Power quality disturbance feature extraction method and system based on segmented multi-resolution s-transform

Abstract

The application discloses a power quality disturbance feature extraction method and system based on segmented multi-resolution S transform, relates to the technical field of power quality monitoring, and aims to solve the problem that traditional time-frequency analysis methods are difficult to accurately capture power quality disturbance features in different frequency bands due to fixed resolution. The application comprises establishing a mathematical model of power quality disturbance signals, including various single and composite disturbance models; discretizing the signals based on continuous S transform and applying one-dimensional discrete S transform; dividing the frequency bands into three segments, i.e., low, medium and high, according to disturbance frequency characteristics; introducing a Gaussian window function with different adjustment factors into each frequency band to adaptively adjust the time-frequency resolution; combining S transform with the window function to obtain a discrete expression of segmented multi-resolution S transform; and extracting disturbance feature parameters based on the time-frequency matrix obtained through transformation. The technical scheme realizes adaptive optimization of time-frequency resolution, and improves the extraction accuracy and reliability of complex power quality disturbance features.

Description

Technical Field

[0001] This invention relates to the field of power quality monitoring, and in particular to a method and system for extracting power quality disturbance features based on piecewise multi-resolution S-transform. Background Technology

[0002] In recent years, to meet the ever-increasing energy demand, renewable energy has been integrated into the power system on a large scale. Unlike traditional large-scale centralized power generation, renewable energy output exhibits significant volatility and intermittency, posing a severe challenge to the stable operation of the power system. Furthermore, the power system contains a large number of nonlinear loads, such as electric vehicle charging stations and power electronic switches, whose interaction with renewable energy further exacerbates power quality problems in the grid.

[0003] Currently, power quality problems mainly stem from the following two aspects:

[0004] From the perspective of renewable energy, there is an unavoidable voltage difference between wind and solar power generation units and the power grid, which can easily cause voltage spurs, voltage dips, and flicker during grid connection or disconnection. At the same time, in order to achieve grid connection of renewable energy, the commonly used power electronic converters, while completing energy conversion, also inject harmonic currents into the grid, resulting in voltage waveform distortion.

[0005] From the perspective of the power grid, electromagnetic transient processes such as the switching of transmission lines, the switching of capacitor banks, and lightning discharges may cause voltage spikes, pulses, and transient oscillations. In addition, internal system factors such as single-phase grounding faults, transformer winding impedance mismatch, and three-phase load imbalance can also cause power quality disturbances.

[0006] Power quality issues not only affect the stable operation of the power system itself but can also cause equipment failures on the user side. Particularly in industries such as papermaking, semiconductors, computers, communications, electronics manufacturing, pharmaceuticals, and data centers, certain transient disturbances can lead to production interruptions, equipment damage, and significant economic losses. Research reports indicate that for large enterprises, a single power outage can cause losses of millions of dollars per hour.

[0007] Therefore, to minimize the negative impact of power quality disturbances, it is essential to first achieve accurate feature extraction and type identification of disturbance signals. By accurately extracting disturbance features and identifying their types, the start and end times of disturbances can be quickly located, and the root cause can be traced, thus providing crucial evidence for the analysis, diagnosis, fault location, and remediation of power quality problems.

[0008] However, existing methods for extracting power quality disturbance features have many limitations: the short-time Fourier transform, due to its fixed window, struggles to balance time and frequency resolution when analyzing non-stationary signals; the traditional S-transform can only reflect the amplitude of a finite number of frequency components at different times, failing to accurately capture fundamental wave fluctuations and interharmonic characteristics; and empirical mode decomposition is limited by mode aliasing and endpoint effects, affecting the accuracy of feature extraction. All these methods struggle to accurately capture power quality disturbance features across different frequency bands. Summary of the Invention

[0009] This invention aims to overcome the shortcomings of existing power quality disturbance feature extraction methods and provides a feature extraction method and system based on piecewise multi-resolution S-transform. This method effectively and accurately extracts the time-frequency features of disturbance signals, thereby providing a reliable technical means for the analysis, diagnosis, fault location, and mitigation of power quality problems. To achieve the above objective, this invention adopts the following technical solution.

[0010] The first technical solution of this invention is: a method for extracting power quality disturbance features based on piecewise multi-resolution S-transform, comprising the following steps:

[0011] 1) Establish a mathematical model for power quality disturbance signals, including multiple single disturbance models and multiple composite disturbance models;

[0012] 2) Based on the continuous S-transform of the time-domain signal, the voltage signal is sampled into a discrete time series and then calculated using a one-dimensional discrete S-transform;

[0013] 3) Based on the frequency characteristics of power quality disturbances, the frequency range is divided into low-frequency, mid-frequency, and high-frequency bands;

[0014] 4) Gaussian window functions with different adjustment factors are introduced in the low-frequency, mid-frequency, and high-frequency bands respectively to adjust the time-frequency resolution of each band;

[0015] 5) Based on frequency segmentation, the S-transform is combined with a Gaussian window function with an adjustment factor to perform transformation processing, resulting in a discrete expression for the piecewise multi-resolution S-transform.

[0016] 6) Based on the time-frequency matrix obtained by the piecewise multi-resolution S-transform, extract the characteristic parameters of power quality disturbance.

[0017] This technical solution innovatively introduces a new adjustment factor and proposes a power quality disturbance feature extraction method based on segmented multi-resolution S-Transform (SMST) through a unique frequency segmentation method. This method can meet the frequency resolution requirements and effectively and accurately extract power quality disturbance features.

[0018] This technical solution segments the main frequency ranges of different types of disturbances (low frequency, mid frequency, and high frequency) and introduces Gaussian window functions with different adjustment factors in different frequency bands. This allows the analysis process to adaptively adjust its time-frequency resolution according to the disturbance characteristics of different frequency bands, creating conditions for more accurate capture of disturbance features. In step 5), by combining segmentation, the introduction of Gaussian window functions with adjustment factors, and S-transform, a segmented multi-resolution S-transform (SMST) is constructed. This achieves higher frequency resolution at low frequencies and higher time resolution at high frequencies, effectively overcoming the limitation of Heisenberg uncertainty principle on single-resolution analysis and improving the method's ability to analyze complex and transient disturbances. Step 6) performs feature extraction based on the optimized time-frequency matrix obtained in step 5). Since this time-frequency matrix contains clearer and more accurate time-frequency domain information than traditional methods, the disturbance features extracted from it (such as energy distribution and amplitude changes) will theoretically have higher discriminative power and reliability, providing a better data foundation for subsequent disturbance classification, diagnosis, and mitigation. This technical solution achieves a leap from "fixed" to "adaptive and adjustable" time-frequency analysis resolution, thereby comprehensively improving the analysis capability and feature extraction quality of complex power quality disturbance signals.

[0019] As a preferred technical means: in step 1), the single disturbance model includes voltage swell, voltage drop, voltage interruption, harmonic, transient oscillation, transient pulse and flicker models; the composite disturbance model includes a model composed of at least two combinations of the single disturbances.

