Power system differential equation modeling method based on data driving

Abstract

The invention relates to the field of differential modeling, in particular to a power system differential equation modeling method based on data driving, which comprises the following steps: collecting time sequence data of a power system, extracting dynamic characteristics of the time sequence data, and preprocessing the time sequence data based on the dynamic characteristics to generate corresponding sequence pre-data; calculating an oscillation coefficient of the power system, selecting a differential equation form, determining a corresponding differential equation parameter, constructing a differential equation model corresponding to the power system to learn the sequence pre-data, generating simulation data within a preset time, and comparing the simulation data with real data corresponding to the preset time; the prediction accuracy of the generated differential equation model is compared with the accuracy threshold value, whether the differential equation model is adjusted or not is judged, the nonlinear relation can be learned from the time sequence data, the prediction performance of the model is objectively evaluated, the defects of the model are found in time, and the actual differential equation model is constructed.

Description

Technical Field

[0001] The present invention relates to the field of differential modeling, and in particular to a data-driven dynamic system differential equation modeling method. Background Art

[0002] Dynamical system modeling is an important field in engineering and scientific research, and is widely used in many systems such as mechanical, fluid, biological, and economic systems.

[0003] The dynamic characteristics of the time series data of the dynamic system are extracted through data-driven algorithms, and a differential equation model is constructed in combination with physical principles, which not only makes full use of data information but also retains the interpretability of the physical model.

[0004] Chinese patent application publication number: CN106227978A discloses a compressor blade suction surface primitive curve modeling method based on a second-order ordinary differential equation. After preprocessing the compressor blade primitive curve data, a second-order constant coefficient linear non-homogeneous ordinary differential system is selected for fitting to obtain the expression of the primitive curve. According to the requirements of the boundary conditions, the problem of obtaining a second-order curve that coincides with the first and last points of the given data is transformed into a two-point boundary value problem, and the implicit Euler method is selected to solve the middle point of the primitive curve to complete the reconstruction of the primitive curve. The invention solves the problem that the first-order system cannot guarantee the interpolation conditions of the first and last points at the same time, obtains a larger optimization operation space, and reduces the sensitivity to the parameter matrix. The invention can accurately interpolate the first and last points of the data scatter points, which has great advantages for the connection of the data scatter points of the slice or segment fitting, and can restore the shape of the compressor blade with high precision.

[0005] Chinese patent application publication number: CN113378310A discloses a fatigue crack propagation modeling method based on uncertain differential equations. For the crack propagation process considering crack closure and high-load hysteresis effects, firstly, based on uncertainty theory, the cognitive uncertainty of four aspects, namely physical properties, external factors, time dimension and threshold, is quantified, and a fatigue crack propagation model based on uncertain differential equations is constructed; then, the model parameters are determined by statistical analysis; then, the confidence reliability function is derived to evaluate the confidence reliability; finally, the crack propagation process and fatigue life are predicted. The above-mentioned fatigue crack propagation modeling method based on uncertain differential equations provided by the invention provides an option for reasonably quantifying cognitive uncertainty in fatigue crack propagation experiments, making the understanding of fatigue laws more accurate, and describing the crack propagation process based on uncertain differential equations, which helps to improve the accuracy of crack propagation and fatigue life prediction.

[0006] However, the above method has the following problems: when the system parameters change or the system structure changes, the model needs to be readjusted and has poor adaptability. Summary of the invention

[0007] To this end, the present invention provides a data-driven dynamic system differential equation modeling method to overcome the problem in the prior art that the model needs to be readjusted when the system parameters or the system structure change, resulting in poor adaptability.

[0008] To achieve the above object, the present invention provides a data-driven dynamic system differential equation modeling method, comprising: Collect time series data of the power system, where The time series data includes experimental measurement data, sensor data and numerical simulation results; The kinetic characteristics of the time series data are extracted using a data-driven algorithm, and the time series data are preprocessed based on the kinetic characteristics to generate corresponding sequence pre-data, wherein: The dynamic characteristics include the oscillation frequency, growth rate and fluctuation of the dynamic system; Calculating the oscillation coefficient of the power system using the dynamic characteristics, selecting a differential equation form according to a comparison result between the oscillation coefficient and the oscillation coefficient threshold, determining corresponding differential equation parameters, and constructing a differential equation model corresponding to the power system; The sequence prediction data is learned by using the differential equation model to generate simulation data within a preset time, and the simulation data is compared with the real data corresponding to the preset time to generate the prediction accuracy of the differential equation model, and the prediction accuracy is compared with the accuracy threshold, and it is determined whether to adjust the differential equation model according to the comparison result, wherein: The accuracy threshold is the minimum standard of the prediction accuracy of the differential equation model and is related to the driving performance of the power system.

