00 to 15:00. The co-directional fluctuations of wind and solar power produce a significant "power superposition effect," leading to a substantial increase in the risk of voltage exceeding limits at the feeder end and exacerbating the voltage deviation. This further illustrates that positive correlation significantly compresses the reactive power regulation space of the distribution network, while negative correlation plays a positive role in "peak shaving and valley filling," effectively improving the system's voltage quality. Therefore, if the positive correlation between wind and solar power output is ignored during modeling, it will lead to an underestimation of voltage deviation risk under extreme operating conditions, thereby threatening the operational safety of the distribution network.

[0079] (2) Comparison of reactive power optimization results without considering correlation and with considering correlation To verify the necessity of considering the correlation between wind and solar power output in the modeling proposed in this paper, this section designs a set of comparative tests. Two optimization schemes are set up: Scheme A (the scheme considering correlation in this paper), which accurately considers the positive correlation between wind and solar power during the modeling stage (ρ=0.5); and Scheme B (the traditional scheme ignoring correlation), which assumes that wind and solar power are independent during the modeling stage (ρ=0). Subsequently, the reactive power compensation control strategies generated by both schemes are uniformly placed under a real ρ=0.5 positive correlation scenario set for performance evaluation, and the results are compared and analyzed.

[0080] From an economic perspective, although Scheme B performs better under its assumed independent environment, its expected active power loss is significantly higher than Scheme A under actual correlated operating conditions. Scheme A generates a smoother network loss curve. This is because Scheme A identifies the current peak superposition effect caused by correlation, optimizes the power flow across the network through reasonable reactive power support, reduces the current peak of heavily loaded feeders, and decreases the total network loss. Statistical data shows that, after considering correlation, the expected daily average active power loss of the system is effectively reduced.

[0081] By comparing the system voltage deviations of Scheme A and Scheme B over a 24-hour period before optimization, it can be observed that Scheme A consistently exhibits a lower voltage deviation than Scheme B for most of the day, with this advantage being most pronounced during peak renewable energy output periods (10:00-15:00). The reason for this is that Scheme B, in its modeling, neglected the positive correlation between wind and solar power output, resulting in its optimization strategy failing to accurately predict the risk of a sharp voltage surge caused by simultaneous high wind and solar power output. In contrast, Scheme A accurately characterizes the physical characteristics of the co-directional fluctuations between wind and solar power, and its resulting control strategy can more proactively allocate reactive power support resources.

[0082] Therefore, if distributed power sources are treated as independent during the reactive power optimization modeling stage, the resulting control strategies will exhibit significant limitations in applicability when facing real-world interconnected operating conditions. Thus, for reactive power optimization in distribution networks with high-penetration renewable energy integration, incorporating the correlation between power outputs into the modeling scope is a prerequisite for ensuring the engineering practicality of the solution. Accurately modeling the wind-solar correlation characteristics not only makes the optimization results closer to real-world conditions but also significantly enhances the system's voltage smoothing capability under extreme superimposed fluctuation scenarios, which is core to achieving distribution network dispatch and operation.

[0083] It should be understood that the various parts of this disclosure can be implemented in hardware, software, firmware, or a combination thereof.

[0084] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for probabilistic reactive power optimization of power distribution network considering wind-photovoltaic correlation, characterized in that, include: Step 1: Construct stochastic models for the output of wind turbine generators and photovoltaic generators. Wind speed is modeled using a two-parameter Weibull distribution and converted into active power output of the wind turbine. Solar intensity is modeled using a Beta distribution and converted into active power output of the photovoltaic generator. Step 2: Introduce the Spearman rank correlation coefficient to quantify the spatial correlation characteristics between the output of wind turbine generators and photovoltaic generators; Step 3: Based on the active power output of wind turbines and photovoltaic power, an initial independent sample matrix of wind and solar power and load is generated by Latin hypercube sampling. Then, according to the Spearman rank correlation coefficient, the initial independent sample matrix is ​​reorganized by Cholesky decomposition and sorting method to generate an initial set of wind and solar power joint output that meets the preset correlation constraints. Step 4: Use the K-means clustering algorithm based on Euclidean distance to reduce the initial scene set of wind and solar power output, extract multiple typical scenes, and determine the probability of occurrence of each typical scene based on the number of original samples clustered in each typical scene. Step 5: Based on typical scenarios and their occurrence probabilities, construct a reactive power optimization model with the comprehensive optimization objectives of minimizing the expected value of system active power loss and the expected value of node voltage deviation under multiple scenarios, and set constraints, including power flow equation constraints, node voltage constraints, reactive power compensation equipment output constraints, and distributed power source reactive power output constraints. Step 6: A hybrid intelligent optimization algorithm combining genetic algorithm and particle swarm optimization algorithm is used to solve the reactive power optimization model to obtain the reactive power optimization scheduling strategy of the distribution network, so as to reduce system network loss and reduce voltage deviation.

