A hybrid wind farm equivalent method considering the interaction between wind farms and power grid

Abstract

The application discloses a kind of considering the equivalent method of mixed wind farm interaction characteristics of follow / network, belong to new energy power system modeling technical field.The method first establishes the output characteristic model of follow network type unit and network type unit, and constructs the interaction relationship between units based on the two-way coupling relationship of voltage and current;Second, construct the grouping index system including inherent characteristic index and coupling interaction characteristic index of unit;Then, the improved DBSCAN algorithm is used to cluster wind turbine units;Further, according to the grouping result, the aggregation processing is carried out on the unit parameters;Finally, the multi-machine equivalent model including coupled power term is constructed.The method can reflect the inherent characteristics of unit and the interaction between units, improve the accuracy and engineering applicability of mixed wind farm equivalent modeling.

Description

Technical Field

[0001] This invention relates to the field of new energy power system modeling and analysis technology, specifically to an equivalent method for hybrid wind farms that considers the interaction characteristics of the grid / network. Background Technology

[0002] With the advancement of new power system construction, the installed capacity of new energy power generation continues to grow, and the proportion of wind power in the power system is constantly increasing. The dynamic response characteristics of wind farms under grid faults and disturbances have a significant impact on the safe and stable operation of the system. Therefore, conducting equivalent modeling research on wind farms has become a key fundamental issue in power system simulation analysis and planning design. Especially in the context of large-scale new energy grid integration, how to construct an equivalent model that can accurately reflect the dynamic characteristics of wind farms has become an important research direction in the field of power system analysis.

[0003] Existing equivalent modeling methods for wind farms primarily target single grid-connected wind farms. These methods typically rely on steady-state operating parameters or dynamic response characteristics of the turbines, employing clustering and parameter aggregation to achieve multi-turbine equivalent modeling. However, in practical engineering, with the application of grid-connected wind turbines, wind farms are increasingly exhibiting a mixed operation of grid-connected and grid-connected turbines. These two types of turbines differ significantly in control methods and external characteristics. Grid-connected turbines exhibit controlled current source characteristics, while grid-connected turbines exhibit controlled voltage source characteristics, forming a bidirectional voltage and current coupling relationship through the grid connection point. Current technologies often rely on clustering indices that only consider the turbine's own operating characteristics, failing to adequately account for the coupling and interaction effects between turbines. Furthermore, commonly used clustering algorithms have limitations in parameter setting and computational efficiency, making them ill-suited for the complex clustering requirements of mixed wind farms. Moreover, existing equivalent modeling methods often employ simple aggregation approaches, failing to reflect the differences in coupling strength between turbines, resulting in insufficient accuracy of the equivalent models.

[0004] Therefore, in wind farms where grid-connected and grid-connected units operate in combination, how to simultaneously consider the inherent characteristics of the units and the interaction characteristics between the units during the clustering process, how to improve the adaptability and computational efficiency of clustering, and how to construct a high-precision equivalent model that can reflect the coupling relationship between the units have become urgent technical problems to be solved. Summary of the Invention

[0005] To address the problems of existing technologies, embodiments of the present invention provide an equivalent method for hybrid wind farms that considers grid-connection interaction characteristics. The technical solution is as follows: An equivalent method for hybrid wind farms that considers grid-connection interaction characteristics includes the following steps: S1: Establish output characteristic models for grid-connected and grid-connected wind turbines, obtain the inherent operating parameters of each unit, and construct the interaction relationship between units based on the bidirectional coupling relationship between voltage and current; S2: Based on the output characteristic model, construct a clustered indicator system that includes inherent characteristic indicators of the unit and coupling and interaction characteristic indicators between units; S3: Based on the aforementioned clustering index system, the improved DBSCAN algorithm is used to cluster the wind turbine units to obtain multiple unit clusters; S4: Based on the unit cluster, the parameters of the wind turbines within the same cluster are aggregated to obtain equivalent parameters; S5: Construct a multi-unit equivalent model of a hybrid wind farm based on the equivalent parameters, wherein the equivalent model includes a coupling power term for characterizing the interaction between units.

[0006] Furthermore, in step S2, the clustering index system includes a set of indexes for grid-connected generating units and a set of indexes for grid-linked generating units. The set of indexes for grid-connected generating units includes grid voltage parameters, virtual impedance characteristic parameters, reactive power voltage regulation parameters, and active power output parameters. The virtual impedance characteristic parameters are obtained through the virtual admittance or equivalent impedance element in the grid-type unit control system and are used to characterize the constraint relationship between the unit port voltage and current.

