A wind farm dynamic equivalent aggregation method based on PCA and kernel-FCM
By combining PCA and Kernel-FCM algorithms, the problems of variable correlation and redundancy in the wind farm equivalent model are solved, achieving efficient dynamic equivalent aggregation of wind farms and improving calculation speed and accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- KUNMING UNIV OF SCI & TECH
- Filing Date
- 2024-03-19
- Publication Date
- 2026-06-05
AI Technical Summary
In equivalent models of wind farms, existing technologies struggle to effectively handle strong correlations and data redundancy among variables, resulting in slow calculation speeds and low accuracy.
The dynamic equivalent aggregation method for wind farms is adopted using PCA and Kernel-FCM algorithms. Clustering indices are selected based on the dynamic characteristics of the units, dimensionality reduction and unit grouping are performed, equivalent unit parameters are calculated, and a dynamic equivalent aggregation model is constructed.
The method improves the rationality and accuracy of clustering and grouping of wind farm grid-connected systems, reduces the amount of computation, and improves simulation speed and accuracy.
Smart Images
Figure CN122153515A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system control technology, and in particular to a dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM. Background Technology
[0002] With the continuous development of wind power technology and the development and utilization of efficient and clean renewable energy sources such as wind power, the construction of large-scale wind farms has become a major trend in the future. When analyzing power systems with large-scale wind farms connected to the grid, it is necessary to reasonably simplify the wind farm, cluster the turbines within the wind farm, and establish their equivalent models. This will greatly simplify the complexity of the wind farm model and improve the speed of simulation operation.
[0003] For equivalent models, multi-machine equivalent models, which can more accurately represent the actual operating state of wind farms, are often used. Multi-machine equivalent models use fewer wind turbines to represent the entire wind farm. Usually, based on the similarity of their operating characteristics, the electrical and mechanical characteristics of wind turbine units are used as clustering indicators for dynamic equivalence.
[0004] However, selecting the number of clustering indicators in multi-machine equivalence models is a challenge. Choosing only one indicator can affect equivalence accuracy, while using more features, although more comprehensive in consideration, increases the workload of acquiring indicators and aggregating classifications due to correlations between variables and data redundancy, without fundamentally improving clustering efficiency. Therefore, if the clustered data cannot be analyzed and processed to eliminate strong correlations between variables and complex redundant information, the data volume will become too large, impacting computational speed.
[0005] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention
[0006] The main objective of this invention is to provide a dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM, aiming to solve the problem of how to analyze and process clustered data to eliminate strong correlations between variables and complex and redundant information in the data.
[0007] To achieve the above objectives, this invention provides a dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM, the method comprising:
[0008] Obtain the dynamic characteristics of the wind turbine in the preset mathematical model, and select multiple clustering indicators based on the dynamic characteristics of the wind turbine;
[0009] Calculate the initial values of the state variables corresponding to each of the clustering indices, and construct a high-dimensional data sample from the initial values of each of the state variables.
[0010] The high-dimensional data sample is reduced in dimensionality using PCA analysis to obtain a low-dimensional data sample.
[0011] The optimal number of clusters is determined based on the gap value and by balancing simulation accuracy and computational cost.
[0012] The low-dimensional data samples are divided into clusters based on the Kernel-FCM algorithm;
[0013] The equivalent parameters of the units in each cluster obtained by clustering are calculated based on the capacity weighting method.
[0014] Based on the fast analytical method, the dynamic equivalent parameters of the power collection network are calculated, and a dynamic equivalent aggregation model of the wind farm is constructed based on the equivalent unit parameters and the dynamic equivalent parameters of the power collection network.
[0015] Optionally, the clustering indices include: pitch angle, rotor speed, mechanical torque, electromagnetic torque, stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, stator active power output, stator reactive power output, wind turbine active power output, and wind turbine reactive power output.
[0016] Optionally, calculating the initial values of the state variables corresponding to each of the clustering indices includes:
[0017] The system acquires the current input wind speed and the first preset variable calculation parameters for each wind turbine. Based on the current input wind speed and the first preset variable calculation parameters, it calculates the blade pitch angle, rotor speed, and active power output of each wind turbine. The first preset variable calculation parameters include the wind turbine blade radius, air density, wind energy utilization coefficient, and tip speed ratio.
[0018] Obtain the current rotor resistance and second preset variable calculation parameters for each wind turbine, and calculate the stator active power output and stator reactive power output for each wind turbine based on the current rotor resistance and the second preset variable calculation parameters. The second preset variable calculation parameters include the stator equivalent two-phase winding self-inductance in the dq coordinate system, the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system, and the stator winding voltage; and...
[0019] Obtain the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and a third preset variable calculation parameter for each wind turbine. Based on the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and the third preset variable calculation parameter, calculate the mechanical torque and electromagnetic torque of each wind turbine. The third preset variable calculation parameter includes the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system and the number of wind turbine pole pairs.
[0020] Optionally, the step of performing dimensionality reduction processing on the high-dimensional data sample based on PCA analysis to obtain a low-dimensional data sample includes:
[0021] Obtain the number of wind turbines n and the number of clustering indicators X of the wind farm, and construct an n*X dimensional matrix based on the number of wind turbines n and the number of clustering indicators X;
[0022] The original data in the matrix is standardized to eliminate the influence of units between data points, resulting in a standardized matrix.
