A wideband oscillation polynomial basis function prediction method for networked converters

Abstract

The present application relates to a kind of network converter broadband oscillation polynomial base function prediction method, belong to the field of power system automation and power electronics control technology, a kind of network converter broadband oscillation polynomial base function prediction method, comprising the following steps: S1: establishing network converter system state space model and extracting time domain analytical solution;S2: construct polynomial frequency domain base function, establish frequency domain analytical characterization framework;S3: derive time-frequency analytical mapping operator matrix;S4: online acquisition system initial value, calculate time domain power series expansion coefficient;S5: execute analytical mapping, solve the frequency domain spectral coefficient of current step;S6: recursive update state, realize the rolling prediction of broadband oscillation frequency spectrum;S7: output frequency spectrum prediction result (frequency, amplitude) and be used for upper layer damping control, the present application, establish a kind of direct mapping mechanism from "time domain analytical solution" to "frequency domain spectral coefficient", realize the unified characterization and closed-form solution of spectral feature in system state evolution process.

Description

Technical Field

[0001] This invention belongs to the field of power system automation and power electronic control technology, and specifically relates to a method for predicting the basis function of a wideband oscillating polynomial in grid converters. Background Technology

[0002] With the deepening construction of new power systems, grid-connected converters have become key equipment for large-scale grid connection of new energy sources due to their advantage of supporting grid frequency and voltage. However, with the integration of a high proportion of power electronic equipment, the system damping characteristics are complex, and broadband oscillations induced by factors such as control loop coupling are beginning to emerge. Given the rapid evolution and wide frequency band coverage of these oscillations, achieving millisecond-level online spectrum prediction is crucial for early warning of oscillation instability and dynamic adjustment of control parameters.

[0003] In the aforementioned scenarios, current research largely relies on traditional signal processing or model simulation methods, failing to fully consider the necessary supporting role of real-time spectrum sensing in assessing system transient stability. Consequently, it lacks a balance between real-time performance and accuracy in spectrum prediction under rapid switching in complex operating conditions. Typically, post-hoc analysis of the acquired time-domain sequences is performed based on Fast Fourier Transform, which, limited by the observation window length, results in significant time delays and makes it difficult to capture millisecond-level instantaneous frequency jumps. Alternatively, offline impedance scanning and eigenvalue analysis can be used to predict oscillation frequencies, but under actual operating conditions where system operating points fluctuate frequently, the calculation results of such models based on fixed operating points cannot reflect the dynamic drift of the spectrum in real time.

[0004] In power systems dominated by grid-connected converters, rapid sensing of oscillation frequency and damping is crucial for achieving active suppression. Existing spectrum analysis techniques exhibit significant deficiencies in predicting rapid transient processes in power electronic systems, particularly in terms of computational response speed, analytical expression, and non-stationary adaptability. Specifically: 1) Lack of analytical mapping: Traditional methods mainly rely on the black-box processing mode of "time-domain sampling-numerical transformation", which fails to establish an explicit mapping relationship between the time-domain analytical solution of the system's dynamic response and the frequency-domain spectral coefficients. This leads to the need to rely on large-scale matrix operations or point-by-point scanning when analyzing broadband oscillations. The calculation process is complex and highly dependent on hardware computing power, making it difficult to achieve lightweight embedding of the algorithm and unable to update the frequency-domain analytical expression in real time according to changes in system parameters.

[0005] 2) Analysis of hysteresis risk: Existing window-sliding spectrum analysis methods inherently suffer from the "observation delay-resolution" conflict, and their accuracy is highly dependent on the signal's stationarity and sampling length. During transient processes caused by load changes or control switching, the prediction results often exhibit "hysteresis feedback" because the signal evolution trend cannot be predicted in advance. This hysteresis makes it difficult for protection devices to respond in a timely manner in the early stages of oscillation instability, posing a risk of system runaway due to slow spectrum update speed.