[0007] Furthermore, the set of grid-connected unit indicators includes grid voltage parameters, active power output parameters, low-voltage ride-through control parameters, and current limiting parameters. The low voltage ride-through control parameters are determined by the grid-side converter control strategy of the unit and are used to characterize the reactive current injection capability during voltage dips. The current limiting parameters are used to constrain the maximum output current of the unit during faults.

[0008] Furthermore, the inter-unit coupling and interaction characteristic index is constructed through the following process: Obtain parameters of the grid-connected unit's ability to regulate the voltage at the grid connection point; Obtain the current characteristic parameters injected by the grid-connected unit into the grid connection point; By combining the impedance or admittance characteristics of the electrical connection lines between units, the voltage regulation effect and the current injection effect are coupled and mapped to obtain a coupling characteristic index for characterizing the interaction strength between units.

[0009] Furthermore, in step S3, the improved DBSCAN algorithm adaptively solves the clustering parameters by introducing a particle swarm optimization algorithm, wherein each particle corresponds to a combination of a neighborhood range parameter and a minimum sample point parameter, and iteratively updates the parameters within a preset parameter range.

[0010] Furthermore, in the particle swarm optimization process, a comprehensive evaluation function is constructed to evaluate the clustering results. The evaluation function is calculated based on the density of sample points within their respective clusters and the degree of separation between different clusters, and the optimal parameter combination is obtained through multiple rounds of iterative screening.

[0011] Furthermore, the improved DBSCAN algorithm organizes the cluster index data by constructing a multi-dimensional spatial index structure. During the neighborhood search process, it filters the set of data points that meet the distance conditions through range queries and skips data branches that do not meet the conditions, thereby reducing the number of distance calculations.

[0012] Furthermore, in step S3, cluster expansion based on density reachability rules includes marking sample points for access, performing neighborhood search, identifying core points and generating clusters, and recursively expanding neighborhood samples based on the core points until the clusters no longer expand.

[0013] Further, in step S4, the parameter aggregation process includes: The generator electrical parameters are weighted and synthesized according to the unit capacity; The shaft system parameters are aggregated based on equivalent inertia and damping characteristics; The parameters of the generator terminal transformer are combined according to resistance, reactance, conductance and susceptance. The control parameters are weighted and averaged according to the unit capacity ratio to ensure the consistency of the equivalent system under the same disturbance.

[0014] Furthermore, in step S5, when constructing the multi-machine equivalent model: Grid-connected generating units will participate in the grid connection point voltage establishment process as voltage regulation sources. The grid-connected generating units will be used as current injection sources to participate in the system current distribution process. Using the grid connection point voltage as the coupling node, the voltage regulation behavior and current injection behavior are linked to form a closed-loop interactive relationship, and the interaction between units is characterized by the coupling power term.

[0015] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows: This invention provides an equivalent method for hybrid wind farms that considers grid-connected / network-connected interaction characteristics. By constructing a clustering index system that includes the inherent characteristics of the units and the coupling and interaction characteristics between the units, the clustering process can not only reflect the operating characteristics of the units themselves, but also reflect the interaction between the voltage regulation effect of grid-connected units and the current injection effect of grid-connected units, thereby improving the rationality and physical consistency of the clustering results.

[0016] This invention introduces a particle swarm optimization mechanism to adaptively solve clustering parameters and combines it with a spatial index structure to accelerate neighborhood search. This reduces the dependence of traditional clustering methods on manual parameter setting, while also reducing computational complexity and improving clustering efficiency and stability in large-scale mixed wind farm scenarios.

[0017] This invention aggregates unit parameters based on clustering results and introduces coupled power terms into the equivalent model. It links the voltage regulation behavior of grid-connected units with the current injection behavior of grid-connected units, enabling the obtained equivalent model to reflect the coupling and interaction characteristics between units. This improves the accuracy of transient response analysis of hybrid wind farms and enhances the applicability of the model in power system simulation and engineering applications. Attached Figure Description

[0018] 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.

[0019] Figure 1 This is a schematic diagram of the grid-connected permanent magnet synchronous generator structure with low voltage ride-through control in this invention. Figure 2 This is a schematic diagram of the grid-type wind turbine control structure based on virtual synchronous generator control in this invention; Figure 3 This is a schematic diagram of the voltage vector changes before and after a short-circuit fault in this invention; Figure 4 This is a simplified model diagram of two wind turbines consisting of grid-connected and grid-connected types in this invention; Figure 5 This is a schematic diagram of the equivalent circuit of the wind farm with integrated wind power and grid in this invention; Figure 6 This is a schematic diagram showing the spatial positional relationship of the voltage vectors of each power source in this invention; Figure 7 This is a schematic diagram of the improved DBSCAN algorithm in this invention. Detailed Implementation

[0020] 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.