[0020] This technical solution covers the most common and typical disturbance types in the field of power quality, ensuring that subsequent feature extraction and identification algorithms are not targeted at individual phenomena, but rather at a complete and representative set of disturbances, fundamentally guaranteeing the universality and completeness of the analysis method. Disturbances are divided into two main categories: "single" and "composite," guiding the entire system to not only identify single, standard disturbance events (such as voltage sags), but also to analyze more complex composite disturbances (such as harmonic-superimposed voltage sags) composed of multiple single disturbances. This establishes a clear direction and requirement for developing high-precision classification and identification algorithms. In actual power grids, both purely single disturbances and more complex composite disturbances can occur. This technical solution does not stop at ideal single disturbance analysis, but actively encompasses complex composite disturbance models, making it closer to engineering practice.

[0021] As a preferred technical means: in step 3), the frequency range is divided as follows: 1Hz to 100Hz is the low frequency band, 100Hz to 700Hz is the mid frequency band, and greater than 700Hz is the high frequency band.

[0022] This technical solution aligns with the occurrence mechanisms and energy concentration areas of different types of power quality disturbances, effectively isolating voltage changes near the fundamental frequency (such as swells, dips, and interruptions), harmonics and interharmonics in the mid-frequency range, and transient oscillations in the high-frequency band. This allows each frequency band to focus on specific types of disturbances in subsequent analyses, enhancing the specificity of the analysis. This technical solution defines the strategy of applying which resolution in which area (which frequency band). For example, in the low-frequency band of 1-100Hz (containing crucial fundamental frequency information), higher frequency resolution is needed to accurately measure amplitude changes; while in the high-frequency band >700Hz (containing rapid transient processes), higher time resolution is needed to capture the onset and morphology of oscillations. This avoids using a single, potentially suboptimal, analysis strategy across the entire frequency range, thereby improving overall computational efficiency and analytical accuracy, allowing computational resources to be more concentrated on the core issues that need to be addressed in each frequency band.

[0023] As a preferred technical approach: In step 4), the adjustment factors introduced for different frequency bands are specifically as follows:

[0024] In the low-frequency range, the window width factor is inversely proportional to the frequency raised to the power of a1. The rate of change of the window width with frequency is controlled by the first adjustment factor a1, and the frequency resolution is guaranteed by the second adjustment factor b1.

[0025] In the mid-frequency band, the window width factor is inversely proportional to the sum of the frequency raised to the power of a² plus the fourth adjustment factor b², in order to balance the time resolution and the window width, where a² is the third adjustment factor.

[0026] In the high-frequency band, the window width factor is inversely proportional to the quarter-th power of the value obtained by multiplying the difference between the sampling frequency and the current frequency by the frequency raised to the power of a3, in order to adjust the window width to an appropriate size. a3 is the fifth adjustment factor.

[0027] This technical solution breaks through the limitation of fixed time-frequency resolution in traditional S-transforms. By introducing factors with clear physical meaning and adjustment functions in different frequency bands, it achieves flexible configuration of adaptive and precisely controllable time-frequency resolution. Specifically, instead of using a uniform window function, this solution designs window width control strategies with different mathematical forms and adjustment factors for the low, medium, and high frequency bands. This allows the shape of the window function to be dynamically adjusted according to the characteristics of the analyzed frequency band, thereby achieving:

[0028] In the low-frequency band, the sensitivity of the window width as a function of frequency is controlled by a1, and the window width is ensured not to be too narrow by b1, thereby prioritizing the critical frequency resolution at and near the fundamental frequency to accurately measure voltage amplitude changes.

[0029] In the mid-frequency band, the introduction of b2 effectively prevents the window width from being too large at specific frequency points, cleverly balancing time resolution and frequency resolution, making it particularly suitable for analyzing harmonics and interharmonics with certain broadband characteristics.

[0030] In the high-frequency band, by introducing This feature, in conjunction with a3, allows for effective control of the window width at high frequencies (close to the Nyquist frequency), avoiding the problem of a sharp drop in frequency resolution caused by excessively narrow window width, and ensuring that usable time-frequency analysis performance can still be maintained in high-frequency transient signal analysis.

[0031] Multiple adjustment factors (a1, b1, a2, b2, a3; specifically, a1 is the low-frequency band window width change rate adjustment factor, b1 is the low-frequency band frequency resolution guarantee factor, a2 is the mid-frequency band time resolution adjustment factor, b2 is the mid-frequency band window width auxiliary control factor, and a3 is the high-frequency band window width adaptation adjustment factor) introduced in the three frequency bands provide rich "tuning parameters" for this method. Users can optimize these factors according to specific signal characteristics and analysis priorities (e.g., whether to focus more on sag depth or oscillation frequency). This adjustability greatly enhances the method's ability to cope with different power grid environments and different disturbance types, upgrading it from a fixed analysis tool to a configurable and highly adaptable analysis platform. The core challenge in the low-frequency band is the need for high frequency resolution, which is guaranteed by b1. The core challenge in the mid-frequency band is resolution balance, which is "smoothed" by b2. The core challenge in the high-frequency band is preventing frequency resolution degradation at high frequencies, which is addressed by b1. The terms are suppressed. This targeted setting based on physical problems makes the entire time-frequency analysis process more accurate and reliable at every stage.

[0032] As a preferred technical means: in step 5), obtaining the discrete expression of the piecewise multi-resolution S-transform includes:

[0033] For the fundamental frequency component, its segmented multi-resolution S-transform coefficients are directly determined by the average value of the discrete Fourier transform coefficients of the signal;

[0034] For the low-frequency band, the piecewise multi-resolution S-transform coefficients are obtained by frequency shifting the discrete Fourier transform spectrum of the signal, multiplying it with an exponential window function whose window width is controlled by a first adjustment factor a1 and a second adjustment factor b1, and then performing an inverse Fourier transform. The window width is inversely proportional to the frequency raised to the power of a1.

[0035] For the mid-frequency band, the piecewise multi-resolution S-transform coefficients are obtained by frequency shifting the discrete Fourier transform spectrum of the signal, multiplying it with an exponential window function whose window width is jointly determined by the third adjustment factor a2 and the fourth adjustment factor b2, and then performing an inverse Fourier transform. The window width is jointly adjusted by the sum of the frequency raised to the power of a2 and b2.

[0036] For the high-frequency band, the piecewise multi-resolution S-transform coefficients are obtained by frequency shifting the discrete Fourier transform spectrum of the signal, multiplying it by a specific exponential window function, and then performing an inverse Fourier transform. The window width of the exponential window function is determined by a fifth adjustment factor a3, the sampling frequency, and the current frequency; specifically, the window width is proportional to the frequency of the signal. It is inversely proportional to the power of a quarter, where Sampling frequency, This is the current frequency.

[0037] This technical solution employs a simplified calculation method for the fundamental frequency component (n=0), directly determined by the average value of the DFT coefficients. This avoids unnecessary complex convolution operations on the fundamental frequency, optimizes the overall calculation process, and improves computational efficiency. For low, medium, and high frequency bands, the solution adopts a unified calculation paradigm of "frequency shift → window function filtering → inverse Fourier transform," performing convolution operations directly in the frequency domain. This method is not only mathematically equivalent but also computationally stable and highly accurate, precisely reflecting the window function adjustment effect carefully designed for each frequency band in step 4). Within the unified algorithm flow (frequency shift, window function multiplication, inverse transform), this technical solution achieves differentiated time-frequency analysis results by embedding window functions specifically designed for different frequency bands and containing specific adjustment factors. For the low frequency band, it embeds... An inversely proportional window achieves high frequency resolution. For the mid-frequency band, an embedded... Adjustable windows achieve resolution balance. For high-frequency bands, [the following is a description of a feature / mechanism] is embedded. The inversely proportional window effectively suppresses performance degradation at high frequencies. This ensures that the entire method maintains the inherent consistency of the algorithm structure while possessing strong flexibility to meet the needs of different frequency bands. This technical solution allows those skilled in the art to directly program and implement the entire SMST transform without additional creative work, lowering the threshold for technical application and ensuring the consistency and reliability of results obtained by different implementers.