[0006] 3) Insufficient dynamic characterization capability: Conventional frequency domain analysis methods have a weak ability to characterize complex envelope signals and non-stationary oscillations; traditional basis functions are difficult to explicitly describe broadband dynamics with exponential decay or polynomial growth characteristics, resulting in spectral leakage when capturing instantaneous frequency drift. Summary of the Invention

[0007] The purpose of this invention is to provide a simple and rationally designed method for predicting the basis function of a wideband oscillating polynomial in a grid converter in order to solve the above-mentioned problems.

[0008] The present invention achieves the above objectives through the following technical solutions: A method for predicting the basis function of a wideband oscillating polynomial in a grid converter includes the following steps: S1: Establish the state-space model of the grid converter system and extract the time-domain analytical solution; S2: Construct polynomial frequency domain basis functions and establish a frequency domain analytical representation framework; S3: Derive the time-frequency analytical mapping operator matrix; S4: Obtain initial system values ​​online and calculate the coefficients of the time-domain power series expansion; S5: Perform analytical mapping to solve for the frequency domain spectral coefficients of the current step size; S6: Recursively update the state to achieve rolling prediction of the wideband oscillation spectrum; S7: Outputs the spectrum prediction results (frequency, amplitude) and uses them for upper-level damping control.

[0009] As a further optimization of the present invention, S4, S5, and S6 constitute a closed-loop process for online recursive prediction. First, S4 obtains a candidate time-domain coefficient vector that reflects the transient evolution trend of the system by Taylor expansion based on the initial system measurement values ​​at the current time t. Then, S5 uses a preset time-frequency mapping operator to perform an analytical transformation on the coefficient vector, and instantly verifies and extracts the frequency domain distribution characteristics within the current step size without waiting for the sampling window to close. That is, as required by S6, the system performs recursive extrapolation of the time-domain state and synchronous correction of the frequency domain spectral coefficients with a preset simulation step size (e.g., 1ms). In each recursive cycle, S4 updates the time-domain dynamic trajectory, and S5 instantly maps the corresponding frequency domain analytical solution, thereby realizing the "evolution and prediction" of the oscillation frequency and amplitude evolution trajectory.

[0010] As a further optimization of the present invention, step S1 involves: establishing a time-frequency analytical mapping model for the grid-connected converter; defining the system's time-domain analytical expression: based on the closed-form solution of the system's dynamic response obtained in the previous chapters, the key state variables of the grid-connected converter are... Consider it as a set of local polynomial approximations within a finite prediction time window; let the power series expansion of the signal in the time domain be: ,in, The coefficients of the nth power series reflect the system's performance in... The dynamic evolution characteristics of time and its domain.

[0011] As a further optimization of the present invention, step S2 involves: constructing polynomial frequency domain basis functions and establishing a frequency domain analytical representation framework; according to Euler's formula, we have: , By taking values ​​for the real and imaginary parts respectively, we obtain: In other words, in the context of In a polynomial space with basis , the frequency is Both the sine and cosine basis functions have corresponding coefficient sequences. , To visually demonstrate this "frequency-polynomial" correspondence, we selected... For different frequencies, the first few coefficients of some sine basis functions and cosine basis functions under the power series basis are listed; .

[0012] As a further optimization of the present invention, step S3 involves deriving the time-frequency analytical mapping operator matrix, considering a time window. The time-domain analytical solution is in the following form: in, These are the power series coefficients obtained from the time-domain residual algorithm in Chapter 3, denoted in matrix form, as shown below: in, ; To ensure consistency with subsequent frequency domain mapping, N discrete sampling points are first selected within this time window. The continuous-time analytical solution within this time window is converted into an N-row, 1-column discrete sampling vector. : in, ; power series base The values ​​at these sampling points are converted into matrix form. First, the polynomial with respect to time is converted into matrix form, as shown in the following equation: The compact expression for the continuous-time analytical solution in discrete time can be written as: The above equation shows that, under a fixed time sampling grid, the continuous time domain Discretizing into N sample points is essentially equivalent to a power series basis matrix. With coefficient vector The product; Since the polynomial frequency domain basis functions are based on the generalized Euler formula, the power series basis matrix... The same applies to polynomial frequency domain basis functions; for any set of frequency domain basis functions... The coefficient of its corresponding order is denoted as (i=0,…,k-1), then the following matrix relationship can be obtained: in, It is an N-row, k-column matrix composed of polynomial frequency domain basis functions; Given a k-row, k-column coefficient matrix constructed from the coefficients of the corresponding basis functions, mapping the original time-domain power series solution to the polynomial frequency-domain basis functions yields the following formula: in, The polynomial frequency domain coefficients (i.e., the weights of each basis function) to be obtained are represented by a k-row, 1-column vector. The transformation matrix between the two sets of basis functions can be obtained using the following formula: This allows the power series basis functions to be projected onto the polynomial frequency domain function, and the vector... Each component corresponds to a predefined "frequency index" and its amplitude of the sine and cosine basis functions. As the time-domain window is updated, the spectrum of the local window is output synchronously.

