Multi-dimensional comparison method for subsynchronous oscillation of direct-drive wind power plant grid-connected system

Abstract

The invention relates to the technical field of grid-connected stability analysis of a new energy power system, and discloses a multi-dimensional comparison method for subsynchronous oscillation of a direct-driven wind power plant grid-connected system. The method comprises the following steps: constructing a whole-system small-signal model covering a wind power plant to a receiving-end power grid under a unified working condition and disturbance, and extracting a theoretical frequency and a damping ratio of a dominant subsynchronous oscillation mode; synchronously acquiring a time domain response of the observed electrical quantity, and extracting a corresponding identification frequency and a damping ratio by using a Prony algorithm after preprocessing; carrying out modal pairing on the dominant oscillation frequency directly extracted from the time domain signal as a reference and a theoretical and identification result to form a candidate theoretical modal and a candidate identification modal; calculating a frequency difference, a damping ratio difference and a Prony fitting quality error among the candidate modals, if the frequency difference, the damping ratio difference and the Prony fitting quality error all meet a threshold value, determining that the three-dimensional result alignment is successful, and outputting a high-confidence parameter set; according to the subsynchronous oscillation identification method and device, the consistency and accuracy of a subsynchronous oscillation identification conclusion are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of grid-connected stability analysis of new energy power systems, in particular to a multi-dimensional comparison method for subsynchronous oscillation of a grid-connected system of a direct-drive wind farm. BACKGROUND

[0002] With the rapid development of the new energy industry, direct-drive wind farms are often far away from load centers and need to be connected to weak power grids at the receiving end through long-distance transmission lines, resulting in low short-circuit ratios and strong coupling characteristics of the grid-connected system, which easily excites subsynchronous oscillation under disturbance, seriously threatening the safe and stable operation of the power grid.

[0003] Existing subsynchronous oscillation identification and verification technologies mainly include small signal eigenvalue analysis, time domain spectral analysis, and Prony algorithm modal identification, but have obvious defects: the small signal model is often simplified and equivalent, missing key coupling characteristics, leading to deviation of modal parameter evaluation from reality; time domain analysis relies on artificial experience and lacks a unified quantitative benchmark, with strong subjectivity in determination; the Prony algorithm is sensitive to data preprocessing and noise, and is prone to false modes, and there is no engineering quality judgment and error correction process; various methods are independently developed, the input conditions and output caliber are not unified, and there is a lack of multi-dimensional mutual verification mechanism, with poor consistency and reproducibility of the conclusions, making it difficult to meet the demand for reliability and reproducibility of the results in engineering applications.

[0004] Therefore, there is an urgent need for a multi-dimensional collaborative comparison technical solution to solve the technical problems of existing technologies and improve the accuracy and engineering applicability of subsynchronous oscillation identification and verification. SUMMARY

[0005] To solve the above technical problems, the present application provides a multi-dimensional comparison method for subsynchronous oscillation of a grid-connected system of a direct-drive wind farm, which is used to improve the accuracy, consistency and engineering usability of subsynchronous oscillation identification and verification.

[0006] The present application provides a multi-dimensional comparison method for subsynchronous oscillation of a grid-connected system of a direct-drive wind farm, which comprises: Step S1: Under the same disturbance conditions, a full-system small signal model covering the key control links of the wind farm, the step-up link, the long-distance transmission line and the receiving end power grid is constructed, and eigenvalue calculation is performed based on the small signal model to extract the theoretical frequency value and the theoretical damping ratio value of the dominant subsynchronous oscillation mode; Step S2: For the target grid-connected system, the observed electrical quantities of the subsynchronous oscillation characteristics are obtained, the time domain response signal after disturbance of the observed electrical quantities is preprocessed, a fitting model of the Prony algorithm is constructed, and the identification frequency value and the identification damping ratio value of the dominant subsynchronous oscillation mode are extracted from the preprocessed time domain response signal based on the fitting model; Step S3: Directly extract the dominant oscillation frequency from the standardized preprocessed time-domain response signal. Using the dominant oscillation frequency as a reference, extract the mode with the closest frequency from the theoretical frequency value and the identified frequency value respectively to form candidate theoretical mode and candidate identified mode. Step S4: Calculate the absolute value of the frequency difference and the absolute value of the damping ratio difference between the candidate theoretical mode and the candidate identified mode, as well as the fitting quality error of the Prony algorithm parameter identification module. If the absolute value of the frequency difference, the absolute value of the damping ratio difference, and the fitting quality error all meet the threshold conditions, then the three-dimensional analysis results are determined to be successfully aligned. Step S5: If the threshold condition is not met, the consistency alignment is determined to have failed, and exception handling is performed.

[0007] Compared with the prior art, the beneficial effects of this application are at least as follows: This application provides a multi-dimensional comparison method for subsynchronous oscillations in grid-connected systems of direct-drive wind farms. First, a high-precision small-signal model of the entire system is established under unified conditions, and theoretical parameters are extracted, ensuring the accuracy of theoretical analysis from the source. Robust Prony parameter identification is performed on the standardized preprocessed time-domain signal to obtain data-driven results that directly reflect the actual system response. Using the objectively extracted dominant oscillation frequency in the time domain as a unified benchmark, accurate pairing of theoretical and identified modes is achieved, solving the problem of difficulty in correlating results from different dimensions. By calculating the frequency difference, damping ratio difference, and fitting quality error and performing threshold judgment, quantitative consistency verification of the analysis results in the theoretical, identified, and time-domain dimensions is achieved. When the verification is successful, a high-confidence fusion parameter set can be directly output.

[0008] When verification fails, the provided exception handling process, including the finite recalculation and degradation output mechanism of the Prony algorithm, ensures that the analysis process can continue even when some results deviate, and outputs reference conclusions and difference information that can be used for engineering review. The whole method forms a standardized verification process with unified input, quantified process and verifiable conclusions, which significantly improves the accuracy, reliability and engineering practical value of subsynchronous oscillation identification and verification. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart of a multi-dimensional comparison method for subsynchronous oscillations in a direct-drive wind farm grid-connected system, as described in an embodiment of this application. Figure 2 This is a schematic diagram of the original time-domain response signal waveform in an embodiment of this application; Figure 3 This application demonstrates the fitting effect of the Prony algorithm on the preprocessed time-domain signal in its embodiments. Figure 4 This is a flowchart illustrating the alignment determination process of the three-dimensional analysis results in an embodiment of this application. Detailed Implementation

[0011] This application provides a multi-dimensional comparison method for subsynchronous oscillations in a direct-drive wind farm grid-connected system. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0012] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of a multi-dimensional comparison method for subsynchronous oscillations in a direct-drive wind farm grid-connected system, as described in this application, includes: Step S1: Under the same preset operating conditions and the same disturbance conditions, construct a small-signal model of the entire system covering the key control links of the wind farm, the boost link, the long-distance transmission line and the receiving-end power grid, and calculate the eigenvalues ​​based on the small-signal model to extract the theoretical frequency value and theoretical damping ratio value of the dominant secondary synchronous oscillation mode.

