A method, system, and medium for dynamic equivalent aggregation of wind farms considering sub-supersynchronous oscillation characteristics

Abstract

This invention relates to the field of smart grid technology, and discloses a dynamic equivalent aggregation method, system, and medium for wind farms that considers sub- to supersynchronous oscillation characteristics. The method calculates the impedance sensitivity of doubly-fed induction generator (DFIG) control parameters in the sub- / supersynchronous frequency band based on the finite difference method, identifying key control parameters affecting the system impedance characteristics. It performs an equivalent transformation on the wind farm collector network, converting the hybrid structure to a parallel structure, and groups the wind turbine output voltages according to their oscillation mode characteristics. Then, it uses a capacity-weighted method to obtain the initial parameters of the equivalent machine. Finally, it uses a particle swarm optimization algorithm to identify and optimize the key control parameters of the equivalent model. This invention's dynamic equivalent aggregation method for wind farms effectively preserves the dominant oscillation modes and key dynamic characteristics of wind farms in the sub- / supersynchronous frequency band, significantly improving the accuracy and efficiency of large-scale wind farm grid-connected oscillation simulation analysis.

Description

Technical Field

[0001] This invention relates to the field of smart grid technology, and in particular to power system modeling and simulation technology. Specifically, it relates to a method, system and medium for dynamic equivalent aggregation of wind farms that takes into account sub-supersynchronous oscillation characteristics. Background Technology

[0002] Modern large-scale wind farms typically consist of dozens or even hundreds of induction wind turbines, which are fed into the power grid through a collection system. However, with the continuous expansion of wind power grid connection and the application of series compensation transmission technology in long-distance power transmission, the interaction between wind farms and the power grid is becoming increasingly complex, leading to more frequent subsynchronous / supersynchronous oscillation (SSO) problems.

[0003] In electromagnetic transient simulation studies of wind farm grid connection, if a detailed model including the detailed control system and electrical components of each wind turbine is used, the number of system nodes will be extremely large, the amount of simulation calculation will increase exponentially, and the time consumption will be extremely long. This makes it difficult to meet the timeliness requirements of large-scale wind farm grid connection oscillation analysis. Therefore, establishing an accurate and efficient wind farm equivalent aggregation model has become the key to engineering applications.

[0004] Currently, the most widely used parameter aggregation method in wind farm equivalent modeling, both domestically and internationally, is based on unit capacity weighting. This method treats multiple wind turbines with similar operating conditions within a wind farm as a single large-capacity unit, and its parameters are typically calculated by weighted averaging based on the proportion of each unit's capacity to the total capacity. This method is simple to operate and has shown good applicability in studying the steady-state operating characteristics or low-frequency electromechanical transient characteristics of wind farms. However, existing capacity-weighted equivalent methods mainly focus on steady-state characteristics near the power frequency, and have significant limitations in studying the dynamic characteristics of subsynchronous / supersynchronous frequency bands covering a frequency range of several hertz to tens of hertz.

[0005] In practical subsynchronous / supersynchronous oscillation analysis, simple capacity-weighted processing often fails to accurately reflect the complex dynamic response of the system. Because the nonlinear influence of controller parameters on high-frequency impedance characteristics is ignored, equivalent models established using the traditional capacity-weighted method frequently exhibit oscillation mode frequency drift during simulation. This means the dominant oscillation frequency obtained in the simulation deviates significantly from the actual detailed model, leading to misjudgments of oscillation risk. Furthermore, when simulating the dynamic process after oscillation occurs, such models often exhibit problems such as excessively fast oscillation convergence speed and peak oscillation amplitudes that do not match the actual situation, failing to accurately reproduce the system's damping characteristics and extreme response. For multi-machine systems, simple single-machine equivalents can easily mask the modal differences between units on different collector branches, resulting in the loss of key local oscillation characteristics. Therefore, how to establish an equivalent modeling method that can significantly reduce computational load while accurately preserving the subsynchronous / supersynchronous oscillation modes and key dynamic characteristics of wind farms is a pressing technical challenge in the field of wind power grid-connected simulation. Summary of the Invention

[0006] Given that existing wind farm equivalent models are unable to accurately reflect the dynamic characteristics of sub- / super-synchronous frequency bands and that detailed model simulations involve excessive computational loads, this invention aims to provide a dynamic equivalent aggregation method for wind farms that considers sub- / super-synchronous oscillation characteristics. This method involves screening key control parameters, transforming the collector network structure, using oscillation mode grouping, and optimizing multi-objective parameters. During the optimization process, a comprehensive objective function is constructed that includes dynamic time warping distance, Pearson correlation coefficient, and peak relative error to minimize the difference in oscillation waveforms between the equivalent model and the detailed model. This results in the establishment of a high-precision wind farm equivalent model, effectively preserving the dominant oscillation modes and key dynamic characteristics of the wind farm in the sub- / super-synchronous frequency bands, and significantly improving the accuracy and efficiency of large-scale wind farm grid-connected oscillation simulation analysis.

[0007] According to a first aspect of the present invention, a dynamic equivalent aggregation method for wind farms that takes into account sub-supersynchronous oscillation characteristics is proposed, comprising the following steps:

[0008] Step 1: Construct the impedance model of the wind turbine in the subsynchronous / supersynchronous frequency band, and use the finite difference method to calculate the impedance sensitivity of the wind turbine control parameters by applying small perturbations to the reference parameters. Based on the impedance sensitivity analysis, select the key control parameters that have the most significant impact on the impedance characteristics of the subsynchronous / supersynchronous frequency band.