[0013] The beneficial effects of this invention are as follows: 1. This invention overcomes the limitations of modeling: considering the complex control loop coupling and dynamic characteristics of grid converters, it establishes a direct mapping mechanism from "time-domain analytical solution" to "frequency-domain spectral coefficients", realizing a unified characterization and closed-loop solution of the spectral characteristics during the system state evolution process, avoiding the computational burden brought by traditional offline impedance analysis or large-scale electromagnetic transient simulation, and improving the lightweight level of the algorithm.

[0014] 2. This invention ensures real-time prediction: For non-stationary processes such as the initial stage of oscillation and sudden changes in operating conditions, it utilizes the constructed polynomial frequency domain basis function and time-frequency mapping operator to break the dependence of traditional analysis methods on the sampling window length. Based on the instantaneously measured system state quantities, it achieves millisecond-level real-time prediction of the spectrum, ensuring timely and accurate frequency information support in the early stage of oscillation instability.

[0015] 3. This invention avoids distortion in predictive spectrum analyzers by introducing a dynamic characterization mechanism based on polynomial basis functions. This mechanism can explicitly characterize non-stationary signals with exponential decay or growth characteristics. While ensuring the accuracy of the frequency domain analytical solution, it dynamically adapts to the frequency drift caused by system operating point switching, reducing the risk of spectral leakage in the transient process of traditional FFT methods. This enables accurate capture of broadband oscillation evolution trends and online analytical characterization and prediction of broadband oscillation characteristics of grid-connected converter-dominated systems. This provides key technical support and data basis for rapid perception of oscillation risks and active damping control in new power systems. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the algorithm of the present invention; Figure 2 This is a comparison between the proposed method and the time-domain results of real-time simulation. Figure 1 ; Figure 3 This is a comparison between the proposed method and the time-domain results of real-time simulation. Figure 2 ; Figure 4 This is a comparison between the proposed method and the frequency domain results of real-time simulation. Figure 1 ; Figure 5 This is a comparison between the proposed method and the frequency domain results of real-time simulation. Figure 2 . Detailed Implementation

[0017] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0018] Example: Figure 1 As shown, this invention proposes a wideband oscillation polynomial basis function prediction method for grid-connected converters. This method addresses the transient stability assessment problem under high-proportion renewable energy integration, constructing a model based on time-frequency analytical mapping theory and designing an online prediction strategy based on polynomial basis functions. Using the time-domain power series expansion coefficients of the system state variables as the driving source, the frequency domain analytical distribution is directly obtained through an offline derived mapping operator, achieving high-speed, high-precision instantaneous spectrum prediction with non-stationary adaptability.

[0019] The problem model driven by the frequency domain analytical solution can be interpreted as follows: by establishing a closed mapping relationship between the time-domain Taylor expansion coefficients and the frequency-domain spectral coefficients, the current spectral distribution can be obtained without long-sequence sampling, thereby ensuring the real-time performance and accuracy of the prediction. It should be noted that the model described in this invention is universally applicable to various oscillation analysis nodes in power-electronic power systems; it only requires updating the mapping matrix for different topologies.

[0020] The specific technical method includes the following steps: S1: Establish the state-space model of the grid converter system and extract the time-domain analytical solution; S2: Construct polynomial frequency domain basis functions and establish a frequency domain analytical representation framework; S3: Derive the time-frequency analytical mapping operator matrix; S4: Obtain initial system values ​​online and calculate the coefficients of the time-domain power series expansion; S5: Perform analytical mapping to solve for the frequency domain spectral coefficients of the current step size; S6: Recursively update the state to achieve rolling prediction of the wideband oscillation spectrum; S7: Outputs the spectrum prediction results (frequency, amplitude) and uses them for upper-level damping control.