[0009] Furthermore, the steps of collecting time series data of the power system include: Determine the measured variables and sampling frequency of the power system, where: The measured variables include physical variables and state variables; Continuously sampling the measurement variable according to the sampling frequency to obtain the time series data; The acquired time series data is stored in a data storage device.

[0010] Furthermore, the steps of extracting dynamic features using a data-driven algorithm include: Using a data-driven algorithm to analyze the time series data and extract corresponding feature vectors; Mapping the feature vector to an infinite dimensional linear space; The characteristic vectors are analyzed using linear algebra tools to extract corresponding dynamic characteristics.

[0011] Furthermore, the steps of preprocessing the time series data based on the dynamic characteristics include: Based on the kinetic characteristics, the time series data is standardized and corresponding sequence prediction data is generated; Wherein, the standardization process is to segment the time series data according to a standard cutting rate; The standard cutting rate is a cutting rate that can be recognized by the differential equation model, and for a single learning, the corresponding standard cutting rate is a single cutting rate.

[0012] Further, the step of calculating the oscillation coefficient of the dynamic system includes: Performing Fourier transformation on the dynamic characteristics and converting the dynamic characteristics into frequency domain data; Fitting the frequency domain data by a sparse regression algorithm to obtain a dynamic spectrum corresponding to the frequency domain data; The highest peak value of the dynamic spectrum is selected and output as the oscillation coefficient.

[0013] Further, when the oscillation coefficient of the power system is greater than the oscillation coefficient threshold, a high-order differential equation is selected, and when the oscillation coefficient of the power system is less than the oscillation coefficient threshold, a linear differential equation is selected.

[0014] Furthermore, the oscillation coefficient threshold is a critical value for judging the oscillation characteristics of the power system, and is related to the driving performance of the power system.

[0015] Furthermore, the steps of learning the sequence pre-data by the differential equation model include: According to the differential equation form, the corresponding differential equation parameters are determined to obtain the corresponding differential equation model: Inputting the preset time and the sequence pre-data into the differential equation model; The output result of the differential equation model at the corresponding preset time is calculated by a numerical solution method, and the output result is output as simulation data.

[0016] Furthermore, real data when the power system reaches the preset time is collected, and the real data is compared with the simulation data to generate a prediction accuracy of the differential equation model, and the prediction accuracy is compared with the accuracy threshold. When the prediction accuracy is greater than the accuracy threshold, the differential equation model is not adjusted.

[0017] Furthermore, when the prediction accuracy is less than the accuracy threshold, the differential equation parameters are adjusted using a gradient descent method.

[0018] Compared with the prior art, the present invention collects time series data of the power system, extracts the dynamic characteristics of the time series data, and pre-processes the time series data based on the dynamic characteristics to generate corresponding sequence pre-data, calculates the oscillation coefficient of the power system and selects the differential equation form, determines the corresponding differential equation parameters, constructs a differential equation model corresponding to the power system to learn the sequence pre-data, generates simulation data within a preset time, and compares the data with the real data corresponding to the preset time, generates a prediction accuracy of the differential equation model and compares it with the accuracy threshold, determines whether to adjust the differential equation model, can learn nonlinear relationships from time series data, objectively evaluate the prediction performance of the model, promptly discover the deficiencies of the model, and construct a differential equation model that meets the actual situation.

[0019] Furthermore, by determining the measured variables of the power system, including physical variables and state variables, the operating status and physical characteristics of the power system can be fully reflected, providing a rich and accurate data basis for subsequent modeling and analysis, and avoiding model deviations caused by omitting important variables. Selecting an appropriate sampling frequency can ensure that the collected data can reflect the dynamic changes of the system without generating unnecessary data redundancy due to too high a sampling frequency or losing important information due to too low a sampling frequency. This helps to improve the quality and availability of data.