[0023] Establish the covariance matrix corresponding to the standardized matrix, and calculate the eigenvalues and eigenvectors of the covariance matrix;
[0024] Calculate the feature contribution rate corresponding to each of the aforementioned feature values, and the cumulative contribution rate corresponding to each feature contribution rate;
[0025] Select the target feature values that are greater than the preset contribution rate threshold from each cumulative contribution rate as principal components;
[0026] Calculate the loading matrix between each principal component and each element in the covariance matrix;
[0027] The data in the load matrix are identified as the low-dimensional data samples.
[0028] The steps for determining the optimal number of clusters based on the Gap Value and balancing simulation accuracy and computational cost include:
[0029]
[0030] in, It is a mathematical operation to calculate the expected value, where n is the sample size and k is the number of clusters being evaluated. It is a set measure of dispersion within a cluster.
[0031] Optionally, the step of performing cluster partitioning on the low-dimensional data samples based on the Kernel-FCM algorithm includes:
[0032] The low-dimensional data samples are mapped to a high-dimensional feature space using a Gaussian kernel function;
[0033] The inner product of data samples in the high-dimensional feature space is calculated based on the Kernel-FCM clustering algorithm, wherein the Kernel-FCM clustering algorithm includes an iterative update function for the membership matrix and an iterative update function for the cluster centers.
[0034] Optionally, the equivalent unit parameters include equivalent parameters of the generator and transformer, equivalent parameters of the shaft system, equivalent parameters of wind speed, and equivalent parameters of the collector lines.
[0035] Optionally, the equivalent parameters of the generator and transformer include the rated capacity, rated active power and rated reactive power of the equivalent unit, the inertial time constant of the wind turbine, the inertial time constant of the generator rotor, the shaft stiffness coefficient, the shaft damping coefficient, and the reactance of the generator. Specific calculation steps include:
[0036]
[0037]
[0038]
[0039]
[0040]
[0041]
[0042]
[0043]
[0044] In the formula, , and These represent the rated capacity, rated active power, and rated reactive power of the wind turbine generator h, respectively. For capacity weighting coefficients, Let h be the wind turbine inertial time constant of the wind turbine unit. The inertial time constant of the generator rotor of the wind turbine unit h represents the inertial time constant. and These are the shaft stiffness coefficient and shaft damping coefficient of wind turbine unit h, respectively. This refers to the reactance of the generator, including stator reactance, rotor reactance, or magnetizing reactance.
[0045] Optionally, the equivalent wind speed parameter includes the input wind speed of the equivalent unit, and the specific calculation steps include:
[0046]
[0047] In the formula, The input wind speed of the equivalent unit. The input wind speed is h for the wind turbine generator.
[0048] Optionally, the equivalent parameters of the collector line include the generator terminal transformer capacity, generator terminal transformer reactance, and equivalent cable impedance. The specific calculation steps include:
[0049]
[0050]
[0051] In the formula, Let h be the capacity of the terminal transformer of the wind turbine generator. Let f be the reactance of the transformer at the turbine terminal of wind turbine h, and f be the number of wind turbines included in the equivalent turbine unit. ;
[0052] The equivalent current corresponding to the equivalent machine formed by the aggregation of wind turbines in group H can be expressed as:
[0053]
[0054] In the formula, This indicates the voltage corresponding to wind turbine unit h. This indicates the current corresponding to wind turbine generator h;
[0055] According to Ohm's law, the equivalent impedance corresponding to the equivalent machine formed by the aggregation of the Hth group of wind turbines can be expressed as:
[0056]
[0057] In the formula, This indicates the voltage at the wind farm's grid connection point. The voltage corresponding to the equivalent machine formed by the aggregation of wind turbines in group H can be expressed as:
[0058]
[0059] It is equal to half the sum of the ground capacitance currents of all the collector networks corresponding to the wind turbines in group A:
[0060]
[0061] In the formula, This represents the current in the collector network corresponding to wind turbine unit h. Let j represent the capacitance of the collector network corresponding to wind turbine generator h. Represents the imaginary part of polar coordinates;
[0062] Corresponding equivalent cable impedance Z eq_Aresistance R eq_A and resistance to X eq_A They are respectively:
[0063]
[0064]
[0065] Re and Im are mathematical operations that calculate the real and imaginary parts, respectively.
[0066] This invention provides a dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM. It selects clustering indicators based on the dynamic characteristics of the turbine units and extracts data at corresponding time points to form high-dimensional data samples. Principal component analysis is applied to reduce the dimensionality of the clustering indicators, thereby reducing the correlation between variables and data redundancy. Based on the low-dimensional data samples, the Kernel-FCM algorithm is applied to partition the turbine clusters, resulting in the clustering results for the wind turbines. This improves the rationality and effectiveness of the clustering method for doubly-fed induction generator (DFIG) wind farm grid-connected systems. The equivalent turbine unit parameters are calculated using a capacity-weighted method, the equivalent wind speed is calculated based on the principle of equal input wind energy, and the equivalent parameters of the collector lines are calculated using the equal power loss method, thereby improving the reliability and accuracy of the clustering results.
