A fine impedance aggregation modeling method for wind farm considering multi-dimensional difference

Abstract

The present disclosure relates to a wind farm fine impedance aggregation modeling method considering multi-dimensional differences. In view of the problem that existing methods ignore the multi-dimensional heterogeneity of units and are difficult to balance accuracy and efficiency, the present disclosure takes single machine impedance and operating state as input, constructs a comprehensive feature vector covering machine type, control mode, capacity, grid-connected position and working condition, and performs principal component dimension reduction and clustering to divide homogeneous machine groups; the capacity, working condition and power collection network parameters of each machine group are weighted and aggregated, the equivalent impedance of the machine group is calculated based on the power weighted admittance parallel strategy, and the total equivalent impedance of the wind farm is synthesized combined with the power collection network topology. Through the "first division, then aggregation, and finally synthesis" process, the system dimension is reduced while the wind farm port broadband impedance characteristics are accurately restored, providing high-precision and high-efficiency frequency domain model support for grid stability analysis.

Description

Technical Field

[0001] This disclosure relates to the field of wind farm aggregation modeling, and more specifically, to a method and apparatus for refined impedance aggregation modeling of wind farms that considers multidimensional differences. Background Technology

[0002] Driven by the "dual carbon" goals and energy structure transformation, the installed capacity of new energy sources such as wind power continues to grow. With the integration of a high proportion of new energy, traditional power systems dominated by synchronous generators are gradually exhibiting characteristics such as decreased inertia, weakened damping capacity, and insufficient short-circuit capacity. Especially under weak grid conditions, large-scale wind turbine grid connection can easily lead to problems such as reactive power voltage fluctuations, limited frequency regulation, and oscillations. Grid-connected wind turbines can actively establish voltage and frequency and provide inertia, damping, and fault support. Therefore, the mixed integration of grid-connected (GFM) and grid-fed (GFL) turbines has become an important form of wind farm development.

[0003] With the expansion of wind farm scale and the increase in phased construction projects, modern wind farms exhibit a high degree of multidimensional heterogeneity. This includes common features such as the mixed connection of permanent magnet direct-drive and doubly-fed induction generator (DFIG) units, the coexistence of GFM and GFL control modes, varying unit capacity levels, different physical topologies and electrical distances of the collector network, and differences in real-time wind speeds and power output conditions for each unit. Due to differences in collector line impedance, electrical distance, and local short-circuit ratios, the dynamic response and frequency domain impedance characteristics of each unit exhibit significant differences; and when a unit triggers amplitude limiting or enters the nonlinear operating region, the overall field impedance displays a complex nonlinear superposition effect.

[0004] For wind farm impedance modeling, existing technologies mainly have the following limitations: Traditional weighted aggregation methods have limited applicability: methods such as single-unit multiplication, single-unit parallel connection, or rated capacity weighting are all based on the ideal assumption of homogeneous unit control and operating conditions within the wind farm. For heterogeneous wind farms with multiple turbine types, mixed control, and complex branch access, these methods cannot characterize the dynamic heterogeneity caused by different control logics, spatial locations, and operating conditions, leading to aggregated impedance distortion.

[0005] Existing cluster partitioning techniques lack multidimensional coupling representation: existing data-driven or clustering partitioning methods mostly rely on steady-state operating data or small-signal linearization models, failing to comprehensively coordinate the multidimensional strong coupling relationship between "machine type-control mode-operating condition-network topology".

[0006] In summary, existing wind farm modeling faces a profound contradiction between "model accuracy" and "computational efficiency": full-detail, unit-by-unit modeling leads to excessively high system dimensionality and computational burden; while overly simplified equivalent modeling loses crucial broadband dynamic characteristics, failing to accurately assess the grid-connected stability of the wind farm. Although existing technologies can obtain impedance data of individual units under current operating conditions through impedance frequency sweeping, online identification, or manufacturer parameters, a refined impedance aggregation modeling method for wind farms that can accurately integrate multi-dimensional differences and balance computational efficiency and impedance accuracy is still lacking.

[0007] Therefore, one or more methods are needed to solve the above problems.

[0008] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] The purpose of this disclosure is to provide a method and apparatus for refined impedance aggregation modeling of wind farms that takes into account multidimensional differences, thereby overcoming, at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0010] According to one aspect of this disclosure, a refined impedance aggregation modeling method for wind farms that considers multidimensional differences is provided, comprising: Acquire the single-unit impedance data and multi-dimensional differential characteristic information of each wind turbine in the wind farm under the current operating state, and preprocess the acquired data to construct a unit impedance database; Based on the multidimensional differential feature information, a comprehensive feature vector is constructed. The comprehensive feature vector is then subjected to dimensionality reduction processing. Based on the dimensionality-reduced feature data, a clustering algorithm is used to divide the wind turbines into homogeneous groups. Weighted aggregation of rated capacity, operating conditions and collector network parameters is performed on each homogeneous generator group to obtain the equivalent rated capacity, equivalent operating conditions and equivalent collector network parameters of each generator group; Based on the individual unit impedance data of each unit and the equivalent collector network parameters, the equivalent impedance of each group of units is calculated, and the equivalent impedance of each group of units is electrically combined with the equivalent impedance of the collector network to obtain the total equivalent impedance of the wind farm grid connection point.

[0011] In one exemplary embodiment of this disclosure, the multidimensional differential feature information includes unit type, control mode, rated capacity, grid connection location electrical distance, operating conditions, and collector line parameters.

[0012] In one exemplary embodiment of this disclosure, the method wherein the comprehensive feature vector is constructed according to the following formula:

[0013] in, Indicates the unit type, encoded as a binary variable; Indicates the control mode, coded as 0 or 1; For the rated capacity, normalized to [0,1]; Electrical distance; This represents the current operating condition and indicates the wind speed output.