[0021] S4, S5, and S6 constitute the closed-loop process of online recursive prediction. First, S4, based on the initial system measurements at the current time t, uses Taylor expansion to obtain a candidate time-domain coefficient vector that reflects the transient evolution trend of the system. Then, S5 uses a preset time-frequency mapping operator to perform an analytical transformation on this coefficient vector, instantly verifying and extracting the frequency domain distribution characteristics within the current step size without waiting for the sampling window to close. That is, as required by S6, the system performs recursive extrapolation of the time-domain state and synchronous correction of the frequency domain spectral coefficients with a preset simulation step size (e.g., 1 ms). Within each recursive cycle, S4 updates the time-domain dynamic trajectory, and S5 instantly maps the corresponding frequency domain analytical solution, thus achieving "evolution and prediction simultaneously" of the oscillation frequency and amplitude evolution trajectory. It should be noted that this recursive mechanism based on analytic mapping avoids the computational overhead caused by data stacking in traditional FFT. Taking a typical broadband oscillation transient process as an example, this method only requires a very small matrix multiplication operation to converge to the spectral characteristics described in S7 in real time with a step size of milliseconds, ensuring that the prediction results are consistent with the physical state of the system.

[0022] Specifically, firstly, step S1: Establish the time-frequency analytical mapping model of the grid converter. This step aims to construct a mapping architecture that directly derives frequency domain characteristics from the time-domain analytical solution, avoiding dependence on discrete sampling points. The technical solution is as follows: Defining the system's time-domain analytical expression: Based on the closed-form solution of the system's dynamic response obtained in previous chapters, the key state signals of the grid converter are expressed... It can be considered as a set of local polynomial approximations within a finite prediction time window. The power series expansion of this signal in the time domain is denoted as: in, The coefficients of the nth power series reflect the system's performance in... The dynamic evolution characteristics of time and its domain.

[0023] Next, step S2: Construct polynomial frequency domain basis functions and establish a frequency domain analytical representation framework; According to Euler's formula, we have By taking values ​​for the real and imaginary parts respectively, we obtain: In other words, in the context of In a polynomial space with basis , the frequency is Both the sine and cosine basis functions have corresponding coefficient sequences. , To visually demonstrate this "frequency-polynomial" correspondence, we selected... For different frequencies, the first few coefficients of a subset of sine and cosine basis functions under the power series basis are listed. Polynomial frequency domain basis functions based on Euler's formula Step S3: Derive the time-frequency analytical mapping operator matrix; Consider a time window The time-domain analytical solution is in the following form: in, These are the power series coefficients obtained from the time-domain residual algorithm in Chapter 3, denoted in matrix form, as shown below: in, .

[0024] To ensure consistency with subsequent frequency domain mapping, N discrete sampling points are first selected within this time window. The continuous-time analytical solution within this time window is converted into an N-row, 1-column discrete sampling vector. : in, .

[0025] power series base The values ​​at these sampling points are converted into matrix form. First, the polynomial with respect to time is converted into matrix form, as shown in the following equation: The compact expression for the continuous-time analytical solution in discrete time can be written as: The above equation shows that, under a fixed time sampling grid, the continuous time domain Discretizing into N sample points is essentially equivalent to a power series basis matrix. With coefficient vector The product of.

[0026] Since the polynomial frequency domain basis functions are based on the generalized Euler formula, the power series basis matrix... This also applies to polynomial frequency domain basis functions. For any set of frequency domain basis functions... The coefficient of its corresponding order is denoted as (i=0,…,k-1), then the following matrix relationship can be obtained: in, It is an N-row, k-column matrix composed of polynomial frequency domain basis functions; Given a k-row, k-column coefficient matrix constructed from the coefficients of the corresponding basis functions, mapping the original time-domain power series solution to polynomial frequency-domain basis functions yields the following formula: in, The polynomial frequency domain coefficients (i.e., the weights of each basis function) to be obtained are represented by a k-row, 1-column vector. The transformation matrix between the two sets of basis functions can be obtained using the following formula: This allows the power series basis functions to be projected onto the polynomial frequency domain function. (Vector) Each component corresponds to a predefined "frequency index" and its amplitude of the sine and cosine basis functions. As the time-domain window is updated, the spectrum of the local window is output synchronously.

