A segmented adaptive fourier transform analysis method for power quality disturbances

Abstract

The application discloses a segmented adaptive Fourier transform analysis method of power quality disturbance. The method firstly collects power quality disturbance signals in a power grid and performs Fourier transform, acquires peak envelope points in a frequency spectrum through a maximum envelope method to dynamically select characteristic frequency points and calculate frequency spectrum segmentation points; subsequently, a composite objective function is used to optimize Gaussian window parameters for each segment; finally, the signal is analyzed by using the optimized window function to obtain time-frequency results with adaptive resolution. The application allocates higher time resolution to strong time-varying components and higher frequency resolution to near steady-state components through segmented adaptive resolution and a composite objective function optimization strategy, effectively avoids the spectrum overlap and energy diffusion problems that are prone to occur in traditional methods, improves the accuracy and robustness of disturbance feature extraction, and can be widely applied to power grid fault diagnosis, disturbance identification and early warning.

Description

Technical Field

[0001] This application relates to the field of power system power quality analysis technology, specifically to a piecewise adaptive Fourier transform analysis method for power quality disturbances. Background Technology

[0002] With the large-scale integration of renewable energy and the widespread application of power electronic equipment, the types and combinations of power quality disturbances in power systems are becoming increasingly complex. Accurate analysis of these disturbances is crucial for equipment fault diagnosis, assessment, and operational optimization.

[0003] Traditional power quality analysis methods mainly rely on time-frequency analysis techniques such as Short-Time Fourier Transform (STFT), Wavelet Transform (WT), and Hilbert-Huang Transform (HHT). Among these, STFT remains the most widely used time-frequency tool in engineering practice due to its simple concept and high computational efficiency. The basic idea of ​​STFT is to localize the signal using a fixed window function. However, the fixed window width results in an invariant time-frequency resolution, which can easily lead to spectral overlap or energy diffusion when analyzing power quality distributions (PQDs) that mix strongly time-varying and steady-state signals.

[0004] To further improve the adaptability of STFT, researchers have proposed several improved methods, including the Generalized Short-Time Fourier Transform (GSTFT) and the Multi-Resolution Short-Time Fourier Transform (MRSTFT). These methods enhance the flexibility of the method or adapt it to different application scenarios by introducing multiple adjustable parameters to control the window function. However, these methods still have some limitations in practical applications, as follows:

[0005] 1. Standard STFT: It uses a fixed window width, which cannot simultaneously meet the time and frequency analysis requirements of time-varying signals, and is prone to spectral overlap.

[0006] 2. GSSTFT: Although window function optimization is introduced, it still lacks the ability to adaptively adjust to different types of disturbances, making it difficult to effectively cope with the complex types of disturbances in modern power systems.

[0007] 3. MRSTFT: Relies on fixed frequency band division and lacks a mechanism to adaptively adjust the resolution according to the real-time characteristics of the signal. It is not effective when processing signals with a mixture of strong time-varying components and near-steady-state components.

[0008] Against this backdrop, there is an urgent need for an improved STFT analysis method that simultaneously possesses high accuracy, high robustness, and high computational efficiency. This method aims to dynamically adjust the time-frequency resolution configuration based on signal characteristics without relying on predefined frequency band divisions, thereby avoiding spectral overlap, improving disturbance localization accuracy, and enhancing analysis performance in complex scenarios. Summary of the Invention

[0009] The technical problem this application aims to solve is: addressing the issues of poor adaptability, severe spectral overlap, and insufficient positioning accuracy in existing PQDs time-frequency analysis methods, a piecewise adaptive Fourier transform (GASTFT) method is proposed. This method does not rely on predefined frequency bands; it dynamically determines the segmented regions based on the spectral structure of the PQDs signal and adaptively optimizes the window function parameters of each segment. This results in higher time resolution for strongly time-varying components and higher frequency resolution for steady-state or near-steady-state components, thereby significantly improving the accuracy and robustness of disturbance detection. The method includes the following steps:

[0010] S101, acquire the PQDs signal in the power system to obtain a discrete signal sequence of length N. ;

[0011] S102, the above discrete signal sequence Perform a Fast Fourier Transform (FFT) to obtain the spectrum. ,in, Frequency index;

[0012] S103, the maximum envelope method is used to obtain the spectrum. China satisfies ;

[0013] The peak envelope points, where, For peak envelope, , The number of peak envelope points selected. This is the envelope threshold;

[0014] S104, Select characteristic frequency points ,in, The number of characteristic frequency points;

[0015] S105, based on characteristic frequency points Calculate the spectrum segmentation points and : ;

[0016] S106, For each segment, a composite objective function is applied ( ) Optimize the corresponding Gaussian window parameters. The composite objective function integrates an energy concentration measure (E... CM ) and 90% peak time width ( );

[0017] S107. The optimized window function is used to perform short-time Fourier analysis on the signal to obtain time-frequency analysis results with adaptive time-frequency resolution.

