Improved DBSCAN algorithm-based network following / constructing hybrid wind power plant equivalence method

Abstract

The invention discloses an improved DBSCAN algorithm-based network tracking / constructing hybrid wind power plant equivalence method. The method comprises the following steps: firstly, acquiring operation parameters of each fan in a wind power plant, and selecting a voltage drop degree, a virtual impedance module value, a reactive droop coefficient, active output power and a power factor as grouping indexes for representing the characteristics of the fan in the aspects of voltage support and power output; secondly, inputting the clustering index into an improved DBSCAN clustering algorithm, realizing adaptive optimization of a neighborhood radius and a minimum point number by introducing particle swarm optimization, constructing a fitness function by combining a contour coefficient and a DBI index to evaluate a clustering effect, and accelerating neighborhood search by using a K-D tree structure, thereby improving clustering efficiency and accuracy; and finally, single-machine multiplication modeling is carried out on the same type of fans according to a clustering result, and a multi-machine equivalent model is formed. The method gives consideration to both modeling precision and calculation speed, and is suitable for transient stability analysis and short-circuit current research of a large-scale hybrid wind power plant.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of new energy power system modeling and analysis, and particularly relates to an equivalent method for follow / network hybrid wind farms based on an improved DBSCAN algorithm. BACKGROUND

[0002] With the rapid construction of new power systems, the installed capacity of new energy units and the proportion of power grids are constantly increasing, among which the large-scale grid connection of wind farms has become the norm. New energy units are usually divided into follow-network and network-construction types according to the control mode, and there are significant differences in their external characteristics. The follow-network type unit behaves as a current source, which needs to rely on the phase-locked loop to detect the grid voltage phase, and can only follow the grid changes and lacks active support capability. The network-construction type unit behaves as a voltage source, and its outer ring directly gives the voltage amplitude and phase, which can provide voltage support and inertia support to the grid. Therefore, under the background of large-scale access of new energy, how to reasonably model and equivalent follow / network hybrid wind farms has become an important problem in power system analysis and simulation.

[0003] Current research work mainly focuses on the equivalent modeling method of follow-network wind farms. The research on the response characteristics of large disturbances usually takes fault output characteristics as the equivalent target. Since the single-machine equivalent method is difficult to balance modeling accuracy and simulation speed, the existing researches mostly use multi-machine equivalent method. The common practice is to divide the characteristics similar wind turbines into a class through clustering aggregation, and establish an aggregated model in the form of single-machine multiplication, so as to obtain an equivalent wind farm model with relatively small size but maintaining the overall characteristics. For the selection of clustering index, the existing technology is mostly based on steady-state tidal flow or voltage and current trajectory. However, these clustering indexes are mostly proposed for follow-network wind farms, and whether they can be directly used for network-construction wind farms still has great uncertainty. In addition, in the clustering method, the research mainly uses clustering algorithms such as K-means, fuzzy C-means and Gaussian mixture model. Although the K-means algorithm is simple in principle and fast in calculation, it is sensitive to the initial clustering center and requires high artificial setting, and the clustering effect is obviously insufficient in the ring or irregular data distribution scene. Fuzzy C-means and Gaussian mixture model also have the problems of strong parameter dependence and poor adaptability. The traditional DBSCAN algorithm can process data with arbitrary shape distribution, and the clustering effect is good, but the algorithm complexity is high, the neighborhood search efficiency is low, and the calculation time is long in the large-scale and high-dimensional data scene.

[0004] This reveals two prominent problems in existing research: First, current clustering index selection methods are mostly designed for grid-connected wind farms, lacking a clustering index system applicable to grid-connected wind farms, making it difficult to guarantee the accuracy of equivalent modeling for hybrid wind farms. Second, existing clustering algorithms have shortcomings in parameter setting, convergence speed, and high-dimensional adaptability, making it difficult to meet the needs of rapid modeling of large-scale hybrid wind farms. Therefore, there is an urgent need to propose a wind farm equivalent method that can take into account the characteristics of both grid-connected and grid-connected wind turbines and improve both clustering efficiency and clustering effect, in order to enhance the accuracy and practicality of hybrid wind farm modeling. Summary of the Invention

[0005] To address the problems of existing technologies, this invention provides an equivalent method for hybrid wind farms (including root / grid structures) based on an improved DBSCAN algorithm. The technical solution is as follows:

[0006] On the one hand, an equivalent method for a hybrid wind farm based on the improved DBSCAN algorithm is provided, including the following steps:

[0007] Step 1: Obtain the operating parameters of each wind turbine in the wind farm, and select the operating parameters as clustering indicators. The clustering indicators include at least the voltage drop, virtual impedance modulus, reactive power droop coefficient, active power output of the wind turbine, and power factor at the outlet.

[0008] Step 2: Input the clustering index into the improved DBSCAN clustering algorithm. The improved DBSCAN clustering algorithm automatically optimizes the neighborhood radius and minimum number of points by introducing the particle swarm optimization algorithm, realizes fast neighborhood search by constructing a KD tree structure, and evaluates the clustering effect by combining the fitness function composed of the silhouette coefficient and the DBI index to obtain the optimal clustering result.

[0009] Step 3: Based on the optimal clustering results, wind turbines belonging to the same class are subjected to single-unit multiplication to form a multi-unit equivalent model.