[0009] Step 2: Perform topology transformation on the wind farm collector network, transforming the radial hybrid collector network into a fully parallel structure in which the branches of each wind turbine are connected in parallel to the common junction point.

[0010] Step 3: Based on the parallel structure obtained by topological transformation, group the wind turbines in the wind farm so that the turbines in the same group have consistent dynamic response characteristics, while preserving the modal differences between different groups of wind turbines.

[0011] Step 4: Based on the wind turbine clustering results, the capacity-weighted aggregation method is used to aggregate the wind turbines in each cluster to obtain the preliminary equivalent model of the wind farm corresponding to each cluster.

[0012] Step 5: Using the particle swarm optimization algorithm, with the goal of minimizing the comprehensive objective function, the selected key control parameters are optimized and identified to obtain the final dynamic equivalent model of the wind farm that can accurately reproduce the subsynchronous / supersynchronous oscillation modes and amplitude characteristics.

[0013] According to a second aspect of the present invention, a computer system is provided, comprising:

[0014] One or more processors;

[0015] The memory stores operable instructions that, when executed by the one or more processors, cause the one or more processors to perform operations, including the process of performing the wind farm dynamic equivalent aggregation method taking into account the sub-supersynchronous oscillation characteristics of the foregoing embodiments.

[0016] In a third aspect of the present invention, a computer-readable storage medium is provided for storing a computer program comprising instructions / instruction set executable by one or more processors, the instructions / instruction set, when executed by the one or more processors, implementing the aforementioned method for dynamic equivalent aggregation of wind farms taking into account sub-supersynchronous oscillation characteristics.

[0017] The significant advantages of the above embodiments of the present invention, which take into account the sub-supersynchronous oscillation characteristics, compared with the prior art, are as follows:

[0018] (1) Compared with the traditional capacity weighting method, the wind farm dynamic equivalent aggregation method of the present invention effectively corrects the frequency shift of the dominant oscillation mode of the equivalent model through parameter optimization, reduces the harmonic distortion rate at the characteristic frequency, can accurately reproduce the oscillation amplitude and convergence trend of the detailed model, and improves the ability to retain sub / supersynchronous oscillation characteristics.

[0019] (2) The wind farm dynamic equivalent aggregation method of the present invention introduces a comprehensive objective function including DTW, correlation coefficient and peak error, which overcomes the defect of traditional error sum of squares being sensitive to phase shift, so that the optimized model performs well in waveform similarity, trend consistency and extreme point matching degree, and improves the robustness of the equivalent model fitting.

[0020] (3) By grouping and aggregation and parameter optimization, large-scale wind farms are simplified into a small number of equivalent units. While significantly reducing the amount of simulation calculations, the dynamic characteristics of the sub / supersynchronous frequency bands are still fully preserved, taking into account both calculation efficiency and accuracy. This provides an efficient and accurate modeling tool for the analysis of grid-connected oscillations in wind farms.

[0021] It should be understood that all combinations of the foregoing concepts and the additional concepts described in more detail below may be considered part of the inventive subject matter of this disclosure, provided that such concepts do not contradict each other. Furthermore, all combinations of the claimed subject matter are considered part of the inventive subject matter of this disclosure.

[0022] The foregoing and other aspects, embodiments, and features of the teachings of the present invention will be more fully understood from the following description in conjunction with the accompanying drawings. Other additional aspects of the invention, such as features and / or beneficial effects of exemplary embodiments, will become apparent from the following description or may be learned through practice of specific embodiments according to the teachings of the present invention. Attached Figure Description

[0023] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown in the various figures may be denoted by the same reference numeral. For clarity, not every component is labeled in each figure. Embodiments of various aspects of the invention will now be described by way of example and with reference to the accompanying drawings.

[0024] Figure 1 This is an overall flowchart of the wind farm dynamic equivalent aggregation method that takes into account the sub-supersynchronous oscillation characteristics according to an embodiment of the present invention.

[0025] Figure 2 This is an impedance sensitivity analysis curve of the proportional coefficient and phase-locked loop parameters of the RSC (rotor-side converter) current controller of the wind turbine in an embodiment of the present invention.

[0026] Figure 3 This is an impedance sensitivity analysis curve of the proportional coefficient and phase-locked loop parameters of the wind turbine GSC (grid-side converter) current controller in an embodiment of the present invention.

[0027] Figure 4 This is an impedance sensitivity analysis curve of the integral coefficients of the wind turbine GSC and RSC current controllers in an embodiment of the present invention.

[0028] Figure 5 This is a comparison diagram of the topology of the wind farm collector network before and after the transformation in an embodiment of the present invention, where (a) is the radial hybrid form before the transformation and (b) is the parallel form after the transformation.

[0029] Figure 6This is a steady-state equivalent circuit diagram of a wind turbine generator (DFIG) used to calculate the equivalent impedance of a branch in an embodiment of the present invention.

[0030] Figure 7 This is a schematic diagram illustrating the principle of the parallel transformation process of the wind farm power collection network in an embodiment of the present invention.