2. The method according to claim 1, characterized in that, The construction process of the stochastic model for the output of the wind turbine generator specifically includes: Based on the power characteristic curve of the wind turbine, the wind speed is divided into three intervals: cut-in wind speed, rated wind speed, and cut-out wind speed, which correspond to the full-load operation, partial output, and shutdown states of the wind turbine, respectively. Among them, the relationship between the active power output of the wind turbine and the wind speed in the partial output interval is represented by a piecewise linear function.

3. The method according to claim 1, characterized in that, The expression for the Spearman rank correlation coefficient is: in, and Let X and Y represent the ranks of each observation in variables X and Y, respectively. Describing covariance, It represents the standard deviation.

4. The method according to claim 1, characterized in that, The step of reorganizing the rank of the initial independent sample matrix using the Cholesky decomposition and sorting method includes: The initial sample matrix generated by Latin hypercube sampling is subjected to Cholesky decomposition to obtain a lower triangular matrix. This matrix is ​​then transformed with the Cholesky decomposition result of the target Spearman rank correlation coefficient matrix. The elements in the initial independent sample matrix are sorted and reorganized so that the rank correlation coefficient matrix of the reorganized sample matrix approximates the preset Spearman rank correlation coefficient matrix.

5. The method according to claim 1, characterized in that, The step of using the K-means clustering algorithm based on Euclidean distance to reduce the initial scene set for combined wind and solar power output includes: Step 4.1: Normalize each feature dimension in the initial scene matrix; Step 4.2: Randomly select K scenes as initial cluster centers; Step 4.3: Calculate the Euclidean distance between each of the remaining scenes and each cluster center, and assign each scene to the nearest cluster. Step 4.4: Calculate the mean of all scenes within each cluster and update the cluster centers; Step 4.5: Repeat steps 4.3 and 4.4 until the cluster centers converge. The final cluster centers are then used as the typical scenario.

6. The method according to claim 5, characterized in that, The expression for the probability of occurrence is: in, To belong to the The number of original sample points in each cluster. This represents the total number of samples.

7. The method according to claim 1, characterized in that, The expression corresponding to the comprehensive optimization objective is: in, For a moment, For the first The probability of each scenario occurring For the system in the first The active power loss of the system in this scenario and These are the weighting coefficients. Let be the voltage deviation of the system in the k-th scenario.

8. The method according to claim 1, characterized in that, The constraints also include: the number of parallel capacitor banks that can be switched on and off, the reactive power output of the static var generator (SVG), the reactive power output of the wind turbine, and the reactive power output of the photovoltaic unit.

9. The method according to claim 1, characterized in that, The hybrid intelligent optimization algorithm that combines genetic algorithm and particle swarm optimization specifically includes: A genetic algorithm is used for global search, and the population is updated through crossover and mutation operations. Periodically extract elite subgroups from the current genetic algorithm population, and use particle swarm optimization algorithm to perform local fine search on the elite subgroups; The elite individuals optimized by the particle swarm optimization algorithm are replaced back into the original population to form a new generation of population. The velocity and position update formulas of the particle swarm optimization algorithm are as follows: in, For particle i, the individual optimality is determined. This is the current optimal solution for the elite subgroup.

10. The method according to claim 1, characterized in that, The reactive power optimization scheduling strategy includes: the reactive power output of wind turbines, the reactive power output of photovoltaic units, the number of parallel capacitor banks switched on and off, and the reactive power output of static var generators (SVG).

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