[0010] Furthermore, the method for determining the voltage drop level in the clustering index obtained in step one includes the following steps:

[0011] (1) Measure the voltage amplitude at the grid connection point before the three-phase short-circuit fault occurs;

[0012] (2) Measure the voltage amplitude at the grid connection point after a three-phase short-circuit fault occurs;

[0013] (3) Divide the difference between the voltage amplitude before the fault and the voltage amplitude after the fault by the voltage amplitude before the fault to determine the degree of voltage drop.

[0014] Furthermore, the method for determining the virtual impedance magnitude in the clustering index obtained in step one includes the following steps:

[0015] (1) Set the resistance component and reactance component of the virtual impedance in the virtual admittance loop control of the grid-type wind turbine;

[0016] (2) Calculate the vector sum of the resistance component and the reactance component;

[0017] (3) The vector sum is used as the virtual impedance modulus to characterize the current support capability of the wind turbine during a short-circuit fault.

[0018] Furthermore, the method for determining the reactive power droop coefficient in the clustering index obtained in step one includes the following steps:

[0019] (1) Set the reference value of the terminal voltage in the reactive power voltage control loop of the grid-type wind turbine;

[0020] (2) Measure the deviation between the actual terminal voltage of the fan and the voltage reference value during operation;

[0021] (3) Determine the reactive power droop coefficient based on the relationship between the deviation and the reactive power change, which is used to characterize the droop characteristics between the terminal voltage and the reactive power.

[0022] Furthermore, the improved DBSCAN clustering algorithm in step two automatically optimizes the neighborhood radius and minimum number of points by introducing a particle swarm optimization algorithm. The automatic optimization includes the following steps:

[0023] (1) Initialize the size of the particle swarm and set the position and velocity information of each particle;

[0024] (2) During the iteration process, the particle velocity is updated based on the inertia weight, the individual historical best position, and the global best position;

[0025] (3) Update the particle positions based on the updated velocity;

[0026] (4) Repeat the iteration steps until the convergence condition is met, and obtain the optimal values ​​of the neighborhood radius and the minimum number of points.

[0027] Furthermore, in step two, the improved DBSCAN clustering algorithm uses a fitness function composed of the silhouette coefficient and the DBI index to evaluate the clustering effect. The evaluation method includes the following steps:

[0028] (1) Calculate the average distance between each sample point and other points in the cluster, and calculate the average distance between the sample point and the nearest neighboring cluster, and determine the profile coefficient accordingly;

[0029] (2) Calculate the dispersion of each cluster and the distance between cluster centers, and determine the DBI index accordingly;

[0030] (3) Combine the average value of the contour coefficients with the DBI index and construct an overall fitness function according to a preset weighting factor;

[0031] (4) The clustering effect is evaluated using the fitness function, and the evaluation results are used to guide the iterative optimization process of the particle swarm optimization algorithm.

[0032] Furthermore, the improved DBSCAN clustering algorithm in step two introduces a KD-tree structure during the neighborhood search process. The neighborhood search method includes the following steps:

[0033] (1) Recursively divide the sample data according to different dimensions and construct a binary tree-like KD tree structure so that the dataset is divided into multiple super rectangular regions;

[0034] (2) When performing a neighborhood query, a hypersphere neighborhood with a radius of the set neighborhood radius is constructed with the query point as the center, and the intersection relationship between the neighborhood and each sub-region of the KD tree is determined.

[0035] (3) Sub-regions that do not intersect with the queried neighborhood are directly discarded and no further distance calculation is performed;

[0036] (4) Calculate the sample points in the sub-regions that intersect with the queried neighborhood and determine whether they are within the radius of the neighborhood;

[0037] (5) The points that meet the conditions are determined as the neighborhood points of the query point, thereby reducing the time complexity from quadratic to logarithmic during the overall search process.

[0038] Furthermore, the single-machine multiplication modeling process in step three includes the following steps:

[0039] (1) Collect and summarize the operating parameters of wind turbines belonging to the same cluster result;

[0040] (2) The wind turbine operating parameters within the cluster are weighted and averaged to obtain the center parameters of the cluster;

[0041] (3) Establish an equivalent unit model based on the cluster center parameters;

[0042] (4) The capacity and current response of the equivalent unit are multiplied according to the number of fans in the cluster;

[0043] (5) Replace the original cluster of multiple wind turbines with the equivalent units after multiplication, and use them for subsequent power system simulation or stability analysis.

[0044] On the other hand, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, is used to perform the method described thereon.

[0045] On the other hand, an electronic device is provided, including at least one processor and at least one memory, wherein the memory stores a computer program that, when executed, causes the processor to perform the method.

[0046] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows:

[0047] This invention provides an equivalent method for hybrid wind farms (including grid-connected wind farms) based on an improved DBSCAN algorithm. Through detailed theoretical derivation, voltage drop, virtual impedance modulus, reactive power droop coefficient, active power output, and power factor are selected as grouping indices. This enables the established multi-machine equivalent model to comprehensively reflect the key characteristics of grid-connected wind farms in terms of voltage support and power response, solving the problem of existing methods lacking grouping indices applicable to grid-connected wind farms.

[0048] Furthermore, an improved DBSCAN algorithm is introduced into the clustering process, which automatically optimizes the clustering parameters through particle swarm optimization, avoiding the difficulty of manually setting parameters. Combined with KD-tree to accelerate neighborhood search and the optimized design of fitness function, this method has stronger applicability and stability when dealing with high-dimensional complex data distributions, and the time complexity is significantly reduced, thus ensuring the efficiency and engineering feasibility of large-scale wind farm clustering calculations.