[0067] This application proposes a dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM, which has at least the following advantages:
[0068] 1. Clustering indicators are selected based on the dynamic characteristics of the unit, and data is extracted at corresponding time points to form a high-dimensional data sample. Principal component analysis is applied to reduce the dimensionality of the clustering indicators, thereby reducing the correlation between variables and the redundancy of data.
[0069] 2. The Kernel-FCM algorithm is applied to the low-dimensional data samples to divide the wind turbine clusters. The division results are the clustering results of the wind turbines, thereby improving the rationality and effectiveness of the clustering method for the doubly fed wind farm grid-connected system.
[0070] 3. The equivalent unit parameters are calculated using the capacity weighting method, the equivalent wind speed is calculated based on the principle of equal input wind energy, and the equivalent parameters of the collector line are calculated based on the equal power loss method, thereby improving the reliability and accuracy of the clustering results. Attached Figure Description
[0071] Figure 1 This is a schematic diagram of the hardware operating environment of the wind farm power control system according to an embodiment of the present invention;
[0072] Figure 2 This is a topology diagram of a wind farm involved in an embodiment of the present invention;
[0073] Figure 3This is a flowchart illustrating the first embodiment of the wind farm dynamic equivalent aggregation method based on PCA and Kernel-FCM of the present invention.
[0074] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation
[0075] To better understand the above technical solutions, exemplary embodiments of this disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of this disclosure to those skilled in the art.
[0076] As one implementation scheme, Figure 1 This is a schematic diagram of the hardware operating environment of the wind farm power control system involved in the embodiments of the present invention.
[0077] like Figure 1 As shown, the wind farm power control system may include: a processor 1001, such as a CPU; a memory 1005; a user interface 1003; a network interface 1004; and a communication bus 1002. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed RAM or a stable, non-volatile memory, such as a disk drive. Optionally, the memory 1005 may also be a storage device independent of the aforementioned processor 1001.
[0078] Those skilled in the art will understand that Figure 1 The wind farm power control system architecture shown does not constitute a limitation on the wind farm power control system, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.
[0079] like Figure 1As shown, the memory 1005, which serves as a storage medium, may include an operating system, a network communication module, a user interface module, and a wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM. The operating system is a program that manages and controls the hardware and software resources of the wind farm power control system, the wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM, and the operation of other software or programs.
[0080] exist Figure 1 In the wind farm power control system shown, the user interface 1003 is mainly used to connect to the terminal and communicate with the terminal; the network interface 1004 is mainly used to communicate with the back-end server; the processor 1001 can be used to call the wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM stored in the memory 1005.
[0081] In this embodiment, the wind farm power control system includes: a memory 1005, a processor 1001, and a dynamic equivalent aggregation program for the wind farm based on PCA and Kernel-FCM, stored in the memory and executable on the processor, wherein:
[0082] When processor 1001 calls the wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM stored in memory 1005, it performs the following operations:
[0083] Obtain the dynamic characteristics of the wind turbine in the preset mathematical model, and select multiple clustering indicators based on the dynamic characteristics of the wind turbine;
[0084] Calculate the initial values of the state variables corresponding to each of the clustering indices, and construct a high-dimensional data sample from the initial values of each of the state variables.
[0085] The high-dimensional data sample is reduced in dimensionality using PCA analysis to obtain a low-dimensional data sample.
[0086] The low-dimensional data samples are divided into clusters based on the Kernel-FCM algorithm;
[0087] The equivalent unit parameters of the wind turbines after the computer cluster is divided are used to construct a dynamic equivalent aggregation model of the wind farm based on the equivalent unit parameters.
[0088] When processor 1001 calls the wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM stored in memory 1005, it performs the following operations:
[0089] The system acquires the current input wind speed and the first preset variable calculation parameters for each wind turbine. Based on the current input wind speed and the first preset variable calculation parameters, it calculates the blade pitch angle, rotor speed, and grid-connected active power output for each wind turbine. The first preset variable calculation parameters include the wind turbine blade radius, air density, wind energy utilization coefficient, and tip speed ratio.
[0090] Obtain the current rotor resistance and second preset variable calculation parameters for each wind turbine, and calculate the stator active power output and stator reactive power output for each wind turbine based on the current rotor resistance and the second preset variable calculation parameters. The second preset variable calculation parameters include the stator equivalent two-phase winding self-inductance in the dq coordinate system, the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system, and the stator winding voltage; and...
[0091] Obtain the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and a third preset variable calculation parameter for each wind turbine. Based on the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and the third preset variable calculation parameter, calculate the mechanical torque and electromagnetic torque of each wind turbine. The third preset variable calculation parameter includes the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system and the number of wind turbine pole pairs.
[0092] When processor 1001 calls the wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM stored in memory 1005, it performs the following operations:
[0093] Obtain the number of wind turbines n and the number of clustering indicators X of the wind farm, and construct an n*X dimensional matrix based on the number of wind turbines n and the number of clustering indicators X;
[0094] The original data in the matrix is standardized to eliminate the influence of units between data points, resulting in a standardized matrix.