[0031] Figure 8 This is a grid-connected topology diagram of a wind turbine generator set used for single-unit equivalent verification in an embodiment of the present invention.

[0032] Figure 9 This is a comparison chart of the output voltage amplitude at the grid connection point between the single-machine equivalent model and the detailed model obtained by the traditional capacity-weighted aggregation method in this embodiment of the invention.

[0033] Figure 10 This is a comparison chart of the spectrum analysis of the output voltage amplitude between the single-machine equivalent model and the detailed model obtained by the traditional capacity-weighted aggregation method in this embodiment of the invention.

[0034] Figure 11 This is a comparison chart of the output voltage amplitude at the grid connection point between the single-machine equivalent model and the detailed model obtained by the parameter optimization method of this invention in this embodiment of the invention.

[0035] Figure 12 This is a comparison chart of the spectrum analysis of the output voltage amplitude between the single-machine equivalent model and the detailed model obtained by the parameter optimization method of this invention in this embodiment of the invention.

[0036] Figure 13 This is a comparison diagram of the dynamic response of the active power output of the single-machine equivalent model before and after parameter optimization in the embodiments of the present invention.

[0037] Figure 14 This is a schematic diagram of the topology and equivalent modeling of a multi-machine wind farm system in an embodiment of the present invention.

[0038] Figure 15 This is a spectrum analysis diagram of the output voltage amplitude of each wind turbine in the multi-machine system of this invention embodiment;

[0039] Figure 16 This is a comparison chart of the output voltage amplitude of the multi-machine equivalent model at the grid connection point before and after parameter optimization in an embodiment of the present invention.

[0040] Figure 17 This is a comparison chart of the spectrum analysis of the output voltage amplitude of each group in the multi-machine equivalent model before and after parameter optimization in the embodiments of the present invention. Detailed Implementation

[0041] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0042] Various aspects of the invention are described in this disclosure with reference to the accompanying drawings, which illustrate numerous illustrative embodiments. The embodiments of this disclosure are not necessarily intended to encompass all aspects of the invention. It should be understood that the various concepts and embodiments described above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0043] Combined with appendix Figure 1 The example shown illustrates a wind farm dynamic equivalent aggregation method considering sub-supersynchronous oscillation characteristics according to an embodiment of the present invention, comprising the following steps:

[0044] Step 1: Construct the impedance model of the wind turbine in the subsynchronous / supersynchronous frequency band, and use the finite difference method to calculate the impedance sensitivity of the wind turbine control parameters by applying small perturbations to the reference parameters. Based on the impedance sensitivity analysis, select the key control parameters that have the most significant impact on the impedance characteristics of the subsynchronous / supersynchronous frequency band.

[0045] Step 2: Perform topology transformation on the wind farm collector network, transforming the radial hybrid collector network into a fully parallel structure in which the branches of each wind turbine are connected in parallel to the common junction point.

[0046] Step 3: Based on the parallel structure obtained by topological transformation, group the wind turbines in the wind farm so that the turbines in the same group have consistent dynamic response characteristics, while preserving the modal differences between different groups of wind turbines.

[0047] Step 4: Based on the wind turbine clustering results, the capacity-weighted aggregation method is used to aggregate the wind turbines in each cluster to obtain the preliminary equivalent model of the wind farm corresponding to each cluster.

[0048] Step 5: Using the particle swarm optimization algorithm, with the goal of minimizing the comprehensive objective function, the selected key control parameters are optimized and identified to obtain the final dynamic equivalent model of the wind farm that can accurately reproduce the subsynchronous / supersynchronous oscillation modes and amplitude characteristics.

[0049] Therefore, this invention first performs sensitivity analysis on the control parameters of wind turbine generators based on the finite difference method. Sensitivity is defined as the partial derivative of the system impedance with respect to the input parameters, and the rate of change of the output impedance is estimated by small perturbations in the input parameters. By calculating the impedance sensitivity in the subsynchronous / supersynchronous frequency band, key control parameters that significantly affect the system impedance characteristics are identified. Combined with... Figure 2 , Figure 3 , Figure 4As shown in the figure, the analysis indicates that the RSC (rotor-side converter) side parameters have a significantly greater impact on the wind turbine impedance characteristics than the GSC (grid-side converter) side parameters, and the proportional coefficient has a greater impact than the integral coefficient. Therefore, in the embodiments of this invention, the RSC current controller proportional coefficient, the RSC phase-locked loop proportional coefficient, and the integral coefficient are selected as key control parameters.

[0050] Secondly, for the hybrid structure caused by the radial topology typically used in wind farm collection networks, this invention performs an equivalent transformation. For example... Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown, based on the principle of maintaining consistent steady-state voltage at the turbine terminals before and after the transformation, the hybrid-connected collector network is transformed into a standardized parallel connection. Specifically, by calculating the steady-state equivalent impedance of the branch where the wind turbine is located, it is combined with the corresponding line impedance and then decomposed into equivalent impedances connected in series in each branch. Ultimately, this achieves a parallel structure where each wind turbine is connected to the point of common coupling (PCC) through a step-up transformer and the transformed collector network's equivalent impedance, providing a topological basis for subsequent clustering and aggregation.

