Doubly-fed wind farm clustering method based on index dimension reduction and weighted fuzzy c-means clustering

Abstract

The present application relates to a kind of double-fed wind farm grouping method based on index dimension reduction and weighted fuzzy C means clustering, belong to power system control technical field.The method includes: S1: the model of double-fed wind farm series compensation is incorporated into weak grid system is built, and the leading variable of sub-synchronous oscillation is selected;S2: considering the dynamic, transient process analysis under the condition of adapting to multiple disturbance scene, the leading variable data of each selected time point before, during the series compensation is incorporated into weak grid, during the series compensation is incorporated into weak grid, during the addition fault and after the removal of fault is used as the initial grouping index of double-fed wind turbine;S3: the initial grouping index is reduced using principal component analysis method;S4: the index after dimension reduction is used as clustering grouping index, and the clustering of wind turbine is realized using weighted fuzzy C means clustering algorithm.The present application improves the rational effectiveness of clustering grouping method in double-fed wind farm series compensation is incorporated into weak grid system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system control, relates to the field of doubly-fed wind turbines and subsynchronous oscillation, and particularly relates to a doubly-fed wind farm grouping method based on index dimension reduction and weighted fuzzy C-means clustering. BACKGROUND

[0002] In the early stage of wind power development, since the scale of wind farms is small, the research focus is mainly on modeling and order reduction of single unit. With the continuous increase of wind power penetration, equivalent modeling of wind farms has attracted attention at home and abroad. In the modeling process, if each unit in the wind farm and the collection network in the field are modeled in detail, not only the complexity of the power system model will be increased, but also many serious problems will be caused, such as the effectiveness of the model, the correction of data, etc., and the time required for power flow calculation will also be increased, especially the time required for time domain simulation, which is not suitable for practical engineering application. Therefore, it is necessary to study the dynamic equivalent modeling method of wind farms to simplify the complexity of the model and reduce the calculation amount. With the continuous increase of the capacity of doubly-fed wind turbine grid-connected wind farms, wind power has a great impact and shock on the operation flexibility and safety and stability of the power system. Under the operation condition of weak power grid, the interaction between the grid impedance and the equivalent impedance of the doubly-fed wind turbine will cause grid-connected oscillation problem, and the series compensation capacitor also has the risk of causing subsynchronous oscillation. Unlike synchronous generators, the single capacity of doubly-fed wind turbines is small, and it is very difficult to model each wind turbine in detail due to the actual system connected with hundreds of wind turbines. Therefore, when simulating and analyzing the actual system, the problem of dimension disaster is prone to occur, and the subsynchronous oscillation situation cannot be correctly reproduced.

[0003] In the study of dynamic characteristics of wind farms and dynamic effects of wind power integration on power systems under wind speed disturbance or grid fault conditions, simplified equivalent models are generally used for dynamic equivalent modeling. One is single-machine equivalent method and the other is multi-machine equivalent method. Single-machine equivalent method equates all wind turbines in a wind farm to one machine, takes equivalent wind speed as the input wind speed of the wind farm, and obtains the input power of the equivalent machine by superimposing the input power of a single machine. The equivalent parameters are usually obtained by weighted summation method. Due to the influence of factors such as terrain, wake effect and time lag, the wind speed distribution of large wind farms is generally uneven, and the actual operating states of the wind turbines in the wind farm are different. In the study of dynamic effects and dynamic characteristics of wind power integrated systems, the accuracy of single-machine equivalent model has gradually failed to meet the actual demand. Multi-machine equivalent method divides the dynamic of wind farm into several groups according to the principle that the operating states of wind turbines are the same or similar, and equates the parameters of wind turbines in the same group. Finally, several machines are used to represent the wind farm to simplify the model of the wind farm. The core idea of multi-machine equivalent is to find the attributes that represent the key characteristics of double-fed wind turbines and use the attributes for clustering in the equivalent modeling process. For the determination of clustering index in multi-machine equivalent, the existing literature often selects the capacity, type, wind speed, output characteristics, state variable, operating control region, wake effect, pitch angle action and other indexes of wind turbines.

