Double-fed wind power plant multi-machine aggregation identification equivalent modeling method considering LVRT power characteristics

Abstract

A doubly-fed wind power plant multi-machine aggregation identification equivalent modeling method considering LVRT power characteristics comprises the following steps: 1) dividing two machine groups with significant difference between a control strategy and a protection logic by comparing power steady-state values before and after a fault; 2) further dividing the second type of units with unrecovered active power in the primary grouping to realize the grouping of the dynamic trajectory; (3) a hierarchical identification strategy is adopted for parameter optimization, single-machine high-sensitivity parameters such as rotor resistance and a Crowbar action threshold value are optimized preferentially, grid-connected point PCC power error minimization is taken as a target to optimize current collection line equivalent impedance, and the influence of line parameter difference is eliminated; 4) aggregating the model parameters according to a grouping result, and optimizing each parameter by adopting a self-adaptive chaos particle swarm optimization algorithm to complete parameter identification of the equivalent wind power plant. The method can more accurately simulate the behavior of the doubly-fed wind power plant when the power grid fails, and provides a reliable basis for planning, operation and control of a power system.

Description

Technical Field

[0001] This invention relates to the field of power system new energy power generation modeling technology, specifically to a multi-machine aggregation identification equivalent modeling method for doubly-fed wind farms that considers low voltage ride-through power characteristics. It is applicable to high-precision dynamic equivalent modeling of wind farms containing doubly-fed induction generators under fault scenarios. Background Technology

[0002] With the accelerated global energy transition, higher requirements are being placed on grid connection technologies for new energy power generation. As an important form of clean energy, wind power's large-scale integration has an increasingly significant impact on the safe and stable operation of the power system. Doubly fed induction generators (DFIGs) have become the mainstream model in wind farms due to their mature technology and significant cost advantages. However, when grid faults cause voltage drops, DFIGs need to maintain grid connection through low-voltage ride-through technology. Their internal Crowbar protection actions, inverter limiting, and reactive power support strategies lead to complex power dynamic characteristics, making it difficult for traditional equivalent modeling methods to accurately reflect the overall behavior of wind farms. Existing equivalent modeling techniques for wind farms have significant shortcomings: Firstly, clustering methods often rely on single indicators such as wind speed and wake effects, or simply use fault characteristics like whether Crowbar protection operates as the basis for division, ignoring the subtle differences in the dynamic trajectory of active power during LVRT (Low Voltage Reduction Time). This results in coarse cluster division and significant deviations between the equivalent model and actual operating characteristics. Secondly, equivalent parameter calculations generally employ analytical methods such as capacity weighting, failing to consider the interactive effects of control parameters and line parameters during fault processes. Furthermore, they lack optimized identification strategies for multi-parameter coupling effects, making it difficult to adapt to the dynamic response requirements of complex doubly-fed induction generator (DFIG) control logic. In addition, existing models lack sufficient generalization ability under different voltage drop levels, fault durations, and asymmetric fault scenarios, failing to meet the engineering needs of multi-scenario simulation and stability analysis of power systems. Summary of the Invention

[0003] To address the aforementioned issues, this invention aims to propose an equivalent modeling method for multi-machine aggregation identification of doubly-fed induction generator (DFIG) wind farms that considers LVRT power characteristics. By deeply exploring the dynamic characteristics of active power of DFIG wind turbines during LVRT, a two-stage refined clustering strategy is constructed: First, initial clustering is performed based on the typical differences in whether the active power recovers to the pre-fault value during the steady-state and transient processes of the fault, effectively distinguishing the unit categories under the influence of Crowbar protection operation status and inverter limiting; then, for units whose dynamic trajectories still differ, Dynamic Time Warping (DTW) distance is introduced to measure the similarity of active power time series, and combined with the Multi-Jet Clustering (NJW) algorithm to achieve secondary clustering, solving the problem of insufficient accuracy of traditional single-index clustering. In the equivalent parameter optimization stage, the impact of each parameter on active and reactive power is quantified through trajectory sensitivity analysis. High-sensitivity parameters such as the reactive power support coefficient and the upper limit of inverter current are identified as key identification points. A strategy combining single-unit step-by-step identification, multi-unit sequential identification, and equivalent impedance identification is proposed. With the goal of minimizing the dynamic characteristic error of the power at the point of grid connection (PCC), the parameters of the clustered and aggregated equivalent model are globally optimized, effectively handling the interactive influence of multiple parameters and improving the fitting accuracy of the equivalent model in fault transient and steady-state processes. This method, based on the LVRT control mechanism of doubly-fed induction generator (DFIG) wind turbines, integrates data-driven cluster analysis and model-driven parameter identification, forming a complete technical chain of "clustering-aggregation-optimization." It provides a systematic solution for high-precision equivalent modeling of DFIG wind farms under complex fault scenarios, significantly enhancing the model's adaptability to different operating conditions and playing a vital role in improving the accuracy of power system simulation analysis and the reliability of new energy grid connection.

[0004] To solve the above-mentioned technical problems, the technical content of this invention is: a method for multi-machine aggregation identification and equivalent modeling of doubly-fed induction generator (LVRT) wind farms considering LVRT power characteristics, the steps of which are as follows:

[0005] Step 1: When a grid fault causes a voltage drop, the doubly-fed induction generator (DFIG) exhibits two typical responses due to the Crowbar protection action and current limiting effect:

[0006] Class I units do not trigger Crowbar protection when they recover to their original power level during the steady-state phase of a fault.

[0007] Class II units experienced a continuous power output lower than the pre-fault value due to protection activation.

[0008] By comparing the steady-state power values ​​before and after the fault, two major machine groups with significant differences in control strategies and protection logic were identified.