[0049] Furthermore, this invention employs a single-machine multiplication modeling method, which merges the characteristics of similar wind turbines using class center parameters. This maintains the overall dynamic response characteristics of the wind farm while effectively reducing the model size. Ultimately, it forms an equivalent method suitable for hybrid wind farms with integrated grids and can be implemented on computer-readable storage media and electronic devices, possessing good simulation accuracy, computational speed, and engineering application value. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0051] Figure 1 This is a flowchart of an equivalent method for a hybrid wind farm based on an improved DBSCAN algorithm, according to an embodiment of the present invention.

[0052] Figure 2This is a diagram of the VSG-type grid-connected wind turbine grid connection system and control structure according to an embodiment of the present invention;

[0053] Figure 3 This is a flowchart of the VSG active-frequency control according to an embodiment of the present invention;

[0054] Figure 4 This is a flowchart of the VSG reactive power-voltage control according to an embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram of the equivalent circuit of an embodiment of the present invention;

[0056] Figure 6 This is a flowchart illustrating the improved DBSCAN algorithm according to an embodiment of the present invention.

[0057] Figure 7 This is a typical wind farm topology diagram according to an embodiment of the present invention;

[0058] Figure 8 This is a comparison diagram of short-circuit currents under typical operating conditions in embodiments of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0060] This invention proposes an equivalent method for wind farms with a hybrid root / grid structure based on an improved DBSCAN algorithm. By introducing particle swarm optimization, fitness function evaluation, and KD tree fast neighborhood search mechanism, wind turbines in the wind farm are clustered and divided. Finally, a multi-turbine equivalent model is formed by using the single-turbine multiplication method.

[0061] like Figure 1 As shown, the types of wind turbines in the hybrid wind farm are first statistically analyzed and classified. Based on the control methods and operating characteristics of different types of wind turbines, corresponding parameter information is imported, including the control mode, terminal voltage, rated parameters, virtual impedance parameters, reactive power droop coefficient, and rated power of the grid-connected wind turbines. The above operating parameters are used as clustering indicators and input into the improved PSK-DBSCAN algorithm for clustering. Based on the clustering results, the number of each type of wind turbine is counted and a single-unit multiplication model is established, finally forming an equivalent model of the hybrid wind farm.

[0062] This method significantly reduces computational complexity while maintaining the accuracy of the equivalent model. It is suitable for modeling and simulation analysis of large-scale integrated wind farms and provides an effective tool for grid dispatching, safety assessment and operation optimization.

[0063] Based on the overall process described above, this embodiment further elaborates on the specific methods and steps. Since wind turbines differ in voltage support characteristics and power output levels, directly affecting the accuracy of subsequent cluster analysis, it is first necessary to establish a clustering index system that comprehensively characterizes the electrical performance of the wind turbines through the measurement and calculation of operating parameters. On this basis, an improved DBSCAN algorithm is then used to conduct cluster analysis, ultimately achieving equivalent modeling of the hybrid wind farm.

[0064] This embodiment provides an equivalent method for a hybrid wind farm (root / grid type) based on an improved DBSCAN algorithm, including the following steps:

[0065] Step 1: Obtain the operating parameters of each wind turbine in the wind farm, and select the operating parameters as clustering indicators. The clustering indicators include at least the voltage drop, virtual impedance modulus, reactive power droop coefficient, active power output of the wind turbine, and power factor at the outlet.

[0066] Specifically, the method for determining the voltage drop level in the clustering index obtained in step one includes the following steps:

[0067] (1) Measure the voltage amplitude at the grid connection point before the three-phase short-circuit fault occurs;

[0068] (2) Measure the voltage amplitude at the grid connection point after a three-phase short-circuit fault occurs;

[0069] (3) Divide the difference between the voltage amplitude before the fault and the voltage amplitude after the fault by the voltage amplitude before the fault to determine the degree of voltage drop.

[0070] The method for determining the virtual impedance magnitude in the clustering index obtained in step one includes the following steps:

[0071] (1) Set the resistance component and reactance component of the virtual impedance in the virtual admittance loop control of the grid-type wind turbine;

[0072] (2) Calculate the vector sum of the resistance component and the reactance component;

[0073] (3) The vector sum is used as the virtual impedance modulus to characterize the current support capability of the wind turbine during a short-circuit fault.

[0074] The method for determining the reactive power droop coefficient in the clustering index obtained in step one includes the following steps:

[0075] (1) Set the reference value of the terminal voltage in the reactive power voltage control loop of the grid-type wind turbine;

[0076] (2) Measure the deviation between the actual terminal voltage of the fan and the voltage reference value during operation;

[0077] (3) Determine the reactive power droop coefficient based on the relationship between the deviation and the reactive power change, which is used to characterize the droop characteristics between the terminal voltage and the reactive power.

[0078] The method for determining the active power output of the wind turbine in the clustering index obtained in step one includes the following steps:

[0079] (1) Collect the output voltage and output current signals under normal operating conditions of the fan;

[0080] (2) The active power output of the fan is determined by averaging the instantaneous product of voltage and current over one power frequency cycle;

[0081] (3) The active power output is used as a grouping index to distinguish the operating characteristics of wind turbines of different power levels.