[0021] This embodiment takes a typical wind farm with a mix of grid-connected and grid-connected wind turbines as an example, and describes an equivalent method for a mixed wind farm that considers the interaction characteristics of the grid and the wind turbines.

[0022] In this embodiment, "considering grid-connected / network-connected interaction characteristics" refers to constructing an interaction characteristic index to characterize the coupling relationship between the voltage regulation capability of grid-connected units and the current injection characteristics of grid-connected units. Based on the interaction characteristic index and the improved DBSCAN algorithm, wind turbines are grouped. On this basis, the parameters of units within the same cluster are aggregated, thereby introducing inter-unit coupled power terms into the equivalent model to reflect the interaction between grid-connected units and grid-connected units.

[0023] In this embodiment, the method includes the following technical process: first, modeling and analyzing the output characteristics of grid-connected and grid-connected wind turbines; second, constructing a clustering index system; then, clustering the turbines based on the improved DBSCAN algorithm; further, aggregating the turbine parameters; and finally, constructing a multi-turbine equivalent model of a hybrid wind farm.

[0024] I. Output Characteristics of Wind Farms Integrated with / Grid To achieve reasonable grouping and equivalent modeling of hybrid wind farm units, this implementation method first analyzes the output characteristics of grid-connected units and grid-connected units, and then extracts key parameters to characterize the operating characteristics of the units and the interaction between the units.

[0025] (a) Output characteristics of grid-connected units Low voltage ride-through control with grid-type PMSG output characteristics Grid-connected direct-drive wind turbine structures with low voltage ride-through control (LVRT) are as follows: Figure 1 As shown, it mainly consists of a wind turbine, a permanent magnet synchronous generator (PMSG), a full-power converter, a load-unloading circuit, and corresponding control components.

[0026] Because the PMSG achieves electrical isolation from the grid through a full-power converter, grid-side electrical disturbances cannot be directly transmitted to the PMSG. Therefore, its output characteristics during faults mainly depend on the control strategy of the grid-side converter. During normal operation, the GSC adopts grid voltage-oriented vector control. The power outer loop achieves maximum power point tracking by adjusting the DC bus voltage and meets grid connection requirements through reactive power regulation. During low-voltage ride-through, the GSC control strategy switches from the power outer loop to LVRT control mode, using the generator terminal voltage as the core input variable and achieving fault ride-through by adjusting the reactive current output.

[0027] According to the national wind farm grid connection technical standard GB / T19963.1-2021, wind turbines must have dynamic reactive power support capability during low-voltage operation, and the injected reactive current should meet the following relationship: (1) In the formula, i gd_ref i gd_ref For the grid-side current reference value dq-axis component, i gd0 i gd0 K is the initial value of the grid-side current. d i is the reactive current gain coefficient. N For the rated current, i max For the maximum limiting current, u g This is the grid voltage.

[0028] Initial value of grid-side converter current i gd0 i gq0 It can be obtained from the operating conditions before the fault. Since grid voltage orientation is used, u... gd =u g u gq =0, at this time the active power and reactive power output by GSC can be represented as (2) In the formula u gd0 u gq0 These are the dq-axis components of the initial grid-side voltage, u g0 Let P be the initial value of the grid voltage. 0_PMSG Q 0_PMSG This is to output the initial values ​​of active and reactive power.

[0029] Substituting equation (2) into equation (1) yields (3) As can be seen from equation (3), the steady-state short-circuit current output by the PMSG during the low-voltage period is determined by the terminal voltage and the operating conditions before the fault. Its power output characteristics during the fault steady state can be equivalent to a controlled current source.

[0030] The transient characteristics of PMSG mainly depend on the dynamic response of the current control inner loop

[21] . In engineering, in order to achieve fast current tracking, the current inner loop can usually complete the transient adjustment within 2ms. When LVRT is triggered, the current reference value jumps from the steady-state value before the fault to the LVRT command value. The current inner loop can quickly adjust the output current to track the active and reactive current reference values. Therefore, the transient process can be approximately ignored.

[0031] The PMSG output current before and after the fault is (4) In summary, the grid-connected PMSG exhibits voltage-controlled current source characteristics during faults, and its output characteristics are mainly affected by the voltage drop, reactive current gain, and active power output of the wind turbine. Considering that the wind turbine typically operates at its rated power factor, the difference in reactive power of the unit before the fault can be ignored.

[0032] Based on the above analysis, it can be seen that the output characteristics of grid-connected units during faults are mainly characterized by controlled current source characteristics, and their output current is affected by voltage levels and control parameters. Therefore, characteristic quantities reflecting the operating characteristics of grid-connected units can be extracted from the perspectives of voltage, current, and control parameters, providing a basis for the subsequent construction of clustering indicators.