[0014] In one exemplary embodiment of this disclosure, after constructing the comprehensive feature vector and before clustering, the comprehensive feature vector is standardized, and the standardization is calculated according to the following formula:

[0015] in, and These are the mean and standard deviation of each feature dimension, respectively.

[0016] In one exemplary embodiment of this disclosure, the dimensionality reduction process employs principal component analysis, and the original feature matrix is ​​assumed to be... Its covariance matrix is .right Perform eigenvalue decomposition to obtain eigenvalues. and corresponding feature vectors The first d principal components are selected to form the projection matrix. Then the data after dimensionality reduction is:

[0017] in, .

[0018] In one exemplary embodiment of this disclosure, the clustering algorithm employs the K-means clustering algorithm, and the number of clusters K is determined using the elbow method, with the sum of squared errors as the criterion. The inflection point of the rate of decrease as a function of the number of clusters is taken as the optimal number of clusters; During clustering, the distance from a sample to the cluster center is calculated using the following formula:

[0019] Cluster centers are updated according to the following formula:

[0020] in, C k For the first k One cluster, Centered on it. With KAs the SSE increases, the rate of decrease gradually slows down, and the inflection point is the optimal point. K， For the first A new cluster center, For the sample points in this cluster, the th j Each cluster contains One sample.

[0021] In one exemplary embodiment of this disclosure, the method involves calculating the weighted aggregation of rated capacity for each homogeneous cluster according to the following formula:

[0022] Among them, C k This is the equivalent rated capacity of the k-th cluster, used to ensure that the total capacity of the cluster remains consistent before and after polymerization.

[0023] In one exemplary embodiment of this disclosure, the method calculates the equivalent wind speed and equivalent output based on the weighted aggregation of the operating conditions according to the following formula:

[0024] in, For the first i The current wind speed of the Taiwan unit, To actually contribute to it; The weighted aggregation of the collector network parameters includes, for radial topologies, the equivalent line impedance of the computer cluster based on the equal power loss method according to the following formula:

[0025] Among them, the single-machine input impedance The impedance information of the i-th unit is pre-acquired under the current operating condition. P i Its output power; For a trunk-type topology, first convert it into an equivalent radial topology. The conversion formula is as follows:

[0026] in, The first in the original trunk line structure i The line impedance of the typhoon generator; All The equivalent impedance is considered as that in a radial structure, and then substituted into the formula to calculate the final equivalent impedance.

[0027] In one exemplary embodiment of this disclosure, calculating the equivalent impedance of each generator group includes: converting the pre-obtained individual unit input impedance of each generator group into admittance form, weighting it according to the power ratio to obtain the weighted admittance of the generator group, and calculating the weighted admittance of the generator group according to the following formula:

[0028] in, N k For the first k The number of units in a cluster For the first i The equivalent input admittance of the unit in advance under the current operating condition; Converting the weighted admittance of the cluster to impedance form yields the equivalent impedance of the cluster:

[0029] Converting the total admittance of the wind farm into impedance form yields the total equivalent impedance at the wind farm's grid connection point:

[0030] In one aspect of this disclosure, a device for refined impedance aggregation modeling of wind farms that considers multidimensional differences is provided, comprising: The data acquisition module is used to acquire the single-unit impedance data and multi-dimensional differential characteristic information of each wind turbine in the wind farm under the current operating state, and to preprocess the acquired data to build a unit impedance database. The turbine clustering module is used to construct a comprehensive feature vector based on the multidimensional differential feature information, perform dimensionality reduction processing on the comprehensive feature vector, and use a clustering algorithm to divide the wind turbines into homogeneous clusters based on the dimensionality-reduced feature data. The parameter aggregation module is used to perform weighted aggregation of rated capacity, operating conditions and power collection network parameters for each homogeneous generator group to obtain the equivalent rated capacity, equivalent operating conditions and equivalent power collection network parameters for each generator group. The impedance synthesis module is used to calculate the equivalent impedance of each turbine group based on the single-unit impedance data of each unit and the equivalent collector network parameters, and to electrically synthesize the equivalent impedance of each turbine group with the equivalent impedance of the collector network to obtain the total equivalent impedance of the wind farm grid connection point.

[0031] This disclosure presents an exemplary method for refined impedance aggregation modeling of wind farms that considers multidimensional differences. Addressing the shortcomings of existing methods that neglect the multidimensional heterogeneity of turbine units and struggle to balance accuracy and efficiency, this invention uses individual turbine impedance and operating status as input to construct a comprehensive feature vector encompassing turbine type, control mode, capacity, grid connection location, and operating conditions. Principal component analysis and clustering are then used to divide the turbine groups into homogeneous clusters. Weighted aggregation of capacity, operating conditions, and collector network parameters is performed on each cluster. The equivalent impedance of the clusters is calculated based on a power-weighted admittance parallel strategy, and the total equivalent impedance of the wind farm is synthesized by combining the collector network topology. Through this "division, aggregation, and synthesis" process, the system dimensionality is reduced while accurately restoring the broadband impedance characteristics of the wind farm ports, providing high-precision and high-efficiency frequency domain model support for grid connection stability analysis.

[0032] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0033] The above and other features and advantages of this disclosure will become more apparent from the detailed description of exemplary embodiments thereof with reference to the accompanying drawings.