[0013] In step S1, a full-system small-signal model is constructed, covering key control links of the wind farm, the booster link, long-distance transmission lines, and the receiving-end power grid. This includes integrating the converter control system of the wind turbine, the impedance characteristics of the two-stage booster transformer, the long-distance transmission lines, and the receiving-end power grid into a full-system small-signal model using a linearization method. The long-distance transmission lines adopt a resistance-inductance-capacitance model, and a mathematical model is established based on the dq rotating coordinate system. The mathematical model is expressed as follows: ,in, This refers to the turns ratio of a two-stage step-up transformer. Let R be the equivalent capacitance to ground in the resistor-inductor-capacitor model, and L be the equivalent inductance in the resistor-inductor-capacitor model. , These are the d-axis and q-axis components of the output voltage of the grid-side converter, respectively. The power grid synchronization angular velocity output by the phase-locked loop. , These are the d-axis and q-axis components of the current flowing through long-distance transmission lines, respectively. , These are the d-axis and q-axis components of the current at the output side of the grid-side converter, respectively. , , , represent the d-axis and q-axis components of the equivalent voltage of the large power grid, respectively, with t being the time point.

[0014] Specifically, regarding the engineering problem of subsynchronous oscillations (SSOs) easily induced in direct-drive wind farm grid-connected systems when new energy bases are connected to weak power grids via long-distance transmission, the effectiveness of existing small-signal analysis methods highly depends on the accuracy of the model. Traditional modeling methods often perform aggregated equivalents on the internal structure of the wind farm or adopt simplified models that ignore capacitance effects for transmission lines. Such simplifications are insufficient in characterizing the distributed parameter characteristics of long lines and the dynamic coupling relationship between the wind farm and the power grid. This may lead to deviations between the modal frequencies and damping ratios output by the small-signal model and the actual system response, thus affecting the reliability of subsequent SSO mechanism analysis and suppression strategy formulation. To improve the accuracy of theoretical analysis from the source and provide a reliable benchmark for subsequent multi-dimensional comparisons, this application constructs a full-system small-signal model covering key control links of the wind farm, booster links, long-distance transmission lines, and the receiving-end power grid. The core of this model is to establish a mathematical model that can accurately reflect the dynamic characteristics of the system, providing a theoretical benchmark for subsequent modal analysis and multi-dimensional comparisons. First, under unified preset operating conditions and the same disturbance conditions, the preset operating conditions specifically refer to the fixed wind power output level of the wind farm, the control parameters of the wind turbine converter such as the proportional-integral coefficient of the current loop, the proportional-integral coefficient of the voltage loop, and the voltage level at the grid connection point. The same disturbance conditions are limited to the same type of disturbance, such as line switching disturbance, power step disturbance, the same application time, duration, and disturbance amplitude, to ensure that the subsequent model calculations and analyses have a unified benchmark and avoid deviations in results due to differences in operating conditions or disturbances. When constructing the small-signal model of the entire system, a linearization method is used to integrate the converter control system of the wind turbine, the impedance characteristics of the two-stage step-up transformer, the long-distance transmission line, and the receiving-end power grid. The converter control system of the wind turbine is the core unit for realizing wind power conversion and grid connection control, covering the current loop and voltage loop control logic of the grid-side converter and the turbine-side converter, as well as the phase-locked loop (PLL) module. Its function is to adjust the output voltage and current to adapt to the grid operation requirements. The impedance characteristics of the two-stage step-up transformer are characterized by parameters such as short-circuit impedance and excitation impedance obtained by actual measurement. The transformer turns ratios K1 and K2 are the primary and secondary voltage ratios of the first-stage and second-stage step-up transformers, respectively, used to match the output voltage of the wind farm with the voltage levels of the transmission line and the receiving-end power grid. The receiving-end power grid is characterized by an equivalent impedance model, which is calculated based on the actual operating parameters of the power grid and reflects the voltage support capacity and equivalent load characteristics of the receiving-end power grid.

[0015] Long-distance transmission lines employ the Resistance-Inductance-Capacitance (RLC) model, an accurate equivalent model considering the distribution characteristics of line resistance, inductance, and capacitance to ground. Compared to the RL model, which only considers resistance and inductance, this model more comprehensively reflects the dynamic coupling characteristics of long-distance transmission lines. Its input data includes inherent line parameters such as line length, resistance per unit length R, inductance per unit length L, and capacitance to ground per unit length C. The model equations are derived using electromagnetic transient theory. The model is established based on the dq rotating coordinate system, a two-dimensional coordinate system rotating at the synchronous angular velocity of the power grid. This system converts AC quantities into DC quantities, simplifying the control and analysis process. In the mathematical equations… , These are the components of the grid-side converter output voltage on the d-axis and q-axis, respectively. The d-axis and q-axis are two orthogonal coordinate axes in the rotating coordinate system, i.e., the dq coordinate system, and are the core characterization parameters of the converter output voltage. The grid synchronization angular velocity output by the phase-locked loop is used to achieve synchronous operation between the converter and the grid, ensuring grid connection stability. , These are the d-axis and q-axis components of the current flowing through long-distance transmission lines, respectively. , These are the d-axis and q-axis components of the current at the output side of the grid-side converter, respectively. Together, they reflect the matching relationship between the line transmission current and the converter output current. , These are the d-axis and q-axis components of the equivalent voltage of the large power grid, directly reflecting the voltage level and phase characteristics of the receiving-end power grid. All these parameters are obtained through measured or simulated data acquisition. Substituting them into mathematical equations allows for a precise description of the dynamic changes in voltage and current in long-distance transmission lines. After integrating all components, the nonlinear equations within the entire system are linearized to eliminate the influence of nonlinear factors, ultimately forming a small-signal model of the entire system covering key control links of the wind farm, the boost link, long-distance transmission lines, and the receiving-end power grid.

[0016] By constructing a high-fidelity small-signal model covering all key components of the system and employing an accurate RLC circuit model, the method avoids the loss of key dynamic characteristics caused by simplified equivalent methods from the source. This method is carried out under uniform operating and disturbance conditions, ensuring the consistency of the modeling benchmark. The extracted theoretical modal parameters have higher accuracy, providing a reliable and reproducible theoretical benchmark for subsequent multi-dimensional comparative analysis.

[0017] In step S1, eigenvalue calculation is performed based on the small-signal model to extract the theoretical frequency and theoretical damping ratio of the dominant secondary synchronous oscillation mode. This includes: at a preset operating point, linearizing all nonlinear equations contained in the small-signal model of the entire system to obtain the linearized state-space equation of the entire grid-connected system. ,in, , These represent the small-signal disturbances of the d-axis and q-axis components of the output voltage of the grid-side converter, respectively. , These are the small-signal disturbances of the d-axis and q-axis components of the current flowing through long-distance transmission lines, respectively. , These are the small-signal disturbances of the d-axis and q-axis components of the current at the output side of the grid-side converter, respectively. , The small-signal disturbances are represented by the d-axis and q-axis components of the equivalent voltage of the large power grid. Eigenvalue decomposition is performed on the system state matrix formed by the linearized state-space equations to obtain all eigenvalues ​​of the system. Each eigenvalue contains a real-part attenuation factor and an imaginary oscillation angular frequency. The corresponding mode frequency is calculated based on the imaginary oscillation angular frequency, and the corresponding mode damping ratio is calculated based on the real-part attenuation factor and the imaginary oscillation angular frequency. Within a preset subsynchronous oscillation frequency range, modes with mode damping ratios less than a preset threshold are selected from all modes and defined as theoretical modes. The mode frequency and mode damping ratio corresponding to the theoretical modes are determined as the theoretical frequency and theoretical damping ratio of the dominant subsynchronous oscillation mode.

