A hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level
By generating typical wind turbine clusters using a hierarchical spatiotemporal clustering method, the problem of high spatiotemporal uncertainty at the turbine level in offshore wind farms is solved. This achieves efficient uncertainty input and a robust scheduling model, while reducing the computational burden.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTH CHINA UNIV OF TECH
- Filing Date
- 2026-06-18
- Publication Date
- 2026-07-17
AI Technical Summary
The increased number of wind turbines in offshore wind farms leads to high spatiotemporal uncertainty at the turbine level. Existing aggregation methods are prone to losing spatial proximity and temporal correlation features, increasing the computational burden of scheduling.
A hierarchical spatiotemporal clustering method for reducing uncertainty at the offshore wind turbine level is adopted, including geographically constrained K-means partitioning, standardization processing, dynamic time-warped distance measurement, Ward hierarchical clustering, and multi-index evaluation, to generate typical wind turbine clusters to reduce uncertainty.
While preserving the wake-related spatiotemporal structure, the uncertainty dimension at the wind turbine level is reduced, improving modeling efficiency and scheduling robustness.
Smart Images
Figure CN122412992A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system uncertainty analysis technology, specifically to a hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainty at the offshore wind turbine level. Background Technology
[0002] As offshore wind farms expand in scale, the number of wind turbines within a single farm increases continuously. These turbines exhibit significant spatiotemporal differences due to spatial layout, wind direction variations, and wake superposition. If turbine-level power deviation trajectories are directly used for grid connection scheduling, the uncertainty dimension will increase rapidly with the number of turbines and the scheduling period, leading to a significant increase in the solution burden for subsequent robust or partially robust scheduling models.
[0003] In existing technologies, offshore wind turbines are numerous and have strong wake coupling, resulting in high spatiotemporal uncertainty at the turbine level. This not only significantly increases the computational burden of scheduling in direct modeling, but also makes existing site-level aggregation methods, while reducing the modeling scale, prone to obscuring the spatial proximity, wake coupling relationship, and time series differences between turbines. In other words, traditional aggregation methods are prone to losing spatial proximity and temporal correlation features. Summary of the Invention
[0004] The purpose of this invention is to provide a hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level. This method not only improves modeling efficiency but also features robustness and scheduling practicality.
[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level, characterized by the following steps: Step S1. Obtain wind turbine spatial coordinates and historical wake correction sequence: Obtain the two-dimensional spatial coordinates of all wind turbines in the offshore wind farm and the wake correction wind speed sequence of each wind turbine at historical time. Step S2. Geographically constrained K-means partitioning based on wind turbine spatial coordinates: Based on the two-dimensional spatial coordinates, the geographically constrained K-means algorithm is used to divide all wind turbines into several non-overlapping geographic partitions, so that wind turbines with similar spatial locations and stronger wake coupling relationships are preferentially assigned to the same geographic partition. Step S3. Standardize the historical wake correction sequence: Standardize the historical wake correction wind speed sequence of each wind turbine in each geographical region to obtain a standardized historical sequence; Step S4. Construct the wind turbine time series distance matrix within each partition: Within each geographical partition, the time similarity between the standardized historical sequences of each wind turbine is measured using dynamic time-normalized distance metric, and the wind turbine time series distance matrix within the partition is constructed. Step S5. Perform Ward hierarchical sub-clustering within each geographic region: Based on the distance matrix, agglomerative hierarchical clustering is performed within each geographic region, and cluster merging is performed using the Ward connection criterion. The time sub-cluster set within each region is obtained by cutting the hierarchical clustering tree diagram. Step S6. Generate distance-weighted representative sequences within the partition: For each time subcluster, calculate its sequence center and assign distance weighting coefficients according to the distance of each wind turbine sequence to the subcluster center to generate distance-weighted representative sequences, while recording the size of each time subcluster; Step S7. Construct a representative sequence set and perform secondary global clustering: Collect distance-weighted representative sequences within all geographic partitions, construct a distance-weighted representative sequence set, and perform secondary global clustering on the representative sequence set again using Ward hierarchical clustering based on dynamic time-warped distance to obtain several global representative sequence clusters; Step S8. Generate the final typical wind turbine cluster and its global representative sequence: Generate a global representative sequence and effective scale based on each global representative sequence cluster, and backtrack to the original wind turbine to obtain the final typical wind turbine cluster; Step S9. Aggregate the wind turbine-level deviation trajectory into a typical wind turbine cluster-level deviation trajectory: map the original wind turbine-level spatiotemporal power deviation vector into a typical wind turbine cluster-level spatiotemporal deviation vector through an aggregation matrix, thereby reducing the dimensionality of the wind turbine-level spatiotemporal uncertainty; Step S10. Determine the number of geographical partitions and the final number of typical clusters based on multi-index evaluation: Based on the silhouette coefficient, Calinski-Harabasz index and Davies-Bouldin index, evaluate the clustering quality of the combination of candidate geographical partitions and the final number of typical wind turbine clusters to determine the number of geographical partitions and the final number of typical clusters.