[0034] Figure 1 A flowchart is shown below illustrating a method for refined impedance aggregation modeling of wind farms that considers multidimensional differences, according to an exemplary embodiment of this disclosure. Figure 2 A flowchart of wind farm aggregation modeling is shown, which is a wind farm aggregation modeling method that considers multidimensional differences according to an exemplary embodiment of the present disclosure. Figure 3 A flowchart illustrating a wind farm cluster partitioning method that considers multidimensional differences in a refined impedance aggregation modeling method for wind farms according to an exemplary embodiment of the present disclosure is shown. Figure 4 A radial topology and its aggregation diagram of a refined impedance aggregation modeling method for wind farms that considers multidimensional differences are shown according to an exemplary embodiment of the present disclosure. Figure 5 The trunk topology and its aggregation diagram of a refined impedance aggregation modeling method for wind farms that considers multidimensional differences are shown in an exemplary embodiment of the present disclosure. Figure 6 A flowchart of wind farm impedance equivalent modeling is shown, which is a wind farm refined impedance aggregation modeling method considering multidimensional differences according to an exemplary embodiment of the present disclosure. Figure 7 A wind farm four-trunk radial collector topology diagram is shown, which is based on an exemplary embodiment of the present disclosure and a wind farm refined impedance aggregation modeling method that considers multidimensional differences. Figure 8The diagram illustrates the variation of the sum of squared errors (SSE) with the number of clusters (K) and its rate of decrease in a refined impedance aggregation modeling method for wind farms that considers multidimensional differences, according to an exemplary embodiment of this disclosure. Figure 9 The diagram illustrates the variance rate and cumulative contribution of each principal component in a refined impedance aggregation modeling method for wind farms that considers multidimensional differences, according to an exemplary embodiment of the present disclosure. Figure 10 A three-dimensional clustering distribution map of 60 wind turbine units is shown, based on an exemplary embodiment of the present disclosure, of a refined impedance aggregation modeling method for wind farms that considers multidimensional differences. Figure 11 A two-dimensional clustering distribution map of 60 wind turbine units is shown, illustrating a refined impedance aggregation modeling method for wind farms that considers multidimensional differences, according to an exemplary embodiment of the present disclosure. Figure 12 A scatter plot of trunk line weighted wind speed-power is shown for a wind farm refined impedance aggregation modeling method that considers multidimensional differences, according to an exemplary embodiment of the present disclosure. Figure 13 The diagram illustrates the electrical distance and loss characteristics and power distribution of each trunk collector line according to an exemplary embodiment of the present disclosure of a refined impedance aggregation modeling method for wind farms that considers multidimensional differences; Figure 14 The positive-sequence impedance frequency domain Bode plot and its modeling error analysis plot are shown for a refined impedance aggregation modeling method for wind farms that considers multidimensional differences, according to an exemplary embodiment of the present disclosure. Figure 15 A comparison diagram of the dynamic response of various electrical quantities at the PCC point is shown in an exemplary embodiment of the present disclosure of a refined impedance aggregation modeling method for wind farms that considers multidimensional differences. Figure 16 A time-domain simulation efficiency comparison chart is shown for three models of a refined impedance aggregation modeling method for wind farms that considers multidimensional differences, according to an exemplary embodiment of the present disclosure. Figure 17 A schematic block diagram of a wind farm refined impedance aggregation modeling apparatus that takes into account multidimensional differences is shown according to an exemplary embodiment of the present disclosure. Detailed Implementation

[0035] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, they are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted.

[0036] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced without one or more of the specific details described, or other methods, components, materials, apparatuses, steps, etc., can be employed. In other instances, well-known structures, methods, apparatuses, implementations, materials, or operations are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0037] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, or in one or more software-hardened modules, or in different network and / or processor devices and / or microcontroller devices.

[0038] In this example embodiment, a refined impedance aggregation modeling method for wind farms that considers multidimensional differences is first provided; refer to Figure 1 As shown, this method for refined impedance aggregation modeling of wind farms that considers multidimensional differences may include the following steps: Step S110: Obtain the single-unit impedance data and multi-dimensional difference characteristic information of each wind turbine in the wind farm under the current operating state, and preprocess the obtained data to build a unit impedance database. Step S120: Construct a comprehensive feature vector based on the multidimensional difference feature information, perform dimensionality reduction processing on the comprehensive feature vector, and use a clustering algorithm to divide the wind turbine into homogeneous groups based on the dimensionality-reduced feature data. Step S130: Perform weighted aggregation of rated capacity, operating conditions and power collection network parameters for each homogeneous generator group to obtain the equivalent rated capacity, equivalent operating conditions and equivalent power collection network parameters for each generator group. Step S140: Based on the single-unit impedance data of each unit and the equivalent collector network parameters, calculate the equivalent impedance of each group of units, and electrically combine the equivalent impedance of each group of units with the equivalent impedance of the collector network to obtain the total equivalent impedance of the wind farm grid connection point.

[0039] This disclosure presents an exemplary method for refined impedance aggregation modeling of wind farms that considers multidimensional differences. Addressing the shortcomings of existing methods that neglect the multidimensional heterogeneity of turbine units and struggle to balance accuracy and efficiency, this invention uses individual turbine impedance and operating status as input to construct a comprehensive feature vector encompassing turbine type, control mode, capacity, grid connection location, and operating conditions. Principal component analysis and clustering are then used to divide the turbine groups into homogeneous clusters. Weighted aggregation of capacity, operating conditions, and collector network parameters is performed on each cluster. The equivalent impedance of the clusters is calculated based on a power-weighted admittance parallel strategy, and the total equivalent impedance of the wind farm is synthesized by combining the collector network topology. Through this "division, aggregation, and synthesis" process, the system dimensionality is reduced while accurately restoring the broadband impedance characteristics of the wind farm ports, providing high-precision and high-efficiency frequency domain model support for grid connection stability analysis.

[0040] The following will further explain a method for refined impedance aggregation modeling of wind farms that considers multidimensional differences in this example embodiment.

[0041] Example 1: In step S110, the single-unit impedance data and multi-dimensional difference characteristic information of each wind turbine in the wind farm under the current operating state can be obtained, and the obtained data can be preprocessed to construct a unit impedance database.

[0042] In this example embodiment, the multidimensional differential characteristic information includes unit type, control mode, rated capacity, grid connection location electrical distance, operating conditions, and collector line parameters.