[0018] Specifically, after completing the construction of the small-signal model of the entire system, in order to accurately obtain the theoretical characteristic parameters of the system's subsynchronous oscillation and provide a reliable theoretical basis for subsequent mode pairing and alignment determination, it is necessary to perform eigenvalue calculation and extract the key parameters of the dominant subsynchronous oscillation mode based on the model. In specific implementation, linearization processing is first carried out at the preset operating point. The preset operating point is the system steady-state operating point corresponding to the unified wind power output, control parameters, and grid connection point voltage determined above. The converter control link covered in the small-signal model of the entire system includes current loop, voltage loop, phase-locked loop control logic, long-distance transmission line transmission link, etc. The equations describing the dynamic relationship between voltage and current are mostly nonlinear equations. These equations contain nonlinear terms such as the product and square of voltage and current variables, which cannot be directly used for eigenvalue analysis to obtain oscillation mode parameters. The core of linearization is to achieve the linear transformation of nonlinear equations through Taylor series expansion. Specifically, using the steady-state value corresponding to a preset operating point as a benchmark, each nonlinear equation is expanded using Taylor series at that benchmark point. The constant terms and first-order terms in the expansion are retained, while higher-order terms (second order and above) are ignored. This is because the values ​​of higher-order terms under small-signal disturbances are extremely small and their impact on the result is negligible. Simultaneously, each electrical quantity in the equation is decomposed into the sum of steady-state components and small-signal disturbances. Substituting these into the expansion eliminates the constant terms corresponding to the steady-state components, ultimately yielding a linear equation containing only small-signal disturbances and their first-order terms. The integration of all the linear equations forms the linearized state-space equation for the entire grid-connected system. In this equation, , These are the small-signal disturbances of the d-axis and q-axis components of the voltage at the output side of the grid-side converter, respectively, i.e., the difference between the steady-state voltage value and the instantaneous value after the disturbance; , These are the small-signal disturbances of the d-axis and q-axis components of the current flowing through long-distance transmission lines, respectively. , These are small-signal disturbances of the d-axis and q-axis components of the current at the grid-side converter output side, respectively, used to characterize the minute changes in current after the disturbance; , These are small-signal disturbances in the d-axis and q-axis components of the equivalent voltage of the main grid, respectively, reflecting minute fluctuations in the grid voltage.

[0019] Subsequently, eigenvalue decomposition is performed on the system state matrix constructed from the linearized state-space equations. The dimension of the system state matrix is ​​determined by the number of independent state variables in the system, and its rows and columns are directly related to the system state variables: each column corresponds to each independent state variable, and each column vector represents the "weight of the influence of a unit small-signal disturbance on the rate of change of all state variables in the corresponding column"; each row corresponds to the rate of change of each state variable, i.e., the terms on the left side of the linearized equation, and each row vector represents the "composite relationship of the rate of change of the state variable in the corresponding row due to the combined effect of small-signal disturbances of all state variables". Eigenvalue decomposition is a common method for diagonalizing matrices in linear algebra. This method decomposes the system state matrix into a set of eigenvalues ​​and eigenvectors. Each eigenvalue and its corresponding eigenvector jointly define a mode. A "mode" refers to the inherent dynamic response pattern of the system under small-signal disturbances. The eigenvectors describe the response amplitude ratio and phase relationship of each state variable, such as voltage and current disturbances, under this mode. The eigenvalues ​​determine the dynamic characteristics of this mode, and each eigenvalue contains a real-part attenuation factor. and the angular frequency of the imaginary part of the oscillation The real part decay factor determines the decay or divergence characteristics of the mode: when the real part is negative, the modal response will gradually decay over time, and the system tends to be stable; when the real part is positive, the modal response will continuously amplify over time, and the system is at risk of instability; when the real part is zero, the modal response maintains constant amplitude oscillation; the imaginary part oscillation angular frequency determines the oscillation frequency of the mode, which is directly related to the modal frequency value and reflects the oscillation speed of the inherent response mode.

[0020] Based on the imaginary part oscillation frequency Through formula The corresponding modal frequency value f is calculated. This modal frequency value is used to accurately characterize the oscillation rate of the corresponding mode and is the core characteristic parameter for identifying subsynchronous oscillations. It directly defines the number of periodic changes of the oscillation signal per unit time and can clearly distinguish subsynchronous oscillations from oscillations in other frequency bands; based on the real part attenuation factor... and the angular frequency of the imaginary part of the oscillation Through the formula: Calculate the corresponding modal damping ratio The modal damping ratio is used to characterize the decay rate of modal oscillations. A smaller value indicates that the oscillation is more difficult to decay and more prone to instability. Within a preset subsynchronous oscillation frequency range, such as 10-50Hz (this range is determined based on the engineering definition of subsynchronous oscillation in power systems), modes with mode damping ratios less than a preset threshold (e.g., 0.05) are selected from all modes and defined as theoretical modes. This preset threshold is set considering the critical requirements for oscillation suppression in engineering. Finally, the mode frequency and mode damping ratio corresponding to the theoretical modes are determined as the theoretical frequency and theoretical damping ratio of the dominant subsynchronous oscillation mode. The theoretical frequency and theoretical damping ratio of the dominant subsynchronous oscillation mode are quantized outputs obtained from eigenvalue analysis based on the small-signal model of the entire system. The theoretical frequency value indicates the specific frequency band in which the dominant subsynchronous oscillation is most likely to be excited under this specific operating condition. The theoretical damping ratio quantitatively characterizes the system's inherent damping capability for this oscillation mode, and its value is directly related to the decay rate of the oscillation amplitude: the smaller the damping ratio, the weaker the system's ability to suppress the oscillation, the easier it is for the oscillation to persist or grow, and the higher the corresponding risk of subsynchronous oscillation; conversely, the larger the damping ratio, the stronger the system stability. This set of theoretical parameters provides a key theoretical benchmark for subsequent oscillation risk assessment, influencing factor analysis, and suppression strategy formulation.

[0021] Through a refined linearization process and standardized eigenvalue calculation method, the core parameters of the dominant subsynchronous oscillation mode were accurately extracted, avoiding parameter distortion caused by traditional simplified linearization. At the same time, the interference of nonlinear factors on theoretical analysis was eliminated, providing a high-precision theoretical benchmark for mode pairing and alignment determination in subsequent multi-dimensional comparisons. This effectively solved the problem of large deviations between the analysis results of small-signal models and the actual response, and significantly improved the overall accuracy and engineering reliability of subsynchronous oscillation identification and verification.