[0006] Further, in step S2, the geographically constrained K-means algorithm: , in, Indicates the number of geographical zones; Indicates the first A collection of wind turbines within a geographical region; Indicates the first The spatial center vector of each partition; Represents the two-dimensional spatial coordinate vector of the wind turbine w; Represents the 2-norm of a vector; Geographical partitioning meets the following conditions: ; This indicates that different geographical zones do not overlap; This indicates that all geographical regions collectively cover the entire set of wind turbines, W.
[0007] Further, in step S3, the specific method of the standardization process is as follows: For the first... Geographical regions wind turbine Calculate the mean and variance of its historical series: , ; in, Indicates wind turbine Mean of historical wake-corrected wind speed series; Indicates wind turbine Variance of historical wake-corrected wind speed series; Indicates the corresponding standard deviation; Further, the standardized historical sequence was obtained: ; in, Indicates wind turbine At a historical moment The standardized sequence value.
[0008] Furthermore, the specific method for step S4 is as follows: For the same geographical region Any two wind turbines The dynamic time-normalized distance metric is used to measure the temporal similarity between the two standardized historical sequences: ; in, Indicates wind turbine With wind turbine The dynamic time-warped distance; and They represent the fans respectively. and The standardized historical sequence vector; Represents the dynamic time-warped distance function; it is calculated from the pairwise distances between all wind turbines within the partition. Composition of partition distance matrix: ; in, Indicates the first Time series distance matrix of wind turbines within a geographical region.
[0009] Furthermore, in step S5, based on the distance matrix... In each geographic region Agglomerative hierarchical clustering is employed, and the Ward connectivity criterion is used for cluster merging. For two candidate clusters A and B within the same geographic partition, the Ward merging cost is expressed as: ; in, This represents the cost of merging candidate cluster A and candidate cluster B; and These represent the number of wind turbines in cluster A and cluster B, respectively. and Let represent the sequence center vectors of cluster A and cluster B, respectively.
[0010] Furthermore, in step S6, for any time sub-cluster... The fan The standardized historical sequence is denoted as Calculate the sequence center of this sub-cluster: ; in, Representing time subclusters The sequence center vector; Subclusters The number of fans inside; Assign a weight to each wind turbine within a sub-cluster based on the distance from the turbine sequence to the sub-cluster center: ; in, Indicates wind turbine In sub-cluster Distance weighting coefficients in the equation; Indicates the fan in the sub-cluster The standardized historical sequence vector. The closer the wind turbine is to the center of the sub-cluster, the more representative it is, and the greater its contribution to the representative sequence.
[0011] Further, in step S4, the method for mapping the original wind turbine-level spatiotemporal power deviation vector to a typical wind turbine cluster-level spatiotemporal deviation vector through an aggregation matrix is as follows: Let the first... Wind turbines in historical samples During the scheduling period The power deviation is For the final typical wind turbine cluster In its first The sample, the first The typical wind turbine cluster deviation under a scheduling period is defined as: ; in, Indicates the first In the historical sample, the first A typical wind turbine cluster during the scheduling period The average power deviation; Indicates the first Wind turbines in historical samples During the scheduling period The original power deviation; All and Typical wind turbine clusters are stacked with deviations to obtain a dimensionality-reduced random vector. ,in, Indicates the first A typical wind turbine cluster-level spatiotemporal deviation vector after hierarchical spatiotemporal clustering dimensionality reduction of a historical sample; Indicates the number of scheduling periods; The dimensionality reduction process can be written in matrix form: ; in, This represents the original wind turbine stage spatiotemporal power deviation vector; Represents an aggregate matrix; Aggregation Matrix The element is defined as: ; in, Represents an aggregate matrix Zhongyou original fan Time period Mapped to a typical wind turbine cluster Time period The elements; when the fan Belongs to a typical wind turbine cluster and When, the element takes Otherwise, take 0.