[0082] The method for determining the power factor at the outlet in the clustering index obtained in step one includes the following steps:

[0083] (1) Obtain the active power and reactive power of the wind turbine at the grid connection point;

[0084] (2) Calculate the power factor based on the relationship between active power and reactive power;

[0085] (3) The power factor is used as a clustering index to reflect the power characteristics and reactive power compensation capability of the wind turbine on the grid side.

[0086] In this specific implementation, to ensure the scientific validity and rationality of the clustering indicators, this embodiment provides the selection principle of the clustering indicators in conjunction with the operating mechanism of grid-connected wind farms. For grid-connected wind turbines controlled by virtual synchronous generators (VSGs), based on their active-frequency control, reactive-voltage control, and virtual admittance loop characteristics, the key factors affecting the short-circuit current component and voltage support capability can be clearly identified through analytical derivation of the current under short-circuit fault conditions. Therefore, this embodiment selects voltage sag, virtual impedance modulus, reactive droop coefficient, active power output, and power factor at the outlet as clustering indicators to comprehensively characterize the response characteristics of the wind turbine under grid disturbances.

[0087] Furthermore, to more clearly illustrate the theoretical basis of the clustering index, this embodiment explains the selection principle of the clustering index for grid-connected wind farms. For VSG-controlled grid-connected wind turbines, such as... Figure 2 As shown, the active frequency loop in its power outer loop achieves active frequency control by simulating the rotor motion equation and primary frequency regulation characteristics of a synchronous generator. Its control flow is as follows: Figure 3 As shown, the corresponding governing equations are:

[0088]

[0089] Where δ is the generator power angle, J is the rotor moment of inertia, and P ref Here, P is the active power reference value, D is the damping coefficient, ω is the system angular velocity, ω0 is the synchronous angular velocity, and k is the synchronous angular velocity. p This is the active power droop factor.

[0090] The reactive voltage loop in the power outer loop achieves reactive voltage regulation by simulating the reactive power regulation and terminal voltage regulation characteristics of a synchronous generator. Its control flowchart is as follows: Figure 4 As shown, its governing equation is

[0091] E=U * +k q (Q ref -Q e (2)

[0092] Where E is the amplitude of the virtual internal potential generated by VSG, and U * k is the voltage base value. q Q is the reactive power droop factor. ref Q is the reactive power reference value. e To output reactive power

[0093] In the main circuit design of the system, considering the voltage stabilizing effect of the DC bus capacitor, the wind turbine, PMSG, turbine-side converter, and DC bus can be treated as an ideal DC voltage source. The AC output characteristics of the grid-connected inverter are determined by the three-phase current i abc and voltage u abc Characterization. The virtual admittance loop simulates the stator resistance and synchronization reactance of the synchronous machine by controlling the output voltage of the VSG. Its control equation is:

[0094]

[0095] The circuit equations for the converter port are as follows:

[0096]

[0097] Neglecting converter delay and equivalent gain, to achieve fast current tracking, the proportional and integral coefficients of the inner current loop are typically designed according to a typical first-order system, and the control equation is as follows:

[0098]

[0099] Performing a Laplace transform on equation (4) and calculating in the frequency domain, we can obtain...

[0100]

[0101] From equation (6), it can be seen that in the expression for the current reference value, the current reference value i at time 0 is... * dq(0) , after short circuit, the grid connection point voltage u dq(s) and virtual internal potential e dq(s) Since the quantities are unknown, it is necessary to solve for the relevant quantities mentioned above.

[0102] Ignoring the current inner loop response, let's examine the voltage vector changes before and after a three-phase short-circuit fault using virtual internal potential orientation. Before the fault, in steady-state operation, the PCC voltage vector is U0 with a phase angle of α0; the virtual internal potential E0 leads the PCC voltage by a phase difference of δ0. When the fault occurs, the PCC voltage amplitude drops sharply to U, and the phase angle jumps to α; although the virtual internal potential amplitude drops to E, and the phase difference with the PCC voltage abruptly changes to δ, due to the virtual inertia of the VSG, the virtual angular frequency can be considered constant during the transient response, i.e., ω≈ω0.

[0103] Based on the phasor relationship between the PCC voltage and the virtual internal potential before and after the fault, we can obtain...

[0104]

[0105] Substituting equation (5) into equation (3), and transforming the expression of the virtual admittance loop control parameters according to Euler's formula, we can obtain the initial value expression of the dq axis current reference value.

[0106]

[0107] Among them, |Z v | represents the virtual impedance magnitude. τ is the virtual impedance angle. v The virtual admittance loop time constant is denoted as .

[0108] After a three-phase short-circuit fault occurs, the VSG maintains virtual internal potential orientation control. Based on the phasor relationship between the grid connection point voltage and the virtual internal potential, the expressions for the grid connection point voltage and the virtual internal potential when approaching quasi-steady state can be obtained as follows:

[0109]

[0110] The transient response of a grid-type converter is divided into multiple time scales. The time scale dominated by the virtual admittance loop and the inner current loop is 0-10ms, and the transient response process is usually completed within 2ms. The time scale dominated by the outer power loop is 10ms-2s. Therefore, when analyzing quasi-steady-state conditions, the current loop response process can be ignored. * dq Approximately equal i dq Substituting equations (6) and (7) into equation (4) and performing a Laplace transform, we can obtain the current i. dq The expression:

[0111]

[0112] Finally, solve for the virtual internal potential E. f When the system approaches quasi-steady-state operation, an equivalent loop is constructed between the virtual internal potential and the PCC. The specific circuit structure is as follows: Figure 5 As shown, Figure 5 Z0 represents the equivalent impedance between the virtual internal potential and the grid connection point voltage. This leads to the VSG output reactive power.