[0022] Step S2: For the target grid-connected system, obtain the observed electrical quantities of the subsynchronous oscillation characteristics, preprocess the time-domain response signal of the observed electrical quantities after disturbance, construct the fitting model of the Prony algorithm, and extract the identification frequency value and identification damping ratio value of the dominant subsynchronous oscillation mode from the preprocessed time-domain response signal based on the fitting model.

[0023] Step S2 involves constructing a fitting model for the Prony algorithm, including: representing the preprocessed time-domain response signal as a discrete-time series. Where n is the sampling point index, a fitting model for the Prony algorithm is constructed. The fitting model is a linear combination of p exponentially decaying sinusoidal components. Based on the fitting model, the discrete time series is fitted to obtain the fitted signal: ,in, Let i represent the number of components in the fitted function, and i denote the modal component number. , , and Let represent the amplitude, attenuation factor, frequency, and initial phase of the i-th modal component, respectively, and N be the total number of sampling points of the signal. Denotes the complex coefficients of the i-th modal component. Let represent the complex exponential root of the i-th modal component.

[0024] Specifically, the theoretical modes calculated using the aforementioned small-signal model of the entire system need to be verified and identified using actual or simulated time-domain data. Key mode parameters of the subsynchronous oscillation are extracted from the system's time-domain response using parameter identification methods. In practice, firstly, for the target grid-connected system, electrical quantities that can sensitively reflect the characteristics of subsynchronous oscillations are selected as observations, including active power, current, or voltage at the grid connection point. After applying the same perturbation as set in the model calculation in step S1, the time-domain response waveforms of the observed electrical quantities are recorded using a data acquisition system to obtain the original time-domain response signal, such as... Figure 2 As shown, a typical original time-domain response signal waveform obtained from the simulation exhibits obvious oscillation decay characteristics after a disturbance is applied, for example, around t=0.5 seconds, with its oscillation frequency in the subsynchronous band. To ensure the accuracy of the identification results and the consistency of subsequent comparisons, the original signal needs to be standardized and preprocessed. The preprocessing process includes filtering and noise reduction, and data standardization: a low-pass filter is used to remove high-frequency noise interference, detrending processing is used to eliminate the DC component and slow drift component in the signal, and then the signal is resampled at a uniform sampling rate to finally obtain a regular discrete-time sequence. , where n is the sampling point number, n=0,1,…,N-1, and N is the total number of signal sampling points.

[0025] Subsequently, a fitting model for the Prony algorithm is constructed. The Prony algorithm is a mode identification method based on fitting exponentially decaying sinusoidal components. Its core principle is to decompose a complex time-domain response signal into a superposition of multiple independent modal components, each component corresponding to the dynamic characteristics of an oscillation mode. In this application, the fitting model is defined as a linear combination of p exponentially decaying sinusoidal components, where p is the number of fitting function components. This number needs to be reasonably set according to the signal complexity and the number of oscillation modes, and is usually determined by trial and error combined with information criteria, such as the AIC criterion. The typical value range is 8-20. The expression of the fitting model is: Where p is the preset model order, i.e., the number of fitted components, and i is the component number. The amplitude of the i-th modal component represents the intensity of the modal oscillation. It is the attenuation factor, which is directly related to the damping characteristics of the mode; The frequency of the i-th modal component is the oscillation frequency to be identified. The initial phase reflects the initial state of the modal oscillation; These are the complex coefficients of the i-th modal component, containing amplitude and phase information. Denotes the power of a complex exponential root, satisfying , The imaginary unit is the modulus, whose magnitude determines the modal decay rate, and whose argument corresponds to the oscillation frequency.

[0026] By using standardized signal preprocessing and scientific Prony algorithm modeling, the modal decomposition of the time-domain response signal was realized, and the core parameters of each oscillation component were accurately extracted. This provided reliable measured data support for subsequent pairing and alignment with theoretical parameters, effectively solving the problems of susceptibility to noise interference and unstable parameter extraction. It improved the accuracy and consistency of subsynchronous oscillation parameter identification and laid a data foundation for multi-dimensional comparison and verification.

[0027] In step S2, extracting the identification frequency and identification damping ratio of the dominant subsynchronous oscillation mode from the preprocessed time-domain response signal includes setting the fitting error function as follows: By using the least squares method, the fitting error function is minimized, and the parameters of each modal component are obtained. , , and The damping ratio of the i-th mode component is calculated based on the attenuation factor and frequency. Mode components whose frequencies are within the preset subsynchronous oscillation frequency band and whose damping ratios are less than the preset threshold are selected from all mode components and defined as the identification modes. The frequency and damping ratio corresponding to the identification modes are determined as the identification frequency value and identification damping ratio value of the dominant subsynchronous oscillation mode.

[0028] Specifically, after constructing the Prony algorithm fitting model, the first step is to set the fitting error function, which is used to quantize the original discrete time series. with model-fitted signal The smaller the error function value, the higher the degree of fidelity of the fitted signal to the original signal, and the closer the model parameters are to the actual oscillation characteristics. Essentially, it calculates the sum of squared differences between the original signal value and the fitted signal value at each sampling point, accumulating the deviations at discrete points into a global error index. This avoids misjudgment caused by the mutual cancellation of positive and negative deviations, providing a clear target for subsequent parameter optimization. For example... Figure 3As shown, the Prony algorithm fits the preprocessed time-domain signal. In the figure, the original signal curve represents the actual observed data after preprocessing, and the Prony-fitted signal curve represents the reconstructed signal after superimposing multiple exponentially decaying sinusoidal components identified by the Prony algorithm. It can be seen that within this time window, the Prony-fitted signal can track the oscillation decay trend of the original signal well, and the two basically overlap in waveform, which initially demonstrates the effectiveness of the Prony algorithm's identification results. The least squares method is used to solve for the fitting model parameters. The least squares method is an optimization method that achieves data fitting by minimizing the sum of squared errors. Its core idea is to adjust the model parameters to fit the error function. The minimum value is reached. The specific solution process is as follows: Substitute the expression of the Prony fitting model into the error function, and adjust the parameters... By taking the partial derivatives and setting them to zero, a system of linear equations about the parameters is obtained. This system of equations is then solved using matrix operations or iterative algorithms to finally obtain the amplitude of each modal component. Attenuation factor ,frequency and initial phase This ensures that the fitted signal matches the original time-domain response signal to the greatest extent possible.