[0009] Initial grouping was performed based on the differences in active power recovery capability during LVRT. By comparing the steady-state power values ​​before and after the fault, two major groups with significant differences in control strategies and protection logic were identified. During low-voltage ride-through, the reactive power output during the fault was calculated based on the values ​​set by the LVRT control strategy. for:

[0010] (1)

[0011] According to equation (1), when the reactive power support coefficient and the rated current of the unit remain constant, the reactive power output of the wind turbine during the fault period depends only on the degree of voltage drop at the turbine terminals. For wind farms with relatively concentrated geographical locations, the voltage drop at the turbine terminals during a fault is similar due to the small difference in the losses of the collector lines, resulting in basically consistent reactive power dynamic characteristics of each wind turbine, which is difficult to use as an effective basis for wind farm grouping. Considering that the wake effect will cause differences in the input wind speed of each wind turbine in the farm, we explore the grouping method from the perspective of differences in active power characteristics. By calculation, the active power P output by the wind turbine during the steady state of the fault can be obtained as follows:

[0012] (2)

[0013] In the formula: The d-axis component of the grid voltage. This represents the active power output under steady-state conditions before the fault.

[0014] According to equation (2), under different operating conditions, there are two typical cases of the active power output of the wind turbine during LVRT, namely whether the active power can be restored to the steady-state value before the fault during the fault. Based on this significant difference, the wind turbine group is initially divided.

[0015] During a fault in a Class I unit, the output power is equal to the power before the fault. The active power of each unit transitions to the fault steady state through a similar transient process when the fault occurs. After the fault is cleared, it recovers to the stable operating state through a similar transient process. Therefore, the dynamic characteristics of Class I units are highly similar and they are directly classified into one group.

[0016] For Class II units, the output power during the fault is lower than the power before the fault. The active power waveforms differ under different wind speeds during the short-term transient process of the fault. Furthermore, the time required for each unit to recover to steady state after the fault is cleared is different, resulting in differences in the disturbed waveforms during the transient process. Therefore, secondary grouping is performed.

[0017] Step 2: For Class II units whose active power has not recovered in the initial clustering, different wind speeds and voltage drops within the unit can cause subtle differences in the active power waveform during the fault transient process, such as transient transition time and waveform oscillation characteristics. To address this, the k-Shape morphological clustering algorithm is used to extract the overall morphological features of the power waveform. Amplitude normalization and cross-correlation are used to maximize the elimination of time axis offset interference. After constructing an association matrix based on waveform morphological similarity, the NJW spectral clustering algorithm and K-means++ clustering are combined. The Laplace matrix eigenvector analysis is used to decouple the coupling features between waveform oscillation mode and transient transition time, thereby achieving dynamic trajectory clustering.

[0018] For the Class II units whose active power failed to recover in step 1, perform secondary clustering of units with similar morphology;

[0019] 2.1) For the Type II units whose active power failed to recover in step 1, due to differences in wind speed and voltage drop, they will exhibit different power waveform characteristics during the fault transient process. The waveform features are extracted and finely grouped by combining the k-Shape morphological clustering algorithm and the NJW spectral clustering algorithm.

[0020] First, the active power waveforms of each wind turbine during LVRT are preprocessed, and the power waveforms are normalized according to the following formula to eliminate the influence of amplitude differences:

[0021] (3)

[0022] (4)

[0023] (5)

[0024] In the formula, The original power waveform. The mean of the waveform. The standard deviation of the waveform. The waveform is the normalized waveform;

[0025] (6)

[0026] Since there is a chance of time axis offset in the waveform during transient processes, the cross-correlation maximization method is used to align the time axis. For any two units i and j, the cross-correlation function of the normalized waveform is calculated as follows:

[0027] Find Maximum time delay , waveform Translation Later and Alignment yields waveforms without time offset. and ;

[0028] 2.2) The k-Shape algorithm is used to extract the overall waveform morphological features. Through template iterative optimization, the clustering results are made robust to the phase shift and amplitude scaling of the time series.

[0029] First, randomly select k waveforms as the initial cluster centers. , ,……, Then calculate the waveform. With template Standardized Euclidean distance:

[0030] (7)

[0031] Each waveform is assigned to the template category with the smallest distance, and the template is updated based on the mean of all waveforms within the category until the template no longer changes significantly. Based on the waveform distances obtained using the k-Shape algorithm, a morphological similarity matrix W is constructed between the units. The matrix elements... Defined as:

[0032] (8)

[0033] In the formula, The waveform distance between units i and j The optimal value is determined by cross-validation, where the Gaussian kernel width is used.

[0034] 2.3) The Ng-Jordan-Weiss spectral clustering algorithm is used to perform dimensionality reduction clustering on the similarity matrix. Using the similarity matrix W, the degree d of each row of the similarity matrix is ​​summed to obtain the degree of the sample points, and the degree matrix D is constructed. Then, the normalized Laplacian matrix is ​​constructed.

[0035] (9)

[0036] Constructing a normalized Laplace matrix ;

[0037] (10)

[0038] right Perform feature decomposition to extract the top k feature vectors, which are then used as input features for subsequent K-means clustering. Let k be the number of clusters. The eigenvectors corresponding to the k smaller eigenvalues ​​form a matrix V. After row standardization, a matrix U is obtained. The K-means++ algorithm is used to cluster matrix U into k classes. By optimizing the selection of the initial cluster centers, K-means++ ultimately classifies units with similar shapes into the same class.