[0038] As a preferred technical approach, the extracted power quality disturbance characteristic parameters include at least one of the following:

[0039] The minimum amplitude of the fundamental frequency component is used to characterize the degree of energy distribution dip in the fundamental frequency component of the power quality disturbance signal;

[0040] The maximum amplitude of the fundamental frequency component is used to characterize the degree of energy distribution expansion of the fundamental frequency component of the power quality disturbance signal;

[0041] The correlation coefficient of the fundamental frequency component is used to check for obvious periodic fluctuations in order to identify voltage flicker;

[0042] The energy of the row vectors of the time-frequency matrix corresponding to the mid-frequency band is used to characterize the energy distribution of the harmonic components of the power quality disturbance.

[0043] The root mean square value of the row vector of the time-frequency matrix corresponding to the high-frequency band is used to characterize the energy distribution of transient oscillations caused by power quality disturbances.

[0044] The five characteristics selected in this technical solution correspond one-to-one with the core physical phenomena of power quality disturbances: the fundamental frequency amplitude characteristics (minimum / maximum) directly quantify the severity of the most common disturbances such as voltage swells, droops, and interruptions. The fundamental frequency correlation coefficient is used to capture the periodic modulation pattern unique to voltage flicker. The mid-frequency energy directly reflects the cumulative intensity of harmonic components in a specific frequency band. The high-frequency root mean square effectively characterizes the impact intensity of high-frequency disturbances such as transient oscillations in the time domain.

[0045] This technical solution constructs a multi-dimensional feature space, which is conducive to accurate classification. The multi-dimensional feature vectors cover the amplitude domain, correlation domain, and energy domain. For example, voltage sag is mainly manifested as a dip in the fundamental frequency amplitude, while harmonic disturbances are manifested as an increase in intermediate frequency energy. By examining these features of different dimensions at the same time, the ability to distinguish different types of disturbances can be greatly enhanced, effectively avoiding misjudgment and laying a solid foundation for building a high-precision automatic classifier.

[0046] This technical solution enables the analysis of complex disturbances. Since these features are extracted from different aspects of the signal (fundamental frequency, intermediate frequency, and high frequency), when a complex disturbance occurs (such as "harmonics + sag"), its feature vector will simultaneously exhibit anomalies in multiple features. For example, the minimum amplitude of the fundamental frequency will decrease (characterizing a sag), while the energy in the intermediate frequency band will increase (characterizing harmonics). This allows the feature set to not only identify single disturbances but also possess the potential to analyze and identify complex complex disturbances.

[0047] Another technical solution of the present invention is: a power quality disturbance feature extraction system based on piecewise multi-resolution S-transform; the power quality disturbance feature extraction system adopts the aforementioned power quality disturbance feature extraction method based on piecewise multi-resolution S-transform, and the system includes:

[0048] The signal modeling module is used to establish a mathematical model of power quality disturbance signals, which includes multiple single disturbance models and multiple composite disturbance models;

[0049] The signal transformation module is used for continuous S-transform based on time-domain signals, sampling the signal into a discrete time series, and applying a one-dimensional discrete S-transform for calculation;

[0050] The frequency band division module is used to divide the frequency range into low-frequency, mid-frequency, and high-frequency bands based on the frequency characteristics of power quality disturbances.

[0051] The window function adjustment module is used to introduce Gaussian window functions with different adjustment factors in the low-frequency band, mid-frequency band and high-frequency band respectively, so as to adjust the time-frequency resolution of each frequency band;

[0052] The piecewise multi-resolution transform module is used to segment according to frequency, combine the S-transform with a Gaussian window function with an adjustment factor, and perform transform processing to obtain the discrete expression of the piecewise multi-resolution S-transform.

[0053] The feature extraction module is used to extract the feature parameters of power quality disturbance based on the time-frequency matrix obtained by the piecewise multi-resolution S-transform.

[0054] The signal modeling module establishes a mathematical model system of "multiple single disturbance models + multiple composite disturbance models," which can comprehensively cover common disturbance types in the power quality field. Compared with traditional solutions that only model single disturbances, this module can avoid the problem of "disturbance omission" caused by incomplete modeling, and provide "full-scenario adaptable" initial model support for subsequent signal transformation and feature extraction, ensuring coverage of various disturbances in complex power grids.

[0055] The signal transformation module leverages the time-frequency analysis advantages of the continuous S-transform (which requires no preset window function type and can simultaneously preserve time and frequency domain information). Through a process of "time-domain signal sampling → discrete time series → one-dimensional discrete S-transform calculation," it transforms continuous-domain disturbance signals into a discrete-domain computable form. This retains the inherent advantage of the S-transform in characterizing the time-frequency features of power quality disturbances while adapting to the numerical computation needs of computers in engineering through "discretization processing," thus solving the problem of "continuous S-transform being difficult to directly implement in engineering" and improving the system's practical application feasibility.

[0056] The frequency band segmentation module precisely divides the frequency range into low-frequency, mid-frequency, and high-frequency bands based on the frequency distribution characteristics of different power quality disturbances: the low-frequency band corresponds to fundamental frequency disturbances such as voltage swells / droops / interruptions, the mid-frequency band corresponds to mid-frequency disturbances such as harmonics, and the high-frequency band corresponds to high-frequency disturbances such as transient oscillations. Compared to the traditional "uniform processing across the entire frequency band" approach, this segmented design avoids mutual interference between disturbances in different frequency bands, allowing subsequent window function adjustment and transformation processing to "precisely target the characteristics of disturbances in each frequency band," thus providing a prerequisite for differentiated optimization of time-frequency resolution.

[0057] The window function adjustment module introduces Gaussian window functions with different adjustment factors for the low, medium, and high frequency bands: In the low-frequency band, the adjustment factor controls the rate of change of the window width with frequency to ensure the time resolution of the fundamental frequency disturbance; in the medium-frequency band, the adjustment factor balances the time resolution and window width to meet the extraction requirements of harmonic disturbances; and in the high-frequency band, the adjustment factor is combined with the sampling frequency to adjust the window width to adapt to the high-frequency characteristics of transient oscillations. This overcomes the limitation of the traditional S-transform's "fixed time-frequency resolution," allowing the window function of each frequency band to precisely match the frequency characteristics of the corresponding disturbance, avoiding problems such as "loss of low-frequency disturbance details" or "high-frequency disturbance aliasing" caused by inappropriate resolution, and maximizing the preservation of disturbance information in each frequency band.