[0004] However, the current equivalent model of wind power integrated system does not consider the correlation between clustering index and subsynchronous oscillation mode, and whether it is suitable for the analysis of subsynchronous oscillation characteristics of double-fed wind farm integrated with weak grid system is still inconclusive. The clustering index should be able to fully describe the operating characteristics of the wind turbines in the wind farm, so multiple clustering indexes are preferred. The data set composed of multiple double-fed wind turbines and multiple clustering indexes may contain strongly correlated variables, which may amplify the weight and influence of a certain index in clustering, resulting in a tendency in the clustering result and affecting the accuracy of clustering. Moreover, the dimension of the data set is high and the data is complex and redundant, so it takes a long time to cluster the data using clustering algorithms. The clustering algorithms currently used focus on the optimization of clustering centers, the determination of the number of clusters and the mining of outlier data, ignoring the differences and correlations between different clustering indexes of wind turbines and the contribution of different clustering indexes to the clustering results.

[0005] Therefore, there is an urgent need for a new clustering method for double-fed wind farms to solve the problem that the current clustering of double-fed wind farms does not consider the correlation between clustering index and subsynchronous oscillation mode and the contribution of different clustering indexes to the clustering results, as well as the inaccuracy of clustering caused by data redundancy. SUMMARY

[0006] Therefore, the present application aims to provide a double-fed wind farm clustering method based on principal component analysis dimension reduction and weighted fuzzy C-means clustering algorithm, select the dominant variables of double-fed wind farm sub-synchronous oscillation mode in series compensation and weak grid system, comprehensively consider the dynamic and transient process analysis in multiple disturbance scenarios, so as to solve the problem that the current double-fed wind farm clustering does not consider the correlation between clustering index and sub-synchronous oscillation mode and the contribution degree of different clustering indexes to clustering results, and the inaccuracy of clustering caused by data redundancy.

[0007] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0008] A double-fed wind farm clustering method based on index dimension reduction and weighted fuzzy C-means clustering, specifically comprising the following steps:

[0009] S1: Constructing a double-fed wind farm series compensation and weak grid system model, and selecting dominant variables of sub-synchronous oscillation, including grid current angular frequency ω s , DC capacitor voltage U dc , stator d-axis current i sd , stator q-axis current i sq , rotor d-axis current i rd , and rotor q-axis current i rq ;

[0010] S2: Considering the dynamic and transient process analysis in multiple disturbance scenarios, selecting dominant variable data at one time point before, during, after adding series compensation and weak grid, and during fault and after fault removal as the initial clustering index of double-fed wind turbine;

[0011] S3: Using principal component analysis method to reduce the dimension of the initial clustering index;

[0012] S4: Using the reduced index as the clustering index, and using the weighted fuzzy C-means clustering algorithm to realize the clustering of wind turbine generators.

[0013] Further, in step S3, the initial clustering index is reduced by using the principal component analysis method, specifically comprising the following steps:

[0014] S31: Establishing an original data sample matrix;

[0015] The extracted wind farm initial clustering index data is constructed into a sample matrix X w as shown in formula (1);

[0016]

[0017] Wherein, n represents the number of samples, i.e. the number of wind turbines in the wind farm; p represents the number of indexes in each sample;

[0018] S32: Calculate the sample covariance matrix R w ;

[0019] The data in the sample matrix X w is standardized by calculating the mean and standard deviation of the sample:

[0020]

[0021]

[0022]

[0023] wherein, is the standardized data of the original sample data x ij of the i-th wind turbine under the j-th index, and are the sample mean and standard deviation of the j-th index, respectively, x ij is the original sample data of the i-th wind turbine under the j-th index;

[0024] The standardized sample matrix X w is According to formula (5), the standardized sample covariance matrix R w can be obtained; the correlation coefficient r ej between x ij and x in the original sample matrix can be calculated by formula (6);

[0025]

[0026]

[0027] wherein, and are the mean values of the e-th and j-th variables, respectively, and are the standardized data of the i-th wind turbine under the e-th and j-th index, respectively;

[0028] S33: Obtain the eigenvalues of the sample covariance matrix R w and the eigenvectors corresponding to the eigenvalues;

[0029] Establish the characteristic equation |λI-R w | = 0, wherein λ represents the eigenvalue of the covariance matrix R w , and I represents the unit matrix. The Jacobi method is used to solve the characteristic equation to obtain the eigenvalues, and the obtained eigenvalues are arranged in descending order, i.e., λ1≥λ2≥…≥λ p ​≥ 0; the corresponding eigenvector is calculated according to the arranged characteristic value as formula (7), and then the eigenvector matrix V is constructed w = [v1, v2, …, v p ];

[0030]

[0031] S34: principal component contribution rate and cumulative contribution rate are calculated;