[0020] Furthermore, by using data-driven algorithms to analyze time series data, hidden patterns and laws can be automatically discovered from a large amount of data without relying on prior physical model assumptions. This method can better adapt to the nonlinear characteristics and dynamic changes of complex dynamic systems, thereby extracting more accurate feature vectors. This automatic adaptability enables the model to better handle different types of dynamic systems and has stronger generalization capabilities.

[0021] Furthermore, by standardizing the time series data based on dynamic characteristics and segmenting it according to the standard cutting rate, the quality and consistency of the data can be significantly improved, and the learning efficiency and prediction accuracy of the model can be enhanced. This process not only simplifies the model construction and adjustment process, but also improves the reliability and stability of the system, providing strong support for the modeling and analysis of dynamic systems.

[0022] Furthermore, through this process of calculating the oscillation coefficient of the dynamic system, key information reflecting the dynamic characteristics of the system can be effectively extracted from the dynamic characteristics, providing an important basis for the selection of differential equation models and parameter determination. This process not only improves the extraction accuracy of the oscillation coefficient, simplifies the model selection and parameter determination process, but also improves the interpretability and understandability of the system, providing strong support for the modeling and analysis of dynamic systems.

[0023] Furthermore, by selecting the differential equation form based on the comparison between the oscillation coefficient and the oscillation coefficient threshold, the dynamic characteristics of the power system can be more accurately matched, thereby building a more accurate differential equation model. This method not only improves the adaptability and accuracy of the model, simplifies the model construction and optimization process, but also improves the interpretability and understandability of the system.

[0024] Furthermore, by learning the sequence pre-data through this differential equation model, the pre-processed data can be effectively used to train and verify the differential equation model, thereby improving the prediction accuracy and reliability of the model. This method not only improves the adaptability and accuracy of the model, simplifies the model construction and optimization process, but also improves the interpretability and understandability of the system, providing strong support for the modeling and analysis of dynamic systems.

[0025] Furthermore, through this model evaluation and adjustment method based on the comparison of real data and simulation data, the parameters of the differential equation model can be dynamically optimized to ensure that its prediction accuracy meets the actual application requirements. This method not only improves the prediction accuracy and adaptability of the model, but also enhances the operating efficiency and stability of the system, providing strong support for the modeling, analysis and optimization of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A flowchart of a data-driven dynamic system differential equation modeling method according to an embodiment of the present invention; Figure 2 A flow chart for collecting time series data of a power system for an embodiment of the present invention; Figure 3 A flow chart of extracting dynamic characteristics using a data-driven algorithm according to an embodiment of the present invention; Figure 4 The present invention is a flowchart of calculating the oscillation coefficient of a power system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0027] In order to make the objects and advantages of the present invention more clearly understood, the present invention is further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0028] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0029] It should be noted that, in the description of the present invention, terms such as "up", "down", "left", "right", "inside" and "outside" indicating directions or positional relationships are based on the directions or positional relationships shown in the drawings. This is only for description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation on the present invention.

[0030] In addition, it should be noted that in the description of the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0031] See also Figure 1 As shown, it is a flow chart of a data-driven dynamic system differential equation modeling method according to an embodiment of the present invention, including: Step S1, collecting time series data of the power system, where: Time series data include experimental measurement data, sensor data, and numerical simulation results; Step S2, using a data-driven algorithm to extract the dynamic characteristics of the time series data, and pre-processing the time series data based on the dynamic characteristics to generate corresponding sequence pre-data, wherein: Dynamical characteristics include the oscillation frequency, growth rate, and fluctuation of the dynamical system; Step S3, using the dynamic characteristics to calculate the oscillation coefficient of the power system, selecting a differential equation form according to the comparison result between the oscillation coefficient and the oscillation coefficient threshold, and determining the corresponding differential equation parameters to construct a differential equation model corresponding to the power system; Step S4, using the differential equation model to learn the sequence prediction data, generate simulation data within a preset time, and compare it with the real data corresponding to the preset time, generate the prediction accuracy of the differential equation model, and compare the prediction accuracy with the accuracy threshold, and determine whether to adjust the differential equation model according to the comparison result, wherein, The accuracy threshold is the minimum standard for the prediction accuracy of the differential equation model and is related to the driving performance of the power system.