[0039] Step 3: Parameter optimization adopts a hierarchical identification strategy. First, key parameters that significantly affect power characteristics are screened through trajectory sensitivity analysis. Priority is given to optimizing high-sensitivity parameters of a single unit, such as rotor resistance and Crowbar action threshold. Then, coupling parameters between multiple units are corrected in layers according to the unit capacity or collector line impedance. Finally, the equivalent impedance of the collector line is optimized with the goal of minimizing the PCC power error at the grid connection point to eliminate the influence of line parameter differences.

[0040] 3.1) Using the aggregated values ​​of each parameter of the clustered and aggregated model as initial values, and taking the minimum error between the dynamic power characteristics of the PCC point of the equivalent model and the detailed system model as the optimization objective, the parameter identification scheme is adopted to optimize the parameters of the equivalent model.

[0041] In the parameter optimization process of double-fed induction generator (DFIG) wind turbines, given the multi-parameter characteristics of the coupling between the electrical and control systems, a trajectory sensitivity analysis method is used to construct a parameter screening system. Considering the winding heating effect and bearing wear factors during long-term operation of rotating machinery, the stator resistance... and direct-axis / quadrature-axis inductors There is a chance that it will produce time-varying characteristics, which will cause deviations from the factory design value. Therefore, it is a key parameter to be identified on the motor side.

[0042] Given that the generator-side converter adopts a dual closed-loop control architecture with stator flux-oriented vector control (DFOC) and the grid-side converter adopts grid voltage-oriented control (VOC), the parameters of the inner-loop current PI controller are involved. Outer loop power PI controller parameters and DC bus voltage control parameters , It has a significant impact on the dynamic response of the system during grid faults, and is therefore considered a key parameter to be identified on the grid side.

[0043] To address the complexity of multi-parameter identification, trajectory sensitivity analysis is first performed to quantify the impact of each parameter on the LVRT power characteristics of the wind turbine. For the parameter vector... The trajectory sensitivity is defined as:

[0044] (11)

[0045] In the formula, For power trajectory, The parameters to be identified are: The average sensitivity of each parameter throughout the entire fault process is calculated using numerical simulation.

[0046] (12)

[0047] Considering that the dynamic characteristics of active power are divided into two categories due to the influence of the amplitude limiting element during model aggregation, and the sensitivity of each parameter differs between the two cases, for the single-equal-scale model, the voltage drop at the PCC point is set to 0.52 pu from 0.05 to 0.15 s. The parameter sensitivity is calculated for wind speed under two conditions: 9 m / s for Type I dynamic characteristic and 11 m / s for Type II dynamic characteristic. Through sensitivity analysis, the LVRT power characteristics of the doubly-fed induction generator are affected by the following parameters: rotor resistance. Crowbar action threshold Overcurrent limiting factor and the mechanical inertia time constant H;

[0048] To avoid coupling interference between parameters, a single-machine step-by-step identification strategy is adopted for the single equivalent machine model. Parameters are identified sequentially in descending order of sensitivity, and parameters with a sensitivity of 0 are not included in the identification. For multiple equivalent machine groups obtained after clustering, a sequential identification strategy is adopted, with groups having higher equivalent capacity and higher parameter sensitivity. Each equivalent machine is identified sequentially in descending order of capacity. When the equivalent machine capacities are the same, the group with the lower equivalent impedance is selected for priority identification. The objective function at this time is:

[0049] (13)

[0050] In the formula, Let be the vector of parameters to be identified for the i-th equivalent unit; , These are the measured active and reactive power at the PCC point, respectively. , These are the simulated active and reactive power values ​​of the equivalent model at the PCC point, respectively. This is a time-weighted function that adjusts the weights according to different fault stages. This is the trade-off coefficient between active and reactive power errors;

[0051] After completing the identification of all equivalent unit parameters, the equivalent impedance of the collector lines is optimized to eliminate errors caused by network topology simplification. An equivalent impedance optimization model is established with the goal of minimizing the PCC power error at the grid connection point.

[0052] (14)

[0053] In the formula, This is the equivalent line impedance parameter matrix, which includes the equivalent impedance from each equivalent generator unit to the PCC point; , These are the simulated values ​​of active and reactive power at the PCC point after adjusting the equivalent impedance.

[0054] Step 4: Build a detailed wind farm model consisting of 20 DFIGs with a capacity of 1.5 MW each in Matlab / Simulink software. Aggregate the model parameters based on the clustering results, and use an adaptive chaotic particle swarm optimization algorithm to optimize each parameter to complete the parameter identification of the equivalent wind farm.

[0055] 4.1) A detailed model of a wind farm consisting of 20 DFIGs with a capacity of 1.5 MW each was built in Matlab / Simulink software. The spacing between wind turbines on the same feeder was 0.5 km, and each feeder was connected to the PCC point via a 1.1 km collector line. An infinite power supply was set to experience an ideal voltage drop from 0.05 to 0.15 s, causing the voltage at the PCC point to drop to 0.625 pu during this period. The time series data of the active power dynamic trajectory of each wind turbine were extracted. Based on the significant difference in active power during the fault period, the units belonging to the first category of dynamic characteristics were grouped into one group. For the remaining units, the k-Shape morphological clustering algorithm was used to extract the overall morphological features of the power waveform, and the NJW algorithm was used for aggregation. Based on the grouping results, the model parameters were aggregated, and the adaptive chaotic particle swarm optimization algorithm was used to optimize each parameter to complete the parameter identification of the equivalent wind farm.

[0056] For further comparison, in addition to the method presented in this paper, a two-stage grouping and conventional equivalent parameter calculation method were used to perform equivalent calculations for this scenario, which was designated as equivalent method 1. The method of grouping based on the steady-state voltage of the fault at the generator terminal and the initial wind speed was designated as equivalent method 2. The equivalent parameters were still calculated using conventional methods. The active and reactive power characteristics and the current and voltage fitting effects before and after the equivalent calculations of the three methods were compared and analyzed, which further verified the effectiveness of the proposed method in improving the fitting accuracy of the equivalent model.