[0051] Then, a spectral analysis was performed on the output voltage amplitude of each turbine in the wind farm to extract the dominant oscillation mode. Based on the similarity of the dominant oscillation frequencies, turbines with similar oscillation modes were grouped into the same subgroup. For each subgroup, the initial parameters of the equivalent wind turbine were calculated using a parameter aggregation method based on turbine capacity weights. Each subgroup was considered equivalent to one wind turbine, and the rotor inertia, damping coefficient, and control parameters of the equivalent turbine were all weighted averages.

[0052] Finally, using operational data from a detailed wind farm model under subsynchronous / supersynchronous oscillation conditions, a comprehensive objective function was constructed. Particle swarm optimization (PSO) was then employed to optimize and identify key control parameters of the equivalent model. The comprehensive objective function considered three metrics: Dynamic Time Warping Distance (DTW), Pearson correlation coefficient (R), and peak relative error. DTW was used to address the time-domain offset of the oscillation waveform, R was used to assess trend consistency, and σ was used to measure the matching degree of key extreme points. By minimizing the comprehensive objective function, the optimal combination of controller parameters was obtained.

[0053] As an optional implementation, in step 1, an impedance model of the wind turbine in the subsynchronous / supersynchronous frequency band is constructed, and sensitivity is defined as the partial derivative of the system impedance with respect to the input parameters, in order to characterize the degree of influence of the input parameters on the impedance characteristics.

[0054] Then, the sensitivity is approximated by the finite difference method. By applying a small perturbation to the reference parameter, the difference in system impedance before and after the perturbation is calculated and combined with the increment of the small perturbation to obtain the sensitivity.

[0055] Based on impedance sensitivity analysis, the key control parameters that have the most significant impact on the impedance characteristics of the subsynchronous / supersynchronous frequency band are selected: the proportional coefficient of the RSC current controller, the proportional coefficient of the RSC phase-locked loop, and the integral coefficient of the RSC phase-locked loop.

[0056] It should be understood that grid-connected oscillation analysis of wind turbine generators (DFIGs) involves numerous control parameters, and performing full-dimensional identification of all parameters would lead to the curse of computational dimensionality. Therefore, this embodiment first introduces a sensitivity analysis method to quantitatively assess the influence of each control parameter on the system impedance characteristics. Sensitivity is defined as the partial derivative of the system impedance Z with respect to the input parameter x, expressed as: ;

[0057] To reduce computational complexity in complex discrete systems, the embodiments of the present invention employ the finite difference method (FMD) for approximate calculations.

[0058] As an example, the specific calculation process is as follows:

[0059] First, the original system impedance Z(x0) under the unperturbed condition is calculated based on the reference parameter x0; then, a small perturbation Δx is applied to the target parameter, and the perturbed system impedance Z(x0 + Δx) is calculated; finally, the sensitivity is obtained using the following difference formula:

[0060] S(x)≈[Z(x0+ Δx) - Z(x0) ] / Δx.

[0061] The sign of the sensitivity value S(x) reflects the correlation between the parameter and the impedance: a positive value indicates that the impedance increases with the increase of the parameter, while a negative value indicates the opposite.

[0062] This embodiment constructs an impedance model of the wind turbine in the subsynchronous / supersynchronous frequency band, and selects parameters such as the proportional / integral coefficients of the current controller and the proportional / integral coefficients of the phase-locked loop for analysis.

[0063] The analysis results show that the sensitivity of the RSC-side parameters is all above 10. -3 The order of magnitude of the difference significantly affects impedance characteristics; while the sensitivity of the GSC side parameters is on the order of 10. -4 The sensitivity of the integral coefficient is significantly lower than that of the RSC side; furthermore, the sensitivity of the integral coefficient is above 10 on both the RSC and GSC sides. -5The impact is minimal, being on the order of magnitude. Specifically, analysis revealed an inflection point in the sensitivity sign change of the RSC side parameters at 15Hz; that is, before 15Hz, the impedance decreases with increasing parameters, while after 15Hz, it increases with increasing parameters. Based on the above analysis, this embodiment ultimately identifies the RSC current controller proportional coefficient, the RSC phase-locked loop proportional coefficient, and the RSC phase-locked loop integral coefficient as the key parameters affecting the wind turbine impedance characteristics, and uses them as the variables to be identified for subsequent equivalent model parameter optimization.

[0064] Because wind farm collection systems typically employ a radial topology, each turbine is interconnected with the grid, making it impossible to directly apply a unified single-unit equivalent model. Therefore, this embodiment proposes a network transformation method based on the principle of constant steady-state turbine terminal voltage. In step 2, a topology transformation is performed on the wind farm collection network, converting the radially interconnected network into a fully parallel structure where each wind turbine branch is connected in parallel to the point of common coupling. This includes:

[0065] The steady-state equivalent impedance of the wind turbine body is calculated and combined with the corresponding line impedance. Under the constraint of keeping the steady-state voltage of the turbine terminals consistent before and after the transformation, the radial hybrid collector network is transformed into a fully parallel structure in which each wind turbine branch is connected to the common junction point by iterative correction of the equivalent impedance.