[0032] By collecting the time series data of the power system, extracting the dynamic characteristics of the time series data, and preprocessing the time series data based on the dynamic characteristics to generate the corresponding sequence pre-data, the oscillation coefficient of the power system is calculated and the differential equation form is selected, the corresponding differential equation parameters are determined, and the differential equation model corresponding to the power system is constructed to learn the sequence pre-data, generate simulation data within a preset time, and compare it with the real data corresponding to the preset time, generate the prediction accuracy of the differential equation model and compare it with the accuracy threshold, determine whether to adjust the differential equation model, learn nonlinear relationships from time series data, objectively evaluate the prediction performance of the model, promptly discover the deficiencies of the model, and construct a differential equation model that meets the actual situation.

[0033] See also Figure 2 As shown, it is a flow chart of collecting time series data of a power system according to an embodiment of the present invention, including: Step S11, determining the measurement variables and sampling frequency of the power system, wherein: The measured variables include physical variables and state variables; Step S12, continuously sampling the measured variables according to the sampling frequency to obtain time series data; Step S13, storing the acquired time series data in a data storage device.

[0034] In the specific implementation, the acquired time series data is stored in the data storage device to facilitate unified management and maintenance of the data. This makes data storage more secure and reliable, and also facilitates subsequent data query and analysis. The stored data can be traced and verified at any time, which is crucial for model verification and optimization. When the model needs to be adjusted or verified, the original data can be directly obtained from the data storage device to ensure the authenticity and integrity of the data.

[0035] High-quality time series data is the basis of data-driven modeling. Through standardized data collection and storage processes, accurate and reliable data support can be provided for subsequent dynamic system differential equation modeling, thereby improving the accuracy and reliability of the model. Through the analysis and modeling of time series data, potential problems and hidden faults of the system can be discovered in time, and measures can be taken in advance to prevent and repair them, thereby enhancing the reliability and stability of the system.

[0036] By determining the measured variables of the power system, including physical variables and state variables, the operating status and physical characteristics of the power system can be fully reflected, providing a rich and accurate data basis for subsequent modeling and analysis, and avoiding model deviations caused by omitting important variables. Selecting an appropriate sampling frequency can ensure that the collected data can reflect the dynamic changes of the system without generating unnecessary data redundancy due to too high a sampling frequency or losing important information due to too low a sampling frequency. This helps to improve the quality and availability of data.

[0037] See also Figure 3 As shown, it is a flow chart of extracting dynamic characteristics using a data-driven algorithm according to an embodiment of the present invention, including: Step S21, using a data-driven algorithm to analyze the time series data and extract the corresponding feature vector; Step S22, mapping the feature vector to an infinite dimensional linear space; Step S23, using linear algebra tools to analyze the characteristic vector and extract the corresponding dynamic characteristics.

[0038] In specific implementations, machine learning or deep learning algorithms (such as principal component analysis (PCA), autoencoders, long short-term memory networks (LSTM), etc.) are used to analyze time series data. These algorithms can automatically learn the inherent structure and pattern of the data from the data. The algorithm extracts the key information from the time series data to form feature vectors. These feature vectors are low-dimensional representations of the data and can capture the main changing trends and dynamic characteristics in the data.

[0039] Through certain mathematical transformations (such as kernel methods, Hilbert space mapping, etc.), the eigenvector is mapped from the original finite-dimensional space to an infinite-dimensional linear space. This mapping can transform nonlinear problems into linear problems, which is convenient for subsequent analysis. In infinite-dimensional linear space, the tools and theories of linear algebra can be used to process data, which enables complex nonlinear relationships to be understood and analyzed in a simpler and more intuitive way.