[0095] Establish the covariance matrix corresponding to the standardized matrix, and calculate the eigenvalues and eigenvectors of the covariance matrix;
[0096] Calculate the feature contribution rate corresponding to each of the aforementioned feature values, and the cumulative contribution rate corresponding to each feature contribution rate;
[0097] Select the target feature values that are greater than the preset contribution rate threshold from each cumulative contribution rate as principal components;
[0098] Calculate the loading matrix between each principal component and each element in the covariance matrix;
[0099] The data in the load matrix are identified as the low-dimensional data samples.
[0100] When processor 1001 calls the wind farm dynamic equivalent aggregation program based on PCA and Kernel-FCM stored in memory 1005, it performs the following operations:
[0101] The low-dimensional data samples are mapped to a high-dimensional feature space using a Gaussian kernel function;
[0102] The inner product of data samples in the high-dimensional feature space is calculated based on the Kernel-FCM clustering algorithm, wherein the Kernel-FCM clustering algorithm includes an iterative update function for the membership matrix and an iterative update function for the cluster centers.
[0103] Based on the hardware architecture of the wind farm power control system based on the above power system control technology, an embodiment of the wind farm dynamic equivalent aggregation method based on PCA and Kernel-FCM is proposed.
[0104] Reference Figure 2 The diagram shown in this embodiment illustrates the topology of the wind farm. The power grid is electrically connected to each wind turbine in the wind farm via a voltage of 220kV / 35kV, and each wind turbine is controlled by a PPC (Performance Optimization With EnhancedRISC – Performance Computing).
[0105] Reference Figure 3 In this embodiment, the wind farm dynamic equivalent aggregation method based on PCA and Kernel-FCM includes the following steps:
[0106] Step S10: Obtain the dynamic characteristics of the wind turbine in the preset wind turbine mathematical model, and select multiple clustering indicators based on the dynamic characteristics of the wind turbine.
[0107] In this embodiment, the system first obtains the dynamic characteristics of the wind turbine from the preset wind turbine mathematical model, and selects multiple clustering indicators based on the dynamic characteristics of the wind turbine.
[0108] The preset wind turbine mathematical model refers to the mathematical model of the doubly fed wind turbine; the dynamic characteristics of the turbine refer to the variable characteristics of the doubly fed wind turbine in the wind farm during the operation of the turbine; and the clustering index is the target turbine dynamic characteristic selected from the dynamic characteristics of each turbine to calculate the initial value of the state variable.
[0109] Optionally, the clustering index may include 12 indicators such as pitch angle, rotor speed, mechanical torque, electromagnetic torque, stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, stator active output, stator reactive output, wind turbine active output, and wind turbine reactive output.
[0110] Step S20: Calculate the initial values of the state variables corresponding to each of the clustering indicators, and construct a high-dimensional data sample from the initial values of each of the state variables.
[0111] In this embodiment, after selecting multiple clustering indicators, the initial values of the state variables corresponding to each clustering indicator are calculated using a preset initial value calculation function for state variables in the system, and the initial values of each state variable are used to form a high-dimensional data sample.
[0112] Optionally, the calculation steps for the initial values of the state variables can be as follows: obtain the current input wind speed of each wind turbine and the first preset variable calculation parameters, and calculate the pitch angle, rotor speed, and grid-connected active power output of each wind turbine based on the current input wind speed and the first preset variable calculation parameters. The first preset variable calculation parameters include the wind turbine blade radius, air density, wind energy utilization coefficient, and tip speed ratio.
[0113] For example, let the pitch angle be... Rotor speed Active power output of wind turbine :
[0114]
[0115] In the formula, Indicates the radius of the wind turbine blades; Indicates air density; Indicates wind speed; The wind energy utilization coefficient represents the extent to which a wind turbine obtains energy from the wind. This indicates the tip speed ratio (the ratio of the blade tip speed to the wind speed).
[0116] Optionally, the calculation steps for the initial values of the state variables can be as follows: obtain the current rotor resistance of each wind turbine and the second preset variable calculation parameters, and calculate the stator active power output and stator reactive power output of each wind turbine according to the current rotor resistance and the second preset variable calculation parameters. The second preset variable calculation parameters include the self-inductance of the equivalent two-phase winding of the stator in the dq coordinate system, the mutual inductance of the equivalent windings of the stator and rotor on the same axis in the dq coordinate system, and the stator winding voltage.
[0117] For example, the sub-active power output is set. Stator reactive power output The assumption is that the fan operates at a unity power factor.
[0118]
[0119] In the formula, R r = diag [ R r R r R r ] Indicates rotor resistance; This represents the self-inductance of the equivalent two-phase stator winding in the dq coordinate system; This represents the equivalent mutual inductance of the stator and rotor windings on the same axis in the dq coordinate system. U s = [ U sa U sb U sc ] T Indicates the stator winding voltage; This is the reactive power output of the wind turbine.
[0120] Optionally, the calculation steps for the initial values of the state variables can be as follows: obtain the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and third preset variable calculation parameters for each wind turbine; calculate the mechanical torque and electromagnetic torque of each wind turbine based on the stator current d-axis component, the stator and rotor current q-axis component, the rotor current d-axis component, the rotor current q-axis component, and the third preset variable calculation parameters, wherein the third preset variable calculation parameters include the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system and the number of wind turbine pole pairs.