[0066] As an optional implementation, the process of topology transformation of the collector network includes:

[0067] Step 2.1: Based on the steady-state equivalent circuit of the wind turbine, set the rotor-side equivalent voltage source to zero, and calculate the equivalent impedance Z of the nth wind turbine body. gen_n And combine it with the corresponding line impedance to obtain the total branch impedance;

[0068] Step 2.2: Transform the original hybrid structure into a parallel structure, decompose the original line impedance and connect it in series to each wind turbine branch. Based on the principle that the terminal voltages before and after the transformation are equal, establish the following equation:

[0069] U term = U PCC + I branch ·Z eq ;

[0070] Among them, U term To change the terminal voltage of the previous unit, U PCC I is the transformed point of common coupling voltage. branch Z is the branch current. eq The equivalent impedance of the transformed branch is used; the equivalent impedance of each branch is corrected through iterative calculation until the collector network is transformed into a structure in which each wind turbine branch is connected in parallel to the common junction point.

[0071] The core constraint of the collector network transformation is to maintain the consistency of the steady-state voltage at the machine terminal before and after the transformation, as shown in the above U. term = U PCC + I branch ·Z eq Constrained, U term U represents the unit's terminal voltage before the conversion. PCC Z represents the transformed voltage at the point of common coupling. eq The equivalent impedance of the transformed branch is characterized, and the equivalent impedance of the wind turbine is iteratively corrected by calculating the correction value ΔZ. new = Z old +ΔZ, until the hybrid circuit is completely transformed into a pure parallel circuit. After the transformation, each wind turbine is connected to the PCC bus through a step-up transformer and a corrected collector network equivalent impedance, such as... Figure 8 As shown.

[0072] For multi-machine systems, direct aggregation can mask the oscillation differences between different units. This embodiment adopts a strategy of first grouping and then aggregating.

[0073] Based on the parallel structure obtained by topological transformation, the output voltage amplitude of each wind turbine in the wind farm is analyzed by spectrum to obtain the dominant oscillation mode frequency in the voltage amplitude curve;

[0074] Based on the similarity of the dominant oscillation frequencies, wind turbines are grouped together. Units with similar dominant oscillation modes are grouped into the same group, so that units in the same group have consistent dynamic response characteristics, while preserving the modal differences between different groups of wind turbines.

[0075] Taking an example of an embodiment with 11 generating units, analysis revealed two main oscillation modes in the system: Mode 1 (subsynchronous 30.29Hz / supersynchronous 69.71Hz) and Mode 2 (subsynchronous 42.57Hz / supersynchronous 57.43Hz). Based on the spectral characteristics, the generating units were divided into three groups: units 1-4 were dominated by Mode 2, units 5-8 were dominated by Mode 1, and units 9-11 were dominated by Mode 1 with a small amount of Mode 2.

[0076] By grouping wind turbines based on the dominant oscillation mode, it is ensured that the turbines within the same group have similar dynamic response characteristics.

[0077] Furthermore, in step 4, based on the wind turbine clustering results, for each cluster, it is equivalent to a single unit. The capacity-weighted aggregation method is used to aggregate the wind turbines within each cluster to obtain the preliminary equivalent model of the wind farm corresponding to each cluster, including the following processes:

[0078] Based on the capacity-weighted aggregation method, wind turbines in each subgroup are aggregated. The ratio of the single unit capacity to the total capacity of the subgroup is used as the weighting coefficient. The weighted average values ​​of the moment of inertia and damping coefficient, stator and rotor impedance parameters and PI controller parameters in the rotor motion equation of the equivalent wind turbine are calculated respectively. These are used as initial values ​​to establish a preliminary equivalent model of the wind farm. Each subgroup corresponds to a preliminary equivalent model of the wind farm.

[0079] As a concrete example, the process of cluster aggregation based on the capacity-weighted aggregation method includes:

[0080] Assuming that the rotational speed of all wind turbines within each cluster is the same, the equivalent rotor moment of inertia of the wind turbines... and damping coefficient Calculate according to the following formulas respectively:

[0081] ;

[0082] ;

[0083] In the formula, S i S is the rated capacity of the i-th fan in the group. sum H represents the total capacity of all wind turbines within the cluster. i D i Let be the rotor moment of inertia and damping coefficient of the i-th fan, respectively;

[0084] The parameters of the PI controller in the equivalent wind turbine control system are calculated according to the following formula:

[0085] ;

[0086] In the formula, K PI_eq For the equivalent wind turbine PI controller parameters, K PI_i The parameters are for the PI controller of the i-th fan.

[0087] Similarly, PI controller parameters (such as the proportional coefficient K) p Integral coefficient K i The equivalent transformer capacity is also linearly superimposed according to capacity weight. The equivalent transformer capacity is the sum of the box-type transformer capacities in the detailed model, and the impedance parameters are calculated based on the principle of parallel circuits.

[0088] Traditional capacity-weighted models often suffer from oscillation frequency shifts (e.g., the dominant mode shifts from 25.6Hz to 28Hz) and amplitude errors. To address this issue, this embodiment introduces the PSO algorithm to correct the aforementioned key control parameters.

[0089] To overcome the sensitivity of traditional error sum-of-squares functions to phase shift, this invention constructs a comprehensive objective function F based on dynamic time warping distance, Pearson correlation coefficient, and peak relative error. fitness , is represented as:

[0090] F fitness = ω1·DTW + ω2·(1-R) ​​+ ω3·σ ;

[0091] In the formula, ω1, ω2, and ω3 are weighting coefficients;

[0092] Wherein, DTW is the Dynamic Time Warping Distance, used to quantify the temporal similarity between the output waveform of the equivalent model and the output waveform of the detailed model. It finds the optimal alignment path between the two time series through dynamic programming, which allows the waveform to be stretched or translated on the time axis, and is used to effectively solve the temporal offset problem of oscillating waveforms; R is the Pearson correlation coefficient, used to evaluate the trend consistency of the two waveform curves, and its value ranges from [-1,1].