[0113]

[0114] By combining the reactive power-voltage control equations in equations (11) and (2), we can obtain...

[0115]

[0116] Substituting equation (12) into equation (10), we obtain the short-circuit current expression in the dq coordinate system. Transforming the expression into steady-state and transient components, we get:

[0117] The expression for the steady-state component of the phase a short-circuit current is:

[0118]

[0119] The expression for the transient component of the phase a short-circuit current is:

[0120]

[0121] As can be deduced above, the influencing factors of the three-phase short-circuit current of a VSG-based direct-drive unit are the voltage drop degree U and the virtual impedance |Z. v | Reactive power droop coefficient K q The active power output of the fan and the power factor at the outlet can be used as grouping indicators to accurately reflect the short-circuit current characteristics of the unit.

[0122] Step 2: Input the clustering index into the improved DBSCAN clustering algorithm. The improved DBSCAN clustering algorithm automatically optimizes the neighborhood radius and minimum number of points by introducing the particle swarm optimization algorithm, realizes fast neighborhood search by constructing a KD tree structure, and evaluates the clustering effect by combining the fitness function composed of the silhouette coefficient and the DBI index to obtain the optimal clustering result.

[0123] The improved DBSCAN clustering algorithm in step two automatically optimizes the neighborhood radius and minimum number of points by introducing a particle swarm optimization algorithm. The automatic optimization includes the following steps:

[0124] (1) Initialize the size of the particle swarm and set the position and velocity information of each particle;

[0125] (2) During the iteration process, the particle velocity is updated based on the inertia weight, the individual historical best position, and the global best position;

[0126] (3) Update the particle positions based on the updated velocity;

[0127] (4) Repeat the iteration steps until the convergence condition is met, and obtain the optimal values ​​of the neighborhood radius and the minimum number of points.

[0128] Furthermore, in step two, the improved DBSCAN clustering algorithm uses a fitness function composed of the silhouette coefficient and the DBI index to evaluate the clustering effect. The evaluation method includes the following steps:

[0129] (1) Calculate the average distance between each sample point and other points in the cluster, and calculate the average distance between the sample point and the nearest neighboring cluster, and determine the profile coefficient accordingly;

[0130] (2) Calculate the dispersion of each cluster and the distance between cluster centers, and determine the DBI index accordingly;

[0131] (3) Combine the average value of the contour coefficients with the DBI index and construct an overall fitness function according to a preset weighting factor;

[0132] (4) The clustering effect is evaluated using the fitness function, and the evaluation results are used to guide the iterative optimization process of the particle swarm optimization algorithm.

[0133] Furthermore, the improved DBSCAN clustering algorithm in step two introduces a KD-tree structure during the neighborhood search process. The neighborhood search method includes the following steps:

[0134] (1) Recursively divide the sample data according to different dimensions and construct a binary tree-like KD tree structure so that the dataset is divided into multiple super rectangular regions;

[0135] (2) When performing a neighborhood query, a hypersphere neighborhood with a radius of the set neighborhood radius is constructed with the query point as the center, and the intersection relationship between the neighborhood and each sub-region of the KD tree is determined.

[0136] (3) Sub-regions that do not intersect with the queried neighborhood are directly discarded and no further distance calculation is performed;

[0137] (4) Calculate the sample points in the sub-regions that intersect with the queried neighborhood and determine whether they are within the radius of the neighborhood;

[0138] (5) The points that meet the conditions are determined as the neighborhood points of the query point, thereby reducing the time complexity from quadratic to logarithmic during the overall search process.

[0139] After obtaining the clustering indicators, a clustering algorithm is needed to classify the wind turbines within the wind farm to form an equivalent model that reflects the overall characteristics. Considering the problems of high parameter sensitivity, unstable clustering results, and insufficient computational efficiency of the traditional DBSCAN algorithm when processing large-scale, high-dimensional data, this embodiment improves upon it and proposes an improved DBSCAN clustering method suitable for wind farms with a hybrid grid / root-grid structure. To more clearly illustrate the design concept of this method, the improved DBSCAN algorithm used is described in detail below.

[0140] In the improved DBSCAN algorithm, a particle swarm optimization (PSO) algorithm is introduced to adaptively obtain the DBSCAN clustering parameters ε (neighborhood radius) and Minpints (minimum number of points), avoiding the difficulty of manual setting and thus enhancing the algorithm's applicability in complex wind farms. The corresponding parameters in the PSO algorithm are defined as follows: the number of particles is N, the particle position data is X, and the velocity data is V.

[0141] The iterative formula for the particle is:

[0142]

[0143] Among them, v i k x is the velocity of the i-th particle in the k-th iteration. i k p is the position of the i-th particle in the k-th iteration. i,best Let p be the local optimal position of particle i after k iterations. g,best Let w be the global optimal position of the population after k iterations, w be the inertia weight that controls the tendency of particles to maintain their original velocity, and c be the global optimal position of the population after k iterations. 1, c2 is the learning factor, used to control the intensity of the particle's learning towards the individual optimum and the global optimum, r 1, r2 is a random number in the interval [0,1], used to enhance the randomness of the algorithm.