[0040] The mapped eigenvectors are analyzed using linear algebra methods (such as singular value decomposition SVD, eigenvalue decomposition, etc.). These tools can effectively extract the main components and dynamic characteristics of the data. The dynamic features finally extracted include oscillation frequency, growth rate, fluctuation, etc. These features can directly reflect the operating state and dynamic behavior of the power system. The data-driven algorithm can handle complex nonlinear relationships, so that the extracted dynamic features can better reflect the actual dynamic characteristics of the power system, thereby improving the model's adaptability to different types of power systems. The extracted dynamic features can be directly used for the construction and optimization of differential equation models, which speeds up the speed of modeling and adjustment and improves modeling efficiency.

[0041] By mapping the eigenvector to an infinite-dimensional linear space, complex nonlinear problems can be transformed into linear problems for processing. In an infinite-dimensional linear space, linear algebra tools can be used to more effectively analyze the eigenvector and extract the corresponding dynamic characteristics, such as oscillation frequency, growth rate, and fluctuation. This mapping method can make full use of the theory and tools of linear algebra to improve the accuracy and efficiency of feature extraction. For dynamic systems with complex dynamic characteristics, traditional feature extraction methods based on physical models may find it difficult to accurately describe their behavior. Data-driven algorithms can effectively extract dynamic characteristics that reflect the dynamic characteristics of the system by learning the essential laws of the system from data, thereby providing support for building more accurate differential equation models.

[0042] By using data-driven algorithms to analyze time series data, hidden patterns and laws can be automatically discovered from large amounts of data without relying on prior physical model assumptions. This method can better adapt to the nonlinear characteristics and dynamic changes of complex dynamic systems, thereby extracting more accurate feature vectors. This automatic adaptability enables the model to better handle different types of dynamic systems and has stronger generalization capabilities. After mapping the feature vectors to infinite-dimensional linear space, linear algebra tools can be used for analysis to more efficiently extract dynamic features and improve the accuracy and efficiency of feature extraction.

[0043] Specifically, the steps for preprocessing time series data based on dynamic characteristics include: Standardize the time series data based on the kinetic characteristics and generate the corresponding sequence pre-data; Among them, the standardization process is to split the time series data according to the standard cutting rate; The standard cutting rate is a cutting rate that can be recognized by the differential equation model, and for a single learning, the corresponding standard cutting rate is a single cutting rate.

[0044] In the specific implementation, the time series data is converted into a unified format or range so that the differential equation model can process this data more effectively. This usually includes normalizing, denoising, smoothing and other operations on the data. The standard cut rate refers to the frequency or time interval at which the time series data is divided into several segments, and this cut rate is recognizable by the differential equation model. For example, if the model needs to learn with a fixed time step, then the standard cut rate is this fixed time step. For a single learning process, the standard cut rate is a fixed value, that is, a single cut rate. This means that the length of the data segment processed each time is the same, which helps the model maintain consistency and stability during the learning process. Through standardization, the time series data is converted into a unified format, eliminating the differences in the data in terms of dimension, range and time step. This enables data from different sources to be directly compared and analyzed, improves the consistency and comparability of the data, and the standardized data reduces the number of parameters that the model needs to adjust when processing the data. This makes the model construction and adjustment process simpler and more direct, reduces the difficulty of modeling, and reduces the complexity and error of the model when processing data in different formats.

[0045] By standardizing the time series data based on dynamic characteristics and segmenting it according to the standard cutting rate, the quality and consistency of the data can be significantly improved, and the learning efficiency and prediction accuracy of the model can be enhanced. This process not only simplifies the model construction and adjustment process, but also improves the reliability and stability of the system, providing strong support for the modeling and analysis of dynamic systems.

[0046] See also Figure 4 As shown, it is a flow chart of calculating the oscillation coefficient of the power system according to an embodiment of the present invention, including: Step S31, performing Fourier transform on the dynamic characteristics and converting the dynamic characteristics into frequency domain data; Step S32, fitting the frequency domain data by a sparse regression algorithm to obtain a dynamic spectrum corresponding to the frequency domain data; Step S33, selecting the highest peak value of the dynamic spectrum and outputting the highest peak value as the oscillation coefficient.

[0047] In practice, Fourier transform is a mathematical method that converts time domain signals into frequency domain signals. By performing Fourier transform on dynamic features (such as oscillation frequency, growth rate, and fluctuation in time series data), these features can be converted from the time domain to the frequency domain, so that the frequency components of the signal can be observed more intuitively. The converted frequency domain data contains the frequency information of the original dynamic features, such as the size, distribution, and intensity of the oscillation frequency.