[0033] (II) Output characteristics of grid-connected units Grid-connected wind turbines using VSG control employ speed outer loop and current inner loop control on the turbine side, while the grid side uses VSG control, consisting of active-frequency and reactive-voltage power outer loops, a virtual admittance loop, and a current inner loop. Its control structure is as follows: Figure 2 As shown.

[0034] The active frequency loop, by simulating the rotor motion equations of a synchronous generator, directly affects the power angle and dynamic response characteristics of active power, and is the core component for maintaining system frequency stability. Its control equation is as follows: (5) In the formula, δ is the generator power angle, J is the rotor moment of inertia, and P... ref Here, P is the active power reference value, and D is the output active power. Let be the system angular velocity. For synchronous angular velocity, k p This is the active power droop factor.

[0035] The reactive power loop, by simulating the excitation regulation characteristics of a synchronous machine, achieves coordinated control of reactive power and terminal voltage. It is the dominant component providing dynamic reactive power support during faults, and its control equation is as follows: (6) In the formula, 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.

[0036] The virtual admittance loop, by controlling the output voltage of the VSG, simulates the stator resistance and synchronous reactance of the synchronous machine, directly affecting the port impedance characteristics of the unit. Its control equation is as follows: (7) In the formula, e d e q For the virtual internal potential dq-axis component, u d u q Terminal voltage dq-axis component, R v L v For virtual resistance and reactance.

[0037] When a fault occurs, due to the voltage stabilizing effect of the DC bus capacitor, the wind turbine, direct-drive wind turbine, turbine-side converter, and DC bus can be treated as an ideal DC voltage source, providing a prerequisite for stable regulation of the grid-side VSG control. The transient response of the grid-type converter exhibits significant multi-time-scale characteristics: the time scale of the loop dominated by the virtual admittance loop and the inner current loop is 0-10ms, and the transient response process is usually completed in 2ms; the time scale dominated by the outer power loop is 10ms-0.5s.

[0038] Therefore, when analyzing quasi-steady state, the transient process of the fast-adjusting stage can be ignored, and the focus can be on the steady-state characteristics dominated by the power outer loop. At this point, the relationships between the key electrical quantities and the power angle of the system are as follows: Figure 3 As shown.

[0039] The current expression can be derived from the virtual admittance loop equation. (8) Depend on Figure 3 achievable (9) When the system approaches quasi-steady state, the output reactive power of the VSG is (10) Combining equations (10) and (6), we can obtain the virtual internal potential as follows: (11) As can be seen from the above derivation, the VSG-based PMSG exhibits the characteristics of a controlled voltage source with multiple control loops coupled during a fault. Its output characteristics are mainly affected by the grid voltage U and the virtual impedance |Z. v | Reactive power droop coefficient k q The active power output P of the wind turbine is affected. Furthermore, if a virtual excitation stage is introduced into the aforementioned VSG control, the complexity of the control strategy will increase, and its voltage regulation will exhibit a dynamic process dominated by excitation regulation. The output characteristics of grid-connected units will be affected by the virtual excitation k. vp k vi Influence.

[0040] As the above analysis shows, grid-connected generating units actively regulate the grid connection point voltage through virtual synchronous generator control, and their output characteristics exhibit controlled voltage source characteristics. Therefore, characteristic quantities reflecting the operating characteristics of grid-connected generating units can be extracted based on their voltage regulation capabilities and control parameters for subsequent cluster analysis.

[0041] (iii) Interaction characteristics of network construction A typical grid-connected / grid-connected hybrid system mainly consists of grid-connected direct-drive wind turbines, grid-connected direct-drive wind turbines, combiner lines, overhead lines, box-type substations (0.69 / 35kV), main transformers (35 / 220kV), and AC power grid. The control structures of the two types of units are consistent with the output characteristic analysis sections of the grid-connected units and grid-connected units mentioned above in this embodiment. Figure 4 The simplified model for the two machines aims to derive the coupling characteristics. Subsequent interaction metrics are obtained through a detailed model and do not depend on equivalent results.

[0042] Based on the characteristic analysis of the two types of units, the grid-connected converter achieves grid connection by tracking the grid voltage, and its external characteristics exhibit that of a controlled current source. In contrast, the grid-connected converter establishes voltage by simulating the characteristics of a synchronous generator, and its external characteristics exhibit that of a voltage source. Therefore, the hybrid wind farm can be equivalently represented as... Figure 5 The circuit model shown uses the grid voltage U g As a reference vector, the vector relationships of each power supply voltage are as follows: Figure 6 As shown. Where θ i =arctan(I GFLq / I GFLd Y GFL Y GFM and Y P I1, I2, and I3 represent the admittance of the corresponding branch, and I1, I2, and I3 represent the injected current of the corresponding branch.