[0029] Based on the attenuation factor obtained by the solution and frequency Calculate the damping ratio of the i-th modal component. The damping ratio is a core parameter characterizing the decay characteristics of oscillation modes, and its calculation formula is as follows: This formula is derived based on the physical relationship between the attenuation factor and the angular frequency. As the attenuation factor, The angular frequency of the mode is calculated. The larger the value, the faster the modal oscillation decays and the stronger the system stability; conversely, the smaller the value, the slower the oscillation decays and the more likely it is to cause continuous oscillation. Next, the identification modes are screened. First, a preset subsynchronous oscillation frequency band is set, consistent with step S1, typically 10-50Hz, to screen out frequencies. Modal components located within this frequency band are excluded from irrelevant modal interference such as power frequency and supersynchronous frequency bands; simultaneously, a preset threshold for the damping ratio is set, consistent with the theoretical modal screening threshold in step S1, typically set to 0.05, to further screen out damping ratios. Modal components below this threshold, due to their weak attenuation capabilities, are the core modes most likely to cause subsynchronous oscillations in the system; these are defined as the identified modes. Finally, the frequencies corresponding to the selected identified modes are... The identified frequency value of the dominant subsynchronous oscillation mode and the corresponding damping ratio were determined. The damping ratio is determined. If multiple identification modes exist, the amplitude is selected. The mode parameter with the highest contribution to the overall oscillation is used as the final output, ensuring that the parameters accurately reflect the actual characteristics of the dominant subsynchronous oscillation. The identified frequency and identified damping ratio of the dominant subsynchronous oscillation mode are quantified results extracted from the parameter identification of the preprocessed time-domain response signal based on the Prony algorithm. The identified frequency reflects the specific frequency band of the dominant subsynchronous oscillation observed in the actual system dynamic response, while the identified damping ratio quantitatively characterizes the actual decay characteristics of the observed oscillation in the time domain. Its value is directly calculated from the decay factor and frequency: a smaller damping ratio indicates a slower decay of the oscillation in the actual response and a higher risk of persistence; conversely, a larger damping ratio indicates rapid decay of the oscillation. This set of identified parameters provides a direct observation and quantitative description of the system's subsynchronous oscillation behavior from the perspective of actual data, providing an empirical basis for comparison and verification with theoretical analysis results.

[0030] By constructing a Prony fitting model and optimizing it using the least squares method, key modal parameters characterizing subsynchronous oscillations can be extracted with high precision from noisy time-domain response signals. This process ensures that the identification results focus on weakly damped risk modes of engineering concern by setting unified frequency bands and damping ratio thresholds for screening. Finally, the dominant mode is determined based on the amplitude, thereby effectively eliminating interference from irrelevant components. The obtained identified frequency and damping ratio values ​​directly and quantitatively reflect the true oscillation characteristics and attenuation capability of the system under actual disturbances, providing objective data for assessing oscillation risk and significantly improving the accuracy and engineering credibility of subsynchronous oscillation analysis conclusions.

[0031] Step S3: Directly extract the dominant oscillation frequency from the standardized preprocessed time-domain response signal. Using the dominant oscillation frequency as a reference, extract the mode with the closest frequency from the theoretical frequency value and the identified frequency value respectively to form candidate theoretical mode and candidate identified mode.

[0032] In step S3, directly extracting the dominant oscillation frequency includes: performing spectral analysis on the time-domain response signal, identifying spectral peaks with energy greater than a preset energy threshold or amplitude higher than a preset threshold within a preset subsynchronous oscillation frequency band, and determining the frequency corresponding to the spectral peak as the dominant oscillation frequency.

[0033] Specifically, to achieve quantitative comparison across the three dimensions of small-signal model, Prony algorithm identification, and time-domain observation, it is essential to first establish an objective, robust, and model-independent frequency benchmark to correlate analysis results from different sources. This frequency benchmark is directly extracted from the time-domain response signal after standardization preprocessing in step S2. Specifically, spectral analysis is used to transform the preprocessed time-domain signal into the frequency domain to visually reveal the concentration of signal energy at different frequencies. A common implementation is the application of the Fast Fourier Transform (FFT) algorithm. This algorithm efficiently decomposes the discrete-time signal into a superposition of sinusoidal components with different frequencies, amplitudes, and phases, thereby directly obtaining the discrete spectrum of the signal, i.e., the amplitude or energy of each frequency component. After obtaining the frequency domain distribution, the analysis focuses on the subsynchronous oscillation frequency band, such as 10Hz to 45Hz, which is pre-defined based on engineering experience. Within this band, spectral peaks significantly higher than the background noise are identified. Reasonable energy or amplitude thresholds are set, and the frequencies corresponding to the peaks with the strongest energy or highest amplitude are determined as the dominant oscillation frequency. This dominant oscillation frequency is directly derived from observational data, unaffected by model assumptions, and possesses objectivity and stability.

[0034] Subsequently, using this frequency as a benchmark, the matching deviation problem caused by the lack of a unified benchmark in modal pairing was solved, ensuring that both the candidate theoretical mode and the candidate identified mode correspond to the same dominant oscillation characteristic of the system. This provides an accurate pairing basis for subsequent consistency verification and alignment determination, and ensures the effectiveness and reliability of multi-dimensional comparative analysis.

[0035] In step S3, forming candidate theoretical modes and candidate identified modes includes: for all theoretical frequency values, calculating the absolute difference between each theoretical frequency value and the dominant oscillation frequency, and selecting the mode corresponding to the theoretical frequency value whose absolute difference is less than a preset threshold as a candidate theoretical mode; for all identified frequency values, calculating the absolute difference between each identified frequency value and the dominant oscillation frequency, and selecting the mode corresponding to the identified frequency value whose absolute difference is less than a preset threshold as a candidate identified mode.

[0036] Specifically, to effectively correlate and compare results from different analytical dimensions, the first step is to determine the most matching modal object based on the dominant oscillation frequency extracted from the time-domain signal, using both the small-signal model calculation results and the Prony algorithm identification results. For this purpose, a frequency pairing threshold is pre-set. This threshold defines the maximum acceptable deviation between the dominant oscillation frequency and the candidate modal frequency. Its value is determined by comprehensively considering the resolution of the spectral analysis, typically inversely proportional to the analysis time window length and engineering experience tolerance. For example, it is set by calculating the reciprocal of the analysis window and taking the larger of it and a preset minimum tolerance value, such as 0.1Hz. After obtaining the dominant oscillation frequency, a parallel screening process is executed. For all theoretical modes calculated from the small-signal model, the absolute difference between their theoretical frequency value and the dominant oscillation frequency is calculated for each mode. Modes whose difference does not exceed the frequency pairing threshold are then selected from all theoretical modes. If there is only one mode that meets this condition, then that mode is directly identified as a candidate theoretical mode. If there are multiple modes that meet the condition, then the one with the smallest absolute difference from the dominant oscillation frequency is selected as the candidate theoretical mode. If no mode meets the condition, then the currently unmatched theoretical mode is recorded. Using the exact same logic and threshold, all identified modes identified by the Prony algorithm are processed in parallel: the absolute difference between each identified frequency and the dominant oscillation frequency is calculated, modes with differences not exceeding the threshold are selected, and the one with the smallest difference is selected as the candidate identified mode. If no mode meets the condition, it is recorded accordingly.

[0037] This process, based on a unified time-domain observation benchmark, identifies a most relevant and directly comparable specific modal object for both theoretical analysis and data identification, namely the candidate theoretical modality and the candidate identification modality, thus establishing a clear input for the consistency quantification verification in subsequent steps.

[0038] Step S4: Calculate the absolute value of the frequency difference and the absolute value of the damping ratio difference between the candidate theoretical mode and the candidate identified mode, as well as the fitting quality error of the Prony algorithm parameter identification module. If the absolute value of the frequency difference, the absolute value of the damping ratio difference, and the fitting quality error all meet the threshold conditions, the three-dimensional analysis results are determined to be successfully aligned.