[0043] In step S120, a comprehensive feature vector can be constructed based on the multidimensional difference feature information, the comprehensive feature vector can be dimensionality reduced, and the wind turbines can be divided into homogeneous groups based on the dimensionality-reduced feature data using a clustering algorithm.

[0044] In this example embodiment, the comprehensive feature vector is constructed according to the following formula:

[0045] in, Indicates the unit type, encoded as a binary variable; Indicates the control mode, coded as 0 or 1; For the rated capacity, normalized to [0,1]; Electrical distance; This represents the current operating condition and indicates the wind speed output.

[0046] In this example embodiment, after constructing the comprehensive feature vector and before clustering, the comprehensive feature vector is standardized, and the standardization is calculated according to the following formula:

[0047] in, and These are the mean and standard deviation of each feature dimension, respectively.

[0048] In this example embodiment, the dimensionality reduction process employs principal component analysis, with the original feature matrix set as follows: Its covariance matrix is .right Perform eigenvalue decomposition to obtain eigenvalues. and corresponding feature vectors The first d principal components are selected to form the projection matrix. Then the data after dimensionality reduction is:

[0049] in, .

[0050] In this example embodiment, the clustering algorithm used is the K-means clustering algorithm, and the number of clusters K is determined using the elbow method, with the sum of squared errors as the criterion. The inflection point of the rate of decrease as a function of the number of clusters is taken as the optimal number of clusters; During clustering, the distance from a sample to the cluster center is calculated using the following formula:

[0051] Cluster centers are updated according to the following formula:

[0052] in, C k For the first k One cluster, Centered on it. With K As the SSE increases, the rate of decrease gradually slows down, and the inflection point is the optimal point. K， For the first A new cluster center, For the sample points in this cluster, the th j Each cluster contains One sample.

[0053] In step S130, the rated capacity, operating conditions and power collection network parameters of each homogeneous generator group can be weighted and aggregated to obtain the equivalent rated capacity, equivalent operating conditions and equivalent power collection network parameters of each generator group.

[0054] In this example embodiment, the weighted aggregation of rated capacity for each homogeneous cluster is calculated according to the following formula:

[0055] Among them, C k This is the equivalent rated capacity of the k-th cluster, used to ensure that the total capacity of the cluster remains consistent before and after polymerization.

[0056] In this example embodiment, the weighted aggregation of the operating conditions is used to calculate the equivalent wind speed and equivalent output according to the following formula:

[0057] in, For the first i The current wind speed of the Taiwan unit, To actually contribute to it; The weighted aggregation of the collector network parameters includes, for radial topologies, the equivalent line impedance of the computer cluster based on the equal power loss method according to the following formula:

[0058] Among them, the single-machine input impedance The impedance information of the i-th unit is pre-acquired under the current operating condition. P i Its output power; For a trunk-type topology, first convert it into an equivalent radial topology. The conversion formula is as follows:

[0059] in, The first in the original trunk line structure i The line impedance of the typhoon generator; All The equivalent impedance is considered as that in a radial structure, and then substituted into the formula to calculate the final equivalent impedance.

[0060] In step S140, the equivalent impedance of each turbine group can be calculated based on the single-unit impedance data of each unit and the equivalent collector network parameters. The equivalent impedance of each turbine group and the equivalent impedance of the collector network are then electrically combined to obtain the total equivalent impedance of the wind farm grid connection point.

[0061] In this example embodiment, calculating the equivalent impedance of each generator group includes: converting the pre-obtained individual unit input impedance of each unit into admittance form, weighting it according to the power ratio to obtain the weighted admittance of the generator group, and calculating the weighted admittance of the generator group according to the following formula:

[0062] in, N k For the first k The number of units in a cluster For the first i The equivalent input admittance of the unit in advance under the current operating condition; Converting the weighted admittance of the cluster to impedance form yields the equivalent impedance of the cluster:

[0063] Converting the total admittance of the wind farm into impedance form yields the total equivalent impedance at the wind farm's grid connection point: .

[0064] Example 2: In this example embodiment, addressing the challenges of existing wind farm aggregation modeling methods in balancing computational efficiency and equivalent impedance accuracy, and the distortion caused by neglecting multidimensional differences in turbine units, this invention provides a refined impedance aggregation modeling method for wind farms that considers multidimensional differences. This method takes pre-obtained individual turbine impedance and operating status as input. It constructs a comprehensive feature vector covering turbine type, control mode, capacity, grid connection location, and operating conditions. Principal component analysis is used to extract key features, and clustering is employed to divide the turbine groups into homogeneous groups. Based on this, capacity-weighted and power-weighted parameter aggregation is performed on each turbine group, and the turbine group impedance is synthesized by combining the collector network topology to obtain the equivalent impedance at the wind farm's grid connection point. Through this "division, aggregation, and synthesis" modeling process, the method significantly reduces the system model order and computational complexity while accurately reproducing the broadband impedance characteristics of the wind farm's ports, providing high-precision and high-efficiency frequency domain model support for system analysis.

[0065] In the embodiments of this example, as Figure 2 As shown, the analysis of multidimensional differential characteristic factors of wind farms in wind farm aggregation modeling includes: Permanent magnet direct-drive wind turbines and doubly-fed induction generators (DFIGs), as well as GFL and GFM turbines, can be mixed and connected within a wind farm. The turbine topology and control method directly affect the sequence impedance characteristics and dynamic response after current limiting. GFLs rely on PLL synchronization, while GFMs generate voltage and frequency through VSGs. Therefore, the control mode and turbine type are the main basis for cluster division.

[0066] Wind capacity, wind speed output, and grid connection location further alter current distribution, limiting probability, and local grid strength. Differences in the electrical distance of collector lines result in variations in the short-circuit ratio and phase margin of each turbine, making it difficult to reflect the overall impedance characteristics of a wind farm using only linear equivalents.

[0067] Table 1 shows the degree of influence of each difference factor. During aggregation, priority is given to ensuring consistency in machine type and control mode, and then adjustments are made for capacity, location, and operating conditions.