[0027] Step S4: Obtain initial system values ​​online and calculate the coefficients of the time-domain power series expansion; Step S5: Perform analytical mapping to solve for the frequency domain spectral coefficients at the current step size; Step S6: Recursively update the state to achieve rolling prediction of the wideband oscillation spectrum; Step S7: Output the spectrum prediction results (frequency, amplitude) and use them for upper-level damping control.

[0028] 1) This method establishes a theoretical framework for time-frequency analytical mapping, breaking through the modeling limitations of traditional discrete sampling analysis: This invention proposes for the first time a novel analytical paradigm of "directly mapping time-domain analytical solutions to frequency-domain analytical distributions." By establishing a closed-form mapping operator between time-domain power series coefficients and frequency-domain spectral coefficients, the complex spectrum acquisition process is transformed from "numerical transformation after signal sampling" to "analytical deduction based on initial values ​​of the physical model." This innovation solves the pain point in traditional methods where spectral information is implicit in long-sequence sampling and difficult to extract explicitly in real time.

[0029] 2) A polynomial frequency domain basis function system was constructed, achieving precise parameterized characterization of non-stationary oscillation characteristics: Unlike the constant amplitude complex exponential basis used in traditional Fourier transforms, this invention constructs a set of discrete frequency domain basis functions corresponding to the order of the time-domain polynomial, specifically targeting the non-stationary characteristics of the transient process of the grid converter. This basis function system can explicitly characterize wideband dynamics with exponential decay or growth characteristics, achieving high-dimensional information compression and parameterized normalized expression of the spectral morphology.

[0030] 3) An online recursive prediction mechanism for dominant oscillation characteristics is proposed, realizing a leap from "post-hoc" to "anti-hoc" spectrum sensing: This invention designs an online recursive calculation process based on a time-frequency mapping matrix. Utilizing the initial instantaneous physical quantities at the current moment, combined with offline pre-derived mapping operators, the spectrum evolution trend for future periods can be output instantaneously without waiting for the observation window to close. This mechanism achieves real-time tracking and anti-hoc prediction of spectrum characteristics, providing a crucial time window for active damping intervention in the early stages of system instability.

[0031] 4) Extremely high real-time performance and "zero-latency" perception: Traditional FFT methods are limited by the Heisenberg uncertainty principle, and high frequency resolution requires a long observation window, resulting in significant computational delay. This invention uses an analytical mapping method, with a computational overhead of only one low-dimensional matrix multiplication operation. The prediction step size can be shortened to the millisecond level (e.g., 1ms), realizing the synchronous update of the spectrum distribution and the physical state of the system, and solving the time delay problem of online monitoring.

[0032] 5) Excellent non-stationary signal processing capabilities: Under sudden changes in system operating conditions, load switching, or control parameter disturbances, signals exhibit strong non-stationary characteristics. Traditional methods are prone to spectral leakage and sidelobe effects, leading to prediction distortion. This invention, based on an analytical representation framework using polynomial basis functions, can natively support the spectral characterization of decaying / growing signals, ensuring prediction accuracy and robustness during transient processes.