[0058] The piecewise multi-resolution transform module generates a discrete expression for the piecewise multi-resolution S-transform (SMST) through an integrated design of "frequency segmentation + combined with an adjusted Gaussian window function + S-transform". This expression is not a simple superposition of the processing results for each frequency band, but rather incorporates the time-frequency resolution optimization effects of each frequency band into the final time-frequency matrix through a coherent process of discrete Fourier transform (frequency shift), exponential window function multiplication, and inverse Fourier transform. Compared to the fixed time-frequency matrix of the traditional S-transform, the SMST matrix output by this module can "preserve key time-frequency information" for perturbations in different frequency bands, providing a data source with "high signal-to-noise ratio and high detail" for subsequent feature extraction.

[0059] The feature extraction module is based on the SMST time-frequency matrix to extract feature parameters directly related to power quality disturbances. These feature parameters are not generalized time-frequency indices, but rather the core characteristics of the disturbances. This avoids redundant calculations caused by extracting irrelevant features, allowing the extracted features to be directly used as the "key basis" for subsequent disturbance identification and fault location, thus improving the efficiency and accuracy of disturbance analysis.

[0060] As a preferred technical means: in the signal modeling module, the single disturbance model includes voltage swell, voltage drop, voltage interruption, harmonic, transient oscillation, transient pulse and flicker models; the composite disturbance model includes a model composed of at least two combinations of the single disturbances; in the frequency band division module, the frequency range is specifically divided as follows: 1Hz to 100Hz is the low frequency band, 100Hz to 700Hz is the mid frequency band, and greater than 700Hz is the high frequency band.

[0061] The signal modeling module provides a standardized set of analysis objects and diagnostic criteria through a comprehensive library of pre-built single and complex disturbance models, ensuring the comprehensiveness and professionalism of the analysis objectives. Simultaneously, the frequency band division module precisely defines the boundaries of low-frequency, mid-frequency, and high-frequency regions based on the physical characteristics of different disturbances, providing a unified and mechanism-compliant frequency analysis framework for all subsequent processing modules. The collaborative work of these two modules, from the two fundamental levels of "object definition" and "analysis strategy," lays a solid foundation for the entire system to achieve accurate and efficient extraction of power quality disturbance characteristics, significantly improving the system's processing specificity and reliability.

[0062] As a preferred technical approach, the window function adjustment module introduces adjustment factors for different frequency bands in the following specific manner:

[0063] In the low-frequency range, the window width factor is inversely proportional to the frequency raised to the power of a1. The rate of change of the window width with frequency is controlled by the first adjustment factor a1, and the frequency resolution is guaranteed by the second adjustment factor b1.

[0064] In the mid-frequency band, the window width factor is inversely proportional to the sum of the frequency raised to the power of a² plus the fourth adjustment factor b², in order to balance the time resolution and the window width, where a² is the third adjustment factor.

[0065] In the high-frequency band, the window width factor is inversely proportional to the quarter-th power of the value obtained by multiplying the difference between the sampling frequency and the current frequency by the frequency raised to the power of a3, in order to adjust the window width to an appropriate size. a3 is the fifth adjustment factor.

[0066] The function adjustment module achieves adaptive and precise control of time-frequency resolution by tailoring mathematical adjustment strategies with clear physical meaning for different frequency bands: in the low-frequency band, it prioritizes frequency resolution to accurately analyze voltage amplitude changes; in the mid-frequency band, it intelligently balances time-frequency resolution to accurately capture harmonic characteristics; and in the high-frequency band, it effectively suppresses frequency resolution degradation to clearly characterize transient oscillation processes. This provides highly optimized analysis conditions for the core conversion module and significantly improves the system's ability and accuracy in resolving complex disturbance characteristics.

[0067] As a preferred technical means, the segmented multi-resolution transformation module includes:

[0068] The fundamental frequency processing unit is used to determine the coefficients of the fundamental frequency component directly from the average value of the discrete Fourier transform coefficients of the signal;

[0069] The low-frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for the low-frequency band, multiplying it with an exponential window function whose window width is controlled by a first adjustment factor a1 and a second adjustment factor b1, and then performing an inverse Fourier transform to obtain its coefficients, wherein the window width is inversely proportional to the frequency to the power of a1.

[0070] The intermediate frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for the intermediate frequency band, multiplying it with an exponential window function whose window width is jointly determined by the third adjustment factor a2 and the fourth adjustment factor b2, and then performing an inverse Fourier transform to obtain its coefficients, wherein the window width is jointly adjusted by the sum of the frequency raised to the power of a2 and b2.

[0071] The high-frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for high-frequency bands, multiplying it with an exponential window function whose window width is jointly determined by the fifth adjustment factor a3, the sampling frequency and the current frequency, and whose window width is inversely proportional to the quarter power of the product of the difference between the sampling frequency and the current frequency and the current frequency raised to the power of a3, and then performing an inverse Fourier transform to obtain its coefficients.

[0072] The segmented multi-resolution transformation module of this technical solution sets up four dedicated processing units for fundamental frequency, low frequency, intermediate frequency, and high frequency. It adopts a unified architecture of "frequency shift-window function multiplication-inverse transformation" but incorporates differentiated window function adjustment strategies. While ensuring the consistency of the algorithm structure, it achieves accurate and efficient parallel processing of signals across the entire frequency band: the fundamental frequency unit improves efficiency by simplifying calculations, the low frequency unit ensures high frequency resolution near the fundamental frequency, the intermediate frequency unit balances the time-frequency resolution of harmonic analysis, and the high frequency unit effectively suppresses performance degradation at the end of the frequency domain to accurately capture transient features. Thus, at the system level, it achieves optimized allocation of computing resources and maximizes the performance of time-frequency analysis across the entire frequency band.

[0073] Beneficial Effects: This technical solution effectively overcomes the limitation of fixed time-frequency resolution in traditional methods by introducing Gaussian window functions with specific adjustment factors in different frequency bands. It maintains high frequency resolution in the fundamental frequency region and high time resolution in the high-frequency region, ultimately extracting characteristic parameters representing the nature of different disturbances from the optimized time-frequency matrix. This significantly improves the accuracy, adaptability, and reliability of power quality disturbance analysis. Specifically:

[0074] 1. Enhanced the relevance and adaptability of time-frequency analysis.

[0075] This technical solution segments the main frequency ranges of different types of disturbances (low frequency, mid frequency, and high frequency) and introduces Gaussian window functions with different adjustment factors in different frequency bands. This enables adaptive adjustment of the time-frequency resolution for different frequency bands.

[0076] 2. It breaks through the limitations of fixed resolution and optimizes the overall analysis performance.

[0077] This technical solution combines piecewise Gaussian window functions with adjustment factors and the S-transform to form a piecewise multi-resolution S-transform (SMST). The SMST transform accurately identifies voltage sags at high frequency resolution in the low-frequency band; it captures harmonic components simultaneously at balanced resolution in the mid-frequency band; and its high time resolution in the high-frequency band is unaffected by low-frequency components, maintaining the independence of transient characteristics. The SMST transform effectively overcomes the limitations of the Heisenberg uncertainty principle on single-resolution analysis, improving the method's ability to analyze complex and transient disturbances. Attached Figure Description

[0078] Figure 1 This is a flowchart of the S-transform calculation of the present invention;

[0079] Figure 2 This is the basic process of the SMST detection method of the present invention. Detailed Implementation

[0080] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0081] Example 1:

[0082] A method for extracting power quality disturbance features based on piecewise multi-resolution S-transform includes the following steps:

[0083] S1: Establish a mathematical model for power quality disturbance signals, which is divided into 7 single disturbance models and 12 composite disturbance models;

[0084] S2: Based on the definition of the continuous S-transform of the time-domain signal x(t), the signal is sampled into a discrete time series, and the calculation formula of the one-dimensional discrete S-transform is derived.