[0043] Write the loop voltage equations for the equivalent circuit. (12) During a fault, based on the current source characteristics of the GFL converter, the current injected into the grid connection point is... (13) The point of common coupling (PCC), as the core node for interaction between the hybrid wind farm and the power grid, directly reflects the system's operating status through its voltage. The PCC voltage is derived using equivalent circuits. (14) Substituting equation (14) into equation (13), we get the GFL port voltage as follows: (15) It is described in the phase plane as follows (16) (17) Transform (16) to the GFL converter's own reference frame to eliminate the influence of reference frame differences on the characteristic analysis. (18) Combining equations (13) and (18), the reactive power output during a GFL fault in a mixed wind farm is (19) The above equation shows that the output characteristics of the GFL in a hybrid wind farm (grid-connected / integrated) are a comprehensive result of its own parameters, the coupling effect of the GFM, and the interaction with the grid. The coupling strength is determined by the amplitude of the GFM virtual internal potential (EGFM), the output current of the GFL (IGFL), and the line impedance, with the coupling angle being the phase difference between the two. This coupling characteristic fundamentally distinguishes the dynamic behavior of hybrid wind farms from that of single grid-connected wind farms. Grid-connected units actively adjust the voltage at the grid connection point, altering the voltage constraints of grid-connected units and further affecting their reactive power support and fault ride-through capabilities.

[0044] Based on the voltage source characteristics of GFM, its output current is determined by the difference between its internal potential and the PCC voltage. (20) Combined equations (12)(20), the reactive power output of GFM is (twenty one) Equation (21) shows that the current injection of GFL will directly change the PCC voltage, causing the voltage regulation loop of GFM to respond, and ultimately affecting its reactive power output.

[0045] After summing and rearranging the reactive power outputs of GFL and GFM, the total reactive power output of the hybrid wind farm is: (twenty two) Equation (22) and the equivalent modeling analysis together show that a bidirectional voltage-current coupling mechanism exists in hybrid wind farms: the GFM acts as a voltage source, dominating the establishment of the PCC voltage and providing a voltage reference for the GFL; the GFL acts as a current source, injecting current under voltage constraints, which in turn affects the voltage regulation process of the GFM, and the two form a closed-loop interaction through the PCC. This coupling relationship results in a significant interactive component in the total power, which cannot be directly obtained by superimposing the characteristics of a single unit. Therefore, for equivalent modeling of hybrid wind farms, the clustering index needs to simultaneously reflect the inherent characteristics of the grid-connected units and embody the coupling interaction characteristics.

[0046] Based on the above derivation, it can be seen that grid-connected units affect the system voltage level by adjusting the grid connection point voltage, while grid-following units inject current into the system under the voltage constraint and generate feedback on the grid connection point voltage, thereby forming a two-way coupling relationship between voltage and current.

[0047] Therefore, in a hybrid wind farm, the output characteristics of each turbine depend not only on its own control parameters but also on the operating status of other turbines. To ensure that the subsequent clustering results reflect this coupling characteristic, this implementation introduces a coupling characteristic index to quantify the interaction strength between turbines during the clustering index construction process.

[0048] Based on the above analysis of the output characteristics of grid-connected and network-structured units, as well as the analysis of coupling relationships between units, key characteristic quantities for characterizing the operating status and interaction relationships of units can be obtained. On this basis, a clustering index system is further constructed, and the improved DBSCAN algorithm is used to realize unit clustering and equivalent modeling.

[0049] II. Equivalence Modeling Method Based on Improved DBSCAN Algorithm (I) Construction of Cluster Indicators To achieve accurate clustering of wind farm units in hybrid wind farms, it is necessary to construct a dual-dimensional clustering index system based on the coupling mechanism and output characteristics of hybrid wind farms, using inherent characteristics to characterize the independent fault response of units and coupling characteristics to quantify the interaction intensity between units.

[0050] For network-type generating units, the cluster index matrix is ​​defined as X. g =[U g ,|Z v |,k q ,P,γ GFM-GFL ] T Among them, the grid voltage U g The difference between the virtual internal potential and the terminal voltage is the core constraint on the fault current amplitude; virtual impedance |Z v The dominant port impedance characteristics directly affect the magnitude of the fault current; the reactive power droop factor k q The dynamic reactive power support capability is determined by adjusting the virtual internal potential; the active power output P affects the active frequency loop response through the power angle. Interactive index γ GFM-GFL =E GFM I GFL Y m Quantify its voltage and current coupling strength with grid-connected units.