[0144] The particle position update formula is as follows

[0145]

[0146] The algorithm randomly generates the positions and velocities of N particles, and sets parameters such as the maximum number of iterations and inertia weights. It then calculates the fitness value of each particle to determine the optimal p for that individual. i,best and the global optimal p g,bestAfter updating the particle state according to the velocity and position formulas, the fitness update is re-evaluated until the maximum number of iterations is reached or convergence is achieved. Finally, the optimal clustering parameters of the DBSCAN algorithm are obtained, ensuring the clustering effect and replacing manual setting.

[0147] The fitness function in this paper is designed based on the silhouette coefficient and DBI. The former directly characterizes the compactness of a single sample with its cluster and the separation from other clusters by calculating the matching degree between individuals and clusters and then taking a global average. The latter does not traverse the samples but calculates the average similarity between clusters from a global perspective to reduce the interference of noise points on the clustering effect and enhance robustness to outliers. Due to its low computational complexity, it is suitable for rapid evaluation of large-scale or high-dimensional data. In clustering calculation, the formula for calculating the silhouette coefficient is:

[0148]

[0149] Where a(i) is the average distance between the sample point and other data points in the cluster, and b(i) is the minimum average distance between the sample point and all data points in other clusters.

[0150] The silhouette coefficient ranges from [-1, 1], where 0 indicates the particle is in a boundary sample, -1 indicates an incorrect cluster, and 1 indicates a correct cluster. The overall silhouette coefficient is obtained by averaging the silhouette coefficients of all particles.

[0151]

[0152] The formula for calculating DBI is:

[0153]

[0154] Where σ is the average distance from cluster i to the cluster center, and c i For the center of cluster i, d(σ) i +σ i R is the inter-cluster distance. ij This represents the discreteness of a single cluster.

[0155] The final fitness function is:

[0156]

[0157] The fitness function combines the clustering performance of individuals and the whole, and has a certain robustness to outliers. The weighting factor α can be adjusted to adjust the proportion of individual and whole performance. In this paper, due to the large amount of data and the relatively uniform distribution of data points, the weighting factor α is set to 0.4.

[0158] The traditional DBSCAN algorithm achieves density reachability based on global linear neighborhood search. For each sample point, it needs to calculate all points in its ε-neighborhood, resulting in a time complexity of O(n^2). 2 This leads to low computational efficiency and a surge in computational load when processing large-scale data. In such cases, introducing a KD-tree can assist in fast neighborhood search, saving time and reducing computational complexity to O(nlogn). As a binary tree data search structure, each node of a KD-tree represents a hyperrectangular region in k-dimensional space. By alternately partitioning data across different dimensions—that is, through hyperplane segmentation—the search range is quickly narrowed. On one hand, range queries find all points clustered less than ε with the query point; on the other hand, if a node's region intersects with the query sphere, the subtree is skipped, prematurely terminating branches with a distance exceeding ε, reducing unnecessary distance calculations. The query data point starts from the root node and is compared with the range of values ​​in each corresponding dimension to determine whether a neighborhood search is successful or to continue iteratively searching the subtree. Segmentation stops when the number of points within a node is less than a threshold or the maximum depth is reached.

[0159] The calculation steps of the DB-SCAN algorithm based on KD-tree are as follows:

[0160] ① The KD tree of the dataset: Construct a KD tree by cyclically partitioning the PDW dataset according to its dimensions, such that the value of the left subtree in a given dimension is less than the value of the parent node, and the value of the right subtree is greater than the value of the parent node.

[0161] ② Perform density reachability search. For unvisited point p: use the range query of the KD tree to find all points in the ε neighborhood of p. If the number of neighborhood points is greater than or equal to Minpints, then p is the core point and a new cluster is formed.

[0162] ③ Recursively expand the cluster until no new core point can be found.

[0163] Final Algorithm Flow Figure 6 As shown.

[0164] Step 3: Based on the optimal clustering results, wind turbines belonging to the same class are subjected to single-unit multiplication to form a multi-unit equivalent model.

[0165] Specifically, the single-machine multiplication modeling process in step three includes the following steps:

[0166] (1) Collect and summarize the operating parameters of wind turbines belonging to the same cluster result;

[0167] (2) The wind turbine operating parameters within the cluster are weighted and averaged to obtain the center parameters of the cluster;

[0168] (3) Establish an equivalent unit model based on the cluster center parameters;

[0169] (4) The capacity and current response of the equivalent unit are multiplied according to the number of fans in the cluster;

[0170] (5) Replace the original cluster of multiple wind turbines with the equivalent units after multiplication, and use them for subsequent power system simulation or stability analysis.

[0171] After grouping and clustering the wind turbines within the wind farm, the clustering results need to be used to establish an equivalent model of the hybrid wind farm. This embodiment uses a single-turbine multiplication method to replace multiple turbines in the same category with a single equivalent turbine, and uses the multiplication coefficient to reflect the number of turbines in that category, thereby achieving a balance between model simplification and preservation of dynamic characteristics.