[0032]

[0033]

[0034] Wherein, δ j is the variance contribution rate of the jth index, μ j is the cumulative variance contribution rate of the first j indexes, λ j is the characteristic value of the jth index; the size of the variance contribution rate represents the description ability to the original sample matrix, the greater the value is, the more information the original sample matrix contains, and the closer the restored matrix is to the original matrix. The number of principal components is determined according to the cumulative variance contribution rate, in order to ensure the effectiveness of the data after dimension reduction and the subsequent clustering and grouping, when μ l ≥ 95%, the first l principal components can reflect the information of p indexes, so the first l principal components play a major role;

[0035] S35: a new sample matrix after dimension reduction is constructed;

[0036] After determining the number of principal components, the first l rows of the eigenvector matrix V w are taken to form a new matrix V wl , and the new sample matrix after dimension reduction can be calculated as

[0037] Further, in step S4, the weighted fuzzy C-means clustering algorithm is used to realize the clustering and grouping of the wind turbine, which specifically includes the following steps:

[0038] S41: the number of clusters is initialized , the maximum number of iterations T m , and the fuzzy index M;

[0039] S42: the membership matrix U and the cluster center matrix C are determined;

[0040] S43: the objective function and the constraint condition are constructed;

[0041] S44: the cluster center C hk and the membership u ih are updated, so that the objective function is minimized, and the above process is repeatedly performed until the number of iterations reaches T m .

[0042] Further, in step S42, the membership matrix U and the cluster center matrix C are determined, specifically comprising: U is an n×c matrix, wherein the element u ih represents the i th sample y w in the matrix Y i , and the membership of the h th cluster center is shown as formula (11) ; C is a c×l matrix, wherein the element C hk is shown as formula (12) ;

[0043]

[0044]

[0045] Wherein, y ik is the i th sample in the matrix Y w , d 2 (y ik , C hk ) = || y ik -C hk || 2 represents the Euclidean distance of the i th sample y ik to the h th cluster center, and || y ik -C mk || 2 Similarly; represents the membership u ih of the fuzzy index M.

[0046] Further, in step S43, the objective function F (U, C, W) is constructed as shown in formula (13), and the constraint condition is shown as formula (14) ;

[0047]

[0048]

[0049] Wherein, ω k represents the weight of the k th principal component index.

[0050] The beneficial effects of the present application are that the principal component analysis method is used to analyze the redundancy of each data, the dimensionality reduction is performed on the selected index, and the corresponding weight is assigned to the reduced index; the reduced index is used as the clustering index, and the weighted fuzzy C-means clustering algorithm is used for clustering, thereby improving the rationality and effectiveness of the clustering method of the double-fed wind farm series compensation into the weak grid system.

[0051] Additional advantages, objects, and features of the application will be apparent to those skilled in the art upon examination of the following specification. It is intended that the application not be limited by any of the details of the specification, unless so expressly desired, but instead be controlled by the full breadth permitted by the claims. It is to be under stood that the application of the underlying principles of the application are applicable with or without the specific details that are indicated in the description and illustrations. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred embodiments of the present application will be described in detail below with reference to the accompanying drawings, in which:

[0053] Figure 1 Flow chart of principal component analysis algorithm;

[0054] Figure 2 Flow chart of weighted FCM clustering algorithm;

[0055] Figure 3 Topology structure diagram of a doubly-fed wind farm;

[0056] Figure 4 Initial cluster index redundancy analysis result;

[0057] Figure 5 Principal component contribution rate;

[0058] Figure 6 Three-dimensional scatter diagram of principal components;

[0059] Figure 7 Weighted FCM clustering result of a doubly-fed wind farm;

[0060] Figure 8 Doubly-fed wind farm unit profile coefficient;

[0061] Figure 9 Average profile coefficient of a doubly-fed wind farm;

[0062] Figure 10 CHI index of a doubly-fed wind farm. DETAILED DESCRIPTION

[0063] The present application is herein described, by way of example only, with reference to the accompanying drawings, wherein:

[0064] Reference will now be made to Figures 1-10The application selects the dominant variable of the double-fed wind farm through series compensation and into the weak grid system subsynchronous oscillation mode, comprehensively considers the dynamic and transient process analysis under the multi-disturbance scene, and proposes a double-fed wind farm grouping method based on principal component analysis dimension reduction and weighted fuzzy C-means clustering algorithm, which is specifically as follows:

[0065] 1. Grouping index dimension reduction based on principal component analysis

[0066] 1) Selection of double-fed wind farm grouping index

[0067] In the double-fed wind farm series compensation and into the weak grid system, through the analysis of the mechanism of system subsynchronous oscillation, it can be known that the phase angle of phase-locked loop will affect the output voltage of the grid-side and rotor-side controllers, and then affect the output current of the double-fed wind turbine, resulting in unstable oscillation of the system. The fluctuation of the direct current voltage will affect the output current of the double-fed wind turbine through the output voltage of the rotor-side and grid-side controllers, and then affect the grid voltage. At the same time, the grid strength, series compensation degree, double-fed wind turbine stator d-axis current and rotor d-axis current and q-axis current are also the main influencing factors of system subsynchronous oscillation. In order to better analyze the subsynchronous oscillation characteristics of the double-fed wind farm series compensation and into the weak grid system, improve the effectiveness of double-fed wind turbine grouping, and then more targetedly design suppression measures, the application selects the dominant variable of subsynchronous oscillation as the grouping index to cluster and group the double-fed wind farm: grid current angular frequency ω s , direct current capacitor voltage U dc , stator d-axis current i sd , stator q-axis current i sq , rotor d-axis current i rd , rotor q-axis current i rq .

[0068] The initial operating point of the double-fed wind farm is an important basis for characterizing its steady-state characteristics. Different initial operating points will affect the dynamic response of the wind turbine during subsynchronous oscillation, thereby causing differences in state. Considering the dynamic and transient process analysis under the multi-disturbance scene, the application selects the data of ω s1 , U dc1 , i sd1 , i sq1 , i rd1 , i rq1 at a time point before the double-fed wind farm series compensation and into the weak grid, selects the data of ω s2 , U dc2 , i sd2 , i sq2 , i rd2 , i rq2 at a time point during the series compensation and into the weak grid, and selects the data of ω s3 , U dc3 , i sd3 , isq3 rd3 rq3 After fault removal, select a time point data ω s4 dc4 sd4 sq4 rd4 rq4 A total of 24 indicators are selected as initial clustering indicators.

[0069] 2) Principal component analysis dimension reduction

[0070] The 24 initial clustering indicators may contain strongly correlated variables, so that the weight and influence of a certain indicator are amplified during clustering, resulting in a tendency of clustering results and affecting the accuracy of clustering. Moreover, the dimension of the data set is high, and the data is complex and redundant. Therefore, before using the initial clustering indicators to cluster the wind turbines, the data needs to be processed to eliminate the strong correlation and redundancy between the indicators, and to reduce the adverse effects of data itself on the clustering results.

[0071] Principal component analysis, as a dimension reduction method of unsupervised learning, is mainly used to reduce the dimension of the data set. By measuring the amount of information through variance, the mutual influencing factors between the original data are eliminated. The modeling process only needs to perform eigenvalue decomposition, and the data dimension reduction is realized by constructing an orthogonal matrix, so as to map high-dimensional data to a few dimensions under the premise of preserving most of the information of the original data, eliminate the correlation between the data, and describe the data characteristics with a small number of indicators, thereby effectively reducing the computational complexity of clustering. The contribution rate of the reduced principal component represents the size of the original characteristic variation information, and the greater the contribution rate, the stronger the explanatory ability of the principal component to the original characteristic information. The present application uses principal component analysis to reduce the dimension of the 24 initial clustering indicators, as shown in formula (2), the algorithm of principal component analysis dimension reduction is specifically divided into five steps: Figure 1

[0072] Step 1: Establish the original data sample matrix. The extracted wind farm initial clustering indicator data is constructed into a sample matrix X w as shown in formula (1), where the number of rows n represents the number of samples, that is, the number of wind turbines in the wind farm, and the number of columns p represents the number of indicators in each sample, and p is 24 in this paper.

[0073]

[0074] Step 2: Calculate the sample covariance matrix. The data in the sample matrix X w is standardized by calculating the mean and standard deviation of the sample:

[0075] ​​​​​​​​

[0076]

[0077]

[0078] in, For x ij The data obtained after standardization For x ij The data obtained after standardization and Let x be the sample mean and standard deviation of the j-th indicator, respectively. ij This represents the original sample data for the j-th indicator of the i-th wind turbine. Sample matrix X w The standardized matrix is The standardized covariance matrix R can be obtained according to equation (5). w In the original sample matrix and The correlation coefficient r between them ej It can be calculated from equation (6), where and Let be the means of the e-th and j-th variables, respectively. and These are the standardized data for the e-th and j-th indicators of the i-th wind turbine, respectively.