[0093] σ is the peak relative error, used to quantify the degree of deviation at key extreme points of the waveform, with a focus on the maximum oscillation amplitude of the unit. Its calculation formula is:

[0094] σ =|(P peak_sin - P peak_mea ) / P peak_mea |;

[0095]

[0096] Among them, P peak_sin To determine the peak value of the waveform in the equivalent model simulation, P peak_mea The peak value of the measured waveform for the detailed model.

[0097] In step 5, the process of optimizing and identifying the selected key control parameters using the particle swarm optimization algorithm includes the following steps:

[0098] (a) Initialize the particle swarm, set the population size and maximum number of iterations, and configure the search range of the parameters to be identified as [-50%, +50%] of the capacity-weighted aggregate value;

[0099] (b) Calculate the fitness value of each particle, i.e., the comprehensive objective function F. fitness The value;

[0100] (c) Update the individual optimal position p of the particle based on the fitness value. best and the global optimal position g best ;

[0101] (d) Update the particle's velocity v and position x, using the following update formula:

[0102]

[0103]

[0104] In the formula, r1, r2 are random numbers, r1, r2∈[0, 1]; ω is the inertia weight, and c1, c2 are learning factors;

[0105] (e) Repeat steps (b) to (d) until the parameter convergence termination condition is met, and output the global optimal position g. best The optimal combination of key control parameters is used to obtain the final dynamic equivalent model of the wind farm.

[0106] In practice, the PSO algorithm parameters are set as follows: particle population size is set to 20, maximum number of iterations is set to 50; learning factors c1=c2=2; inertia weight ω decreases linearly from 0.9 to 0.4. The search range for the parameters to be identified is set to the range of [-50%, +50%] of the capacity-weighted aggregate value.

[0107] When the improvement rate of the fitness function decreases by less than 1% for five consecutive generations or the number of iterations reaches the upper limit, the optimization stops, and the output is the result that makes the comprehensive objective function F... fitness The smallest optimal parameter combination.

[0108] Combined with appendix Figures 9-17 As shown, we constructed a detailed simulation system including wind turbine generators, step-up transformers, and collector networks for testing, to verify the effectiveness and engineering applicability of the proposed dynamic equivalent aggregation method for wind farms based on sensitivity analysis and parameter optimization. The simulation was set at t=3.5s, with a 25% series compensation capacitor added at the grid connection point to trigger subsynchronous / supersynchronous oscillations of the system. The voltage output oscillation trajectory and active power dynamic response at the grid connection point were used as the main observations. The performance of the single-unit equivalent model and the multi-unit cluster equivalent model was compared and analyzed in depth from two dimensions: time-domain waveform fitting degree and frequency-domain modal consistency.

[0109] As one example, single-machine equivalence verification, combined with Figures 9-13As shown, four wind turbines with different operating states and control parameters were selected as the objects to be aggregated. When using the traditional capacity-weighted aggregation method to establish an equivalent model, the simulation results revealed obvious limitations. Specifically, the detailed model before aggregation showed obvious dominant oscillation modes at 25.6Hz and 74.4Hz; however, the corresponding oscillation mode frequencies of the traditional equivalent model shifted to 28Hz and 72Hz, respectively, showing a large frequency deviation. In addition, the traditional model showed a faster oscillation convergence speed in the time domain than the actual situation, and the peak value of the oscillation amplitude was larger, indicating that simple capacity weighting cannot accurately preserve the dynamic damping characteristics of the system in the subsynchronous / supersynchronous frequency band.

[0110] To address the aforementioned problems, the equivalent model was modified using the parameter optimization method proposed in this invention. As shown in the accompanying drawings, during the optimization process, the particle swarm optimization algorithm adaptively adjusted key control parameters based on the comprehensive objective function. For example, the d-axis proportional coefficient of the RSC current controller was corrected from 0.25 (capacity-weighted calculation) to 0.3503, the q-axis proportional coefficient from 1.96 to 1.6368, and the RSC phase-locked loop integral coefficient from 20.71 to 27.8820. Figure 9 , Figure 10 , Figure 11 , Figure 12 As shown, the optimized simulation results demonstrate that the equivalent model established in this invention exhibits extremely high consistency with the measured data of the detailed model in terms of output voltage amplitude waveform, and the retention rate of oscillation amplitude is significantly improved. Spectrum analysis further confirms that the frequency offset of the dominant oscillation mode in the optimized model is significantly reduced, and the harmonic distortion rate at the characteristic frequency is also effectively improved. Simultaneously, combined with… Figure 13 As shown, output active power is introduced as an auxiliary verification index. The results show that the optimized equivalent model is highly consistent with the original model in terms of active power trajectory, which verifies the dynamic fidelity of the method in multidimensional physical quantities.