[0012] Further, in step S10, the clustering quality evaluation includes: a larger silhouette coefficient indicates a more reasonable clustering result; a larger Calinski-Harabasz index indicates better inter-cluster separation and intra-cluster compactness; a smaller Davies-Bouldin index indicates a more compact clustering result and higher inter-cluster separation; by comprehensively comparing the three indicators under different combinations of candidate parameters, the final number of geographical zones and the final number of typical wind turbine clusters are determined.
[0013] Furthermore, the method is applied to the offshore wind power grid-connected scheduling scenario, using the dimensionality-reduced typical wind turbine cluster-level spatiotemporal deviation vector as uncertainty input to construct a robust scheduling model or a partially robust scheduling model.
[0014] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level.
[0015] The beneficial effects of this invention are as follows: The dimensionality reduction method of this invention addresses the problem of high spatiotemporal uncertainty at the wind turbine level. While preserving the wake-related spatiotemporal structure, it compresses a large number of wind turbines into a small number of representative typical wind turbine clusters, providing more efficient uncertainty input for large-scale offshore wind power grid-connected scheduling. This not only improves modeling efficiency but also has the characteristics of robustness and scheduling practicality. Attached Figure Description
[0016] The present invention will be further described with reference to the accompanying drawings, but the embodiments in the drawings do not constitute any limitation on the present invention. For those skilled in the art, other drawings can be obtained based on the following drawings without creative effort: Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is the first-stage geographic partitioning result for OWF1; Figure 3 This is the final typical wind turbine cluster distribution diagram. Detailed Implementation
[0017] like Figure 1 As shown, a hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level includes the following steps: Step S1. Obtain wind turbine spatial coordinates and historical wake correction sequence: Obtain the two-dimensional spatial coordinates of all wind turbines in the offshore wind farm and the wake correction wind speed sequence of each wind turbine at historical time.
[0018] Assume that all wind turbines within an offshore wind farm form a set. For any wind turbine Its two-dimensional spatial coordinate vector representation
[0019] in, Indicates wind turbine Two-dimensional spatial coordinate vector; and They represent the fans respectively. The horizontal and vertical spatial coordinates; It represents a two-dimensional real number space.
[0020] Let the set of historical moments be For wind turbines Its historical wake-corrected wind speed sequence is represented as follows: , in, Indicates wind turbine Historical wake-corrected wind speed sequence vector; Indicates wind turbine At a historical moment The wake correction wind speed; Indicates the number of historical moments.
[0021] Step S2. Geographically constrained K-means partitioning based on wind turbine spatial coordinates: Based on the two-dimensional spatial coordinates, the geographically constrained K-means algorithm is used to divide all wind turbines into several non-overlapping geographic partitions, so that wind turbines with similar spatial locations and stronger wake coupling relationships are preferentially assigned to the same geographic partition.
[0022] Specifically, a large number of wind turbines can lead to a high computational burden. Therefore, this invention employs a hierarchical spatiotemporal clustering method to reduce the dimensionality of wind turbine-level uncertainties.
[0023] First, perform geographically constrained K-means partitioning based on the spatial coordinates of the wind turbines:
[0024] in, Indicates the number of geographical zones; Indicates the first A collection of wind turbines within a geographical region; Indicates the first The spatial center vector of each partition; This represents the 2-norm of a vector.
[0025] Geographic partitioning satisfies: in, This indicates that different geographical zones do not overlap; This indicates that all geographical regions collectively cover the entire set of wind turbines, W.
[0026] This step prioritizes wind turbines with similar spatial locations and stronger wake coupling relationships into the same geographical partition, thus narrowing the calculation scope for subsequent time series clustering within the partition.
[0027] Step S3. Standardize the historical wake correction sequence: Standardize the historical wake correction wind speed sequence of each wind turbine in each geographical region to obtain a standardized historical sequence.
[0028] For the Geographical regions wind turbine Calculate the mean and variance of its historical series: in, Indicates wind turbine Mean of historical wake-corrected wind speed series; Indicates wind turbine Variance of historical wake-corrected wind speed series; Indicates the corresponding standard deviation; Indicates wind turbine At a historical moment The wake correction wind speed; Indicates the number of historical moments.
[0029] Further, the standardized historical sequence was obtained: in, Indicates wind turbine At a historical moment The standardized sequence values are used to mitigate the impact of differences in the dimensions and amplitudes of wind speed sequences from different wind turbines on the time series similarity measure.