[0048] Sparse regression algorithms (such as LASSO, Elastic Net, etc.) are algorithms that introduce regularization terms into regression models, which can effectively select the most important features from a large number of features while suppressing overfitting. By fitting frequency domain data with a sparse regression algorithm, a dynamic spectrum can be obtained, which shows the intensity and distribution of different frequency components in the frequency domain data. The dynamic spectrum can intuitively reflect the oscillation characteristics of the dynamic system. In the dynamic spectrum, the highest peak represents the frequency component with the highest intensity in the frequency domain data, that is, the main oscillation frequency of the dynamic system. Outputting the highest peak as the oscillation coefficient can provide an important basis for the selection and parameter determination of the differential equation model. The size and position of the oscillation coefficient can reflect the oscillation characteristics of the dynamic system, such as the intensity and frequency of the oscillation.

[0049] By converting the dynamic characteristics into frequency domain data through Fourier transform, the frequency components of the signal can be observed more intuitively, thereby improving the extraction accuracy of the oscillation coefficient. The sparse regression algorithm can effectively select the most important frequency components from the frequency domain data, while suppressing the overfitting phenomenon, further improving the extraction accuracy of the oscillation coefficient. Outputting the highest peak value as the oscillation coefficient can provide a direct basis for the selection and parameter determination of the differential equation model. This simplifies the process of model selection and parameter determination and reduces the difficulty of modeling.

[0050] Accurate oscillation coefficients can provide important references for system decision-making and control, help predict potential system problems in advance, and take corresponding control measures to improve system operation efficiency and reliability.

[0051] Through this process of calculating the oscillation coefficient of the dynamic system, key information reflecting the dynamic characteristics of the system can be effectively extracted from the dynamic characteristics, providing an important basis for the selection of differential equation models and parameter determination. This process not only improves the extraction accuracy of the oscillation coefficient, simplifies the model selection and parameter determination process, but also improves the interpretability and understandability of the system, providing strong support for the modeling and analysis of dynamic systems.

[0052] Specifically, when the oscillation coefficient of the power system is greater than the oscillation coefficient threshold, a high-order differential equation is selected, and when the oscillation coefficient of the power system is less than the oscillation coefficient threshold, a linear differential equation is selected.

[0053] Specifically, the oscillation coefficient threshold is a critical value used to determine the oscillation characteristics of the power system, and is related to the driving performance of the power system.

[0054] In the specific implementation, the oscillation coefficient is calculated through the above process (Fourier transform, sparse regression fitting dynamic graph, and selecting the highest peak value), which reflects the main oscillation characteristics of the power system, such as the intensity and frequency of the oscillation. This is a preset critical value used to determine whether the oscillation characteristics of the power system are significant. This threshold is closely related to the driving performance of the power system, and different power systems may have different threshold settings.

[0055] When the oscillation coefficient is greater than the oscillation coefficient threshold, it means that the oscillation characteristics of the power system are more significant, and there may be complex nonlinear dynamic behaviors. At this time, choosing a high-order differential equation to model can better capture the complex dynamic characteristics of the system.

[0056] When the oscillation coefficient is less than the oscillation coefficient threshold, it means that the oscillation characteristics of the dynamic system are relatively weak, and the system may be closer to linear dynamic behavior. At this time, choosing a linear differential equation to model can simplify the model structure and improve computational efficiency.

[0057] Selecting the appropriate differential equation form based on the comparison between the oscillation coefficient and the threshold can more accurately match the actual dynamic characteristics of the power system. For systems with significant oscillation characteristics, higher-order differential equations can better capture nonlinear dynamics; for systems with weaker oscillation characteristics, linear differential equations can simplify the model structure and improve the adaptability and accuracy of the model. This method can automatically adapt to different types of power systems and has strong generalization capabilities. Regardless of how the oscillation characteristics of the system change, the model can select the appropriate equation form based on the size of the oscillation coefficient, thereby improving the applicability of the model in different scenarios.