[0057] The beneficial effects of this invention are as follows: The proposed method for multi-machine aggregation identification and equivalent modeling of doubly-fed induction generator (DFIG) wind farms, considering the power characteristics of LVRT (Low Voltage Reduction Test), breaks through the limitations of traditional single-index clustering. It performs two-stage clustering based on the active power recovery capability during LVRT and complex clustering algorithms, uses parameter sensitivity analysis to determine key optimization parameters, and combines single-machine step-by-step, multi-machine sequential, and equivalent impedance identification strategies to effectively solve the problem of multi-parameter interaction. The model after two-stage clustering and parameter optimization maintains low error under complex operating conditions such as different wind speeds, voltage drops, fault durations, and asymmetrical short-circuit faults, demonstrating strong adaptability. This accurate equivalent model can more accurately simulate the behavior of DFIG wind farms during grid faults, providing a reliable basis for power system planning, operation, and control. It helps to formulate reasonable grid operation strategies, improve the grid's ability to absorb new energy sources, and ensure the safe and stable operation of the power system. Attached Figure Description

[0058] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0059] Figure 1 This is a flowchart of the secondary grouping process for wind farms according to the present invention;

[0060] Figure 2 This is a flowchart of the steps of the present invention;

[0061] Figure 3 This is the average sensitivity diagram of the unit corresponding parameters for the type I dynamic characteristics in the embodiment;

[0062] Figure 4 This is the average sensitivity diagram of the unit corresponding parameters for the type II dynamic characteristics in the embodiment;

[0063] Figure 5 This is a detailed model structure diagram of the wind farm in the embodiment;

[0064] Figure 6 This is a comparison chart of the power response and voltage and current curves at the PCC point of the wind farm before and after the equivalent values ​​in the embodiment. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0066] Example 1:

[0067] Reference Figures 1-4 This is the first embodiment of the present invention, which provides an equivalent modeling method for multi-machine aggregation identification of doubly-fed wind farms considering low-voltage ride-through power characteristics, including:

[0068] Step 1: When a grid fault causes a voltage drop, doubly-fed induction generators (DFIGs) exhibit two typical responses due to Crowbar protection activation and current limiting effects: Type I units recover to their original power level during the fault steady-state phase (without triggering Crowbar protection), while Type II units experience a sustained power drop below pre-fault values ​​due to protection activation. By comparing the steady-state power values ​​before and after the fault, two major groups of units with significantly different control strategies and protection logic can be quickly identified, overcoming the limitations of traditional grouping methods in representing dynamic control mechanisms.

[0069] Step 2: For Class II units whose active power has not recovered in the initial clustering, different wind speeds and voltage drops within the unit can still cause subtle differences in the active power waveform during the fault transient process, such as transient transition time and waveform oscillation characteristics. Therefore, a k-Shape clustering algorithm is used to extract the overall morphological features of the power waveform. Amplitude normalization and cross-correlation are used to maximize the elimination of time axis offset interference. After constructing an association matrix based on waveform morphological similarity, spectral clustering (NJW algorithm) and K-means++ clustering are combined. The Laplace matrix eigenvector analysis is used to decouple the coupling characteristics of waveform oscillation modes and transient transition time, achieving accurate clustering of dynamic trajectories.

[0070] Step 3: Parameter Optimization employs a hierarchical identification strategy to improve model accuracy. First, trajectory sensitivity analysis is used to screen key parameters significantly impacting power characteristics. Priority is given to optimizing high-sensitivity parameters for individual units, such as rotor resistance and Crowbar action threshold. Then, coupling parameters between multiple units are corrected hierarchically based on unit capacity or collector line impedance. Finally, the equivalent impedance of the collector line is optimized to minimize the power error at the point of connection (PCC), eliminating the influence of line parameter differences. By decoupling the interaction of multiple parameters, the dynamic fitting error of the power curve in the equivalent model during fault transients and steady-state processes can be effectively reduced, significantly improving adaptability to complex voltage drop scenarios.

[0071] Step 4: Build a detailed wind farm model consisting of 20 DFIGs with a capacity of 1.5 MW each in Matlab / Simulink software. Then, aggregate the model parameters based on the clustering results and use an adaptive chaotic particle swarm optimization algorithm to optimize each parameter to complete the parameter identification of the equivalent wind farm.

[0072] Further details of the complete steps: As described in step 1, initial grouping is performed based on the differences in active power recovery capabilities during LVRT. By comparing the steady-state power values ​​before and after the fault, two major groups with significant differences in control strategies and protection logic are identified.

[0073] 1.1) During low-voltage ride-through, the reactive power output during a fault can be calculated based on the values ​​set by the LVRT control strategy. for:

[0074] (1)

[0075] As shown in equation (1), when the reactive power support coefficient and the rated current of the unit remain constant, the reactive power output of the wind turbine during the fault period depends only on the degree of voltage drop at the turbine terminals. For wind farms with relatively concentrated geographical locations, the voltage drop at the turbine terminals during a fault is similar due to the small difference in the losses of the collector lines, resulting in basically consistent reactive power dynamic characteristics of each wind turbine, which is difficult to use as an effective basis for wind farm grouping. Considering that the wake effect will cause differences in the input wind speed of each wind turbine in the farm, we can explore grouping methods based on the differences in active power characteristics. The active power P output by the wind turbine during the fault steady state can be calculated as follows:

[0076] (2)