[0018] Optionally, the envelope threshold mentioned in step S103 Set to 1-5% of the fundamental amplitude, with a preferred value of 1%.

[0019] Optionally, the composite objective function described in step S106 is: ,in, This is a weighting parameter, with a value ranging from 1 to 3, and an optimal value of 2.

[0020] Optionally, the energy concentration measure E in step S106 CM The calculation is as follows:

[0021] ,

[0022] in, The normalized result of the short-time Fourier transform matrix modulus is as follows:

[0023] .

[0024] Optionally, step S106 The calculation method is as follows: record the time sample corresponding to a 10% amplitude increment between the baseline value and the peak value. and and calculate .

[0025] Optionally, the Gaussian window parameter optimization in step S106 satisfies:

[0026] ,

[0027] Its constraints are:

[0028] ,

[0029] in, The standard deviation factor for each segment, For frequency resolution, This represents the minimum distance to the adjacent segment point.

[0030] Compared with traditional PQDs signal time-frequency analysis methods, the GASTFT method of this application has the following significant technical advantages:

[0031] 1. Adaptive segmentation strategy based on dominant frequency components (DFCs): By analyzing the distribution of the dominant energy components in the spectrum, the frequency axis is dynamically divided, enabling the time-frequency analysis window to be automatically adjusted according to the spectral structure of different types of PQDs, thereby significantly improving the method's adaptability to different types of disturbances.

[0032] 2. Adopting integrated E CM and The COF enables dynamic optimization of time-frequency resolution: it automatically improves time resolution in regions with strong time-varying components and increases frequency resolution in regions with steady-state or near-steady-state components, effectively improving the analysis distortion caused by fixed resolution in traditional STFTs.

[0033] 3. Significantly improved disturbance localization accuracy: The average error in voltage sag localization is only 2.58%, and the error in transient disturbance localization is as low as 1.25%, which is significantly better than existing methods such as standard STFT, GSTFT, and MRSTFT.

[0034] 4. Effectively suppresses spectral overlap and improves the accuracy of disturbance identification: By allocating differentiated time-frequency resolution, spectral overlap between harmonic components is effectively avoided, making disturbance characteristics clearer and more identifiable.

[0035] 5. Simple parameter optimization and high computational efficiency: directly optimizing the standard deviation of the Gaussian window function. Optimization can be performed without introducing additional constraints or complex nonlinear variables, making the overall optimization process stable and controllable, and reducing the amount of computation.

[0036] 6. Excellent engineering application results, applicable to a variety of practical scenarios: It can clearly reveal the disturbance evolution process, modal characteristics and frequency migration in practical scenarios such as wind turbine grid connection and resonant overvoltage, and has good engineering applicability and promotion value. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the overall process of the GASTFT method described in the embodiments of this application.

[0038] Figure 2 This is a schematic diagram of the segmented adaptive strategy described in an embodiment of this application. The thin line represents the spectrum obtained by FFT, the thick line represents the maximum envelope curve identified, and the dashed line represents the envelope threshold. Hollow triangles are used to mark the selected characteristic frequency points.

[0039] Figure 3The figures show a comparison of voltage sag and time-varying harmonic analysis results in the embodiments of this application. 3(a) represents the standard ST analysis result; 3(b) represents the IST analysis result; 3(c) represents the DRST analysis result; and 3(d) represents the GASTFT analysis result.

[0040] Figure 4 The figures show a comparison of voltage flicker, steady-state harmonics, and high-frequency transient analysis results in the embodiments of this application. 4(a) represents the standard ST analysis result; 4(b) represents the IST analysis result; 4(c) represents the DRST analysis result; and 4(d) represents the GASTFT analysis result. Detailed Implementation

[0041] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. These embodiments are only used to illustrate the technical solutions of the present invention and do not constitute a limitation on the scope of protection.

[0042] Example 1: Voltage Sag and Time-Varying Harmonic Analysis

[0043] This example provides a typical PQDs signal that includes voltage sags and time-varying harmonics, expressed as follows:

[0044] in, This represents the voltage sag depth, with a value of 0.3. This represents the start time of the voltage sag, with a value of 0.1s. The voltage sag end time is set to 0.2s. The values ​​are harmonic amplitudes, taken as 0.2, 0.15, and 0.1 respectively. The values ​​are the harmonic orders, which are 3, 5, and 7 respectively.