[0068] Table 1 Analysis of the impact of differential factors on system stability

[0069] In this example embodiment, the wind farm aggregation modeling process includes: To address the conflict between accuracy and efficiency, this invention adopts a modeling process of "first dividing, then aggregating, and finally synthesizing".

[0070] A comprehensive feature vector is constructed based on the model, control mode, capacity, grid connection location, and operating conditions. After principal component dimensionality reduction, K-means is used to divide homogeneous clusters, so that the same cluster maintains a high dynamic similarity.

[0071] Rated capacity, wind speed output, and power collection network parameters are aggregated for each generator group; the input impedance of a single unit is based on pre-acquired data that reflects the current operating status.

[0072] Finally, the equivalent models of each turbine group are combined to form the total impedance of the wind farm. After obtaining the equivalent impedance of each turbine group, they are treated as independent equivalent power sources and synthesized into the overall impedance of the wind farm through parallel connection. Its equivalent form can be expressed as: (1) In the formula, the equivalent impedance of each unit group is the input impedance of each unit in the group obtained in advance under the current operating conditions. For the first The equivalent impedance of each machine group is obtained by power weighting or admittance paralleling.

[0073] In this example embodiment, principal component dimensionality reduction and K-means homogeneous cluster partitioning include: (1) Preprocessing of single-unit impedance information and operating status Before aggregation, the individual unit impedance and status information of each unit under its current operating condition are obtained. The status information includes unit type, control mode, rated capacity, connected branch, electrical distance, line parameters, wind speed, power, and limiting status.

[0074] The impedance of a single unit can be obtained from existing models, frequency sweep tests, online identification, or manufacturer data; this invention does not limit the specific method of obtaining it.

[0075] Data with inconsistent frequency sampling points, capacity references, and dimensions are resampled, normalized, and missing values ​​are corrected to form a unit impedance database that can be directly used for feature construction and grouping.

[0076] (2) Construction of comprehensive feature vectors The comprehensive feature vector of each unit It can be constructed as: (2) In the formula, Indicates the unit type, encoded as a binary variable; Indicates the control mode, coded as 0 or 1; For the rated capacity, normalized to [0,1]; Electrical distance; This represents the current operating condition and the wind speed output. This vector comprehensively describes the static parameters and dynamic operating status of the unit, and forms the basis for subsequent cluster analysis.

[0077] (3) Data preprocessing Before clustering, the original feature data needs to be standardized to eliminate dimensional differences between different dimensions. Let the first... The feature vector of the Taiwanese unit is Its standardized form It can be represented as: (3) In the formula, and These are the mean and standard deviation of each feature dimension, respectively.

[0078] (4) Principal Component Analysis and Dimensionality Reduction Because the features of the generator set have high dimensionality, direct clustering may lead to the curse of dimensionality. Therefore, principal component analysis is first used to reduce the dimensionality of the features. Let the original feature matrix be... Its covariance matrix is .right Perform eigenvalue decomposition to obtain eigenvalues. and corresponding feature vectors The first d principal components are selected to form the projection matrix. Then the data after dimensionality reduction is: (4) In the formula, This effectively reduces the computational complexity of subsequent clustering.

[0079] (5) Determine the number of clusters K Cluster number K The choice of [aspect / factor] directly affects the clustering effect. This paper uses the elbow method to determine the optimal [aspect / factor]. K The value of is determined by the key metric, which is the sum of squared errors (SSE) of all clusters, used to evaluate the quality of clustering. (5) In the formula, C k For the first k One cluster, Centered on it. With K As the SSE increases, the rate of decrease gradually slows down, and the inflection point is the optimal point. K .

[0080] (6) K-means clustering algorithm Based on the dimensionality-reduced data Perform K-means clustering. The specific steps are as follows: First, initialize randomly. K Cluster centers Then calculate the distance from the sample to each center: (6) In the formula, For the first A new cluster center, These are the sample points in this cluster.

[0081] Then assign the sample to the nearest cluster, update the cluster centers, and let the i-th cluster be the nearest cluster. j Each cluster contains For each sample, the update formula is: (7) Repeated sample allocation and cluster center updates until cluster centers converge; see the flowchart below. Figure 3 .

[0082] In this example embodiment, the aggregation of cluster capacity, operating conditions, and power collection network parameters includes: Within a homogeneous power plant cluster, the unit types and control modes remain consistent, and the rated capacity, operating conditions, and power collection network parameters are aggregated using a weighted method to form an equivalent model of the power plant cluster.

[0083] (1) Rated capacity polymerization Let the first k The individual machine group includes The rated capacities of the units are as follows: Then the equivalent rated capacity of the generator group is: (8) C k This is the equivalent rated capacity of the k-th cluster, used to ensure that the total capacity of the cluster remains consistent before and after polymerization.

[0084] (2) Aggregation of operating conditions Since the wind speed and output vary depending on the operating conditions of different units, they need to be reasonably aggregated. This paper uses the weighted average method to calculate the equivalent wind speed. and equivalent output : (9) In the formula, For the first i The current wind speed of the Taiwan unit, This method takes into account both capacity weights and operational status, avoiding the distortion caused by simple averaging.

[0085] (3) Aggregation of collector network parameters The collector network is processed according to the actual topology: the radial type is equivalent to the power loss, and the trunk type is first converted into an equivalent radial type.

[0086] Figure 4 The collector network topology is radial, with each wind turbine connected in parallel to the PCC. According to the equal power loss method, let the first... k The individual machine group includes n Taiwanese generator set, its equivalent line impedance for: (10) In the formula, the single-machine input impedance The impedance information of the i-th unit is pre-acquired under the current operating condition. P i Its output power.