[0085] S3: Based on the different frequency ranges in which different disturbances occur, the region from 1Hz to 100Hz is set as the low frequency band, the region from 100Hz to 700Hz is set as the mid frequency band, and the region greater than 700Hz is set as the high frequency band.

[0086] S4: Based on the idea of ​​generalized S-transform, new adjustment factors are introduced into the Gaussian window function in the low-frequency, mid-frequency and high-frequency regions respectively to obtain the window width factor of the new Gaussian window function in different regions.

[0087] S5: The S-transform is segmented according to the low-frequency, mid-frequency, and high-frequency regions. A Gaussian window function with an adjustment factor is introduced to change the time-frequency resolution of the S-transform. After performing a Fourier transform, the expression for the segmented multi-resolution S-transform (SMST) is obtained.

[0088] S6: Extract the disturbance characteristics based on the distribution characteristics of power quality disturbances in the time and frequency domains.

[0089] This embodiment extracts the disturbance characteristics of power quality disturbances based on their distribution in the time and frequency domains, providing a basis for analyzing, diagnosing, locating faults, and studying power quality problems. Accurate extraction of power quality disturbance signals can reduce and control the negative impacts of power quality disturbances.

[0090] In this embodiment, the models for the seven single perturbation models are established as follows:

[0091] This represents a disturbance signal. The rated angular frequency of the disturbance signal. For the rated frequency, Rated frequency The corresponding signal period, It is a step signal. This represents the start time of the disturbance. This represents the end time of the disturbance.

[0092] The standard signal model is: U Its model parameters are .

[0093] I. The voltage sag model is as follows:

[0094] ,

[0095] Its model parameters are: , , This is the adjustment factor for the transient increase amplitude;

[0096] II. The voltage sag model is as follows:

[0097] ,

[0098] Its model parameters are , , This is the attenuation factor for the transient amplitude.

[0099] III. The voltage interruption model is as follows:

[0100] ,

[0101] Its model parameters are: , , This is the interruption amplitude attenuation factor;

[0102] IV. The harmonic model is as follows:

[0103] ,

[0104] Its model parameters are , ; The amplitude coefficient of the i-th harmonic;

[0105] V. The transient oscillation model is as follows:

[0106] ,

[0107] Its model parameters are:

[0108] , , , , ; For the amplitude coefficient of the oscillation component, The oscillation decay time constant is The oscillation angular frequency, The oscillation frequency;

[0109] VI. The transient pulse model is as follows:

[0110] ,

[0111] Its model parameters are: , , The amplitude of the pulse component;

[0112] VII. The flicker model is as follows:

[0113] ,

[0114] Its model parameters are: , , is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient;

[0115] The following twelve composite disturbance models are established:

[0116] I. The harmonic + transient rise model is as follows:

[0117] ,

[0118] Its model parameters are: , , , ; This is the adjustment factor for the transient increase. The amplitude coefficient of the i-th harmonic;

[0119] II. The harmonic + sag model is as follows:

[0120] ,

[0121] Its model parameters are: , , , ; This is the attenuation factor for the transient amplitude. The amplitude coefficient of the i-th harmonic;

[0122] III. The harmonic + interruption model is as follows:

[0123] ,

[0124] Its model parameters are: , , , ; This is the interruption amplitude attenuation factor. The amplitude coefficient of the i-th harmonic;

[0125] IV. The harmonic + oscillation model is as follows:

[0126] ,

[0127] Its model parameters are:

[0128] , , , , , , ; For the amplitude coefficient of the oscillation component, The oscillation decay time constant is The oscillation angular frequency, The oscillation frequency is... The amplitude coefficient of the i-th harmonic;

[0129] V. The flicker + harmonic model is as follows:

[0130] ,

[0131] Its model parameters are: , , , ; b is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient. The amplitude coefficient of the i-th harmonic;

[0132] VI. The flicker + transient rise model is as follows:

[0133] ,

[0134] Its model parameters are: , , , ; This is the adjustment factor for the transient increase. is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient;

[0135] VII. The flicker + temporary drop model is as follows:

[0136] ,

[0137] Its model parameters are: , , , ; This is the attenuation factor for the transient amplitude. is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient;

[0138] 8. The flicker + oscillation model is as follows:

[0139] ,

[0140] Its model parameters are:

[0141] , , , , , , ; For the amplitude coefficient of the oscillation component, The oscillation decay time constant is The oscillation angular frequency, The oscillation frequency is... is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient;

[0142] IX. The oscillation + temporary rise model is as follows:

[0143] ,

[0144] Its model parameters are:

[0145] , , , , , , , For the amplitude coefficient of the oscillation component, The oscillation decay time constant is The oscillation angular frequency, The oscillation frequency is... t3 is the transient rise amplitude adjustment factor, t4 is the transient rise start time, and t4 is the transient rise end time.

[0146] 10. The flicker + harmonic + transient rise model is as follows:

[0147] ,

[0148] Its model parameters are:

[0149] , , , , , ; This is the adjustment factor for the transient increase. b is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient. The amplitude coefficient of the i-th harmonic;

[0150] XI. The flicker + harmonics + sag model is as follows:

[0151] ,

[0152] Its model parameters are:

[0153] , , , , ; This is the attenuation factor for the transient amplitude. b is the flicker modulation amplitude coefficient, and b is the flicker modulation frequency coefficient. The amplitude coefficient of the i-th harmonic;

[0154] 12. The harmonic + oscillation + sag model is as follows:

[0155]

[0156] Its model parameters are:

[0157] , , , , , , , , ; This is the attenuation factor for the transient amplitude. The amplitude coefficient of the i-th harmonic. For the amplitude coefficient of the oscillation component, The oscillation decay time constant is The oscillation angular frequency, t3 is the oscillation frequency, t4 is the start time of the sag, and t4 is the end time of the sag.

[0158] In step S2, based on the time-domain signal Definition of the continuous S-transform:

[0159]

[0160] In the formula, f is the frequency and t is the time. As a time shift factor; the signal Sampled discrete time series In the formula, T is the sampling time interval of the signal. If the total number of sampling points is N, k = 0, 1, ..., N 1, then The discrete Fourier transform is:

[0161]

[0162] In the formula, n represents the time sampling points, which take values ​​of 0, 1, ..., N-1. Let... , Then the expression for the one-dimensional discrete S-transform is obtained as follows:

[0163]

[0164] like Figure 1 The diagram shows the calculation flowchart for the S-transform.

[0165] In step S3, the region from 1Hz to 100Hz is designated as the low-frequency band, the region from 100Hz to 700Hz as the mid-frequency band, and the region above 700Hz as the high-frequency band. The main reason for this is that in the field of power quality analysis, there are various types of disturbances, and the frequency ranges corresponding to different types of disturbances differ significantly. Based on the mathematical expression of the disturbance signal, it is clear that common disturbances such as voltage swells, voltage dips, and voltage interruptions mainly occur around the fundamental frequency (50Hz). Given that this region requires higher monitoring accuracy and better time resolution, the frequency range of 1Hz to 100Hz can be defined as the low-frequency region.