[0079]

[0080]

[0081] Step 3: Calculate the sample covariance matrix R w The eigenvalues ​​and their corresponding eigenvectors are established. The characteristic equation |λI-R| is constructed. w |=0, where λ represents the covariance matrix R w The eigenvalues ​​are denoted by λ, where I represents the identity matrix. The eigenvalues ​​are obtained by solving the characteristic equation using the Jacobi method. These eigenvalues ​​are then arranged in descending order such that λ₁ ≥ λ₂ ≥ ... ≥ λₙ. p ≥0. Based on the arranged eigenvalues, the corresponding eigenvectors are obtained as shown in equation (7), and then the eigenvector matrix V is constructed. w .

[0082]

[0083] Step 4: Calculate the principal component contribution rate and cumulative contribution rate.

[0084]

[0085]

[0086] Where, δj is the variance contribution rate of the jth indicator, μ j is the cumulative variance contribution rate of the first j indicators, λ j is the eigenvalue of the jth indicator. The size of the variance contribution rate represents the description ability of the original sample matrix, the larger the value, the more information the original sample matrix contains, and the closer the restored matrix is to the original matrix. The number of principal components is determined according to the cumulative variance contribution rate. In order to ensure the effectiveness of the data after dimension reduction and subsequent clustering, when μ l ≥ 95%, the first l principal components can reflect the information of p indicators, so the first l principal components play a major role.

[0087] Step 5: Constructing the new sample matrix after dimension reduction. After determining the number of principal components, the first l rows of the eigenvector matrix V w are taken to form a new matrix V wl , and the new sample matrix after dimension reduction can be calculated as

[0088] Compared with the initial grouping indicator data of the doubly-fed wind turbine, the reliability and effectiveness of the data after dimension reduction by the principal component analysis method are improved, and the clustering result can be improved by using the data as the grouping indicator of the doubly-fed wind turbine.

[0089] 2. Clustering of doubly-fed wind farm based on weighted fuzzy C-means

[0090] 1) Weighted fuzzy C-means clustering algorithm

[0091] Fuzzy C-means (FCM) clustering algorithm is a method based on the description and division of things with fuzziness or uncertainty. Among many fuzzy clustering algorithms, FCM clustering algorithm is the most widely used and successful one. It combines the essence of fuzzy theory and provides more flexible clustering results compared to the hard clustering of k-means. In most cases, the objects in the data set cannot be divided into obviously separated classes, and it is too rigid and may be wrong to assign an object to a specific class. Therefore, FCM clustering algorithm divides the samples into several classes and assigns each sample a weight, i.e. membership degree, representing the degree of belonging to each class, thereby obtaining a membership matrix. The clustering center matrix and membership matrix are updated through iterative calculation to ensure that the objective function is minimized. By optimizing the objective function, the membership of each sample point to all class centers is obtained, thereby determining the class of the sample point to achieve the purpose of automatically classifying sample data.

[0092] The traditional FCM clustering algorithm considers all sample features as equally important, that is, the contribution degree to the clustering result is the same, and ignores the difference between the sample features. When the traditional FCM clustering algorithm is used for clustering and grouping of wind turbines, the contribution degree of different operating characteristics of the wind turbines to the clustering result is ignored, resulting in unreasonable grouping result. It is known from principal component analysis that the contribution degrees of various indexes are different and greatly different, therefore, the contribution degree of different indexes to the clustering result is considered, the corresponding weight of each index is given, a weighted FCM clustering algorithm is proposed, and clustering and grouping of wind turbines are realized. The weight of each index can be calculated by formula (10):

[0093]

[0094] Among them, PC l represents the lth principal component index, λ l is the characteristic value of the lth principal component index, ω k is the weight of the kth principal component index, and the weight vector of the l principal component indexes is W={ω1,ω2,...,ω l}.

[0095] The principal component indexes after dimension reduction are used as the clustering and grouping indexes of the doubly-fed wind farm, the new sample matrix Y w after dimension reduction is the sample data set, y i ={y i1 ,y i2 ,...,y il} represents the lth principal component of the ith sample. The data is divided into c classes, and the corresponding c class centers are C. As shown in the formula (13), the FCM clustering algorithm calculation process is as follows: Figure 2

[0096] 1) Initialize the number of clusters , the maximum number of iterations T m , and the fuzzy index M. M is a constant that characterizes the degree of fuzzification, and the value range is [1, 2.5], and generally M is 2.