[0033] This invention achieves instantaneous sensing of wideband oscillation signals by introducing a frequency domain analytical mapping operator into the grid converter control system. This is based on simulation and experimental data analysis of embodiments of this invention (see appendix for details). Figure 2 , Figure 3 , Figure 4 , Figure 5 Its specific technical effects are as follows: The effects of this invention are as follows: Figure 2 , Figure 3 , Figure 4 , Figure 5 As shown in the attached figure: the results were obtained under the condition of high-frequency oscillation around 1000Hz caused by a non-ideal DC bus. and The response is highly consistent with the time-domain power series solution, where It is the frequency of oscillation (in angular frequency form). This represents the d-axis component of the DC bus voltage in the dq coordinate system. If we disregard the effects of measurement errors such as oscilloscope sampling, channel noise, and signal conditioning, both exhibit consistent trends in oscillation frequency, phase, and amplitude envelope variation. As can be seen from the magnified view, the deviation between the real-time simulation result curve and the time-domain power series solution during the short-time transition is minimal, with no significant phase drift or amplitude distortion. To verify the effectiveness of the time-frequency mapping algorithm in characterizing the oscillation spectrum, we... Figure 3 and Figure 4 It can be seen that within the selected 18-21ms time window, if the influence of measurement errors such as oscilloscope sampling, channel noise, and signal conditioning is not considered, the dominant frequency obtained by the spectrum mapping algorithm based on the explicit time-domain solution is basically consistent with that obtained by the FFT experiment. For For the variable, both methods showed a unique significant spectral line near 1000 Hz, with its dominant frequency center at approximately 1060 Hz and a corresponding amplitude of approximately 4.96%. For Similarly, the dominant frequency center of the variable is approximately 1060 Hz, corresponding to an amplitude of approximately 34.21%. It should be noted that, besides the main peak near 1060 Hz, some smaller spectral lines with amplitudes much smaller than the main peak can still be seen in the figure. These frequency components are mainly introduced by the inherent limitations of finite-time-window FFT. For a short period of time, Fourier analysis based on a large number of samples must make a trade-off between time resolution and frequency resolution when dealing with signals exhibiting non-stationary characteristics. That is, the shorter the time window, the better it can track transient processes, but the worse the frequency resolution and the more severe the leakage. Therefore, the dominant oscillation component at 1060 Hz has multiple adjacent frequency points, leading to main lobe expansion and sidelobe elevation, presenting a series of small-amplitude frequency components. In contrast, the spectrum algorithm proposed in this paper explicitly uses time-domain power series to analytically model the frequency domain solution of the signal within a local time window. While maintaining a high time resolution, it significantly improves the concentration of spectral energy, making the 1060 Hz dominant component appear as a more uniform spectral line in both figures. Thus, it has a better frequency resolution than FFT in the fast transient analysis scenario of grid-type converter-dominated power systems.

[0034] The effects of each technical step in this invention are as follows: 1) This invention establishes an analytical mapping model between time-domain power series coefficients and discrete frequency-domain basis functions, which explicitly links the physical evolution mechanism of the system with the frequency-domain distribution characteristics, thereby transforming the spectrum prediction process from "data-driven" to "model-driven". This significantly reduces the dependence on long sequence sampling while ensuring the closed nature of the calculation process.

[0035] 2) This invention constructs a polynomial frequency domain basis function system, and outputs an analytical spectral distribution under the premise of considering the non-stationarity and strong damping characteristics of broadband oscillation signals. This enables the accurate capture of transient oscillation components with exponential decay or polynomial growth characteristics, thereby improving the reliability of spectrum analysis under complex transient conditions, enhancing the fit and robustness of prediction results to instantaneous frequency drift, and improving identification accuracy and early warning level while eliminating spectral leakage.

[0036] 3) This invention uses time-domain order recursion and online operator mapping to track and verify the system state evolution in real time, so that the spectrum boundary can be updated synchronously at the millisecond level as the operating point switches or control changes. This reduces computational delay while avoiding prediction failure caused by signal non-stationarity, and balances the real-time performance of online sensing with engineering deployability, thereby improving the operational safety and transient stability of the grid converter-dominated system.

[0037] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for predicting the basis function of a wideband oscillating polynomial in a grid-connected converter, characterized in that: Includes the following steps: S1: Establish the state-space model of the grid converter system and extract the time-domain analytical solution; S2: Construct polynomial frequency domain basis functions and establish a frequency domain analytical representation framework; S3: Derive the time-frequency analytical mapping operator matrix; S4: Obtain initial system values ​​online and calculate the coefficients of the time-domain power series expansion; S5: Perform analytical mapping to solve for the frequency domain spectral coefficients of the current step size; S6: Recursively update the state to achieve rolling prediction of the wideband oscillation spectrum; S7: Outputs the frequency and amplitude of the spectrum prediction results and uses them for upper-level damping control.