[0166] From the perspective of disturbance characteristics in the mid-frequency region, the main disturbance forms in this frequency band are harmonics and interharmonics (in actual analysis, only the 3rd to 11th harmonics are usually considered). Based on this characteristic, the frequency range of 100Hz to 700Hz can be defined as the mid-frequency band. In the high-frequency region, transient oscillations are the most typical type of disturbance. Combining their frequency characteristics, the region with frequency values ​​greater than 700Hz can be defined as the high-frequency band.

[0167] In step S4, since the time-frequency resolution of the S-transform is relatively fixed and is limited by the Heisenberg uncertainty principle, its time-frequency resolution can only be controlled by adjusting the window width of the window function at different frequencies.

[0168] Based on the idea of ​​generalized S-transform, a Gaussian window function with an adjustment factor is introduced to change the time-frequency resolution of the S-transform.

[0169] Define the window width factor of the Gaussian window function in the low-frequency region from 1Hz to 100Hz:

[0170]

[0171] By introducing a new adjustment factor a1, the window width changes faster with frequency at low frequencies, while the adjustment factor b1 is used to ensure that the window width is not too narrow and loses the required frequency resolution.

[0172] Define the window width factor of the Gaussian window function in the mid-frequency region from 100Hz to 700Hz:

[0173]

[0174] The adjustment factor a2 ensures the time resolution of the S-transform, while the new adjustment factor b2 can assist in the control of the window width.

[0175] Define the window width factor of the Gaussian window function in the high-frequency region above 700Hz:

[0176]

[0177] In the formula This represents the signal sampling frequency. The adjustment factor a3 is used to adjust the window width to an appropriate size.

[0178] In step S5, based on the above analysis, the discretization formula for the piecewise multi-resolution S-transform (SMST) obtained after Fourier transform in discrete signal processing is as follows:

[0179]

[0180] See Figure 2 The basic process of the SMST detection method is obtained.

[0181] In step S6, using the aforementioned analysis method, a two-dimensional time-frequency matrix SMST(m,n) containing massive amounts of time-frequency information can be obtained. Based on this SMST matrix, a perturbation feature extraction method for SMST(m,n) is proposed.

[0182] From a matrix function perspective, the SMST, as a dedicated two-dimensional matrix for time-frequency analysis of power quality disturbance signals, encompasses rich time-frequency domain information. The characteristics of each power quality signal require the use of its own energy and frequency parameters to be represented. To effectively improve the extraction efficiency of signal time-frequency information, based on the distribution characteristics of power quality disturbances in the time-frequency domain, this embodiment extracts the following five core power quality features:

[0183] (1) Feature 1: Minimum amplitude of fundamental frequency component, used to characterize the degree of energy distribution depression of fundamental frequency component of power quality disturbance signal.

[0184]

[0185] (2) Feature 2: Maximum amplitude of the fundamental frequency component, used to characterize the degree of energy distribution expansion of the fundamental frequency component of the power quality disturbance signal.

[0186]

[0187] In the formula, R(m) represents the average value of the fundamental frequency content of the power quality disturbance signal. This represents the average value of the fundamental frequency content of the standard signal. R(m) can be obtained using the following formula:

[0188]

[0189] The J() expression is shown below:

[0190]

[0191] In the formula J( () represents time location The surrounding fundamental frequency curves, This is the starting point of the time window; during the course of this study, parameters have been... The value is set to 50. The number of sampling points in the time window, where This is the time-frequency matrix corresponding to SMST. Features 1 and 2 are mainly used to characterize the variation law of the fundamental frequency component. Since the energy distribution of the power quality disturbance signal will show a significant expansion and contraction, features 1 and 2 can be used to accurately describe the characteristics of the fundamental frequency component in the power quality disturbance signal.

[0192] (3) Feature 3: Fundamental frequency component correlation coefficient

[0193] Periodic fluctuation patterns are one of the key features for voltage flicker detection, and voltage flicker within different amplitude ranges exhibits certain similarities in fluctuation characteristics. Therefore, effective identification of voltage flicker requires determining whether the signal exhibits significant periodic fluctuations. Based on this identification approach, this study defines the correlation coefficient between voltage flicker and the fundamental frequency component as feature 3, and its corresponding mathematical expression is as follows:

[0194]

[0195] In the formula, J(t) and J0(t) represent the fundamental frequency components of the analysis signal and voltage flicker, respectively, and Cov[ , ] represents the covariance function (used to calculate the degree of linear correlation between two signals), Var[ ] is the variance function (which calculates the degree of dispersion of the signal).

[0196] (4) Feature 4: The energy of the row vector corresponding to frequency f is used to characterize the energy distribution of the intermediate frequency component of power quality disturbance, such as harmonic components.

[0197] ;

[0198] In the formula, This represents the row vector energy of the time-frequency matrix in the mid-frequency band (100Hz-700Hz), where t is the time sampling point and N is the total number of sampling points. These are elements of the SMST time-frequency matrix.

[0199] (5) Feature 5: The root mean square of the row vector corresponding to frequency f, used to characterize the energy distribution of high-frequency components of power quality disturbances, such as transient oscillations. t represents the sampling point, and N is the number of sampling points of the interference signal.

[0200]

[0201] In the formula, The root mean square value of the row vectors of the time-frequency matrix in the high-frequency band (>700Hz) is... N represents the mid-frequency energy, and N represents the total number of sampling points.

[0202] The technical effects of this embodiment will be verified below.

[0203] First, we model and output the disturbance signals. Through simulation, we generate standardized power quality disturbance signals, including: voltage swell, voltage sag, voltage interruption, harmonics, transient oscillations, transient impulses, flicker, and composite signals with multiple disturbances (such as Harmonic+Sag, Flicker+Swell, etc.). We then encapsulate these disturbance operators (including transient oscillations, transient impulses, harmonics, flicker, etc.) into standard input / output interface functions using function handles, thus forming an extensible disturbance modeling rule base. This generates 7 single and 12 composite power quality data types, covering typical disturbance types such as voltage swell, sag, harmonics, oscillations, and flicker.

[0204] Then, the five-dimensional features are extracted and output. Table 1 shows the numbering, meaning, and physical significance of the five power quality disturbance feature vectors.

[0205] Table 1. Characteristic vectors of five types of power quality disturbances

[0206]

[0207] The five-dimensional features (F1~F5) extracted from GST_5Features.m reveal that in the low-frequency band, frequency resolution is ensured through adjustment factors, thus accurately capturing fundamental frequency amplitude changes; in the mid-frequency band, time-frequency resolution is balanced through window functions, effectively extracting harmonic energy; and in the high-frequency band, resolution degradation is avoided through window function adjustment, clearly capturing transient characteristics. Therefore, this technical solution can adaptively adjust its time-frequency resolution to suit the disturbance characteristics of different frequency bands, enhancing the relevance and adaptability of time-frequency analysis.

[0208] This demonstrates that the present technical solution has successfully achieved accurate capture of disturbance characteristics in different frequency bands through segmented multi-resolution S-transform.