[0097] 2) Determine the membership matrix U and the clustering center matrix C. U is an n×c matrix, wherein the element u ih represents the membership degree of the ith sample y w in the matrix Y i to the hth clustering center, as shown in formula (11). C is a c×l matrix, wherein the element C hk C jk is shown in formula (12).

[0098]

[0099] ​

[0100] where y ik is the matrix Y w , d 2 is the i-th sample in Y ik , C hk is the h-th cluster center, and ||y ik -C hk || is the Euclidean distance between the i-th sample y 2 and the h-th cluster center C ik . ik -C mk || is the Euclidean distance between the i-th sample y 2 and the h-th cluster center C hk .

[0101] 3) Construct the objective function F(U,C,W) as shown in equation (13) and the constraint condition as shown in equation (14).

[0102]

[0103]

[0104] 4) Update the cluster center C hk and the membership u ih to minimize the objective function, and repeat the above process until the iteration number reaches T m .

[0105] 3. Clustering validity test

[0106] The clustering validity research is a process of establishing a validity index, evaluating the clustering quality and determining the optimal cluster number. Typical clustering validity indexes include the SSE index (sum of squared error), the CHI index (Calinski-Harabasz Index), the DBI index (Davies-Bouldin Index), the SC index (Silhouette coefficient), the XB index (Xie-Beni Index), etc. In order to ensure the accuracy and objectivity of the clustering grouping result, the XB index widely used in fuzzy clustering is selected to determine the optimal cluster number in the present application, which is defined as follows.

[0107]

[0108] where the numerator of V XB reflects the compactness within the class, and the smaller the value is, the more compact it is; and the denominator reflects the separation degree between classes, and the larger the value is, the better the separation is. Therefore, the smaller the value of V XB is, the better the grouping effect is. When V XB is the smallest, the corresponding c is the optimal cluster number.

[0109] To verify the rationality of the wind farm grouping index of the present application, and further illustrate the effectiveness of the weighted FCM clustering algorithm and the rationality of the clustering grouping result, the SC index and the CHI index are selected for evaluation. The SC index is defined as:

[0110]

[0111]

[0112] wherein, α i is the intra-class compactness, indicating the average distance between the sample y i in the same group and all other samples, the smaller the value, the more compact the intra-class; β i is the inter-class dispersion, indicating the average distance between the sample y i in any group and all samples in the nearest group, the larger the value, the more dispersed the inter-class. SC i is the silhouette coefficient of the i-th group, SC i ∈[-1,1], SC i <0 indicates that the grouping is unreasonable, and the larger the SC i value, the more reasonable the grouping. SC m is the average silhouette coefficient of the group, the larger the value, the more effective the clustering grouping result.

[0113] The CHI index comprehensively considers the dispersion B between classes and the compactness W within classes, and the calculation formula is as follows, I CHI the larger the value, the better the dispersion between class clusters and the compactness within class clusters.

[0114]

[0115]

[0116] Embodiment:

[0117] 1. Parameter setting

[0118] A time-domain simulation model of a double-fed wind farm connecting a weak grid through series compensation is built in Matlab / Simulink as shown in the figure. Figure 3 The double-fed wind farm in the simulation includes 25 double-fed wind turbines of the same type, and the parameters of the wind farm are shown in Table 1. The distance between adjacent double-fed wind turbines is 500 m, and the double-fed wind farm is connected to a 35 kV medium voltage bus through a machine-end transformer and overhead lines, and then connected to a 220 kV power grid through a main transformer and transmission lines. According to the wind speed and wind direction, and considering the wake effect, the wind speed of each wind turbine in the double-fed wind farm can be calculated as shown in Table 2.

[0119] Table 1 Parameters of double-fed wind farm

[0120]

[0121]

[0122] Table 2 Wind speeds of each turbine in a doubly fed wind farm

[0123]

[0124] The initial short-circuit ratio of the power grid is set to 3, and the series compensation degree is set to 20%. At 2.1s, the short-circuit ratio is changed to 2, and the series compensation degree is changed to 50%. At 3.1s, the initial short-circuit ratio and series compensation degree are changed back. A three-phase-to-ground short-circuit fault is added at 4s and cleared at 4.15s. ω s1 U dc1 i sd1 i sq1 i rd1 i rq1 The data was collected at 2 seconds, ω s2 U dc2 i sd2 i sq2 i rd2 i rq2 The data was collected at 3 seconds, ω s3 U dc3 i sd3 i sq3 i rd3 i rq3 The data was collected at 4.1 seconds, ω s4 U dc4 i sd4 i sq4 i rd4 i rq4 The data was collected at 4.6 seconds. The dataset, consisting of 25 wind turbines and 24 initial cluster indicators, is a 25×24 sample matrix X. w .