[0051] For grid-connected generating units, define a cluster index matrix X. f =[U g ,P,K d ,I N ,γ GFM-GFL ] T , grid voltage U g The active power P determines the initial amplitude of the reactive current command during the low-voltage breakout period; the low-voltage breakout reactive current gain K d The limiting current I affects the magnitude of reactive power regulation. NConstrained peak fault current; Interaction index γ GFM-GFL It reflects the change of the voltage constraint condition of the grid-forming unit during voltage establishment. The above indexes take into account both the inherent characteristics and the coupling interaction.

[0052] The above clustering index system mainly characterizes the output characteristics of a hybrid wind farm dominated by the control strategy differences of grid-side converters and coupling interactions. The machine-side operating mode is indirectly reflected in the existing indexes by affecting the steady-state operating point. If the differences in the machine-side operating modes in the wind farm are significant, the resulting differences in dynamic response characteristics will affect the clustering accuracy, and the operating mode should be further incorporated into the clustering indexes.

[0053] The clustering index system constructed in the above way contains both the inherent characteristic indexes of the units and the coupling interaction characteristic indexes between the units, making the clustering results not only able to reflect the operating characteristics of the units themselves, but also able to reflect the interaction influence relationship between the units, thus improving the clustering rationality.

[0054] (2) Improved DBSCAN algorithm for clustering 1. Basic principle As a classic unsupervised clustering method, the core of the traditional DBSCAN algorithm is to automatically identify the cluster structure in the dataset through the density reachability criterion to achieve unsupervised clustering, and its mathematical expression and core definitions are as follows: Minpints is the minimum number of points, ɛ is the neighborhood radius.

[0055] Core point: Given a dataset D, for a sample p, if |N ɛ (p)|≥Minpints, then p is a core point, where Nɛ(p) represents the neighborhood with p as the center and radius ɛ, and dist(p,q) is the Euclidean distance between sample points p and q.

[0056] Border point: If a sample point q satisfies |N ɛ (q)|<Minpints, and there exists a core point p such that q is density-reachable from p, then q is a border point. Among them, density reachability is defined as the existence of a sequence of sample points p1, p2,... p n n, satisfying p1 = p, p n n = q, and for 1 ≤ i ≤ n - 1, pi+1∈Nɛ(pi) and pi+1 is a core point of p i i.

[0057] This algorithm continuously starts from the core points and expands the clustering clusters along the high-density regions, so as to adaptively identify cluster structures of arbitrary shapes without presetting the number of clusters. However, its clustering effect depends on The values ​​of the Minpints parameter are determined, and the computational complexity is O(n) for large-scale datasets. 2 It is difficult to directly adapt to the needs of mixed wind field clustering.

[0058] 2. Adaptive parameter optimization To address the issue that traditional DBSCAN parameters rely on manual setting, a particle swarm optimization (PSO) algorithm is introduced to achieve adaptive parameter solving.

[0059] The parameters in the particle swarm are defined as follows: the number of particles is N, and the particle position vector X corresponds to a set of... The parameter, velocity data is V. The iterative formula for the particle is: (twenty three) v i k Let x be the velocity of the i-th particle in the k-th iteration. i k Let p be 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 is the global optimal position of the population after k iterations, w is the inertia weight, which controls the tendency of the particle to maintain its original speed, c1 and c2 are learning factors, which are used to control the intensity of the particle's learning towards the individual optimal and the global optimal, and r1 and r2 are random numbers in the interval [0,1], which are used to enhance the randomness of the algorithm.

[0060] Next, the silhouette coefficient and the DBI index (Davies-Bouldin) are combined to optimize the fitness function in order to quantitatively evaluate the clustering effect.

[0061] Profile coefficient is (twenty four) This is used to characterize the compactness of a single sample within its cluster and its separation from other clusters, where a(i) is the average distance between the sample point and other data points within its cluster, and b(i) is the minimum average distance between the sample point and all data points in other clusters. The overall silhouette coefficient is obtained by averaging the silhouette coefficients of all particles. (25) The silhouette coefficient ranges from [-1, 1], and the closer it is to 1, the better the clustering effect.

[0062] The DBI index is (26) (27) in Let c be the average distance from cluster i to the cluster center. i As the center of cluster i, R is the Euclidean distance between clusters. ij The smaller the DBI, the better the clustering effect.

[0063] The final fitness function is (28) The fitness function balances the clustering quality of individual samples with the rationality of the global cluster structure. The weight factor β is adjusted to adjust the proportion of individual and overall performance. In this paper, due to the large amount of data and the relatively uniform distribution of data points, the weight factor β is set to 0.4.