[0209] Finally, a feature statistics table is output, showing the five-dimensional feature values ​​of all samples in a structured table format for easy analysis and subsequent processing, as shown in Table 2. The SMST transform maintains the independence of each component feature in complex perturbations, avoiding feature aliasing caused by fixed resolution in traditional methods. The simultaneous and accurate extraction of multiple features from complex perturbations proves that the SMST transform successfully overcomes the fixed resolution limitation of the traditional S-transform, achieving coordinated optimization of time-frequency resolution across the entire frequency band and improving the method's analytical capability for complex perturbations.

[0210] Table 2. Generation results of five types of power quality disturbance characteristics.

[0211]

[0212] As shown in Table 2, this embodiment achieves adaptive optimization of time-frequency resolution, preserving frequency at low frequencies and time at high frequencies; it improves the ability to resolve complex disturbances, ensuring that features in each frequency band do not interfere with each other; and the output features have clear physical meaning and classification discrimination, laying the foundation for subsequent intelligent diagnosis.

[0213] Example 2:

[0214] This embodiment provides a power quality disturbance feature extraction system based on piecewise multi-resolution S-transform. The system can implement all the processes of the above-described method.

[0215] A power quality disturbance feature extraction system based on piecewise multi-resolution S-transform; the power quality disturbance feature extraction system employs the aforementioned power quality disturbance feature extraction method based on piecewise multi-resolution S-transform, and the system includes:

[0216] 1. Signal modeling module, used to establish mathematical models of power quality disturbance signals, including multiple single disturbance models and multiple composite disturbance models;

[0217] In the signal modeling module, the single disturbance model includes voltage swell, voltage drop, voltage interruption, harmonic, transient oscillation, transient pulse, and flicker models; the composite disturbance model includes a model composed of at least two combinations of the single disturbances.

[0218] II. Signal Transformation Module: This module is used for continuous S-transform based on time-domain signals. It samples the signal into a discrete time series and applies a one-dimensional discrete S-transform for calculation.

[0219] 3. Frequency band division module, used to divide the frequency range into low frequency band, mid frequency band and high frequency band according to the frequency characteristics of power quality disturbances; the frequency range is specifically divided as follows: 1Hz to 100Hz is low frequency band, 100Hz to 700Hz is mid frequency band, and greater than 700Hz is high frequency band.

[0220] IV. Window function adjustment module, used to introduce Gaussian window functions with different adjustment factors in the low frequency band, mid frequency band and high frequency band respectively, so as to adjust the time-frequency resolution of each frequency band;

[0221] In the low-frequency range, the window width factor is inversely proportional to the frequency raised to the power of a1. The rate of change of the window width with frequency is controlled by the first adjustment factor a1, and the frequency resolution is guaranteed by the second adjustment factor b1.

[0222] In the mid-frequency band, the window width factor is inversely proportional to the sum of the frequency raised to the power of a² plus the fourth adjustment factor b², in order to balance the time resolution and the window width.

[0223] In the high-frequency band, the window width factor is inversely proportional to the quarter-th power of the value obtained by multiplying the difference between the sampling frequency and the current frequency by the frequency raised to the power of a³, in order to adjust the window width to an appropriate size.

[0224] V. Piecewise Multiresolution Transform Module: This module divides the S-transform into segments based on frequency, combines the S-transform with a Gaussian window function incorporating an adjustment factor, and performs the transformation to obtain a discrete expression for the piecewise multiresolution S-transform; it includes:

[0225] The fundamental frequency processing unit is used to determine the coefficients of the fundamental frequency component directly from the average value of the discrete Fourier transform coefficients of the signal;

[0226] The low-frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for the low-frequency band, multiplying it with an exponential window function whose window width is controlled by a first adjustment factor a1 and a second adjustment factor b1, and then performing an inverse Fourier transform to obtain its coefficients, wherein the window width is inversely proportional to the frequency to the power of a1.

[0227] The intermediate frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for the intermediate frequency band, multiplying it with an exponential window function whose window width is jointly determined by the third adjustment factor a2 and the fourth adjustment factor b2, and then performing an inverse Fourier transform to obtain its coefficients, wherein the window width is jointly adjusted by the sum of the frequency raised to the power of a2 and b2.

[0228] The high-frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for high-frequency bands, multiplying it with an exponential window function whose window width is jointly determined by the fifth adjustment factor a3, the sampling frequency and the current frequency, and whose window width is inversely proportional to the quarter power of the product of the difference between the sampling frequency and the current frequency and the current frequency raised to the power of a3, and then performing an inverse Fourier transform to obtain its coefficients.

[0229] VI. A feature extraction module, used to extract feature parameters of power quality disturbance based on the time-frequency matrix obtained by the piecewise multi-resolution S-transform. In this embodiment, the power quality disturbance feature parameters extracted by the feature extraction module include at least one of the following:

[0230] Minimum amplitude of the fundamental frequency component; maximum amplitude of the fundamental frequency component; correlation coefficient of the fundamental frequency component; energy of the row vector of the time-frequency matrix corresponding to the mid-frequency band; root mean square value of the row vector of the time-frequency matrix corresponding to the high-frequency band.

[0231] In specific implementation, the working principle, control process and technical effect of the power quality disturbance feature extraction system based on piecewise multi-resolution S-transform provided in this embodiment of the invention are the same as the power quality disturbance feature extraction method based on piecewise multi-resolution S-transform in the above embodiment, and will not be repeated here.

[0232] The above-described method and system for extracting power quality disturbance features based on piecewise multi-resolution S-transform is a specific embodiment of the present invention, demonstrating the substantial features and progress of the present invention. Equivalent modifications can be made to it according to actual usage needs, under the guidance of the present invention, and all such modifications are within the scope of protection of this solution.

Claims

1. A method for extracting power quality disturbance features based on piecewise multi-resolution S-transform, characterized in that, Includes the following steps: 1) Establish a mathematical model for power quality disturbance signals, including multiple single disturbance models and multiple composite disturbance models; 2) Based on the continuous S-transform of the time-domain signal, the signal is sampled into a discrete time series and then calculated using the one-dimensional discrete S-transform; 3) Based on the frequency characteristics of power quality disturbances, the frequency range is divided into low-frequency, mid-frequency, and high-frequency bands; 4) Gaussian window functions with different adjustment factors are introduced into the low-frequency, mid-frequency, and high-frequency bands respectively to adjust the time-frequency resolution of each band; wherein, In the low-frequency range, the window width factor is inversely proportional to the frequency raised to the power of a1. The rate of change of the window width with frequency is controlled by the first adjustment factor a1, and the frequency resolution is guaranteed by the second adjustment factor b1. In the mid-frequency band, the window width factor is inversely proportional to the sum of the frequency raised to the power of a² plus the fourth adjustment factor b², in order to balance the time resolution and the window width, where a² is the third adjustment factor. In the high-frequency band, the window width factor is inversely proportional to the one-quarter power of the value obtained by multiplying the difference between the sampling frequency and the current frequency by the frequency raised to the power of a3, so as to adjust the window width to an appropriate size. a3 is the fifth adjustment factor. 5) Based on frequency segmentation, the S-transform is combined with a Gaussian window function with adjustment factors a1, b1, a2, b2, and a3 to perform transformation processing, resulting in a discrete expression for the piecewise multi-resolution S-transform. 6) Based on the time-frequency matrix obtained by the piecewise multi-resolution S-transform, extract the characteristic parameters of power quality disturbance; the characteristic parameters include: minimum amplitude of fundamental frequency component, maximum amplitude of fundamental frequency component, correlation coefficient of fundamental frequency component, energy of the row vector of time-frequency matrix corresponding to mid-frequency band frequency, and root mean square value of row vector of time-frequency matrix corresponding to high-frequency band frequency.