[0121] For example, let mechanical torque Electromagnetic torque d-axis component of stator current q-axis component of stator current d-axis component of rotor current q-axis component of rotor current Number of wind turbine pole pairs Synchronous rotational angular velocity ;
[0122]
[0123] in,
[0124] in,
[0125] In this embodiment, after calculating the initial values of the aforementioned state variables, the dataset constructed from the initial values of each state variable is used as a high-dimensional data sample.
[0126] For example, in some specific implementations, the obtained high-dimensional data samples are shown in Tables 1 and 2 below:
[0127] Table 1. Wind speed parameters for each wind turbine
[0128] Table 2. Characteristic Quantities of Each Typhoon
[0129] Step S30: Dimensionality reduction of the high-dimensional data sample is performed based on PCA analysis to obtain a low-dimensional data sample;
[0130] In this embodiment, after obtaining high-dimensional data samples, as the scale of wind farms continues to increase, selecting all state variables as clustering indicators would result in an immeasurable amount of computation and time. Therefore, considering the correlation between the various state variables, principal component analysis (PCA) is used to reduce dimensionality and extract dominant variables from these state variables, which can significantly reduce the amount of computation while maintaining accuracy.
[0131] Optionally, the method for reducing the dimensionality of the high-dimensional data sample using PCA analysis can be specified.
[0132] 1. Obtain the number of wind turbines n and the number of clustering indices X of the wind farm, and construct an n*X dimensional matrix based on the number of wind turbines n and the number of clustering indices X;
[0133] For example, an n*X dimensional matrix is as follows:
[0134] x = [ x 11 x 12 ⋯ x 1 p x 21 x 22 ⋯ x 2 p ⋯ ⋯ ⋱ ⋯ x n 1 x n 2 ⋯ x np ] = ( x 1 , x 2 , ⋯ , x p )
[0135] 2. Standardize the original data in the matrix to eliminate the influence of units between the data, and obtain a standardized matrix;
[0136] Specific standardization processes include: calculating the mean of the matrix column by column. and standard deviation :
[0137]
[0138]
[0139] Calculated standardized data :
[0140]
[0141] The obtained standardized matrix is:
[0142] X = [ X 11 X 12 ⋯ X 1 p X 21 X 22 ⋯ X 2 p ⋯ ⋯ ⋱ ⋯ X n 1 X n 2 ⋯ X np ] = ( X 1 , X 2 , ⋯ , X p )
[0143] 3. Establish the covariance matrix corresponding to the standardized matrix, and calculate the eigenvalues and eigenvectors of the covariance matrix;
[0144] Specifically, the expression for the covariance matrix R is:
[0145] R = [ r 11 r 12 ⋯ r 1 p r 21 r 22 ⋯ r 2 p ⋯ ⋯ ⋱ ⋯ r n 1 r n 2 ⋯ r np ]
[0146] In the formula, .
[0147] Specifically, the steps for calculating the eigenvalues and eigenvectors of the covariance matrix are as follows:
[0148]
[0149] The eigenvalues can be obtained ,and (R is a positive semi-definite matrix, and tr(R) = )
[0150] From the following formula
[0151]
[0152] Obtain the eigenvectors { a 1 = [ a 11 , a 21 , ⋯ , a p 1 ] T a 2 = [ a 21 , a 22 , ⋯ , a p 2 ] T ⋮ a p = [ a 1 p , a 2 p , ⋯ , a pp ] T
[0153] IV. Calculate the feature contribution rate corresponding to each of the aforementioned feature values, and the cumulative contribution rate corresponding to each feature contribution rate;
[0154] Specifically, let the eigenvalue contribution rate be... and cumulative contribution rate The calculation formula is as follows:
[0155]
[0156] In the formula, This represents the i-th eigenvalue; This represents the j-th eigenvalue;
[0157] 5. Select target feature values that are greater than the preset contribution rate threshold from each cumulative contribution rate as principal components;
[0158] Optionally, the preset contribution rate threshold can be 80% or 85%.
[0159] 6. Calculate the loading matrix between each principal component and each element in the covariance matrix;
[0160] Specifically, let principal components be defined. The elements in the covariance matrix are Load matrix The expression is as follows:
[0161]
[0162] In the formula, Let represent the element in the i-th row and i-th column of the covariance matrix. This represents the i-th row of the k-th eigenvector.
[0163] Finally, the data in the load matrix is determined as the low-dimensional data sample.
[0164] For example, in some specific embodiments, reference is made to the principal component values corresponding to each state variable shown below:
[0165] It can be seen that, after considering redundancy and correlation, among the variables characterizing the operating state of a doubly-fed wind turbine, the pitch angle is... Rotor speed Active power output of wind turbine This approach can relatively completely reflect the dynamic characteristics of a doubly-fed wind turbine. Wind speed v, as the most direct and representative state variable, is also selected as the grouping index in this specific implementation. That is, the selected grouping index is the pitch angle. Rotor speed Active power output of wind turbine And wind speed v.
[0166] Step S40: Determine the optimal number of clusters based on the Gap Value and by balancing simulation accuracy and computational cost;
[0167] Specifically, it includes:
[0168]
[0169] in, It is a mathematical operation to calculate the expected value, where n is the sample size and k is the number of clusters being evaluated. It is a set measure of dispersion within a cluster.