[0058] By selecting the differential equation form based on the comparison between the oscillation coefficient and the oscillation coefficient threshold, the dynamic characteristics of the power system can be more accurately matched, thereby building a more accurate differential equation model. This method not only improves the adaptability and accuracy of the model, simplifies the model construction and optimization process, but also improves the interpretability and understanding of the system.

[0059] Specifically, the steps of learning the sequence pre-data by the differential equation model include: Determine the corresponding differential equation parameters according to the differential equation form and obtain the corresponding differential equation model: Inputting preset time and sequence data into the differential equation model; The output result of the differential equation model at the corresponding preset time is calculated by a numerical solution method, and the output result is output as simulation data.

[0060] In the specific implementation, for the selected differential equation form, its corresponding parameters need to be determined. These parameters can be determined by data fitting, optimization algorithms (such as least squares method, gradient descent method, etc.) or machine learning methods (such as neural networks). The parameter determination process is intended to enable the differential equation model to better fit the sequence data.

[0061] Preset time: The preset time refers to the time range or time point for which prediction is required.

[0062] Pre-sequence data: Pre-sequence data is the time series data that has been preprocessed (standardized, segmented, etc.) and will serve as the input of the differential equation model.

[0063] Input model: Input preset time and sequence data into the differential equation model to prepare for model solving and prediction.

[0064] Numerical solution methods (such as Euler's method, Runge-Kutta method, etc.) are commonly used methods for solving differential equations. These methods can convert continuous differential equations into discrete difference equations, which can then be solved on a computer. Through numerical solution methods, the output results of the differential equation model at a preset time can be calculated. These output results are the predicted values ​​of the model, also known as simulation data.

[0065] By comparing the simulated data with the real data, the prediction performance and reliability of the model can be verified. If the simulated data is highly consistent with the real data, it means that the model has a high reliability. If there is a large difference between the simulated data and the real data, the model can be adjusted and optimized to improve the reliability of the model.

[0066] Through the steps of learning the sequence pre-data by this differential equation model, the pre-processed data can be effectively used to train and verify the differential equation model, thereby improving the prediction accuracy and reliability of the model. This method not only improves the adaptability and accuracy of the model, simplifies the model construction and optimization process, but also improves the interpretability and understanding of the system, providing strong support for the modeling and analysis of dynamic systems.

[0067] Specifically, real data when the power system reaches the preset time is collected, and the real data is compared with the simulation data to generate the prediction accuracy of the differential equation model, and the prediction accuracy is compared with the accuracy threshold. When the prediction accuracy is greater than the accuracy threshold, the differential equation model is not adjusted.

[0068] Specifically, when the prediction accuracy is less than the accuracy threshold, the gradient descent method is used to adjust the differential equation parameters.

[0069] In the specific implementation, at a preset time point, the real operating data of the power system is obtained through sensors, experimental measurements or other data collection methods. These data reflect the real state of the power system in actual operation. Ensure that the collected real data and simulation data are synchronized in time for accurate comparison.

[0070] Calculate the error between the real data and the simulated data. Common error indicators include mean square error (MSE), mean absolute error (MAE), etc. Calculate the prediction accuracy of the model based on the error indicator. The accuracy can be expressed as the inverse of the error or other forms to reflect the accuracy of the model prediction.

[0071] The gradient descent method calculates the gradient of the loss function (such as the sum of squared errors) and gradually adjusts the model parameters to minimize the loss function.

[0072] Parameter adjustment: When the prediction accuracy is less than the accuracy threshold, the gradient descent method is used to adjust the parameters of the differential equation. The specific steps are as follows: Define loss function: Choose an appropriate loss function, such as mean squared error (MSE).

[0073] Calculate gradients: Calculate the gradient of the loss function with respect to the model parameters.

[0074] Update parameters: Update model parameters according to gradient direction and learning rate.

[0075] Iterative optimization: Repeat the above steps until the prediction accuracy reaches or exceeds the accuracy threshold.

[0076] Through this model evaluation and adjustment method based on the comparison of real data and simulation data, the parameters of the differential equation model can be dynamically optimized to ensure that its prediction accuracy meets the actual application requirements. This method not only improves the prediction accuracy and adaptability of the model, but also enhances the operating efficiency and stability of the system, providing strong support for the modeling, analysis and optimization of the power system.