2. The method for predicting the wideband oscillating polynomial basis function of a grid converter according to claim 1, characterized in that: S4, S5, and S6 constitute the closed-loop process of online recursive prediction. First, S4 obtains candidate time-domain coefficient vectors that reflect the transient evolution trend of the system by Taylor expansion based on the initial system measurement values ​​at the current time t. Then, S5 uses a preset time-frequency mapping operator to perform an analytical transformation on the coefficient vector, and instantly verifies and extracts the frequency domain distribution characteristics within the current step size without waiting for the sampling window to close. As required by S6, the system performs recursive extrapolation of the time-domain state and synchronous correction of the frequency-domain spectral coefficients with a preset simulation step size. In each recursive cycle, the time-domain dynamic trajectory is updated by S4, and the corresponding frequency-domain analytical solution is mapped out in real time by S5, thereby realizing "evolution and prediction" of the oscillation frequency and amplitude evolution trajectory.

3. The method for predicting the wideband oscillating polynomial basis function of a grid converter according to claim 2, characterized in that: Step S1: Establish the time-frequency analytical mapping model of the grid-connected converter; define the system time-domain analytical expression: based on the closed-form solution of the system dynamic response obtained in the previous chapters, the key state signals of the grid-connected converter are... Consider it as a set of local polynomial approximations within a finite prediction time window; let the power series expansion of the signal in the time domain be: ,in, The coefficients of the nth power series reflect the system's... The dynamic evolution characteristics of time and its domain.

4. The method for predicting the wideband oscillating polynomial basis function of a grid converter according to claim 3, characterized in that: Step S2 involves constructing polynomial frequency domain basis functions and establishing a frequency domain analytical representation framework. According to Euler's formula, we have: ， By taking values ​​for the real and imaginary parts respectively, we obtain: In other words, in the context of In a polynomial space with basis , the frequency is Both the sine and cosine basis functions have corresponding coefficient sequences. , To visually demonstrate this "frequency-polynomial" correspondence, we selected... For different frequencies, the first few coefficients of some sine basis functions and cosine basis functions under the power series basis are listed; 。 5. The method for predicting the wideband oscillating polynomial basis function of a grid converter according to claim 4, characterized in that: Step S3 involves deriving the time-frequency analytical mapping operator matrix, considering a time window. The time-domain analytical solution is in the following form: in, These are the power series coefficients obtained from the time-domain residual algorithm in Chapter 3, denoted in matrix form, as shown below: in, ; To ensure consistency with subsequent frequency domain mapping, N discrete sampling points are first selected within this time window. The continuous-time analytical solution within this time window is converted into an N-row, 1-column discrete sampling vector. : in, ; power series base The values ​​at these sampling points are converted into matrix form. First, the polynomial with respect to time is converted into matrix form, as shown in the following equation: The compact expression for the continuous-time analytical solution in discrete time can be written as: The above equation shows that, under a fixed time sampling grid, the continuous time domain Discretizing into N sample points is essentially equivalent to a power series basis matrix. With coefficient vector The product; Since the polynomial frequency domain basis functions are based on the generalized Euler formula, the power series basis matrix... The same applies to polynomial frequency domain basis functions; for any set of frequency domain basis functions... The coefficient of its corresponding order is denoted as (i=0,…,k-1), then the following matrix relationship can be obtained: in, It is an N-row, k-column matrix composed of polynomial frequency domain basis functions; Given a k-row, k-column coefficient matrix constructed from the coefficients of the corresponding basis functions, mapping the original time-domain power series solution to the polynomial frequency-domain basis functions yields the following formula: in, The polynomial frequency domain coefficients (i.e., the weights of each basis function) to be obtained are k-row, 1-column vectors. The transformation matrix between the two sets of basis functions can be obtained, as shown in the following formula: This allows the power series basis functions to be projected onto the polynomial frequency domain function, and the vector... Each component corresponds to a predefined "frequency index" and its amplitude of the sine and cosine basis functions. As the time-domain window is updated, the spectrum of the local window is output synchronously.

Images