[0125] 2. Dimensionality reduction results of principal component analysis

[0126] For sample matrix X w Using principal component analysis for dimensionality reduction, the variance contribution rate of each component can be obtained as follows: Figure 4 As shown. By Figure 4 It can be seen that the 24 initial clustering indicators include strongly correlated indicators, which will cause the clustering results to be biased. Therefore, it is necessary to perform dimensionality reduction on the data to reduce the inaccuracy of the clustering results caused by the interference of the data itself.

[0127] The eigenvalues ​​corresponding to each component are arranged in descending order, and the corresponding variance contribution rate and cumulative variance contribution rate are calculated, as shown in Table 3.

[0128] Table 3 Principal Component Variance Contribution Rate

[0129]

[0130]

[0131] From Table 3, the cumulative contribution rate of the first three principal components reaches 96.7319%, which is greater than 95%, satisfying the selection requirement of principal components in the principal component analysis method, and the remaining indicators have little impact on the contribution rate. The contribution rates of the first three principal components are 51.4265%, 33.9819%, and 11.3236%, respectively. Therefore, the first three principal components are selected for dimension reduction, that is, the initial clustering indicators are reduced to three dimensions. The component with an eigenvalue of 12.34236 is the first principal component, the component with an eigenvalue of 8.155651 is the second principal component, and the component with an eigenvalue of 2.717655 is the third principal component, which basically retains the information of the original data. The contribution rates of the three principal components are as follows Figure 5 , the broken line represents the cumulative contribution rate, and the blue rectangle represents the variance contribution rate.

[0132] The principal component scatter plot obtained according to the data is as follows Figure 6 , which refers to the data of each double-fed wind turbine in the sample and the contribution of each initial clustering indicator to each principal component. Different coordinate axes in the figure represent different principal components, and points represent the data of 25 groups of wind turbines. The intercept of each point on each coordinate represents the contribution of the data of this group to this principal component, and the greater the intercept, the greater the contribution of the data of this group to this principal component. The direction and length of the straight line vector represent the contribution of each original indicator to the new principal component, and the greater the intercept, the greater the contribution of the indicator to this principal component.

[0133] From Figure 6 , it can be seen that the distribution of each group of data represented by the points is relatively scattered and has no obvious regularity. The seventh indicator has the greatest contribution to the first principal component, the fourth indicator has the greatest contribution to the second principal component, and the fifteenth indicator has the greatest contribution to the third principal component.

[0134] At this point, the 24 initial clustering indicators are reduced to three principal component indicators through principal component analysis, and the new sample matrix Y w after dimension reduction is a 25x3 matrix. According to formula (10), the weight vector of the three principal component indicators is W = {0.5316, 0.3513, 0.1171}.

[0135] 3. Double-fed wind farm clustering results based on weighted FCM clustering algorithm

[0136] The new sample matrix Y w after dimension reduction is clustered using the weighted FCM clustering algorithm, the initial cluster number c is set to 2, and the maximum number of iterations T mFor 100, fuzzy index M is 2. According to iterative calculation of formula (15), the optimal cluster number c of 25 double-fed wind turbines is 4 op =4, so as to obtain the clustering and grouping results of three principal component indexes as multi-grouping indexes, as shown in Table 4 and Figure 7

[0137] Table 4 Weighted FCM clustering and grouping results of double-fed wind farm

[0138]

[0139] In order to verify the effectiveness of the weighted FCM clustering algorithm and the rationality of the clustering and grouping results of the present application, Figure 8 is the silhouette coefficient of 25 double-fed wind turbines when the clustering number is 4, Figure 9 is the average silhouette coefficient result, Figure 10 is the CHI index result.