[0170] Step S50: Perform cluster partitioning on the low-dimensional data samples based on the Kernel-FCM algorithm;
[0171] In this embodiment, after obtaining low-dimensional data samples, the low-dimensional data samples are divided into clusters based on the Kernel-FCM algorithm.
[0172] It should be noted that the Kernel-FCM algorithm, also known as the kernel function method, is based on the core idea of using a nonlinear mapping to transform the input pattern space (in this example, the dataset) into a nonlinear space. The spatial location is mapped to a high-dimensional feature space, which can be represented as: Then, machine learning algorithms are used; in this embodiment, the Kernel-FCM algorithm is used for cluster analysis. Since the algorithm only uses the inner product between data points for calculation, as long as a kernel function satisfying the Mercer condition is selected, it is not necessary to know the nonlinear mapping. The specific form.
[0173] Specifically, the low-dimensional data samples are first mapped to a high-dimensional feature space using a Gaussian kernel function;
[0174] For example, let K be a value defined in the dataset. The kernel function on the high-dimensional feature space characterizes the similarity between data, and its expression is:
[0175] K ( x , y ) = [ φ ( x ) , φ ( y ) ]
[0176] Next, the inner product of the data samples in the high-dimensional feature space is calculated based on the Kernel-FCM algorithm, wherein the Kernel-FCM clustering algorithm includes an iterative update function for the membership matrix and an iterative update function for the cluster centers.
[0177] For example, let the objective function of the Kernel-FCM algorithm be as follows:
[0178]
[0179] In the formula, This represents the feature vector corresponding to the c-th cluster center in high-dimensional space; This represents the distance metric between the i-th data point and the c-th cluster center. To represent dataset X n The membership degree of the i-th (1≤i≤C) class in the cluster, where U represents the membership degree matrix, n represents the number of samples, C represents the total number of cluster centers, and m represents the degree of fuzziness;
[0180] in, The specific form is shown in the following formula:
[0181]
[0182] Among them, the membership matrix in the Kernel-FCM clustering algorithm The expression for the iterative update function can be as follows:
[0183] u ic = 1 / ∑ k = 1 C [ d ( φ ( x i ) , θ c ) d ( φ ( x i ) , θ r ) ] m − 1
[0184] Among them, the feature vectors corresponding to the cluster centers The iterative update formula is shown below:
[0185]
[0186] The formula for the Gaussian kernel function K is shown below:
[0187]
[0188] In the formula, Indicates kernel parameters.
[0189] For example, in some specific implementations, the Kernel-FCM algorithm is applied to partition the wind turbine cluster based on low-dimensional data samples. The resulting wind turbine clustering results are shown in Table 5.
[0190] Step S60: Calculate the equivalent parameters of each cluster of units obtained by clustering based on the capacity weighting method.
[0191] Optionally, in this embodiment, the capacity-weighted method can be used to calculate the equivalent unit parameters.
[0192] Specifically, equivalent unit parameters can include four types of equivalent parameters: equivalent parameters of generator and transformer, equivalent parameters of shaft system, equivalent parameters of wind speed, and equivalent parameters of collector lines.
[0193] Specifically, the equivalent parameters of the generator and transformer include the rated capacity, rated active power and rated reactive power of the equivalent unit, the inertial time constant of the wind turbine, the inertial time constant of the generator rotor, the shaft stiffness coefficient, the shaft damping coefficient, and the reactance of the generator; the equivalent parameters of the wind speed include the input wind speed of the equivalent unit; and the equivalent parameters of the collector line include the capacity of the generator terminal transformer, the reactance of the generator terminal transformer, and the equivalent cable impedance.
[0194] Optionally, the formulas for calculating the equivalent parameters of the generator and transformer are as follows:
[0195]
[0196]
[0197]
[0198]
[0199]
[0200]
[0201]
[0202]
[0203] In the formula, , and These represent the rated capacity, rated active power, and rated reactive power of the wind turbine generator h, respectively. For capacity weighting coefficients, Let h be the wind turbine inertial time constant of the wind turbine unit. The inertial time constant of the generator rotor of the wind turbine unit h represents the inertial time constant. and These are the shaft stiffness coefficient and shaft damping coefficient of wind turbine unit h, respectively. This refers to the reactance of the generator, including stator reactance, rotor reactance, or magnetizing reactance.
[0204] Optionally, the formula for calculating the wind speed equivalent parameter is as follows:
[0205]
[0206] In the formula, The input wind speed of the equivalent unit. The input wind speed is h for the wind turbine generator.
[0207] Optionally, the formula for calculating the equivalent parameters of the collector line is as follows:
[0208]
[0209]
[0210] In the formula, Let h be the capacity of the terminal transformer of the wind turbine generator. Let f be the reactance of the transformer at the turbine terminal of wind turbine h, and f be the number of wind turbines included in the equivalent turbine unit. ;
[0211] The equivalent current corresponding to the equivalent machine formed by the aggregation of wind turbines in group H can be expressed as:
[0212]
[0213] In the formula, This indicates the voltage corresponding to wind turbine unit h. This represents the current corresponding to wind turbine generator h;
[0214] According to Ohm's law, the equivalent impedance corresponding to the equivalent machine formed by the aggregation of the Hth group of wind turbines can be expressed as:
[0215]
[0216] In the formula, This indicates the voltage at the wind farm's grid connection point. The voltage corresponding to the equivalent machine formed by the aggregation of wind turbines in group H can be expressed as:
[0217]
[0218] It is equal to half the sum of the ground capacitance currents of all the collector networks corresponding to the wind turbines in group A:
[0219]
[0220] In the formula, This represents the current in the collector network corresponding to wind turbine unit h. Let j represent the capacitance of the collector network corresponding to wind turbine generator h. Represents the imaginary part of polar coordinates;
[0221] Corresponding equivalent cable impedance Z eq_A resistance R eq_A and resistance to X eq_A They are respectively:
[0222]
[0223]
[0224] Re and Im are mathematical operations that calculate the real and imaginary parts, respectively.