[0039] Step S4 includes: calculating the absolute value of the difference between any two of the frequency values ​​of the candidate theoretical mode, the candidate identified mode, and the dominant oscillation frequency, and taking the largest absolute value of the frequency difference as the final absolute value of the frequency difference; calculating the absolute value of the difference between the damping ratio of the candidate theoretical mode and the damping ratio of the candidate identified mode, and taking this as the absolute value of the damping ratio difference; the fitting quality error is the normalized reconstruction error of the Prony algorithm, which is obtained by analyzing the preprocessed time-domain response signal. Fitted signal generated by Prony algorithm The calculation is performed, and the formula is as follows: Where N is the total number of sampling points of the signal; the final absolute value of frequency difference, absolute value of damping ratio difference, and fitting quality error are compared with the preset frequency threshold, preset damping ratio threshold, and preset reconstruction error threshold. When all are less than or equal to the corresponding preset threshold, the threshold condition is satisfied, the three-dimensional analysis result is successfully aligned, and a high confidence parameter set containing the dominant oscillation frequency, the theoretical damping ratio value after alignment verification, and the identified damping ratio value is output.

[0040] Specifically, after screening and pairing candidate theoretical modes and candidate identification modes, a three-dimensional consistency check needs to be performed to determine the alignment between theoretical analysis and experimental identification results, ensuring high confidence of the output parameters. In practical implementation, such as... Figure 4 The diagram shows a flowchart of the alignment judgment process for the three-dimensional analysis results. First, various differences and fitting quality errors are calculated. One such calculation is the final absolute value of the frequency difference. Specifically, this involves extracting three frequency parameters: the frequency values ​​of the candidate theoretical mode, the frequency values ​​of the candidate identified mode, and the determined dominant oscillation frequency. The absolute value of the difference between any two of these parameters is calculated, resulting in three sets of absolute frequency difference values. The maximum value from these three sets is then selected as the final absolute frequency difference value. The core significance of this final absolute frequency difference value lies in quantifying the maximum deviation range of the three-dimensional frequency parameters (theoretical, measured, and directly extracted). Its magnitude directly reflects the degree of consistency of the three-dimensional frequency characteristics. If this value is within a preset threshold, it indicates that there is no significant discrepancy in the frequency analysis results across the three dimensions. The first step involves identifying discrepancies. If the value exceeds a preset threshold, it indicates that at least two dimensions of frequency results have excessive deviations, requiring re-verification of the model or identification process. This method comprehensively covers the frequency deviations of the theoretical, measured, and directly extracted dimensions, avoiding omissions caused by single-dimensional comparisons. The second step is calculating the absolute value of the damping ratio difference. This involves directly extracting the damping ratio values ​​of candidate theoretical modes and candidate identified modes, and calculating the absolute value of the difference between the two to quantify the degree of deviation between the theoretical and measured damping characteristics. The third step is calculating the fitting quality error. Here, the fitting quality error is the normalized reconstruction error of the Prony algorithm, which is used to evaluate the accuracy of the Prony fitting model in restoring the original time-domain signal. It is obtained by analyzing the preprocessed time-domain response signal. Fitted signal generated by Prony algorithm The calculation is obtained, specifically based on the calculation formula. The solution is performed, where N is the total number of sampling points of the signal, the numerator is the sum of squared errors between the original signal and the fitted signal, and the denominator is the sum of squared energy of the original signal. This normalization process can eliminate the influence of the signal amplitude on the error assessment, so that the fitting quality error has a unified and comparable standard.

[0041] Subsequently, various preset thresholds are set for threshold comparison. The preset frequency threshold is set in conjunction with the engineering accuracy requirements for identifying the subsynchronous oscillation frequency of the power system, and is usually set to 0.5~2Hz. The preset damping ratio threshold is set in conjunction with the reasonable deviation range between theoretical and measured damping ratios, and is usually set to 0.02~0.05. The preset reconstruction error threshold is set in conjunction with the engineering accuracy requirements for fitting the Prony algorithm, and is usually set to 0.05~0.1, i.e. 5%~10%. Each threshold can be adaptively adjusted according to the specific operating conditions and accuracy requirements of the target grid-connected system. The absolute values ​​of the final frequency difference, damping ratio difference, and fitting quality error obtained from the aforementioned calculations are compared with the corresponding preset frequency threshold, preset damping ratio threshold, and preset reconstruction error threshold, respectively. If all three conditions are simultaneously met—the absolute value of the final frequency difference being less than or equal to the preset frequency threshold, the absolute value of the damping ratio difference being less than or equal to the preset damping ratio threshold, and the fitting quality error being less than or equal to the preset reconstruction error threshold—then the threshold conditions are considered met, meaning the three-dimensional analysis results are successfully aligned. This signifies that the analysis results based on the theoretical analysis of the whole system small-signal model, the experimental identification based on the Prony algorithm, and the extraction of the dominant oscillation frequency based on spectral analysis have all met the engineering-preset consistency requirements in terms of frequency characteristics, damping characteristics, and fitting accuracy. This judgment provides high-confidence quantitative support for the risk assessment and suppression strategy formulation of the subsynchronous oscillation of the target grid-connected system. First, it verifies the effectiveness and practicality of the whole system small-signal model, which can be used as a basis for subsequent system operating condition optimization. The tool for analyzing subsynchronous oscillation characteristics in scenarios such as topology adjustments eliminates the need for repeated large-scale field measurements or simulations, significantly reducing analysis costs and timelines. Secondly, it confirms the accuracy of the Prony algorithm parameter identification process; its signal preprocessing standards, model order selection rules, and parameter screening thresholds can be solidified into a universal process for subsynchronous oscillation measurement and identification in similar grid-connected systems, providing a standardized reference for engineering applications. Thirdly, it outputs a high-confidence parameter set, which includes the dominant oscillation frequency, the aligned and verified theoretical damping ratio, and the identified damping ratio. The aligned and verified parameters correspond to the candidate theoretical mode and the candidate identified mode, ensuring that the output parameters possess both theoretical reliability and experimental accuracy. This high-confidence parameter set can directly guide the precise design of subsynchronous oscillation suppression measures. For example, it allows for configuring dedicated damping controller parameters for the dominant oscillation frequency, evaluating system stability margin based on the damping ratio, and defining risk warning thresholds, ensuring the suppression strategy is targeted and effective.

[0042] This three-dimensional alignment verification process achieves comprehensive consistency verification across three dimensions: theory, experimental results, and direct signal extraction. It effectively avoids parameter distortion caused by single-dimensional verification, ensures the confidence level of output parameters, and provides accurate and reliable quantitative basis for subsequent subsynchronous oscillation mechanism analysis and suppression strategy formulation.

[0043] Step S5: If the threshold condition is not met, the consistency alignment is determined to have failed, and exception handling is performed.