[0030] Step S4. Construct the wind turbine time series distance matrix within each partition: Within each geographical partition, the time similarity between the standardized historical sequences of each wind turbine is measured using dynamic time-normalized distance, and the wind turbine time series distance matrix within the partition is constructed.
[0031] For the same geographical region Any two wind turbines The dynamic time-normalized distance metric is used to measure the temporal similarity between the two standardized historical sequences: in, Indicates wind turbine With wind turbine The dynamic time-warped distance; and They represent the fans respectively. and The standardized historical sequence vector; This represents the dynamic time-warped distance function.
[0032] The intervals between all the fans in the zone Composition of partition distance matrix: in, Indicates the first Time series distance matrix of wind turbines within a geographical region.
[0033] Step S5. Perform Ward hierarchical sub-clustering within each geographic region: Based on the distance matrix, agglomerative hierarchical clustering is performed within each geographic region, and cluster merging is performed using the Ward connection criterion. The time sub-cluster set within each region is obtained by cutting the hierarchical clustering dendrogram.
[0034] Based on distance matrix In each geographic region Agglomerative hierarchical clustering is employed, and the Ward join criterion is used for cluster merging. The Ward merge cost for two candidate clusters A and B within the same geographic partition is expressed as: in, This represents the cost of merging candidate cluster A and candidate cluster B; and These represent the number of wind turbines in cluster A and cluster B, respectively. and Let represent the sequence center vectors of cluster A and cluster B, respectively.
[0035] By cutting the hierarchical clustering tree diagram, in geographical partitioning The set of time subclusters is obtained internally: And satisfy: ,in, Indicates the first Within the first geographical region A time sub-cluster; Indicates the first Number of time subclusters within a geographic partition; This indicates the maximum number of time subclusters allowed for this geographic partition.
[0036] Step S6. Generate distance-weighted representative sequences within the partition: For each time subcluster, calculate its sequence center and assign distance weighting coefficients according to the distance from each wind turbine sequence to the subcluster center to generate distance-weighted representative sequences, while recording the size of each time subcluster.
[0037] For any time sub-cluster The fan The standardized historical sequence is denoted as First, calculate the sequence center of this sub-cluster: in, Representing time subclusters The sequence center vector; Subclusters The number of fans inside.
[0038] Assign a weight to each wind turbine within a sub-cluster based on the distance from the turbine sequence to the sub-cluster center: in, Indicates wind turbine In sub-cluster Distance weighting coefficients in the equation; Indicates the fan in the sub-cluster The standardized historical sequence vector. The closer the wind turbine is to the center of the sub-cluster, the more representative it is, and the greater its contribution to the representative sequence.
[0039] Further, the distance-weighted representation sequence of the subclusters is obtained: And define the size of the sub-cluster corresponding to this representative sequence: in, Indicates the first Within the first geographical region Distance-weighted representative sequences of time subclusters; This indicates the number of wind turbines contained within the sub-cluster at that time.
[0040] Step S7. Construct a representative sequence set and perform secondary global clustering: Collect distance-weighted representative sequences within all geographic partitions, construct a representative sequence set, and perform secondary global clustering on the representative sequence set again using Ward hierarchical clustering based on dynamic time-warped distance to obtain several global representative sequence clusters.
[0041] Collect distance-weighted representative sequences within all geographic regions to obtain a set of representative sequences: The number of representative sequences is: in, This represents the set of all sequences within each partition. This represents the total number of sequences.
[0042] Subsequently, for the representative sequence set DTW-Ward hierarchical clustering was used again to divide it into: The final representative cluster , Indicates the first There are global representative sequence clusters that satisfy: .
[0043] This step further compresses the multiple local temporal subclusters formed within the partition into a small number of global typical clusters to reduce the dimensionality of subsequent uncertainty modeling.
[0044] Step S8. Generate the final typical wind turbine cluster and its global representative sequence: Generate the global representative sequence and effective scale based on each global representative sequence cluster, and backtrack to the original wind turbine to obtain the final typical wind turbine cluster.
[0045] For the A global representative sequence cluster Its global representative sequence is defined as: Its effective size is defined as: in, Indicates the first A global representative sequence of a final typical wind turbine cluster; Indicates the first The effective size of a typical final wind turbine cluster; Indicates the first The first geographical region The representative sequence of the time sub-cluster is assigned to the . A global representative sequence cluster.