[0077] In the formula: The d-axis component of the grid voltage. The active power output is the value of the wind turbine in steady state before the fault. As can be seen from equation (2), under different operating conditions, there are two typical situations for the active power output of the wind turbine during LVRT, namely, whether the active power can recover to the steady state value before the fault during the fault. Based on this significant difference, the wind turbine group can be initially divided. The output power of the Class I units during the fault is equal to the power before the fault. The active power of each unit transitions to the fault steady state through a similar transient process when the fault occurs. After the fault is cleared, it recovers to the stable operating state through a similar transient process. Therefore, the dynamic characteristics of the Class I units are highly similar and can be directly divided into one group. For the Class II units, the output power during the fault is lower than the power before the fault. The active power waveforms are different in the short transient process when the fault occurs at different wind speeds. Moreover, the time required for each unit to recover to the steady state after the fault is cleared is different, which leads to the difference in the disturbed waveform during the transient process. In order to further improve the equivalence accuracy, it is necessary to perform secondary grouping.

[0078] Further complete steps: As described in step 2, more accurate clustering is achieved among the morphologically similar units in the Class II units where active power failed to recover in step I.

[0079] 2.1) For Class II wind turbines where active power failed to recover in Step I, different wind speeds and voltage drops will result in varying power waveform characteristics during the fault transient. To achieve more accurate clustering, a method combining k-Shape clustering and NJW spectral clustering is used to extract waveform features and perform fine-grained grouping. First, the active power waveforms of each wind turbine during LVRT are preprocessed, normalized using the following formula to eliminate the influence of amplitude differences:

[0080] (3)

[0081] (4)

[0082] (5)

[0083] In the formula, The original power waveform. The mean of the waveform. The standard deviation of the waveform. This is the normalized waveform.

[0084] Because the waveform may have time axis offset during transient processes (e.g., different start times during the transient process), a cross-correlation maximization method is used to align the time axis. For any two units i and j, the cross-correlation function of their normalized waveforms is calculated:

[0085] (6)

[0086] Find Maximum time delay , waveform Translation Later and Alignment yields waveforms without time offset. and .

[0087] 2.2) The k-Shape algorithm is used to extract the overall waveform morphology features. This algorithm is optimized through template iteration to ensure that the clustering results are robust to the phase shift and amplitude scaling of the time series.

[0088] First, randomly select k waveforms as the initial cluster centers. , ,……, Then calculate the waveform. With template Standardized Euclidean distance:

[0089] (7)

[0090] Each waveform is assigned to the template category with the smallest distance, and the template is updated based on the mean of all waveforms within the category until the template no longer changes significantly. Based on the waveform distances obtained using the k-Shape algorithm, a morphological similarity matrix W is constructed between the units. The matrix elements... Defined as:

[0091] (8)

[0092] In the formula, The waveform distance between units i and j The optimal value is determined by cross-validation, where is the width of the Gaussian kernel.

[0093] 2.3) The Ng-Jordan-Weiss (NJW) spectral clustering algorithm is used to perform dimensionality reduction clustering on the similarity matrix. Using the similarity matrix W, the degree d of each row is summed to obtain the degree matrix D of the sample points. Then, the normalized Laplacian matrix is ​​constructed. .

[0094] (9)

[0095] Constructing a normalized Laplace matrix .

[0096] (10)

[0097] right Perform feature decomposition to extract the top k feature vectors, which will serve as the input features for subsequent K-means clustering. Let k be the number of clusters, and take... The eigenvectors corresponding to the k smaller eigenvalues ​​are used to form a matrix V, which is then row-normalized to obtain a matrix U. The K-means++ algorithm is applied to matrix U to cluster it into k classes. K-means++ improves the stability and accuracy of clustering by optimizing the selection of initial cluster centers, ultimately grouping similar morphological units into the same class.

[0098] Further complete steps: As described in step 3, a hierarchical identification strategy is used to optimize parameters and improve model accuracy.

[0099] 3.1) Using the aggregated values ​​of each parameter of the clustered model as initial values, and taking the minimum error between the dynamic characteristics of the power at PCC point of the equivalent model and the detailed system model as the optimization objective, a reasonable parameter identification scheme is proposed to optimize the parameters of the equivalent model.

[0100] In the parameter optimization process of doubly-fed induction generator (DFIG) wind turbines, given the multi-parameter characteristics of the coupling between its electrical and control systems, a trajectory sensitivity analysis method is required to construct a parameter screening system. Considering factors such as winding heating and bearing wear during long-term operation of rotating machinery, the stator resistance... and direct-axis / quadrature-axis inductors It may exhibit time-varying characteristics, leading to deviations from the factory design values. Therefore, it is listed as a key parameter to be identified on the motor side.

[0101] Given that the generator-side converter adopts a dual closed-loop control architecture based on stator flux orientation vector control (DFOC) and the grid-side converter adopts grid voltage orientation control (VOC), the parameters of the inner-loop current PI controller involved are... Outer loop power PI controller parameters and DC bus voltage control parameters , It has a significant impact on the dynamic response of the system during grid faults, and is therefore listed as a key parameter to be identified on the grid side.

[0102] To effectively address the complexity of multi-parameter identification, trajectory sensitivity analysis is first performed to quantify the impact of each parameter on the LVRT power characteristics of the wind turbine. For the parameter vector... The trajectory sensitivity is defined as:

[0103] (11)

[0104] In the formula, For power trajectory, These are the parameters to be identified. The average sensitivity of each parameter throughout the entire fault process is calculated using numerical simulation.