[0064] By introducing the particle swarm optimization algorithm, we can achieve adaptive search and optimization of clustering parameters, avoid the uncertainty caused by manually setting parameters, and improve the stability and accuracy of clustering results.

[0065] 3. Accelerated neighborhood search The traditional DBSCAN algorithm achieves density reachability through a global linear traversal, requiring the computation of its density for each sample point. The distance between all samples in the neighborhood has a time complexity of O(n). 2 When processing large-scale mixed wind field cluster index data, the computational load is large and the processing time is long.

[0066] To address this, a KD-tree is introduced to assist in fast neighborhood search, reducing the algorithm complexity to O(nlogn). The KD-tree uses a binary tree structure to represent hyperrectangular regions in N-dimensional space. Through alternating multi-dimensional partitioning and hyperplane segmentation, it narrows the search range and directly filters regions with distances less than [a certain value]. The point, and for Subtrees with no overlap are skipped to reduce unnecessary computation. The fast clustering process based on KD-trees is as follows: Construct a KD tree by cyclically partitioning the cluster index dataset along 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.

[0067] Perform density-reachable point search; for unvisited point p: find p using a range query of the KD-tree. If the number of neighboring points is greater than or equal to Minpints, then p is the core point, forming a new cluster.

[0068] The cluster is recursively expanded until no new core point can be found.

[0069] The final algorithm flowchart is as follows Figure 7 As shown.

[0070] By constructing a spatial index structure and performing range queries, the number of distance calculations during the neighborhood search process is effectively reduced, thereby reducing the overall computational complexity of the algorithm and improving computational efficiency in large-scale wind farm scenarios.

[0071] Based on the improved DBSCAN algorithm, after completing parameter optimization and neighborhood search acceleration, the units are clustered and expanded through density reachability rules to obtain multiple unit clusters. The units in each cluster have similar operating characteristics and coupling relationships.

[0072] (III) Equivalent Parameter Aggregation After completing the unit clustering, in order to construct an equivalent model of the hybrid wind farm, it is necessary to aggregate the electrical and control parameters of the units within the same cluster to form equivalent unit parameters.

[0073] After grouping the turbines using the improved DBSCAN algorithm, it is necessary to aggregate the turbine parameters within the same cluster to construct an equivalent model. The specific aggregation method is as follows: 1) Generator parameters (29) In the formula, subscript i represents the parameters of the i-th wind turbine, subscript eq represents the aggregate parameters, S and P are the unit capacity and active power, respectively; n is the number of units in the group; R s R r X s X r These are the stator and rotor resistance and reactance, respectively.

[0074] 2) Shaft system parameters (30) In the formula, H g H t , respectively, are the rotor inertia constants of the wind turbine and generator; K and D are the shaft stiffness coefficient and damping coefficient, respectively.

[0075] 3) Parameters of the generator terminal transformer (31) In the formula, R Ti X Ti G Ti B Ti These are the resistance, reactance, conductance, and susceptance of the transformer at the generator terminal.

[0076] 4) Control parameters Control parameters are typically per-unit values ​​at the unit's own capacity. Based on the principle that the total regulation is equal under the same disturbance, the equivalent system control parameters are the capacity-weighted average of the control parameters of each unit. (32) In the formula K p_i K i_i These are the proportional and integral control parameters for the i-th unit, Z. v_i Let k be the virtual impedance of the i-th unit. q_i Let be the reactive voltage droop coefficient of the i-th generator unit.

[0077] 5) Collection lines In wind farms, different topologies are used between the turbines. The basic collector line wiring methods are mainly radial and trunk types. The equivalent impedance of a radial line is... (33) In the formula, I i Z i These represent the current flowing through the i-th line and the line impedance, respectively; P i This represents the active power flowing through the i-th line.

[0078] The equivalent impedance of the trunk line is (34).

[0079] By aggregating the parameters as described above, the equivalent unit maintains consistency with the original unit group in terms of power output characteristics and dynamic response characteristics, thereby ensuring the accuracy of the equivalent model.

[0080] III. Construction of Equivalence Model After parameter aggregation is completed, a multi-unit equivalent model of a hybrid wind farm is constructed based on the equivalent parameters. In the equivalent model, grid-connected units participate as voltage regulation sources in the grid connection point voltage establishment process, while grid-following units participate as current injection sources in the system current distribution. A closed-loop interaction relationship is formed through the grid connection point voltage as a coupling node, thereby reflecting the interaction between units through the coupled power term.