[0046] Based on the relationship between the representative sequences and the original wind turbines, the final wind turbine classification is obtained: And satisfy: .
[0047] in, Indicates the first A final typical wind turbine cluster; This indicates the number of wind turbines in this typical wind turbine cluster.
[0048] Step S9. Aggregate the wind turbine-level deviation trajectory into a typical wind turbine cluster-level deviation trajectory: Map the original wind turbine-level spatiotemporal power deviation vector into a typical wind turbine cluster-level spatiotemporal deviation vector through an aggregation matrix, thereby reducing the dimensionality of the wind turbine-level spatiotemporal uncertainty.
[0049] Let the first Wind turbines in historical samples During the scheduling period The power deviation is For the final typical wind turbine cluster In its first The sample, the first The typical wind turbine cluster deviation under a scheduling period is defined as: in, Indicates the first In the historical sample, the first A typical wind turbine cluster during the scheduling period The average power deviation; Indicates the first Wind turbines in historical samples During the scheduling period The original power deviation.
[0050] All and Typical wind turbine clusters are stacked with deviations to obtain a dimensionality-reduced random vector. ,in, Indicates the first A typical wind turbine cluster-level spatiotemporal deviation vector after hierarchical spatiotemporal clustering dimensionality reduction of a historical sample; Indicates the number of scheduling periods.
[0051] The dimensionality reduction process described above can be written in matrix form: in, This represents the original wind turbine stage spatiotemporal power deviation vector; This represents an aggregate matrix.
[0052] Aggregation Matrix The element is defined as: in, Represents an aggregate matrix Zhongyou original fan Time period Mapped to a typical wind turbine cluster Time period The elements. When the fan Belongs to a typical wind turbine cluster and When, the element takes Otherwise, take 0.
[0053] Through this step, the original dimension is... The spatiotemporal uncertainty of wind turbines is reduced to Spatiotemporal uncertainty at the typical wind turbine cluster level.
[0054] Step S10. Determine the number of geographical partitions and the final number of typical clusters based on multi-index evaluation: Based on the silhouette coefficient, Calinski-Harabasz index and Davies-Bouldin index, evaluate the clustering quality of the combination of candidate geographical partitions and the final number of typical wind turbine clusters to determine the number of geographical partitions and the final number of typical clusters.
[0055] To determine the number of geographic zones and the final typical number of wind turbine clusters For candidate parameter combinations Cluster quality was evaluated using metrics including the silhouette coefficient, Calinski-Harabasz (CH) index, and Davies-Bouldin (DB) index. A higher CH index indicates better inter-cluster separation and intra-cluster compactness. A lower DB index indicates more compact clustering and higher inter-cluster separation.
[0056] By comprehensively comparing different candidates Profile coefficients below CH and DB are used to determine the final number of geographic partitions and the final number of typical wind turbine clusters.
[0057] Application examples of this invention To verify the hierarchical spatiotemporal clustering method for dimensionality reduction of turbine-level uncertainties proposed in this invention, this embodiment selects OWF1 in the improved IEEE 39-node system as the case study. OWF1 consists of 73 offshore wind turbines, using the MingYang MySE5.5-155 Offshore turbine, with a rated power of 5.5 MW per unit, a rotor diameter of 155 m, and a hub height of 103 m. The scheduling cycle is 24 time periods. For the unreduced turbine-level spatiotemporal uncertainty, its dimension is... After adopting the method of this invention, the number of geographical zones is selected. The final typical number of wind turbine clusters The uncertainty dimension is reduced to Therefore, while preserving the spatiotemporal structure of the wind turbine level, the model input dimension is significantly compressed. Clustering parameter selection results show that a larger CH index indicates better cluster separation, while a smaller DB index indicates more compact clusters and more pronounced inter-cluster separation.
[0058] Figure 2 The results of the first-stage geographic partitioning of OWF1 are presented. It can be seen that the geographic partitioning forms relatively continuous spatial regions, which prioritizes wind turbines with similar spatial locations and strong wake coupling relationships into the same local area, thereby narrowing the calculation scope of subsequent time series clustering.
[0059] Figure 3 This is the final distribution map of typical wind turbine clusters. The map shows five typical wind turbine clusters after hierarchical spatiotemporal clustering. Compared to modeling each of the original 73 wind turbines individually, this invention compresses the uncertainty of the wind turbine level into five typical wind turbine clusters while still maintaining a certain degree of spatial interpretability. This result demonstrates that this invention does not simply randomly remove wind turbines, but rather forms representative clusters with physical meaning based on spatial location and historical time series similarity.