[0087] And for Figure 5 The trunk-type collector network topology in the example needs to be converted into an equivalent radial structure first. m Taking a typhoon generator as an example, let its position on the main line correspond to the equivalent line impedance as follows: : (11) In the formula, The first in the original trunk line structure i The line impedance of the typhoon generator. Then, all of them... The equivalent impedance is considered as that in a radial structure, and then substituted into the formula to calculate the final equivalent impedance.

[0088] In this example embodiment, the calculation of the equivalent impedance of the wind farm cluster, based on the pre-obtained individual unit impedances, includes: Units within a homogeneous generator group share similar generator types, control modes, and operating conditions. A power-weighted admittance parallel strategy is adopted to optimize the equivalent impedance of the generator group.

[0089] First, based on basic circuit principles, the total admittance of a multi-unit parallel system... It equals the sum of the admittances of each individual machine: (12) In the formula, N k For the first k The number of units in a cluster For the firsti The equivalent input admittance of the unit in advance under the current operating state.

[0090] However, in actual operation, the output power of each unit differs, and their contributions to the system's dynamic response are not equal. Simply using equal-weighted parallel operation would lead to an underestimation of the dynamic characteristics of high-power units. Therefore, a power-ratio weighting mechanism is adopted to weight the admittance of each individual unit: (13) In the formula, For the first i Normalized weights for generator units. This method assigns greater aggregation weights to high-power generator units, improving the fidelity of the equivalent model in the dominant frequency band.

[0091] Finally, the first k Equivalent impedance of a cluster for: (14) The equivalent impedance of the generator group obtained in this way takes into account both the power contribution and electrical parallel relationship of the units, and can be used for subsequent network synthesis.

[0092] In this example embodiment, the total impedance synthesis of the wind farm includes: After calculating the equivalent impedance of each turbine group, it is necessary to further connect it electrically to the internal collector network of the wind farm to construct the equivalent impedance model of the entire wind farm. Since multiple turbines in the wind farm are connected to the substation via collector lines, their electrical topology is usually star or radial. Therefore, the collector network can be equivalent to a lumped parameter impedance. It is connected in parallel with the equivalent impedance of each machine group.

[0093] Suppose the wind farm is divided into 10 parts. K The first cluster, k The equivalent impedance of each cluster is Then the total admittance of the wind farm is: (15) In the formula, This is the equivalent impedance of the collector network. If the distributed parameter effect is ignored, it can be approximated as a purely inductive impedance: (16) In the formula, and It can be estimated based on actual engineering data or typical values. Ultimately, the total impedance of the wind farm... It can be represented as: (17) In this example embodiment, the wind farm impedance equivalent modeling process includes: Figure 6 The modeling path from raw unit data and group parameters to the equivalent impedance of the wind farm is presented.

[0094] Example 3: In this example embodiment, the simulation system configuration includes: Taking a general-purpose 200MW onshore wind farm as an example, a detailed electromagnetic transient model containing 60 turbine units and a four-trunk radial collector network was established in MATLAB / Simulink. The farm includes three types of turbine units: 2.0MW, 3.0MW, and 5.0MW, covering typical scenarios of multi-generational mixed installation and mixed control modes.

[0095] The wind farm adopts a four-trunk 35kV radial collection network, connected to the 220kV power grid via a 35kV / 220kV step-up substation. Lines A, B, C, and D are located 0.5–2.1km, 2.0–3.5km, 3.6–6.0km, and 6.2–10.0km from the step-up substation, respectively, corresponding to the existing, hybrid transition, technology verification, and mainstream turbine areas. The topology is as follows: Figure 7 As shown.

[0096] The entire site has 60 units with a total capacity of 200MW, including 32 doubly fed wind turbines, 28 permanent magnet direct-drive wind turbines, 50 GFLs and 10 GFMs; their configuration is shown in Table 2, and detailed electrical parameters are shown in Table 3.

[0097] Table 2 Overview of Wind Farm Four Trunk Line Unit Configuration

[0098] The simulation system has a grid connection voltage of 220kV and a short-circuit ratio of 3. The collector line is modeled as 35kV, and the impedance of the A-D line is set according to the distance gradient. The wind speed is taken as three typical operating conditions of 4m / s, 8m / s and 12m / s and randomly distributed.

[0099] Table 360 ​​Detailed Electrical Parameters of Wind Turbine Units

[0100] In this example embodiment, cluster partitioning and parameter aggregation include: (1) Division of wind farm clusters The elbow method was used to determine the number of clusters. Figure 8 The sum of squared errors (SSE) and its rate of decrease are given as a function of K.

[0101] SSE decreases rapidly when K=1 to 4, and then levels off after K>4, so K=4 is chosen. This setting preserves the main technological generation and control differences, and compresses 60 units into 4 equivalent groups.

[0102] Based on K=4, principal component dimensionality reduction was performed using five-dimensional features: machine type, control mode, rated capacity, actual output, and distance to grid connection point. The results are shown in […]. Figure 9 .

[0103] The variance contribution rates of PC1 and PC2 were 48.2% and 30.8%, respectively, totaling 79.0%. PC1 primarily reflects the control mode, while PC2 mainly reflects differences in turbine models; capacity, wind speed, and location are used to correct for parameter differences within the same turbine group. Therefore, clustering is mainly based on PC1 and PC2, while also considering other features.

[0104] Based on the feature space constructed from the first three-dimensional principal components, the three-dimensional cluster distribution of the 60 wind turbine units is as follows: Figure 10 As shown.

[0105] Figure 10 The data shows that PC1 distinguishes the control characteristics of GFL and GFM, PC2 reflects the differences between doubly-fed induction generator (DFIG) and permanent magnet direct-drive (PMD) wind turbine models, and PC3 reflects the discreteness of operating conditions and network locations. The distribution of the four types of units is consistent with the technical configuration of each trunk line, indicating that this characteristic space can effectively support the division of the turbine group.

[0106] (2) Wind farm parameter aggregation After grouping, the group parameters are aggregated according to capacity, wind speed, output, and line parameters. The results are as follows: Figure 11 — Figure 13 As shown.