[0081] This implementation method constructs a multi-unit equivalent model that reflects the coupling characteristics of wind farms using a hybrid grid / rooted system. This model is achieved through analysis of the output characteristics of the wind farm, construction of a two-dimensional clustering index, improved DBSCAN clustering, and parameter aggregation. The method can simultaneously characterize both the inherent characteristics of the units and the interactions between them, making it suitable for power system transient analysis and engineering applications.

[0082] 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 hybrid wind farms considering grid-connection interaction characteristics, characterized in that, Includes the following steps: S1: Establish output characteristic models for grid-connected and grid-connected wind turbines, obtain the inherent operating parameters of each unit, and construct the interaction relationship between units based on the bidirectional coupling relationship between voltage and current; S2: Based on the output characteristic model, construct a clustered indicator system that includes inherent characteristic indicators of the unit and coupling and interaction characteristic indicators between units; S3: Based on the aforementioned clustering index system, the improved DBSCAN algorithm is used to cluster the wind turbine units to obtain multiple unit clusters; S4: Based on the unit cluster, the parameters of the wind turbines within the same cluster are aggregated to obtain equivalent parameters; S5: Construct a multi-unit equivalent model of a hybrid wind farm based on the equivalent parameters, wherein the equivalent model includes a coupling power term for characterizing the interaction between units.

2. The method according to claim 1, characterized in that: In step S2, the cluster index system includes a set of indexes for grid-connected generating units and a set of indexes for grid-following generating units. The set of indexes for grid-connected generating units includes grid voltage parameters, virtual impedance characteristic parameters, reactive voltage regulation parameters, and active power output parameters. The virtual impedance characteristic parameters are obtained through virtual admittance or equivalent impedance links in the grid-connected generating unit control system and are used to characterize the constraint relationship between the unit port voltage and current.

3. The method according to claim 1, characterized in that: The grid-connected unit index set includes grid voltage parameters, active power output parameters, low voltage ride-through control parameters, and current limiting parameters. The low voltage ride-through control parameters are determined by the grid-side converter control strategy of the unit and are used to characterize the reactive current injection capability during voltage dips. The current limiting parameters are used to constrain the maximum output current of the unit during faults.

4. The method according to claim 1, characterized in that: The inter-unit coupling and interaction characteristic index is constructed through the following process: Obtain parameters of the grid-connected unit's ability to regulate the voltage at the grid connection point; Obtain the current characteristic parameters injected by the grid-connected unit into the grid connection point; By combining the impedance or admittance characteristics of the electrical connection lines between units, the voltage regulation effect and the current injection effect are coupled and mapped to obtain a coupling characteristic index for characterizing the interaction strength between units.

5. The method according to claim 1, characterized in that: In step S3, the improved DBSCAN algorithm adaptively solves the clustering parameters by introducing a particle swarm optimization algorithm, wherein each particle corresponds to a combination of a neighborhood range parameter and a minimum sample point parameter, and iteratively updates the parameters within a preset range.

6. The method according to claim 5, characterized in that: In the particle swarm optimization process, a comprehensive evaluation function is constructed to evaluate the clustering results. The evaluation function is calculated based on the density of sample points within their respective clusters and the degree of separation between different clusters, and the optimal parameter combination is obtained through multiple rounds of iterative screening.

7. The method according to claim 1, characterized in that: The improved DBSCAN algorithm organizes the cluster index data by constructing a multi-dimensional spatial index structure. During the neighborhood search process, it filters the set of data points that meet the distance conditions through range queries and skips data branches that do not meet the conditions, thereby reducing the number of distance calculations.

8. The method according to claim 1, characterized in that: In step S3, cluster expansion based on density reachability rules includes marking sample points for access, performing neighborhood search, identifying core points and generating clusters, and recursively expanding neighborhood samples based on the core points until the clusters no longer expand.

9. The method according to claim 1, characterized in that: In step S4, the parameter aggregation process includes: The generator electrical parameters are weighted and synthesized according to the unit capacity; The shaft system parameters are aggregated based on equivalent inertia and damping characteristics; The parameters of the generator terminal transformer are combined according to resistance, reactance, conductance and susceptance. The control parameters are weighted and averaged according to the unit capacity ratio to ensure the consistency of the equivalent system under the same disturbance.

10. The method according to claim 1, characterized in that: In step S5, when constructing the multi-machine equivalent model: Grid-connected generating units will participate in the grid connection point voltage establishment process as voltage regulation sources. The grid-connected generating units will be used as current injection sources to participate in the system current distribution process. Using the grid connection point voltage as the coupling node, the voltage regulation behavior and current injection behavior are linked to form a closed-loop interactive relationship, and the interaction between units is characterized by the coupling power term.

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