[0044] Step S5 includes: when the absolute value of the frequency difference, the absolute value of the damping ratio difference, or the fitting quality error exceeds the corresponding preset threshold, the Prony algorithm recalculation process is triggered. After each recalculation, the absolute value of the frequency difference, the absolute value of the damping ratio difference, and the fitting quality error between the current identification result and the candidate theoretical mode are recalculated, and it is re-determined whether the threshold condition is met. If the re-determined result still does not meet the threshold condition after the preset number of recalculations is reached, a reference parameter set is output based on the dominant oscillation frequency and the theoretical frequency value and theoretical damping ratio value corresponding to the candidate theoretical mode, and the difference information between the Prony algorithm identification result and the benchmark is recorded as the verification difference information.

[0045] Specifically, after completing the 3D alignment determination, if any one or more of the final absolute value of frequency difference, absolute value of damping ratio difference, or fitting quality error exceeds the corresponding preset threshold, the consistency alignment is deemed to have failed. At this point, an anomaly handling process is initiated to ensure the continuity and availability of the subsynchronous oscillation analysis results. In practice, when the Prony algorithm recalculation process is triggered, the re-identification work is mainly achieved through two core methods: adjusting the model order or the identification time window. This is to specifically address the deviation problems caused by improper parameter settings in the original identification process. For adjusting the model order, fine-tuning is required within a reasonable range based on the original Prony fitted model order: if the original order is too low (easily leading to mode omission), it is increased by 2-4; if the original order is too high (easily introducing spurious modes), it is decreased by 2-4. Simultaneously, the adjusted orders are evaluated using the AIC information criterion, and the order with the smallest fitting error and the most stable mode identification is selected as the new model order. The core of adjusting the identification time window is to optimize the analysis segment of the time-domain response signal: if the original time window does not fully cover the oscillation decay process, the time window is extended until the oscillation signal decays to less than 5% of the steady-state amplitude; if the original time window contains too much invalid data in the transition phase after disturbance, the time window is shortened, the transition data of the first 0.2 to 0.5 seconds is removed, and only the signal segment with stable oscillation characteristics is retained. At the same time, it is ensured that the number of sampling points in the adjusted time window is not less than 70% of the original number of sampling points to ensure the sufficiency of identification data.

[0046] After each adjustment of the model order or identification time window, the Prony algorithm is re-identified based on the optimized parameters of the time-domain response signal. After re-identification, the parameter extraction process in step S2 is repeated to obtain new identification frequency values, damping ratio values, and other parameters. Then, the candidate identification mode screening in step S3 is performed to determine new candidate identification modes. Subsequently, the absolute values ​​of the frequency difference and damping ratio difference between the candidate identification mode and the original candidate theoretical mode, as well as the new fitting quality error, are recalculated. The threshold comparison process in step S4 is repeated to determine whether the alignment conditions are met. To avoid infinite recalculation, a threshold for the number of recalculations needs to be preset. This threshold is set based on engineering efficiency and identification accuracy requirements, and is usually set to 3 to 5 times. If, within the preset number of recalculations, the result of a recalculation meets all threshold conditions, it is considered that the anomaly handling is successful, the alignment of the 3D analysis results is successfully determined, and the corresponding high-confidence parameter set is output. If, after reaching the preset number of recalculations, the result of the re-judgment still does not meet the threshold conditions, the Prony algorithm recalculation is stopped, and the fallback output mechanism is activated: based on the dominant oscillation frequency determined in step S3 and the theoretical frequency value and theoretical damping ratio value corresponding to the candidate theoretical mode obtained in step S1, a reference parameter set is output. Simultaneously, detailed records of the differences between the Prony algorithm's identification results and the baseline parameters are required as verification difference information. This includes the frequency values, damping ratios, differences from the baseline parameters and their percentages, fitting quality error values, parameter types and adjustment magnitudes during recalculation, etc. This difference information can be used for subsequent backtracking analysis of the root causes of deviations, such as verifying whether it is a modeling deviation of the small signal model under specific working conditions, excessive noise interference during time-domain signal acquisition, or the adaptability of the Prony algorithm to the characteristics of this system. This provides data support for subsequent optimization of modeling methods, improvement of identification algorithms, or enhancement of signal acquisition accuracy.

[0047] This anomaly handling process not only attempts to correct identification deviations to achieve alignment to the greatest extent possible, but also ensures the availability of output parameters when deviations cannot be corrected. At the same time, it retains deviation information to provide a basis for subsequent optimization, effectively improving the robustness and engineering practicality of the entire subsynchronous oscillation analysis process.

[0048] In summary, this application proposes a multi-dimensional comparative method for identifying and verifying subsynchronous oscillations in grid-connected systems of direct-drive wind farms. By constructing a collaborative analysis framework of "theoretical model calculation - data-driven identification - direct time-domain observation," it effectively solves the problems of unreliable and unverifiable conclusions caused by model simplification, noise sensitivity, or reliance on subjective experience in traditional single methods. This method first establishes a high-fidelity small-signal model of the entire system under unified operating conditions and disturbances, and extracts oscillation mode parameters from measured data based on the Prony algorithm and spectrum analysis, providing an accurate and comparable data foundation for multi-dimensional analysis. Subsequently, through mode pairing and quantization alignment based on the dominant time-domain oscillation frequency, cross-validation and consistency verification of results from different technical paths are achieved.

[0049] More importantly, this application designs an engineered anomaly handling mechanism that includes finite recalculation of the Prony algorithm and degraded output, ensuring that reliable conclusions with clear evidence and traceability information can still be output even when deviations occur during the analysis process. Ultimately, this method can output a set of high-confidence parameters verified across multiple dimensions, significantly improving the accuracy, consistency, and engineering usability of subsynchronous oscillation characteristic analysis, mechanism tracing, and risk assessment, providing strong technical support for the safe and stable operation of new energy grid-connected systems.

[0050] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0051] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0052] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A multi-dimensional comparison method for subsynchronous oscillation of direct-drive wind farm grid-connected system, characterized in that, The method comprises: Step S1: under unified preset operating conditions and same disturbance conditions, a full-system small signal model covering key control links of a wind farm, a step-up link, a long-distance power transmission line and a receiving end power grid is constructed, and based on the small signal model, eigenvalue calculation is performed to extract a theoretical frequency value and a theoretical damping ratio value of a dominant subsynchronous oscillation mode; Step S2: for a target grid-connected system, an observed electrical quantity of a subsynchronous oscillation characteristic is obtained, a time-domain response signal after disturbance of the observed electrical quantity is preprocessed, a fitting model of a Prony algorithm is constructed, and based on the fitting model, an identified frequency value and an identified damping ratio value of a dominant subsynchronous oscillation mode are extracted from the preprocessed time-domain response signal; Step S3: a dominant oscillation frequency is directly extracted from the preprocessed time-domain response signal, and based on the dominant oscillation frequency, a mode closest in frequency is extracted from the theoretical frequency value and the identified frequency value respectively to form a candidate theoretical mode and a candidate identified mode; Step S4: a frequency difference absolute value and a damping ratio difference absolute value between the candidate theoretical mode and the candidate identified mode are calculated, and a fitting quality error of a Prony algorithm parameter identification module is calculated, and if the frequency difference absolute value, the damping ratio difference absolute value and the fitting quality error all satisfy threshold conditions, it is determined that three-dimensional analysis result alignment is successful; Step S5: if the threshold conditions are not satisfied, it is determined that consistency alignment fails, and then exception handling is performed.

2. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 1, characterized in that, In step S1, the full-system small signal model covering key control links of a wind farm, a step-up link, a long-distance power transmission line and a receiving end power grid is constructed, comprising: The converter control system of the wind turbine, the impedance characteristics of the two-stage step-up transformer, the long-distance power transmission line and the receiving end power grid are integrated into a full-system small signal model through a linearization method; The long-distance transmission line adopts a resistance-inductance-capacitance model, and a mathematical model is established based on a d-q rotating coordinate system, and the mathematical model is expressed as: wherein, is a turns ratio of the two-stage step-up transformer, is an equivalent capacitance to ground in the resistance-inductance-capacitance model, R is an equivalent resistance in the resistance-inductance-capacitance model, and L is an equivalent inductance in the resistance-inductance-capacitance model, , are respectively d-axis and q-axis components of an outlet side voltage of a grid-side converter, is a grid synchronous angular velocity output by a phase-locked loop, , are respectively d-axis and q-axis components of a current flowing through the long-distance transmission line, , are respectively d-axis and q-axis components of an outlet side current of the grid-side converter, , are respectively d-axis and q-axis components of an equivalent voltage of a large power grid, and t is a time point.

3. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 2, characterized in that, In step S1, based on the small signal model, eigenvalue calculation is performed to extract a theoretical frequency value and a theoretical damping ratio value of a dominant subsynchronous oscillation mode, comprising: In a preset operating condition point, linearize all nonlinear equations contained in the full system small signal model to obtain linearized state space equations of the entire grid-connected system: wherein, , are small signal disturbances of d-axis and q-axis components of the voltage at the outlet side of the grid-side converter, , are small signal disturbances of d-axis and q-axis components of the current flowing through the long-distance transmission line, , are small signal disturbances of d-axis and q-axis components of the current at the outlet side of the grid-side converter, , are small signal disturbances of d-axis and q-axis components of the equivalent voltage of the large power grid. The system state matrix formed by the linearized state space equation is subjected to eigenvalue decomposition to obtain all eigenvalues of the system, each eigenvalue containing a real part attenuation factor and an imaginary part oscillation angular frequency; the corresponding mode frequency value is calculated according to the imaginary part oscillation angular frequency, and the corresponding mode damping ratio is calculated according to the real part attenuation factor and the imaginary part oscillation angular frequency; in a preset subsynchronous oscillation frequency range, the mode whose mode damping ratio value is less than a preset threshold is selected from all modes to be defined as a theoretical mode, and the mode frequency value and the mode damping ratio corresponding to the theoretical mode are determined as the theoretical frequency value and the theoretical damping ratio value of the dominant subsynchronous oscillation mode.

4. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 1, characterized in that, In step S2, the fitting model of the Prony algorithm is constructed, comprising: The pre-processed time-domain response signal is represented as a discrete time series where n is the sample point number, a fitting model of Prony algorithm is constructed, the fitting model is a linear combination of p exponential decay sinusoidal components, the discrete time series is fitted based on the fitting model to obtain a fitting signal: where is the number of fitting function components, i represents the number of modal components, , , and respectively represent the amplitude, the attenuation factor, the frequency and the initial phase of the i-th modal component, and N is the total number of signal sampling points, represents the complex coefficient of the i-th modal component, represents the complex exponential root of the i-th modal component.

5. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 4, characterized in that, In step S2, the identified frequency value and the identified damping ratio value of the dominant subsynchronous oscillation mode are extracted from the preprocessed time-domain response signal, comprising: The fitting error function is set as: The parameters of each modal component are obtained by solving the least square method to minimize the fitting error function 、 、 and The damping ratio of the i-th modal component is calculated according to the attenuation factor and the frequency. The modal component with a frequency in the preset subsynchronous oscillation frequency band and a damping ratio less than a preset threshold is screened from all modal components, and is defined as a recognized modal. The frequency and the damping ratio corresponding to the recognized modal are determined as a recognized frequency value and a recognized damping ratio value of the dominant subsynchronous oscillation modal.

6. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 1, characterized in that, The dominant oscillation frequency is directly extracted in step S3, including: The time domain response signal is subjected to spectral analysis, and a spectral peak with energy greater than a preset energy threshold or amplitude higher than a preset threshold is identified in a preset subsynchronous oscillation frequency band. The frequency corresponding to the spectral peak is determined as the dominant oscillation frequency.

7. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 6, characterized in that, The candidate theoretical modal and the candidate recognized modal are formed in step S3, including: For all theoretical frequency values, the absolute difference between each theoretical frequency value and the dominant oscillation frequency is calculated. The modal corresponding to the theoretical frequency value with an absolute difference less than a preset threshold is selected as a candidate theoretical modal. For all recognized frequency values, the absolute difference between each recognized frequency value and the dominant oscillation frequency is calculated. The modal corresponding to the recognized frequency value with an absolute difference less than a preset threshold is selected as a candidate recognized modal.

8. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 1, characterized in that, Step S4 includes: The absolute value of the difference between any two of the frequency value of the candidate theoretical modal, the frequency value of the candidate recognized modal, and the dominant oscillation frequency is calculated. The maximum frequency difference absolute value among the three is taken as the final frequency difference absolute value. The absolute value of the difference between the damping ratio value of the candidate theoretical modal and the damping ratio value of the candidate recognized modal is calculated as a damping ratio difference absolute value. The fitting quality error is a normalized reconstruction error of the Prony algorithm, and the preprocessed time domain response signal The fitting signal generated by the Prony algorithm The calculation formula is: Wherein, N is the total number of signal sampling points; The final frequency difference absolute value, the damping ratio difference absolute value, and the fitting quality error are compared with a preset frequency threshold, a preset damping ratio threshold, and a preset reconstruction error threshold. When all are less than or equal to the corresponding preset threshold, it is determined that the threshold condition is met, the three-dimensional analysis result is successfully aligned, and a high-confidence parameter set containing the dominant oscillation frequency, the theoretical damping ratio value, and the recognized damping ratio value after alignment verification is output.

9. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 1, characterized in that, Step S5 includes: When the frequency difference absolute value, the damping ratio difference absolute value, or the fitting quality error exceeds the corresponding preset threshold, a Prony algorithm recalculation process is triggered. After each recalculation, the frequency difference absolute value, the damping ratio difference absolute value, and the fitting quality error between the current recognition result and the candidate theoretical modal are recalculated, and it is re-determined whether the threshold condition is met. If the re-determined result still does not meet the threshold condition after a preset number of recalculation, a reference parameter set is output based on the dominant oscillation frequency and the theoretical frequency value and the theoretical damping ratio value corresponding to the candidate theoretical modal, and the difference information between the Prony algorithm recognition result and the reference is recorded as verification difference information.

10. The multi-dimensional comparison method for subsynchronous oscillation of direct drive wind farm grid integration system according to claim 9, characterized in that, The Prony algorithm recalculation process re-recognizes the time domain response signal. The re-recognition is achieved by adjusting the model order or the recognition time window. The total number of recalculation does not exceed a preset maximum number of recalculation.

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