[0225] Step S70: Equivalent unit parameters of the wind turbine units after the computer cluster is divided, and a dynamic equivalent aggregation model of the wind farm is constructed based on the equivalent unit parameters.
[0226] In this embodiment, after the wind turbine cluster is divided, the equivalent unit parameters of the wind turbines after the cluster division are used to construct a dynamic equivalent aggregation model of the wind farm based on the equivalent unit parameters.
[0227] In this embodiment, after obtaining the above-mentioned equivalent parameter calculation formulas, the various equivalent parameter calculation formulas are integrated into a set of formulas to obtain the dynamic equivalent aggregation model of the wind farm.
[0228] After obtaining the model, the operation of wind turbines in the wind farm can be simulated based on the established equivalent aggregation model, thereby simplifying the analysis complexity of the wind farm model.
[0229] In the technical solution provided in this embodiment, clustering indicators are selected based on the dynamic characteristics of the units, and data is extracted at corresponding time points to form high-dimensional data samples. Principal component analysis is applied to reduce the dimensionality of the clustering indicators, thereby reducing the correlation between variables and the redundancy of data. The Kernel-FCM algorithm is applied to divide the wind turbine clusters based on the low-dimensional data samples, and the division results are the clustering results of the wind turbines, thereby improving the rationality and effectiveness of the clustering method for the doubly-fed wind farm grid-connected system. The equivalent unit parameters are calculated using the capacity-weighted method, the equivalent wind speed is calculated based on the principle of equal input wind energy, and the equivalent parameters of the collection lines are calculated based on the equal power loss method, thereby improving the reliability and accuracy of the clustering results.
[0230] Furthermore, those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program includes program instructions and can be stored in a storage medium, which is a computer-readable storage medium. The program instructions are executed by at least one processor in the wind farm power control system to implement the process steps of the embodiments of the above methods.
[0231] Therefore, the present invention also provides a computer-readable storage medium storing a dynamic equivalent aggregation program for wind farms based on PCA and Kernel-FCM. When the dynamic equivalent aggregation program for wind farms based on PCA and Kernel-FCM is executed by a processor, it implements the various steps of the dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM as described in the above embodiments.
[0232] The computer-readable storage medium can be any computer-readable storage medium capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), magnetic disk, or optical disk.
[0233] It should be noted that, since the storage medium provided in the embodiments of this application is the storage medium used to implement the methods of the embodiments of this application, those skilled in the art can understand the specific structure and variations of the storage medium based on the methods described in the embodiments of this application, and therefore will not be repeated here. All storage media used in the methods of the embodiments of this application fall within the scope of protection of this application.
[0234] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0235] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0236] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0237] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0238] It should be noted that any reference signs placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.
[0239] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.
[0240] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
Claims
1. A dynamic equivalent aggregation method for wind farms based on PCA and Kernel-FCM, characterized in that, The wind farm dynamic equivalent aggregation method based on PCA and Kernel-FCM includes the following steps: Obtain the dynamic characteristics of the wind turbine in the preset mathematical model, and select multiple clustering indicators based on the dynamic characteristics of the wind turbine; Calculate the initial values of the state variables corresponding to each of the clustering indices, and construct a high-dimensional data sample from the initial values of each of the state variables. The high-dimensional data sample is reduced in dimensionality using PCA analysis to obtain a low-dimensional data sample. The optimal number of clusters is determined based on the gap value and by balancing simulation accuracy and computational cost. The low-dimensional data samples are divided into clusters based on the Kernel-FCM algorithm; The equivalent parameters of the units in each cluster obtained by clustering are calculated based on the capacity weighting method. Based on the fast analytical method, the dynamic equivalent parameters of the power collection network are calculated, and a dynamic equivalent aggregation model of the wind farm is constructed based on the equivalent unit parameters and the dynamic equivalent parameters of the power collection network.
2. The method as described in claim 1, characterized in that, The clustering indices include: pitch angle, rotor speed, mechanical torque, electromagnetic torque, stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, stator active power output, stator reactive power output, wind turbine active power output, and wind turbine reactive power output.