[0060] The clustering quality of different clustering methods is compared in Table 1: Table 1 compares the clustering quality of different clustering methods.
[0061] As shown in Table 1, the DB index of the method of the present invention is the lowest, at 1.40, indicating that its clustering results perform well in terms of compactness and inter-cluster separation. At the same time, its average silhouette coefficient and CH index remain at a high level, indicating that the method can achieve a good trade-off between spatial interpretability and temporal pattern distinguishability.
[0062] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainty at the offshore wind turbine level as described in this embodiment.
[0063] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.
[0064] The computer-readable storage medium is a memory, which may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.
[0065] Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described herein, as well as the features of those embodiments or examples, without contradiction. Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.
Claims
1. A hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level, characterized in that, Includes the following steps: Step S1. Obtain wind turbine spatial coordinates and historical wake correction sequence: Obtain the two-dimensional spatial coordinates of all wind turbines in the offshore wind farm and the wake correction wind speed sequence of each wind turbine at historical time. Step S2. Geographically constrained K-means partitioning based on wind turbine spatial coordinates: Based on the two-dimensional spatial coordinates, the geographically constrained K-means algorithm is used to divide all wind turbines into several non-overlapping geographic partitions, so that wind turbines with similar spatial locations and stronger wake coupling relationships are preferentially assigned to the same geographic partition. Step S3. Standardize the historical wake correction sequence: Standardize the historical wake correction wind speed sequence of each wind turbine in each geographical region to obtain a standardized historical sequence; Step S4. Construct the wind turbine time series distance matrix within each partition: Within each geographical partition, the time similarity between the standardized historical sequences of each wind turbine is measured using dynamic time-normalized distance metric, and the wind turbine time series distance matrix within the partition is constructed. Step S5. Perform Ward hierarchical sub-clustering within each geographic region: Based on the distance matrix, agglomerative hierarchical clustering is performed within each geographic region, and cluster merging is performed using the Ward connection criterion. The time sub-cluster set within each region is obtained by cutting the hierarchical clustering tree diagram. Step S6. Generate distance-weighted representative sequences within the partition: For each time subcluster, calculate its sequence center and assign distance weighting coefficients according to the distance of each wind turbine sequence to the subcluster center to generate distance-weighted representative sequences, while recording the size of each time subcluster; Step S7. Construct a representative sequence set and perform secondary global clustering: Collect distance-weighted representative sequences within all geographic partitions, construct a distance-weighted representative sequence set, and perform secondary global clustering on the representative sequence set again using Ward hierarchical clustering based on dynamic time-warped distance to obtain several global representative sequence clusters; Step S8. Generate the final typical wind turbine cluster and its global representative sequence: Generate a global representative sequence and effective scale based on each global representative sequence cluster, and backtrack to the original wind turbine to obtain the final typical wind turbine cluster; Step S9. Aggregate the wind turbine-level deviation trajectory into a typical wind turbine cluster-level deviation trajectory: map the original wind turbine-level spatiotemporal power deviation vector into a typical wind turbine cluster-level spatiotemporal deviation vector through an aggregation matrix, thereby reducing the dimensionality of the wind turbine-level spatiotemporal uncertainty; Step S10. Determine the number of geographical partitions and the final number of typical clusters based on multi-index evaluation: Based on the silhouette coefficient, Calinski-Harabasz index and Davies-Bouldin index, evaluate the clustering quality of the combination of candidate geographical partitions and the final number of typical wind turbine clusters to determine the number of geographical partitions and the final number of typical clusters.
2. The hierarchical spatiotemporal clustering method for dimensionality reduction of uncertainties at the offshore wind turbine level according to claim 1, characterized in that: In step S2, the geographically constrained K-means algorithm is as follows: ， in, Indicates the number of geographical zones; Indicates the first A collection of wind turbines within a geographical region; Indicates the first The spatial center vector of each partition; Represents the two-dimensional spatial coordinate vector of the wind turbine w; Represents the 2-norm of a vector; Geographical partitioning meets the following conditions: ; This indicates that different geographical regions do not overlap; This indicates that all geographical regions collectively cover the entire set of wind turbines, W.