[0105] (12)

[0106] Considering that the dynamic characteristics of active power are divided into two categories due to the influence of the amplitude limiting element during model aggregation, the sensitivity of each parameter obviously differs between the two cases. Therefore, for the single-equal-scale model, the voltage drop at the PCC point is set to 0.52 pu from 0.05 to 0.15 s, and the parameter sensitivity is calculated for wind speeds of 9 m / s (Category I dynamic characteristics) and 11 m / s (Category II dynamic characteristics). Sensitivity analysis reveals that the LVRT power characteristics of the doubly-fed induction generator (DFIG) are mainly affected by the following parameters: rotor resistance. Crowbar action threshold Overcurrent limiting factor And the mechanical inertia time constant H.

[0107] To avoid coupling interference between parameters, a single-machine step-by-step identification strategy is adopted for the single equivalent machine model. Parameters are identified sequentially in descending order of sensitivity, and parameters with a sensitivity of 0 are excluded from identification. For multiple equivalent machine groups obtained after clustering, a sequential identification strategy is adopted. Groups with larger equivalent capacities typically have higher parameter sensitivity; therefore, each equivalent machine is identified sequentially in descending order of capacity. When equivalent machine capacities are the same, the group with the smaller equivalent impedance is selected for priority identification. The objective function at this point is:

[0108] (13)

[0109] In the formula, Let be the vector of parameters to be identified for the i-th equivalent unit; , These are the measured active and reactive power at the PCC point, respectively. , These are the simulated active and reactive power values ​​of the equivalent model at the PCC point, respectively. This is a time-weighted function, and the weights can be adjusted according to different fault stages; It is the weighting factor for the error between active and reactive power.

[0110] After identifying all equivalent unit parameters, the equivalent impedance of the collector lines is further optimized to eliminate errors caused by network topology simplification. An equivalent impedance optimization model is established with the goal of minimizing the power error at the point of connection (PCC):

[0111] (14)

[0112] In the formula, This is the equivalent line impedance parameter matrix, which includes the equivalent impedance from each equivalent generator unit to the PCC point; , These are the simulated values ​​of active and reactive power at the PCC point after adjusting the equivalent impedance.

[0113] Further complete steps: As described in step 4, build a detailed model of the doubly fed wind farm in Matlab / Simulink software, and perform clustering and parameter identification.

[0114] 4.1) A detailed model of a wind farm consisting of 20 DFIGs with a capacity of 1.5 MW each was built in Matlab / Simulink software. The turbine spacing on the same feeder was 0.5 km, and each feeder was connected to the PCC point via a 1.15 km collector line. An infinite power supply was set to experience an ideal voltage drop from 0.05 to 0.15 s, causing the voltage at the PCC point to drop to 0.625 pu during this period. The time series data of the active power dynamic trajectory of each turbine were extracted. Based on the significant difference in active power during the fault period, the turbines belonging to the first category of dynamic characteristics were grouped into one group. For the remaining turbines, the k-Shape clustering algorithm was used to extract the overall morphological features of the power waveform, and the NJW algorithm was further used for aggregation. Then, the model parameters were aggregated based on the grouping results, and the adaptive chaotic particle swarm optimization algorithm was used to optimize each parameter to complete the parameter identification of the equivalent wind farm.

[0115] For further comparison, in addition to the method of this invention, a two-stage grouping and conventional equivalent parameter calculation method were used to perform equivalent calculations for this scenario, which was taken as equivalent method 1. The method of grouping based on the steady-state voltage of the fault at the generator terminal and the initial wind speed was taken as equivalent method 2. The equivalent parameters were still calculated using conventional methods. The active and reactive power characteristics and current and voltage fitting effects before and after the equivalent calculations of the three methods were compared and analyzed, which further verified the effectiveness of the method proposed in this paper in improving the fitting accuracy of the equivalent model.

[0116] Example 2

[0117] Reference Figures 5-6 To verify the feasibility of the proposed method for multi-machine aggregation identification and equivalent modeling of doubly fed wind farms that considers low voltage ride-through power characteristics, a detailed model of a wind farm consisting of 20 DFIGs with a capacity of 1.5 MW was built in Matlab / Simulink software as an example to perform cluster aggregation and parameter identification.

[0118] The final clustering results are shown in Table 1:

[0119] Table 1: Final Clustering Results

[0120]

[0121] The results of the equivalent wind farm parameter identification are shown in the table below:

[0122] Table 2: Parameter Identification Results of Equivalent Wind Farm

[0123]

[0124] The test results show that in the field of multi-machine equivalent model parameter optimization, the strategy of combining single-machine step-by-step identification, multi-machine sequential identification, and equivalent impedance identification can effectively address the challenges of numerous equivalent model parameters and complex interactions between parameters. Under different wind speeds and voltage dip conditions, the wind farm model after two-stage clustering and parameter optimization exhibits significantly improved equivalent accuracy. When the equivalent model constructed using this method is placed in different operating scenarios, such as encountering various short-circuit faults, changes in voltage dip amplitude, or variations in fault duration, it demonstrates good adaptability and performs better under complex conditions compared to the equivalent model without optimized parameters.

[0125] The specific embodiments of this invention are not exhaustive and do not constitute a limitation on the scope of protection of the claims. Those skilled in the art, upon learning from the embodiments of this invention, can conceive of other substantially equivalent alternatives without inventive effort, all of which are within the scope of protection of this invention.