[0172] Specifically, based on the clustering results obtained in step two, wind turbines belonging to the same category are first grouped together. For each category of wind turbines, the operating parameters such as voltage sag, virtual impedance modulus, reactive power droop coefficient, active power, and power factor are used to determine the class center feature value through weighted averaging, which is used as the parameter input for constructing the equivalent wind turbine model.

[0173] During the modeling process, the capacity of the equivalent wind turbine is set according to the product of the number of turbines of this type and the capacity of a single turbine. Its control parameters are kept consistent with the class center characteristics to ensure the consistency of the equivalent model in transient response and steady-state operation. Specifically, when a three-phase short circuit or voltage disturbance occurs in the power system, the equivalent wind turbine can reproduce the current support and voltage recovery characteristics of a group of similar wind turbines, thereby accurately reflecting the overall dynamic behavior of the wind farm.

[0174] Furthermore, the single-machine multiplication model is applicable not only to the clustering results of grid-connected wind turbines but also to the grid-connected wind turbine portion included in hybrid wind farms. Through a unified clustering-multiplication modeling process, a large-scale multi-machine equivalent model is finally obtained, which can be directly embedded into the transient stability analysis, short-circuit current calculation, and dispatch simulation of power systems.

[0175] A detailed model of a typical wind farm was built in PSCAD / EMTDC and compared with the established equivalent model. The wind farm topology is as follows: Figure 7 As shown, the equivalent results are as follows: Figure 8 As shown in Table 1, the results indicate that, compared with existing equivalence methods, the single-machine multiplication modeling in this embodiment maintains the physical consistency of clustering results while avoiding complex electrical topology reconstruction, significantly reducing modeling complexity and improving the efficiency of large-scale wind farm simulation calculations.

[0176] Table 1 Comparison of short-circuit current results in equivalent models under typical operating conditions

[0177]

[0178] In some embodiments, a computer-readable storage medium is provided having computer program instructions stored thereon. When executed by a processor, the instructions are used to implement the steps of the equivalent method for a rooted / grid-connected hybrid wind farm based on the improved DBSCAN algorithm described in this invention, including:

[0179] Obtain the operating parameters of each wind turbine in the wind farm, and determine the clustering index based on the voltage drop, virtual impedance modulus, reactive power droop coefficient, active power and power factor;

[0180] The clustering index is input into the improved DBSCAN clustering algorithm, and adaptive optimization of neighborhood radius and minimum number of points is achieved by introducing particle swarm optimization.

[0181] A fitness function is constructed by combining the silhouette coefficient and the DBI index to evaluate the clustering effect, and a fast neighborhood search is achieved using the KD tree structure.

[0182] After obtaining the optimal clustering results, the single-unit multiplication method is used to replace the wind turbines of the same type to form a multi-unit equivalent model.

[0183] The execution of the computer program enables the automation and efficiency of wind farm equivalent modeling.

[0184] In other embodiments, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it is configured to implement the steps of the equivalent method for a root / grid hybrid wind farm based on the improved DBSCAN algorithm described in this invention.

[0185] The electronic device may be an industrial control computer, a power system simulation analysis server, a wind farm dispatching main control platform, or a scientific research computing terminal, and may include:

[0186] The data acquisition module is used to acquire wind turbine operating parameters and generate cluster indicators;

[0187] Clustering computation module, used to execute the improved DBSCAN clustering algorithm;

[0188] The optimization module is used to optimize clustering parameters using the particle swarm optimization algorithm.

[0189] A fast search module is used to accelerate the neighborhood search process using KD trees;

[0190] The equivalent modeling module is used to construct multi-machine equivalent models based on clustering results;

[0191] The results output module is used to apply the equivalent model to power system stability analysis and dispatch simulation.

[0192] The aforementioned electronic devices enable rapid modeling and simulation analysis of large-scale hybrid wind farms, reducing computational complexity and improving system analysis efficiency.

[0193] In summary, this implementation method, focusing on grid-connected equivalent modeling, acquisition of terminal voltage phasor mutations under fault triggering, current inner-loop control and constraints during low-voltage ride-through, phase-locked loop dynamic modeling, and Runge-Kutta numerical integration, presents a coherent and consistent implementation process and parameter organization, forming a path directly applicable to engineering calculations. The above steps are decoupled and reused through an interface relationship of "initial conditions—external input—control constraints—coupled equations—numerical advancement"; relevant parameters can be described in per-unit or actual units and can be adjusted according to grid strength, short-circuit location, and controller settings. The accompanying drawings and terminology are used to illustrate the implementation idea rather than limiting specific values ​​and structures. Without departing from the overall concept and key features, equivalent circuit refinement, control loop implementation details, integration order and step size settings, and result post-processing methods are all allowed to be equivalently replaced and adapted. Those skilled in the art can implement this method accordingly.

[0194] In summary, the proposed equivalent method for wind farms based on the improved DBSCAN algorithm in this embodiment achieves the equivalent processing of large-scale wind farms by following the technical process of obtaining clustering indicators, cluster analysis, and single-unit multiplication modeling. By introducing adaptive parameter optimization and a fast search mechanism in the clustering stage, not only is the accuracy and computational efficiency of clustering improved, but the dynamic response characteristics of the wind turbine group are also effectively maintained during the modeling process. Combined with the implementation form of computer-readable storage media and electronic devices, this invention can be implemented in various application scenarios, providing reliable support for power system transient stability research, short-circuit current analysis, and dispatch simulation.