[0107] Figure 11 The results show that the polymerization capacities of lines A through D are 28MW, 24MW, 48MW, and 100MW, respectively, with line D having the highest capacity and playing a major role in impedance polymerization.

[0108] Figure 12 This reflects the differences in weighted wind speed and power output among the main lines. The equivalent wind speed for line A is 8.0 m / s, and the equivalent power is 0.8 MW; for line D, the equivalent wind speeds are 8.8 m / s and the equivalent power is 2.6 MW. This result is used for subsequent power weighting calculations in impedance aggregation.

[0109] Figure 13 This indicates that line losses vary with electrical distance and generator configuration. The equivalent losses of each trunk line after weighted aggregation are approximately 0.6% to 1.1%, with the aggregation points all within an error band of ±0.5%.

[0110] In this example embodiment, the comparison of impedance polymerization results includes: A detailed parallel model of 60 generating units was used as a benchmark, and compared with a traditional single-unit multiplication model with average parameters across the entire field. The three models were evaluated under the same operating conditions in the 10Hz–10kHz frequency domain, fault transients, power step, and computational efficiency.

[0111] (1) Comparison of frequency domain results A detailed parallel model of 60 generating units was constructed as a benchmark based on the pre-obtained individual unit impedances. Considering that the overall variation patterns of positive and negative sequence impedances are similar, the following comparison focuses on positive sequence impedances.

[0112] Figure 14 In the diagram, the blue line represents the detailed parallel model, the red line represents the proposed aggregation model, and the green line represents the traditional single-machine multiplication model.

[0113] Figure 14 The left figure shows that the amplitude-frequency and phase-frequency characteristics of the proposed aggregation model are basically consistent with those of the detailed model; the traditional model shows a significant deviation in the mid-frequency band because the averaging process does not preserve the differences between the groups.

[0114] Figure 14 The right figure shows that the proposed model has an amplitude error of 1.0–2.0 dB and a phase error of 2.0–4.0°; while the traditional model has an amplitude error of 2.2–9.0 dB and a maximum phase error of 16.3°. The difference decreases in the high-frequency band, mainly due to the distributed parameters of the collector line.

[0115] (2) Comparison of time-domain results Time-domain verification was performed at a short-circuit ratio of 3.0: a three-phase short-circuit fault was applied at t=1.0s, the fault was cleared at t=1.15s, and an active power step was applied at t=4.0s. The results are shown in […]. Figure 15 .

[0116] During the fault, the voltage in the detailed model dropped to approximately 0.78 pu. The proposed model can track reactive power support and fault current response better; the reactive power support of the traditional model is approximately 60 Mvar, which is lower than the approximately 90 Mvar of the detailed model and the proposed model.

[0117] After the fault is cleared, the proposed model can reproduce the voltage overshoot and damped oscillation characteristics of the detailed model at approximately 1.12 pu; the traditional model has larger overshoot and oscillation deviations and a longer active power recovery time.

[0118] Under power step conditions, the steady-state error of the proposed model in tracking the 180MW target value is less than 2%, and its reactive power, voltage and current responses are basically consistent with the detailed model; the steady-state power deviation of the traditional model is about 5%, and the reactive power support is insufficient.

[0119] (3) Comparison of computational efficiency results Figure 16 The computational efficiency of three models in completing a 6-second time-domain simulation was compared.

[0120] from Figure 16 As can be seen, the detailed simulation of 60 models taking 6 seconds to complete a dynamic simulation took 1627 seconds, while the equivalent traditional single-machine model took 774 seconds, resulting in a speedup ratio of [missing information]. The aggregation model in this paper only takes 483 seconds, which is a speedup of [previous time]. According to the evaluation criteria of the wind farm equivalent aggregation model, the acceleration ratio This is considered a significant improvement in computational efficiency. The proposed aggregation model not only meets this threshold but also exhibits superior acceleration performance compared to traditional models. Combined with the aforementioned accuracy verification results, the proposed aggregation model achieves significant computational acceleration while meeting the high accuracy threshold set in the evaluation criteria for wind farm equivalent aggregation models; while traditional models, although achieving a similar speedup ratio, suffer from severely excessive accuracy, failing to meet the requirements for high-fidelity modeling. This verifies the effectiveness of the proposed aggregation method within the comprehensive evaluation system.

[0121] It should be noted that although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0122] Furthermore, in this example embodiment, a refined impedance aggregation modeling apparatus for wind farms that considers multidimensional differences is also provided. (Refer to...) Figure 17 As shown, the wind farm refined impedance aggregation modeling device 200 considering multidimensional differences may include: a data acquisition module 210, a turbine cluster division module 220, a parameter aggregation module 230, and an impedance synthesis module 240. Wherein: The data acquisition module 210 is used to acquire the single-unit impedance data and multi-dimensional difference characteristic information of each wind turbine in the wind farm under the current operating state, and to preprocess the acquired data to build a unit impedance database. The turbine cluster division module 220 is used to construct a comprehensive feature vector based on the multidimensional differential feature information, perform dimensionality reduction processing on the comprehensive feature vector, and use a clustering algorithm to divide the wind turbines into homogeneous clusters based on the dimensionality-reduced feature data. The parameter aggregation module 230 is used to perform weighted aggregation of rated capacity, operating conditions and collector network parameters for each homogeneous generator group to obtain the equivalent rated capacity, equivalent operating conditions and equivalent collector network parameters of each generator group. Impedance synthesis module 240 is used to calculate the equivalent impedance of each group of turbines based on the single-unit impedance data of each unit and the equivalent collector network parameters, and to electrically synthesize the equivalent impedance of each group of turbines with the equivalent impedance of the collector network to obtain the total equivalent impedance of the wind farm grid connection point.