[0077] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A data-driven dynamic system differential equation modeling method, characterized in that: include: Collecting time series data of the power system, wherein the time series data includes experimental measurement data, sensor data and numerical simulation results; Extracting the dynamic characteristics of the time series data using a data-driven algorithm, and preprocessing the time series data based on the dynamic characteristics to generate corresponding sequence pre-data, wherein the dynamic characteristics include the oscillation frequency, growth rate and fluctuation of the power system; Calculating the oscillation coefficient of the power system using the dynamic characteristics, selecting a differential equation form according to a comparison result between the oscillation coefficient and the oscillation coefficient threshold, determining corresponding differential equation parameters, and constructing a differential equation model corresponding to the power system; The sequence prediction data is learned by using the differential equation model to generate simulation data within a preset time, and the simulation data is compared with the real data corresponding to the preset time to generate the prediction accuracy of the differential equation model, and the prediction accuracy is compared with the accuracy threshold, and it is determined whether to adjust the differential equation model according to the comparison result, wherein: The accuracy threshold is the minimum standard of the prediction accuracy of the differential equation model and is related to the driving performance of the power system.

2. The data-driven dynamic system differential equation modeling method according to claim 1, characterized in that: The steps to collect time series data for a power system include: Determining measurement variables and sampling frequencies of the power system, wherein the measurement variables include physical variables and state variables; Continuously sampling the measurement variable according to the sampling frequency to obtain the time series data; The acquired time series data is stored in a data storage device.

3. The data-driven dynamic system differential equation modeling method according to claim 2, characterized in that: The steps of extracting dynamic features using data-driven algorithms include: Using a data-driven algorithm to analyze the time series data and extract corresponding feature vectors; Mapping the feature vector to an infinite dimensional linear space; The characteristic vectors are analyzed using linear algebra tools to extract corresponding dynamic characteristics.

4. The data-driven dynamic system differential equation modeling method according to claim 3 is characterized in that: The steps of preprocessing time series data based on dynamic characteristics include: Based on the kinetic characteristics, the time series data is standardized and corresponding sequence pre-data is generated; wherein the standardization is to segment the time series data according to a standard cutting rate; The standard cutting rate is a cutting rate that can be recognized by the differential equation model, and for a single learning, the corresponding standard cutting rate is a single cutting rate.

5. The data-driven dynamic system differential equation modeling method according to claim 4 is characterized in that: The steps to calculate the oscillation coefficient of a dynamical system include: Performing Fourier transformation on the dynamic characteristics and converting the dynamic characteristics into frequency domain data; Fitting the frequency domain data by a sparse regression algorithm to obtain a dynamic spectrum corresponding to the frequency domain data; The highest peak value of the dynamic spectrum is selected and output as the oscillation coefficient.

6. The data-driven dynamic system differential equation modeling method according to claim 5, characterized in that: When the oscillation coefficient of the power system is greater than the oscillation coefficient threshold, a high-order differential equation is selected, and when the oscillation coefficient of the power system is less than the oscillation coefficient threshold, a linear differential equation is selected.

7. The data-driven dynamic system differential equation modeling method according to claim 6, characterized in that: The oscillation coefficient threshold is a critical value used to determine the oscillation characteristics of the power system, and is related to the driving performance of the power system.

8. The data-driven dynamic system differential equation modeling method according to claim 7, characterized in that: The steps of learning the differential equation model on the sequence pre-data include: According to the differential equation form, the corresponding differential equation parameters are determined to obtain the corresponding differential equation model: Inputting the preset time and the sequence pre-data into the differential equation model; The output result of the differential equation model at the corresponding preset time is calculated by a numerical solution method, and the output result is output as simulation data.

9. The data-driven dynamic system differential equation modeling method according to claim 8, characterized in that: Collect real data when the power system reaches the preset time, compare the real data with the simulation data, generate the prediction accuracy of the differential equation model, and compare the prediction accuracy with the accuracy threshold. When the prediction accuracy is greater than the accuracy threshold, do not adjust the differential equation model.

10. The data-driven dynamic system differential equation modeling method according to claim 9, characterized in that: When the prediction accuracy is less than the accuracy threshold, the differential equation parameters are adjusted using a gradient descent method.

Images