3. The hierarchical spatiotemporal clustering method for uncertainty reduction at the offshore wind turbine level according to claim 2, characterized in that, In step S3, the specific method of the standardization process is as follows: For the first... Geographical regions wind turbine Calculate the mean and variance of its historical series: ， ； in, Indicates wind turbine Mean of historical wake-corrected wind speed series; Indicates wind turbine Variance of historical wake-corrected wind speed series; Indicates the corresponding standard deviation; Further, the standardized historical sequence was obtained: ； in, Indicates wind turbine At a historical moment The standardized sequence value.
4. The hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines according to claim 1, characterized in that, The specific method for step S4 is as follows: For the same geographical region Any two wind turbines The dynamic time-normalized distance metric is used to measure the temporal similarity between the two standardized historical sequences: ； in, Indicates wind turbine With wind turbine The dynamic time-warped distance; and They represent the fans respectively. and The standardized historical sequence vector; Represents the dynamic time-warped distance function; The intervals between all the fans in the zone Composition of partition distance matrix: ； in, Indicates the first Wind turbine time series distance matrix within each geographical region.
5. The hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines according to claim 4, characterized in that... In step S5, based on the distance matrix In each geographic region Agglomerative hierarchical clustering is employed, and the Ward join criterion is used for cluster merging. For two candidate clusters A and B within the same geographic partition, the Ward merge cost is expressed as: ； in, This represents the cost of merging candidate cluster A and candidate cluster B; and These represent the number of wind turbines in cluster A and cluster B, respectively. and Let represent the sequence center vectors of cluster A and cluster B, respectively.
6. The hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines according to claim 5, characterized in that, In step S6, for any time sub-cluster The fan The standardized historical sequence is denoted as Calculate the sequence center of this subcluster: ； in, Representing time subclusters The sequence center vector; Subclusters The number of fans inside; Assign a weight to each wind turbine within a sub-cluster based on the distance from the turbine sequence to the sub-cluster center: ； in, Indicates wind turbine In sub-cluster Distance weighting coefficients in the equation; Indicates the fan in the sub-cluster The standardized historical sequence vector; the closer the wind turbine is to the center of the sub-cluster, the stronger its representativeness and the greater its contribution to the representative sequence.
7. The hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines according to claim 6, characterized in that, In step S4, the method for mapping the original wind turbine-level spatiotemporal power deviation vector to a typical wind turbine cluster-level spatiotemporal deviation vector through an aggregation matrix is as follows: Let the first... Wind turbines in historical samples During the scheduling period The power deviation is For the final typical wind turbine cluster In its first The sample, the first The typical wind turbine cluster deviation under a scheduling period is defined as: ； in, Indicates the first In the historical sample, the first A typical wind turbine cluster during the scheduling period The average power deviation; Indicates the first Wind turbines in historical samples During the scheduling period The original power deviation; All and Typical wind turbine clusters are stacked with deviations to obtain a dimensionality-reduced random vector. ,in, Indicates the first A typical wind turbine cluster-level spatiotemporal deviation vector after hierarchical spatiotemporal clustering dimensionality reduction of a historical sample; Indicates the number of scheduling periods; The dimensionality reduction process can be written in matrix form: ； in, This represents the original wind turbine stage spatiotemporal power deviation vector; Represents an aggregate matrix; Aggregation Matrix The element is defined as: ； in, Represents an aggregate matrix Zhongyou original fan Time period Mapped to a typical wind turbine cluster Time period The elements; when the fan Belongs to a typical wind turbine cluster and When, the element takes Otherwise, take 0.
8. The hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines according to claim 1, characterized in that, In step S10, the clustering quality evaluation includes: a larger silhouette coefficient indicates a more reasonable clustering result; a larger Calinski-Harabasz index indicates better inter-cluster separation and intra-cluster compactness; a smaller Davies-Bouldin index indicates a more compact clustering result and higher inter-cluster separation; by comprehensively comparing the three indicators under different combinations of candidate parameters, the final number of geographical zones and the final number of typical wind turbine clusters are determined.
9. The hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines according to claim 1, characterized in that... The method is applied to the offshore wind power grid-connected scheduling scenario. It uses the dimensionality-reduced typical wind turbine cluster-level spatiotemporal deviation vector as uncertainty input to construct a robust scheduling model or a sub-bluish robust scheduling model.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the hierarchical spatiotemporal clustering method for uncertainty reduction of offshore wind turbines as described in any one of claims 1-9.