2. The power quality disturbance feature extraction method based on piecewise multi-resolution S-transform according to claim 1, characterized in that: In step 1), the single disturbance model includes voltage swell, voltage drop, voltage interruption, harmonic, transient oscillation, transient pulse and flicker models; the composite disturbance model includes a model composed of at least two combinations of the single disturbances.

3. The power quality disturbance feature extraction method based on piecewise multi-resolution S-transform according to claim 2, characterized in that: In step 3), the frequency range is divided as follows: 1Hz to 100Hz is the low frequency band, 100Hz to 700Hz is the mid frequency band, and greater than 700Hz is the high frequency band.

4. The power quality disturbance feature extraction method based on piecewise multi-resolution S-transform according to claim 1, characterized in that: In step 5), the discrete expression for obtaining the piecewise multi-resolution S-transform includes: For the fundamental frequency component, its segmented multi-resolution S-transform coefficients are directly determined by the average value of the discrete Fourier transform coefficients of the signal; For the low-frequency band, the piecewise multi-resolution S-transform coefficients are obtained by frequency shifting the discrete Fourier transform spectrum of the signal, multiplying it with an exponential window function whose window width is controlled by a first adjustment factor a1 and a second adjustment factor b1, and then performing an inverse Fourier transform. The window width is inversely proportional to the frequency raised to the power of a1. For the mid-frequency band, the piecewise multi-resolution S-transform coefficients are obtained by frequency shifting the discrete Fourier transform spectrum of the signal, multiplying it with an exponential window function whose window width is jointly determined by the third adjustment factor a2 and the fourth adjustment factor b2, and then performing an inverse Fourier transform. The window width is jointly adjusted by the sum of the frequency raised to the power of a2 and b2. For the high-frequency band, the piecewise multi-resolution S-transform coefficients are obtained by frequency shifting the discrete Fourier transform spectrum of the signal, multiplying it by a specific exponential window function, and then performing an inverse Fourier transform. The window width of the exponential window function is determined by a fifth adjustment factor a3, the sampling frequency, and the current frequency; specifically, the window width is proportional to the frequency of the signal. It is inversely proportional to the power of a quarter, where Sampling frequency, This is the current frequency.

5. The power quality disturbance feature extraction method based on piecewise multi-resolution S-transform according to claim 4, characterized in that: The extracted power quality disturbance characteristic parameters include at least one of the following: The minimum amplitude of the fundamental frequency component is used to characterize the degree of energy distribution dip in the fundamental frequency component of the power quality disturbance signal; The maximum amplitude of the fundamental frequency component is used to characterize the degree of energy distribution expansion of the fundamental frequency component of the power quality disturbance signal; The correlation coefficient of the fundamental frequency component is used to check for obvious periodic fluctuations in order to identify voltage flicker; The energy of the row vectors of the time-frequency matrix corresponding to the mid-frequency band is used to characterize the energy distribution of the harmonic components of the power quality disturbance. The root mean square value of the row vector of the time-frequency matrix corresponding to the high-frequency band is used to characterize the energy distribution of transient oscillations caused by power quality disturbances.

6. A power quality disturbance feature extraction system based on piecewise multi-resolution S-transform, characterized in that, The power quality disturbance feature extraction system employs a power quality disturbance feature extraction method based on piecewise multi-resolution S-transform as described in any one of claims 1-5, and the system comprises: The signal modeling module is used to establish a mathematical model of power quality disturbance signals, which includes multiple single disturbance models and multiple composite disturbance models; The signal transformation module is used for continuous S-transform based on time-domain signals, sampling the signal into a discrete time series, and applying a one-dimensional discrete S-transform for calculation; The frequency band division module is used to divide the frequency range into low-frequency, mid-frequency, and high-frequency bands based on the frequency characteristics of power quality disturbances. The window function adjustment module is used to introduce Gaussian window functions with different adjustment factors in the low-frequency band, mid-frequency band and high-frequency band respectively, so as to adjust the time-frequency resolution of each frequency band; The piecewise multi-resolution transform module is used to segment according to frequency, combine the S-transform with a Gaussian window function with an adjustment factor, and perform transform processing to obtain the discrete expression of the piecewise multi-resolution S-transform. The feature extraction module is used to extract the feature parameters of power quality disturbance based on the time-frequency matrix obtained by the piecewise multi-resolution S-transform.

7. The power quality disturbance feature extraction system based on piecewise multi-resolution S-transform according to claim 6, characterized in that: In the signal modeling module, the single disturbance model includes voltage swell, voltage drop, voltage interruption, harmonics, transient oscillation, transient pulse, and flicker models; The composite disturbance model includes a model composed of at least two combinations of the single disturbance; in the frequency band division module, the frequency range is specifically divided as follows: 1Hz to 100Hz is the low frequency band, 100Hz to 700Hz is the mid frequency band, and greater than 700Hz is the high frequency band.

8. The power quality disturbance feature extraction system based on piecewise multi-resolution S-transform according to claim 6, characterized in that: The window function adjustment module introduces adjustment factors for different frequency bands in the following specific ways: In the low-frequency range, the window width factor is inversely proportional to the frequency raised to the power of a1. The rate of change of the window width with frequency is controlled by the first adjustment factor a1, and the frequency resolution is guaranteed by the second adjustment factor b1. In the mid-frequency band, the window width factor is inversely proportional to the sum of the frequency raised to the power of a² plus the fourth adjustment factor b², in order to balance the time resolution and the window width, where a² is the third adjustment factor. In the high-frequency band, the window width factor is inversely proportional to the quarter-th power of the value obtained by multiplying the difference between the sampling frequency and the current frequency by the frequency raised to the power of a3, in order to adjust the window width to an appropriate size. a3 is the fifth adjustment factor.

9. The power quality disturbance feature extraction system based on piecewise multi-resolution S-transform according to claim 6, characterized in that: The segmented multi-resolution transformation module includes: The fundamental frequency processing unit is used to determine the coefficients of the fundamental frequency component directly from the average value of the discrete Fourier transform coefficients of the signal; The low-frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for the low-frequency band, multiplying it with an exponential window function whose window width is controlled by a first adjustment factor a1 and a second adjustment factor b1, and then performing an inverse Fourier transform to obtain its coefficients, wherein the window width is inversely proportional to the frequency to the power of a1. The intermediate frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for the intermediate frequency band, multiplying it with an exponential window function whose window width is jointly determined by the third adjustment factor a2 and the fourth adjustment factor b2, and then performing an inverse Fourier transform to obtain its coefficients, wherein the window width is jointly adjusted by the sum of the frequency raised to the power of a2 and b2. The high-frequency processing unit is used to perform frequency shifting on the discrete Fourier transform spectrum of the signal for high-frequency bands, multiplying it with an exponential window function whose window width is jointly determined by the fifth adjustment factor a3, the sampling frequency and the current frequency, and whose window width is inversely proportional to the quarter power of the product of the difference between the sampling frequency and the current frequency and the current frequency raised to the power of a3, and then performing an inverse Fourier transform to obtain its coefficients.

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