Claims

1. A method for multi-machine aggregation identification and equivalent modeling of doubly-fed induction generator (LVRT) wind farms considering LVRT power characteristics, characterized in that, The steps are as follows: Step 1: When a grid fault causes a voltage drop, the doubly-fed induction generator (DFIG) exhibits two typical responses due to the Crowbar protection action and current limiting effect: Class I units do not trigger Crowbar protection when they recover to their original power level during the steady-state phase of a fault. Class II units experienced a continuous power output lower than the pre-fault value due to protection activation. By comparing the steady-state power values ​​before and after the fault, two major machine groups with significant differences in control strategies and protection logic were identified. Step 2: For Class II units whose active power has not recovered in the initial clustering, different wind speeds and voltage drops within the unit can cause subtle differences in the active power waveform during the fault transient process, such as transient transition time and waveform oscillation characteristics. To address this, the k-Shape morphological clustering algorithm is used to extract the overall morphological features of the power waveform. Amplitude normalization and cross-correlation are used to maximize the elimination of time axis offset interference. After constructing an association matrix based on waveform morphological similarity, the NJW spectral clustering algorithm and K-means++ clustering are combined. The Laplace matrix eigenvector analysis is used to decouple the coupling features between waveform oscillation mode and transient transition time, thereby achieving dynamic trajectory clustering. Step 3: Parameter optimization adopts a hierarchical identification strategy. First, key parameters that have a significant impact on power characteristics are screened through trajectory sensitivity analysis. Priority is given to optimizing high-sensitivity parameters of a single unit, such as rotor resistance and Crowbar action threshold. Then, the coupling parameters between multiple units are corrected in layers according to the unit capacity or collector line impedance. Finally, the equivalent impedance of the collector line is optimized with the goal of minimizing the PCC power error at the grid connection point to eliminate the influence of line parameter differences. Step 4: Build a detailed wind farm model consisting of 20 DFIGs with a capacity of 1.5 MW each in Matlab / Simulink software. Aggregate the model parameters based on the clustering results, and use an adaptive chaotic particle swarm optimization algorithm to optimize each parameter to complete the parameter identification of the equivalent wind farm.

2. A method for equivalent modeling of multi-machine aggregation identification in doubly-fed wind farms considering LVRT power characteristics, characterized in that, The specific steps in step 1 are as follows: Initial grouping was performed based on the differences in active power recovery capability during LVRT. By comparing the steady-state power values ​​before and after the fault, two major groups with significant differences in control strategies and protection logic were identified. During low-voltage ride-through, the reactive power output during the fault was calculated based on the values ​​set by the LVRT control strategy. for: （1） According to equation (1), when the reactive power support coefficient and the rated current of the unit remain constant, the reactive power output of the wind turbine during the fault period depends only on the degree of voltage drop at the turbine terminals. For wind farms with relatively concentrated geographical locations, the voltage drop at the turbine terminals during a fault is similar due to the small difference in the losses of the collector lines, resulting in basically consistent reactive power dynamic characteristics of each wind turbine, which is difficult to use as an effective basis for wind farm grouping. Considering that the wake effect will cause differences in the input wind speed of each wind turbine in the farm, we explore the grouping method from the perspective of differences in active power characteristics. By calculation, the active power P output by the wind turbine during the steady state of the fault can be obtained as follows: （2） In the formula: The d-axis component of the grid voltage. This represents the active power output under steady-state conditions before the fault. According to equation (2), under different operating conditions, there are two typical cases of the active power output of the wind turbine during LVRT, namely whether the active power can be restored to the steady-state value before the fault during the fault. Based on this significant difference, the wind turbine group is initially divided. During a fault in a Class I unit, the output power is equal to the power before the fault. The active power of each unit transitions to the fault steady state through a similar transient process when the fault occurs. After the fault is cleared, it recovers to the stable operating state through a similar transient process. Therefore, the dynamic characteristics of Class I units are highly similar and they are directly classified into one group. For Class II units, the output power during the fault is lower than the power before the fault. The active power waveforms differ under different wind speeds during the short-term transient process of the fault. Furthermore, the time required for each unit to recover to steady state after the fault is cleared is different, resulting in differences in the disturbed waveforms during the transient process. Therefore, secondary grouping is performed.

3. A method for multi-machine aggregation identification and equivalent modeling of doubly-fed wind farms considering LVRT power characteristics, characterized in that, The specific steps in step 2 are as follows: For the Class II units whose active power failed to recover in step 1, perform secondary clustering of units with similar morphology; Step 2.1) For the Type II units whose active power failed to recover in Step 1, due to differences in wind speed and voltage drop, they will exhibit different power waveform characteristics during the fault transient process. The waveform features are extracted and finely grouped by combining the k-Shape morphological clustering algorithm and the NJW spectral clustering algorithm. First, the active power waveforms of each wind turbine during LVRT are preprocessed, and the power waveforms are normalized according to the following formula to eliminate the influence of amplitude differences: （3） （4） （5） In the formula, The original power waveform. The mean of the waveform. The standard deviation of the waveform. The waveform is the normalized waveform; （6） Since there is a chance of time axis offset in the waveform during transient processes, the cross-correlation maximization method is used to align the time axis. For any two units i and j, the cross-correlation function of the normalized waveform is calculated as follows: Find Maximum time delay , waveform Translation Later and Alignment yields waveforms without time offset. and ; Step 2.2) Use the k-Shape algorithm to extract the overall waveform morphology features, and optimize the template iteratively to make the clustering results robust to the phase shift and amplitude scaling of the time series; First, randomly select k waveforms as the initial cluster centers. , ,……, Then calculate the waveform. With template Standardized Euclidean distance: （7） Each waveform is assigned to the template category with the smallest distance, and the template is updated based on the mean of all waveforms within the category until the template no longer changes significantly. Based on the waveform distances obtained using the k-Shape algorithm, a morphological similarity matrix W is constructed between the units. The matrix elements... Defined as: （8） In the formula, The waveform distance between units i and j The optimal value is determined by cross-validation, where the Gaussian kernel width is used. Step 2.3) The Ng-Jordan-Weiss spectral clustering algorithm is used to perform dimensionality reduction clustering on the similarity matrix. Using the similarity matrix W, the elements in each row of the similarity matrix are summed to obtain the degree d of the sample points, and the degree matrix D is constructed. Then, the normalized Laplacian matrix is ​​constructed. （9） Constructing a normalized Laplace matrix ; （10） right Perform feature decomposition to extract the top k feature vectors, which are then used as input features for subsequent K-means clustering. Let k be the number of clusters. The eigenvectors corresponding to the k smaller eigenvalues ​​form a matrix V. After row standardization, a matrix U is obtained. The K-means++ algorithm is used to cluster matrix U into k classes. By optimizing the selection of the initial cluster centers, K-means++ ultimately classifies units with similar shapes into the same class.