[0111] As one example, multi-machine cluster equivalence verification, combined with Figures 14-17As shown, in the multi-unit grouping equivalent verification, 11 units were divided into 3 groups according to modes. By performing spectrum analysis on the output voltage of each unit, two distinct dominant oscillation modes were identified in the system: Mode 1 (subsynchronous 30.29Hz / supersynchronous 69.71Hz) and Mode 2 (subsynchronous 42.57Hz / supersynchronous 57.43Hz). Based on the grouping strategy of this invention, the units were divided into three groups. Simulation results show that the three equivalent groups after parameter optimization accurately retain the complex oscillation characteristics of their respective groups. Specifically, equivalent group 1 successfully retains the original unit group's dominant oscillation mode 2, while accurately reflecting the small amount of Mode 1 components; equivalent group 2 accurately reproduces the single dominant oscillation mode 1; and equivalent group 3 accurately simulates the mixed oscillation characteristics dominated by Mode 1 and accompanied by a small amount of Mode 2 components.

[0112] In summary, compared with traditional methods, the dynamic equivalent aggregation method for wind farms based on sensitivity analysis and parameter optimization proposed in this invention not only effectively eliminates frequency drift but also accurately reproduces the oscillation attenuation trend and amplitude envelope under multimodal coupling. Verification results fully demonstrate that this method simplifies large-scale wind farms to a small number of equivalent units, significantly reducing the computational load of simulations while maintaining extremely high modeling accuracy, thus meeting the practical needs of wind farm grid connection / supersynchronous oscillation analysis.

[0113] Based on the above embodiments of the dynamic equivalent aggregation method for wind farms based on sensitivity analysis and parameter optimization, the present invention also proposes a computer system, comprising: one or more processors; and a memory for storing operable instructions.

[0114] When the instruction is executed by the one or more processors, it causes the one or more processors to perform an operation, which includes the process of executing the wind farm dynamic equivalent aggregation method taking into account the sub-supersynchronous oscillation characteristics of the foregoing embodiments.

[0115] In conjunction with the above embodiments of the dynamic equivalent aggregation method for wind farms based on sensitivity analysis and parameter optimization, the present invention also proposes a computer-readable storage medium storing a computer program, wherein the computer program includes instructions / instruction sets executable by one or more processors, and the instructions / instruction sets, when executed by the one or more processors, implement the process of the dynamic equivalent aggregation method for wind farms taking into account sub-supersynchronous oscillation characteristics of any of the foregoing embodiments.

[0116] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for dynamic equivalence aggregation of wind farms considering sub-super synchronous oscillation characteristics, characterized in that, The method comprises the following steps: Step 1, constructing an impedance model of the wind turbine in the sub / super synchronous frequency band, and calculating impedance sensitivity of the control parameter of the wind turbine by applying a small perturbation to the reference parameter by using the finite difference method, and screening the key control parameters most significantly affecting the impedance characteristics in the sub / super synchronous frequency band according to the impedance sensitivity analysis; Step 2, topological transformation is performed on the power collection network of the wind farm, and the power collection network in the radial mixed structure is transformed into a complete parallel structure in which each wind turbine branch is connected in parallel to a common connection point; Step 3, based on the parallel structure obtained by the topological transformation, the wind turbines in the wind farm are grouped, so that the wind turbines in the same group have consistent dynamic response characteristics, and the modal differences of the wind turbines in different groups are retained; Step 4, based on the grouping result of the wind turbines, the wind turbines in each group are aggregated by using a capacity-weighted aggregation method, and a preliminary equivalent model of the wind farm corresponding to each group is obtained; Step 5, by using a particle swarm optimization algorithm, the key control parameters screened are optimized and identified to minimize the comprehensive objective function, and finally a wind farm dynamic equivalent model capable of accurately reproducing the sub / super synchronous oscillation mode and amplitude characteristics is obtained.

2. The method of claim 1, wherein the method further comprises: In step 1, an impedance model of the wind turbine in the sub / super synchronous frequency band is constructed, and the sensitivity is defined as the partial derivative of the system impedance to the input parameter, which is used to represent the influence degree of the input parameter on the impedance characteristics; Then the sensitivity is approximately solved by using the finite difference method, the system impedance difference before and after the perturbation is calculated by applying a small perturbation to the reference parameter, and the sensitivity is obtained by combining the small perturbation increment; According to the impedance sensitivity analysis, the key control parameters most significantly affecting the impedance characteristics in the sub / super synchronous frequency band are screened: the proportional coefficient of the RSC current controller, the proportional coefficient of the RSC phase-locked loop, and the integral coefficient of the RSC phase-locked loop.

3. The method of claim 1, wherein the method further comprises: In step 2, the topological transformation is performed on the power collection network of the wind farm, and the power collection network in the radial mixed structure is transformed into a complete parallel structure in which each wind turbine branch is connected in parallel to a common connection point, including: The steady-state equivalent impedance of the wind turbine body is calculated, and the corresponding line impedance is combined, and under the constraint condition that the steady-state voltage at the terminal before and after the transformation is consistent, the equivalent impedance is iteratively corrected, so that the power collection network in the radial mixed structure is transformed into a complete parallel structure in which each wind turbine branch is connected in parallel to a common connection point.