3. The method as described in claim 1 or 2, characterized in that, The calculation of the initial values of the state variables corresponding to each of the clustering indices includes: The system acquires the current input wind speed and the first preset variable calculation parameters for each wind turbine. Based on the current input wind speed and the first preset variable calculation parameters, it calculates the blade pitch angle, rotor speed, and active power output of each wind turbine. The first preset variable calculation parameters include the wind turbine blade radius, air density, wind energy utilization coefficient, and tip speed ratio. Obtain the current rotor resistance and second preset variable calculation parameters for each wind turbine, and calculate the stator active power output and stator reactive power output for each wind turbine based on the current rotor resistance and the second preset variable calculation parameters. The second preset variable calculation parameters include the stator equivalent two-phase winding self-inductance in the dq coordinate system, the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system, and the stator winding voltage; and... Obtain the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and a third preset variable calculation parameter for each wind turbine. Based on the stator current d-axis component, stator current q-axis component, rotor current d-axis component, rotor current q-axis component, and the third preset variable calculation parameter, calculate the mechanical torque and electromagnetic torque of each wind turbine. The third preset variable calculation parameter includes the equivalent winding mutual inductance of the stator and rotor on the same axis in the dq coordinate system and the number of wind turbine pole pairs.
4. The method as described in claim 1, characterized in that, The step of performing dimensionality reduction processing on the high-dimensional data sample based on PCA analysis to obtain a low-dimensional data sample includes: Obtain the number of wind turbines n and the number of clustering indicators X of the wind farm, and construct an n*X dimensional matrix based on the number of wind turbines n and the number of clustering indicators X; The original data in the matrix is standardized to eliminate the influence of units between data points, resulting in a standardized matrix. Establish the covariance matrix corresponding to the standardized matrix, and calculate the eigenvalues and eigenvectors of the covariance matrix; Calculate the feature contribution rate corresponding to each of the aforementioned feature values, and the cumulative contribution rate corresponding to each feature contribution rate; Select the target feature values that are greater than the preset contribution rate threshold from each cumulative contribution rate as principal components; Calculate the loading matrix between each principal component and each element in the covariance matrix; The data in the load matrix are identified as the low-dimensional data samples.
5. The method as described in claim 1, characterized in that, The steps for determining the optimal number of clusters based on the Gap Value and balancing simulation accuracy and computational cost include: ； in, It is a mathematical operation to calculate the expected value, where n is the sample size and k is the number of clusters being evaluated. It is a set measure of dispersion within a cluster.
6. The method as described in claim 1, characterized in that, The step of performing cluster partitioning on the low-dimensional data samples based on the Kernel-FCM algorithm includes: The low-dimensional data samples are mapped to a high-dimensional feature space using a Gaussian kernel function; The inner product of data samples in the high-dimensional feature space is calculated based on the Kernel-FCM clustering algorithm, wherein the Kernel-FCM clustering algorithm includes an iterative update function for the membership matrix and an iterative update function for the cluster centers.
7. The method as described in claim 1, characterized in that, The equivalent unit parameters include equivalent parameters of the generator and transformer, equivalent parameters of the shaft system, equivalent parameters of wind speed, and equivalent parameters of the collector lines.
8. The method as described in claim 7, characterized in that, The equivalent parameters of the generator and transformer include the rated capacity, rated active power and rated reactive power of the equivalent unit, the inertial time constant of the wind turbine, the inertial time constant of the generator rotor, the shaft stiffness coefficient, the shaft damping coefficient, and the reactance of the generator. The specific calculation steps include: ； ； ； ； ； ； ； ； In the formula, , and These represent the rated capacity, rated active power, and rated reactive power of the wind turbine generator h, respectively. For capacity weighting coefficients, Let h be the wind turbine inertial time constant of the wind turbine unit. The inertial time constant of the generator rotor of the wind turbine unit h represents the inertial time constant. and These are the shaft stiffness coefficient and shaft damping coefficient of wind turbine unit h, respectively. This refers to the reactance of the generator, including stator reactance, rotor reactance, or magnetizing reactance.
9. The method as described in claim 7, characterized in that, The equivalent wind speed parameter includes the input wind speed of the equivalent unit, and the specific calculation steps include: ； In the formula, The input wind speed of the equivalent unit. The input wind speed is h for the wind turbine generator.
10. The method as described in claim 7, characterized in that, The equivalent parameters of the collector line include the generator terminal transformer capacity, generator terminal transformer reactance, and equivalent cable impedance. The specific calculation steps include: ； ； In the formula, Let h be the capacity of the terminal transformer of the wind turbine generator. Let f be the reactance of the transformer at the turbine terminal of wind turbine h, and f be the number of wind turbines included in the equivalent turbine unit. ; The equivalent current corresponding to the equivalent machine formed by the aggregation of wind turbines in group H can be expressed as: ； In the formula, This indicates the voltage corresponding to wind turbine unit h. This indicates the current corresponding to wind turbine generator h; According to Ohm's law, the equivalent impedance corresponding to the equivalent machine formed by the aggregation of the Hth group of wind turbines can be expressed as: ； In the formula, This indicates the voltage at the wind farm's grid connection point. The voltage corresponding to the equivalent machine formed by the aggregation of wind turbines in group H can be expressed as: ； It is equal to half the sum of the ground capacitance currents of all the collector networks corresponding to the wind turbines in group A: ； In the formula, This represents the current in the collector network corresponding to wind turbine unit h. Let j represent the capacitance of the collector network corresponding to wind turbine generator h. Represents the imaginary part of polar coordinates; Corresponding equivalent cable impedance Z eq_A resistance R eq_A and resistance to X eq_A They are respectively: ； ； Re and Im are mathematical operations that calculate the real and imaginary parts, respectively.