4. A method for multi-machine aggregation identification and equivalent modeling of doubly-fed induction generator (LVRT) wind farms considering LVRT power characteristics, characterized in that, The specific steps in step 3 are as follows: The aggregated values ​​of each parameter of the clustered and aggregated model are used as initial values. The optimization objective is to minimize the error between the dynamic power characteristics of the PCC point power of the equivalent model and the detailed system model. The parameter identification scheme is used to optimize the parameters of the equivalent model. In the parameter optimization process of double-fed induction generator (DFIG) wind turbines, given the multi-parameter characteristics of the coupling between the electrical and control systems, a trajectory sensitivity analysis method is used to construct a parameter screening system. Considering the winding heating effect and bearing wear factors during long-term operation of rotating machinery, the stator resistance... and direct-axis / quadrature-axis inductors There is a chance that it will produce time-varying characteristics, which will cause deviations from the factory design value. Therefore, it is a key parameter to be identified on the motor side. Given that the generator-side converter adopts a dual closed-loop control architecture with stator flux-oriented vector control (DFOC) and the grid-side converter adopts grid voltage-oriented control (VOC), the parameters of the inner-loop current PI controller are involved. Outer loop power PI controller parameters and DC bus voltage control parameters , It has a significant impact on the dynamic response of the system during grid faults, and is therefore considered a key parameter to be identified on the grid side. To address the complexity of multi-parameter identification, trajectory sensitivity analysis is first performed to quantify the impact of each parameter on the LVRT power characteristics of the wind turbine. For the parameter vector... The trajectory sensitivity is defined as: （11） In the formula, For power trajectory, The parameters to be identified; The average sensitivity of each parameter throughout the entire fault process was calculated using numerical simulation. （12） Considering that the dynamic characteristics of active power are divided into two categories due to the influence of the amplitude limiting element during model aggregation, and the sensitivity of each parameter differs between the two cases, for the single-equal-scale model, the voltage drop at the PCC point is set to 0.52 pu from 0.05 to 0.15 s. The parameter sensitivity is calculated for wind speed under two conditions: 9 m / s for Type I dynamic characteristic and 11 m / s for Type II dynamic characteristic. Through sensitivity analysis, the LVRT power characteristics of the doubly-fed induction generator are affected by the following parameters: rotor resistance. Crowbar action threshold Overcurrent limiting factor and the mechanical inertia time constant H; To avoid coupling interference between parameters, a single-machine step-by-step identification strategy is adopted for the single equivalent machine model. Parameters are identified sequentially in descending order of sensitivity, and parameters with a sensitivity of 0 are not included in the identification. For multiple equivalent machine groups obtained after clustering, a sequential identification strategy is adopted, with groups having higher equivalent capacity and higher parameter sensitivity. Each equivalent machine is identified sequentially in descending order of capacity. When the equivalent machine capacities are the same, the group with the lower equivalent impedance is selected for priority identification. The objective function at this time is: （13） In the formula, Let be the vector of parameters to be identified for the i-th equivalent unit; , These are the measured active and reactive power at the PCC point, respectively. , These are the simulated active and reactive power values ​​of the equivalent model at the PCC point, respectively. This is a time-weighted function that adjusts the weights according to different fault stages. This is the trade-off coefficient between active and reactive power errors; After completing the identification of all equivalent unit parameters, the equivalent impedance of the collector lines is optimized to eliminate errors caused by network topology simplification. An equivalent impedance optimization model is established with the goal of minimizing the PCC power error at the grid connection point. （14） In the formula, This is the equivalent line impedance parameter matrix, which includes the equivalent impedance from each equivalent generator unit to the PCC point; , These are the simulated values ​​of active and reactive power at the PCC point after adjusting the equivalent impedance.

5. A method for multi-machine aggregation identification and equivalent modeling of doubly-fed induction generator (LVRT) wind farms considering LVRT power characteristics, characterized in that, The specific steps in step 4 are as follows: A detailed model of a wind farm consisting of 20 DFIGs with a capacity of 1.5 MW each was built in Matlab / Simulink software. The turbines on the same feeder were spaced 0.5 km apart, and each feeder was connected to the PCC point via a 1.1 km collector line. An infinite power supply was set to experience an ideal voltage drop from 0.05 to 0.15 s, causing the voltage at the PCC point to drop to 0.625 pu during this period. Time series data of the active power dynamic trajectory of each turbine were extracted. Based on the significant differences in active power during the fault period, the turbines belonging to the first category of dynamic characteristics were grouped into one group. For the remaining turbines, the k-Shape morphological clustering algorithm was used to extract the overall morphological features of the power waveform, and the NJW algorithm was used for aggregation. Based on the grouping results, the model parameters were aggregated, and the adaptive chaotic particle swarm optimization algorithm was used to optimize each parameter to complete the parameter identification of the equivalent wind farm.

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