4. The method of claim 3, wherein the method further comprises: The process of the topological transformation of the power collection network comprises: Step 2.1, based on the steady-state equivalent circuit of the wind turbine generator, set the equivalent voltage source on the rotor side to zero, calculate the equivalent impedance Z of the nth wind turbine generator gen_n , and combine it with the corresponding line impedance to obtain the total branch impedance; Step 2.2, transforming the original mixed structure into a parallel structure, decomposing and connecting the original line impedance in series to each wind turbine branch, and establishing an equation based on the principle that the terminal voltages before and after the transformation are equal: U term = U PCC + I branch ·Z eq ; wherein U term is the terminal voltage of the generator before transformation, U PCC is the voltage at the point of common coupling after transformation, I branch is the branch current, and Z eq is the equivalent impedance of the branch after transformation; the equivalent impedance of each branch is corrected through iterative calculation until the collection network is transformed into a structure in which each wind turbine generator branch is connected in parallel to the point of common coupling.

5. The method of claim 3, wherein the method further comprises: In step 3, based on the parallel structure obtained by the topological transformation, the wind turbines in the wind farm are grouped, so that the wind turbines in the same group have consistent dynamic response characteristics, and the modal differences of the wind turbines in different groups are retained, including the following steps: The output voltage amplitude of each wind turbine in the wind farm is subjected to frequency spectrum analysis, and the dominant oscillation modal frequency in the voltage amplitude curve is obtained; According to the closeness of the dominant oscillation frequency, the wind turbine is grouped, and the wind turbines with similar dominant oscillation modes are divided into the same group, so that the wind turbines in the same group have consistent dynamic response characteristics, and the modal differences of different groups of wind turbines are retained.

6. The method of claim 1, wherein the method further comprises: In step 4, based on the wind turbine grouping result, the wind turbines in each group are aggregated by using the capacity-weighted aggregation method to obtain the preliminary equivalent model of the wind farm corresponding to each group, including the following processes: Based on the capacity-weighted aggregation method, the wind turbines in each group are aggregated, and the weighted average values of the moment of inertia and damping coefficient in the rotor motion equation, the stator-rotor impedance parameters and the PI controller parameters of the equivalent wind turbine are calculated as the initial values to establish the preliminary equivalent model of the wind farm, and each group corresponds to obtain a preliminary equivalent model of the wind farm.

7. The method of claim 6, wherein the method further comprises: In step 4, the process of grouping and aggregation based on the capacity-weighted aggregation method includes: Assuming that the rotational speed of each wind turbine in each cluster is consistent, the rotor moment of inertia of the equivalent wind turbine and the damping coefficient are calculated according to the following formulas, respectively: ； ； where S i is the rated capacity of the i-th fan in the subgroup, S sum is the total capacity of all fans in the subgroup, H i , D i are the moment of inertia and damping coefficient of the rotor of the i-th fan, respectively. The PI controller parameters in the equivalent wind turbine control link are calculated according to the following formula: ； where K PI_eq is the equivalent wind turbine PI controller parameter, K PI_i is the i-th wind turbine PI controller parameter.

8. The method of aggregating dynamic equivalents of a wind farm considering sub- hyper-synchronous oscillation characteristics according to any of claims 1-7, characterized in that, In step 5, a comprehensive objective function F based on dynamic time warping distance, Pearson correlation coefficient and relative error of peak is constructed fitness is expressed as: F fitness = ω1·DTW + ω2·(1-R) + ω3·σ ; In the formula, ω1, ω2, ω3 are weight coefficients; DTW is a dynamic time warping distance, which is used to quantify the time domain similarity between the output waveform of the equivalent model and the output waveform of the detailed model, and the optimal alignment path of the two time series is found through dynamic programming; R is a Pearson correlation coefficient, which is used to evaluate the trend consistency of two waveform curves, and the value range is [-1, 1]; σ is a peak relative error, which is used to quantify the deviation degree of the key extreme points of the waveform, and the calculation formula is: σ = |(P peak_sin - P peak_mea ) / P peak_mea |; ； where P peak_sin is the peak value of the equivalent model simulation waveform, and P peak_mea is the peak value of the detailed model measured waveform.

9. The method of claim 8, wherein the method further comprises: In step 5, the process of optimizing and identifying the selected key control parameters by using the particle swarm optimization algorithm includes the following steps: (a) initialize the particle swarm, set the population size, the maximum number of iterations, and configure the search interval of the to-be-identified parameters as [-50%, +50%] of the capacity-weighted aggregation value; (b) calculating a fitness value for each particle, i.e. the value of the composite objective function F fitness . (c) updating the individual best position p of the particle according to the fitness value best and the global best position g best ; (d) update the velocity v and position x of the particle, and the update formula is ； ； In the formula, r1, r2 are random numbers, r1, r2 ∈ [0, 1]; ω is an inertia weight, c1, c2 are learning factors; (e) repeating steps (b) to (d) until a parameter convergence termination condition is met, outputting a global optimal position g best As the optimal key control parameter combination, the final wind farm dynamic equivalent model is obtained.

10. A computer system, characterized by including: One or more processors; A memory stores instructions that can be operated, which, when executed by the one or more processors, cause the one or more processors to perform operations, the operations including executing the process of the wind farm dynamic equivalent aggregation method considering the sub-super synchronous oscillation characteristics according to any one of claims 1-9.

11. A computer readable storage medium storing a computer program, characterized in that, The computer program includes instructions / instruction sets that can be executed by one or more processors, which, when executed by the one or more processors, implement the process of the wind farm dynamic equivalent aggregation method considering the sub-super synchronous oscillation characteristics according to any one of claims 1-9.

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