[0195] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An equivalent method for a hybrid wind farm based on an improved DBSCAN algorithm, characterized in that, Includes the following steps: Step 1: Obtain the operating parameters of each wind turbine in the wind farm, and select the operating parameters as clustering indicators. The clustering indicators include at least the voltage drop, virtual impedance modulus, reactive power droop coefficient, active power output of the wind turbine, and power factor at the outlet. Step 2: Input the clustering index into the improved DBSCAN clustering algorithm. The improved DBSCAN clustering algorithm automatically optimizes the neighborhood radius and minimum number of points by introducing the particle swarm optimization algorithm, realizes fast neighborhood search by constructing a KD tree structure, and evaluates the clustering effect by combining the fitness function composed of the silhouette coefficient and the DBI index to obtain the optimal clustering result. Step 3: Based on the optimal clustering results, wind turbines belonging to the same class are subjected to single-unit multiplication to form a multi-unit equivalent model.

2. The method according to claim 1, characterized in that, The method for determining the voltage drop level in the clustering index obtained in step one includes the following steps: (1) Measure the voltage amplitude at the grid connection point before the three-phase short-circuit fault occurs; (2) Measure the voltage amplitude at the grid connection point after a three-phase short-circuit fault occurs; (3) Divide the difference between the voltage amplitude before the fault and the voltage amplitude after the fault by the voltage amplitude before the fault to determine the degree of voltage drop.

3. The method according to claim 1, characterized in that, The method for determining the virtual impedance magnitude in the clustering index obtained in step one includes the following steps: (1) Set the resistance component and reactance component of the virtual impedance in the virtual admittance loop control of the grid-type wind turbine; (2) Calculate the vector sum of the resistance component and the reactance component; (3) The vector sum is used as the virtual impedance modulus to characterize the current support capability of the wind turbine during a short-circuit fault.

4. The method according to claim 1, characterized in that, The method for determining the reactive power droop coefficient in the clustering index obtained in step one includes the following steps: (1) Set the reference value of the terminal voltage in the reactive power voltage control loop of the grid-type wind turbine; (2) Measure the deviation between the actual terminal voltage of the fan and the voltage reference value during operation; (3) Determine the reactive power droop coefficient based on the relationship between the deviation and the reactive power change, which is used to characterize the droop characteristics between the terminal voltage and the reactive power.

5. The method according to claim 1, characterized in that, The improved DBSCAN clustering algorithm in step two automatically optimizes the neighborhood radius and minimum number of points by introducing a particle swarm optimization algorithm. The automatic optimization includes the following steps: (1) Initialize the size of the particle swarm and set the position and velocity information of each particle; (2) During the iteration process, the particle velocity is updated based on the inertia weight, the individual historical best position, and the global best position; (3) Update the particle positions based on the updated velocity; (4) Repeat the iteration steps until the convergence condition is met, and obtain the optimal values ​​of the neighborhood radius and the minimum number of points.

6. The method according to claim 1, characterized in that, The improved DBSCAN clustering algorithm in step two uses a fitness function composed of silhouette coefficient and DBI index to evaluate the clustering effect. The evaluation method includes the following steps: (1) Calculate the average distance between each sample point and other points in the cluster, and calculate the average distance between the sample point and the nearest neighboring cluster, and determine the profile coefficient accordingly; (2) Calculate the dispersion of each cluster and the distance between cluster centers, and determine the DBI index accordingly; (3) Combine the average value of the contour coefficients with the DBI index and construct an overall fitness function according to a preset weighting factor; (4) The clustering effect is evaluated using the fitness function, and the evaluation results are used to guide the iterative optimization process of the particle swarm optimization algorithm.

7. The method according to claim 1, characterized in that, The improved DBSCAN clustering algorithm in step two introduces a KD tree structure during the neighborhood search process. The neighborhood search method includes the following steps: (1) Recursively divide the sample data according to different dimensions and construct a binary tree-like KD tree structure so that the dataset is divided into multiple super rectangular regions; (2) When performing a neighborhood query, a hypersphere neighborhood with a radius of the set neighborhood radius is constructed with the query point as the center, and the intersection relationship between the neighborhood and each sub-region of the KD tree is determined. (3) Sub-regions that do not intersect with the queried neighborhood are directly discarded and no further distance calculation is performed; (4) Calculate the sample points in the sub-regions that intersect with the queried neighborhood and determine whether they are within the radius of the neighborhood; (5) The points that meet the conditions are determined as the neighborhood points of the query point, thereby reducing the time complexity from quadratic to logarithmic during the overall search process.

8. The method according to claim 1, characterized in that, The single-machine multiplication modeling process in step three includes the following steps: (1) Collect and summarize the operating parameters of wind turbines belonging to the same cluster result; (2) The wind turbine operating parameters within the cluster are weighted and averaged to obtain the center parameters of the cluster; (3) Establish an equivalent unit model based on the cluster center parameters; (4) The capacity and current response of the equivalent unit are multiplied according to the number of fans in the cluster; (5) Replace the original cluster of multiple wind turbines with the equivalent units after multiplication, and use them for subsequent power system simulation or stability analysis.

9. A computer-readable storage medium having a computer program stored thereon, the program being executed by a processor to perform the method according to any one of claims 1 to 8.

10. An electronic device comprising at least one processor and at least one memory, the memory storing a computer program that, when executed, causes the processor to perform the method according to any one of claims 1 to 8.

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