[0123] The specific details of each of the wind farm refined impedance aggregation modeling device modules that consider multidimensional differences have been described in detail in the corresponding wind farm refined impedance aggregation modeling method that considers multidimensional differences, so they will not be repeated here.

[0124] It should be noted that although several modules or units of a wind farm refined impedance aggregation modeling device 200 considering multidimensional differences have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0125] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0126] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

[0127] It should be understood that this disclosure is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this disclosure is limited only by the appended claims.

Claims

1. A refined impedance aggregation modeling method for wind farms considering multidimensional differences, characterized in that, The method includes: Acquire the single-unit impedance data and multi-dimensional differential characteristic information of each wind turbine in the wind farm under the current operating state, and preprocess the acquired data to construct a unit impedance database; Based on the multidimensional differential feature information, a comprehensive feature vector is constructed. The comprehensive feature vector is then subjected to dimensionality reduction processing. Based on the dimensionality-reduced feature data, a clustering algorithm is used to divide the wind turbines into homogeneous groups. Weighted aggregation of rated capacity, operating conditions and collector network parameters is performed on each homogeneous generator group to obtain the equivalent rated capacity, equivalent operating conditions and equivalent collector network parameters of each generator group; Based on the individual unit impedance data of each unit and the equivalent collector network parameters, the equivalent impedance of each group of units is calculated, and the equivalent impedance of each group of units is electrically combined with the equivalent impedance of the collector network to obtain the total equivalent impedance of the wind farm grid connection point.

2. The method as described in claim 1, characterized in that, The multidimensional differential characteristic information includes unit type, control mode, rated capacity, grid connection location and electrical distance, operating conditions and collector line parameters.

3. The method as described in claim 1, characterized in that, In the method described above, the comprehensive feature vector is constructed according to the following formula: in, Indicates the unit type, encoded as a binary variable; Indicates the control mode, coded as 0 or 1; For the rated capacity, normalized to [0,1]; Electrical distance; This represents the current operating condition and indicates the wind speed output.

4. The method as described in claim 3, characterized in that, After constructing the comprehensive feature vector and before clustering, the comprehensive feature vector is standardized. The standardization is calculated according to the following formula: in, and These are the mean and standard deviation of each feature dimension, respectively.

5. The method as described in claim 4, characterized in that, The dimensionality reduction process employs principal component analysis, assuming the original feature matrix is... Its covariance matrix is .right Perform eigenvalue decomposition to obtain eigenvalues. and corresponding feature vectors The first d principal components are selected to form the projection matrix. Then the data after dimensionality reduction is: in, .

6. The method as described in claim 5, characterized in that, The clustering algorithm used is K-means clustering, and the number of clusters K is determined using the elbow method, with the sum of squared errors as the criterion. The inflection point of the rate of decrease as a function of the number of clusters is taken as the optimal number of clusters; During clustering, the distance from a sample to the cluster center is calculated using the following formula: Cluster centers are updated according to the following formula: in, C k For the first k One cluster, Centered on it. With K As the SSE increases, the rate of decrease gradually slows down, and the inflection point is the optimal point. K， For the first A new cluster center, For the sample points in this cluster, the first... j Each cluster contains One sample.

7. The method as described in claim 6, characterized in that, In the method, the weighted aggregation of rated capacity for each homogeneous cluster is calculated according to the following formula: Among them, C k This is the equivalent rated capacity of the k-th cluster, used to ensure that the total capacity of the cluster remains consistent before and after polymerization.

8. The method as described in claim 7, characterized in that, In the method, the weighted aggregation of the operating conditions is calculated according to the following formula to determine the equivalent wind speed and equivalent output: in, For the first i The current wind speed of the Taiwan unit, To actually contribute to it; The weighted aggregation of the collector network parameters includes, for radial topologies, the equivalent line impedance of the computer cluster based on the equal power loss method according to the following formula: Among them, the single-machine input impedance The impedance information of the i-th unit is pre-acquired under the current operating condition. P i Its output power; For a trunk-type topology, first convert it into an equivalent radial topology. The conversion formula is as follows: in, The first in the original trunk line structure i The line impedance of the typhoon generator; All The equivalent impedance is considered as that in a radial structure, and then substituted into the formula to calculate the final equivalent impedance.

9. The method as described in claim 8, characterized in that, The calculation of the equivalent impedance of each generator group includes: converting the pre-obtained individual unit input impedance of each unit into admittance form, and weighting it according to the power ratio to obtain the weighted admittance of the generator group. The weighted admittance of the generator group is calculated according to the following formula: in, N k For the first k The number of units in a cluster For the first i The equivalent input admittance of the unit in advance under the current operating condition; Converting the weighted admittance of the cluster to impedance form yields the equivalent impedance of the cluster: Converting the total admittance of the wind farm into impedance form yields the total equivalent impedance at the wind farm's grid connection point: 。 10. A device for refined impedance aggregation modeling of wind farms considering multidimensional differences, characterized in that, The device includes: The data acquisition module is used to acquire the single-unit impedance data and multi-dimensional differential characteristic information of each wind turbine in the wind farm under the current operating state, and to preprocess the acquired data to build a unit impedance database. The turbine clustering module is used to construct a comprehensive feature vector based on the multidimensional differential feature information, perform dimensionality reduction processing on the comprehensive feature vector, and use a clustering algorithm to divide the wind turbines into homogeneous clusters based on the dimensionality-reduced feature data. The parameter aggregation module is used to perform weighted aggregation of rated capacity, operating conditions and power collection network parameters for each homogeneous generator group to obtain the equivalent rated capacity, equivalent operating conditions and equivalent power collection network parameters for each generator group. The impedance synthesis module is used to calculate the equivalent impedance of each turbine group based on the single-unit impedance data of each unit and the equivalent collector network parameters, and to electrically synthesize the equivalent impedance of each turbine group with the equivalent impedance of the collector network to obtain the total equivalent impedance of the wind farm grid connection point.

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