[0140] It can be obtained from Figure 8 that the silhouette coefficient of 25 double-fed wind turbines is greater than 0 when the clustering number is 4, which indicates that the grouping is reasonable and effective. It can be obtained from Figure 9 and Figure 10 that the average silhouette coefficient and the CHI index of the unit are maximum when the clustering number is 4, which is consistent with the optimal clustering number determined by the XB index, so the 25 double-fed wind turbines built in the present embodiment can be divided into four equivalent groups.

[0141] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application but not limit the present application. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the purpose and scope of the present technical solutions, which should be covered in the scope of the claims of the present application.​

Claims

1. A method for clustering doubly-fed wind farms based on index dimension reduction and weighted fuzzy C-means clustering, characterized in that, The method specifically comprises the following steps: S1: Constructing a series compensation and weak grid system model of a doubly-fed wind farm, and selecting dominant variables of subsynchronous oscillation, including grid current angle frequency, DC capacitor voltage, stator d, q axis current, rotor d, q axis current; S2: Considering dynamic and transient process analysis in multiple disturbance scenarios, selecting dominant variable data at a time point before, during, after adding series compensation and weak grid, during fault addition, and after fault removal as initial grouping indexes of the doubly-fed wind turbine; S3: Using principal component analysis to reduce the initial grouping indexes; S4: Using the reduced indexes as clustering grouping indexes, and using a weighted fuzzy C-means clustering algorithm to realize clustering and grouping of the wind turbine; Using the dimensionality-reduced principal component index as the clustering index for doubly-fed wind farms, the new sample matrix after dimensionality reduction... For the sample dataset, Indicates the first one sample Principal components; divide the data into... Class, corresponding The category center is The weighted fuzzy C-means clustering algorithm is used to cluster wind turbine units, specifically including the following steps: S41: initialize the number of clusters , maximum iteration number , fuzzy index M ; S42: determining a membership matrix and a cluster center matrix ; Determine the membership matrix and cluster center matrix ; It is A matrix, where elements Representation matrix The Middle Sample For the first The membership degree of each cluster center is shown in Equation (1); It is A matrix, where elements As shown in equation (2); (1) (2) in, For matrix The Middle One sample, Indicates the first Sample To the Euclidean distance between cluster centers Similarly; The fuzziness index is represented as M membership degree ; S43: constructing an objective function As shown in equation (3), the constraint condition is shown in equation (4); (3) (4) wherein, represents the weight of the first k principal component index. S44: update the cluster center and membership minimize the objective function, repeat the above process until the iteration number reaches .

2. The doubly-fed wind farm grouping method according to claim 1, characterized in that, In step S3, the initial grouping indexes are reduced by using principal component analysis, specifically comprising the following steps: S31: Establishing an original data sample matrix; The extracted initial clustering index data of the wind farm is constructed into a sample matrix as shown in equation (5) ; (5) wherein, n represents the number of samples, i.e. the number of wind turbines within the wind farm; represents the number of indicators in each sample; S32: Calculate sample covariance matrix ; The data in the sample matrix is normalized by calculating the mean and standard deviation of the sample: The data in the sample matrix is normalized by calculating the mean and standard deviation of the sample: (6) (7) (8) wherein, is the data obtained after standardization, and are the sample mean and standard deviation of the th index, respectively, is the original sample data under the th index of the typhoon machine, and th index. sample matrix The normalized matrix is The normalized sample covariance matrix is obtained according to equation (9) The correlation coefficient between and is calculated by equation (10) 9) (10) wherein, and are the first and the second and are the first the second and the third normalized data under the first, second and third index, respectively.​ S33: Obtain the eigenvalues of the sample covariance matrix and their corresponding eigenvectors S33: Obtain the eigenvalues of the sample covariance matrix and their corresponding eigenvectors establishing a characteristic equation wherein λ denotes eigenvalues of the covariance matrix I denotes an identity matrix; eigenvalues are obtained by solving the characteristic equation using the Jacobi method, and the obtained eigenvalues are arranged in descending order to make ; the corresponding eigenvectors are obtained according to the arranged eigenvalues as shown in equation (11), and an eigenvector matrix is constructed.​ (11) S34: Calculating principal component contribution rate and cumulative contribution rate; (12) (13) wherein, is the variance contribution rate of the first index, is the cumulative variance contribution rate of the first index, is the eigenvalue of the first index; when , the first principal components reflect the information of the first index, so the first principal components play a major role; S35: Constructing a new sample matrix after dimension reduction; After determining the number of principal components, the eigenvector matrix is ​​taken. The former Rows form a new matrix The new sample matrix after dimensionality reduction is calculated as follows: .

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