[0045] The analysis was performed using the GASTFT method, and the specific steps are as follows:

[0046] S101, Acquire the above PQDs signals to obtain a discrete signal sequence. The sampling frequency is 2048Hz, and the signal length is 2048 points;

[0047] S102, for discrete signal sequences Perform an FFT transform to obtain the spectrum. ;

[0048] S103, using the maximum envelope method to identify the spectrum. The peak envelope point in the data is set with a threshold. ;

[0049] S104, Select characteristic frequency point This includes the fundamental frequency and all harmonic frequencies;

[0050] S105, based on characteristic frequency points Calculate the spectrum segmentation points and ;

[0051] S106, a composite objective function is used to optimize the Gaussian window parameters for each segment, and weight parameters are set. ;

[0052] S107. Use the optimized window function to perform time-frequency analysis on the signal to obtain time-frequency analysis results with adaptive time-frequency resolution.

[0053] The experimental comparison results are shown in Table 1.

[0054] Table 1. Comparison of errors of different methods in voltage sag localization

[0055] 50Hz 150Hz 250Hz 350Hz average error ST 8.72% 9.15% 8.93% 8.51% 8.83% IST 11.91% 12.27% 12.20% 11.13% 11.88% DRST 7.34% 7.89% 7.62% 7.18% 7.51% GASTFT 2.45% 2.61% 2.59% 2.67% 2.58%

[0056] Analysis of the data in Table 1 shows that: compared with the standard ST method, the GASTFT method effectively avoids spectral overlap of harmonic components above 150Hz; compared with IST method, the GASTFT method retains the time-varying characteristics of voltage sags and harmonics; and compared with DRST method, the GASTFT method has better flexibility and adaptability. The average voltage sag positioning error is 2.58%, significantly better than the comparative methods.

[0057] Example 2: Analysis of Voltage Flicker, Steady-State Harmonics and High-Frequency Transient Disturbances

[0058] This embodiment constructs a PQDs signal containing voltage flicker, steady-state harmonics, and high-frequency transient disturbances, and its expression is:

[0059]

[0060] in, This is the flicker amplitude value, which is 0.1. The flicker frequency is set to 10Hz. The values ​​are harmonic amplitudes, taken as 0.2, 0.15, and 0.1 respectively. The harmonic orders are 3, 5, and 7, respectively. The value is the transient disturbance amplitude, which is 0.3. This is the transient disturbance attenuation coefficient, with a value of 50. This represents the start time of the voltage sag, with a value of 0.1s. The frequency of the transient disturbance is 13.

[0061] The analysis was performed using the GASTFT method, following the same steps as in Example 1.

[0062] The performance comparison is shown in the table below.

[0063] Table 2 Comparison of errors of different methods in transient disturbance localization

[0064] Transient positioning error ST 8.72% IST 11.91% DRST 7.34% GASTFT 2.45%

[0065] Table 3 Comparison of performance metrics of different methods

[0066] <![CDATA[1 / E cm ]]> <![CDATA[T 90% ]]> COF IST 362.34 6203 12768.34 DRST 430.78 6979 14388.78 GASTFT 584.67 2799 6182.67

[0067] Analysis of the data in Table 2 shows that the GASTFT method can assign higher time resolution to strong time-varying components such as flicker and transient disturbances, and higher frequency resolution to steady-state harmonics. The transient disturbance localization error is only 2.45%, which is significantly better than IST (11.91%) and DRST (7.34%). The composite objective function value is the smallest, indicating that it performs best in terms of balancing time and frequency resolution.

[0068] Example 3: Parameter Sensitivity Analysis

[0069] This embodiment aims to analyze the impact of key parameters on the performance of the GASTFT method, specifically including the threshold. The value of the parameter affects the weighting parameters. The value of the signal is affected by the sampling frequency and the signal length.

[0070] The parameter settings for this example are shown in Table 4.

[0071] Table 4 Parameter settings for parameter sensitivity analysis

[0072] Range of values Step length ε 0.5%~5% 0.5% α 1~5 1 Sampling frequency 1024~8192Hz 1024Hz signal length 1024~8192 points 1024 points

[0073] The parameter sensitivity of the method is evaluated using indicators such as voltage sag location error, transient disturbance location error, calculation time, and spectral overlap. The results show that:

[0074] 1. Threshold Impact: When The positioning error is minimized when the error is within the range of 1% to 2%; threshold When the threshold is too small, it is easily affected by noise; If the value is too large, important characteristic frequency points may be lost.

[0075] 2. Weighting parameters Impact: When weight parameters When the value is 2, Minimum value; When the energy level is too low, there is an overemphasis on energy concentration. When the value is too large, the high time resolution leads to a decrease in frequency resolution.

[0076] 3. Impact of sampling frequency: The performance is best when the sampling frequency is in the range of 2048~4096Hz; when the sampling frequency is too low, the frequency resolution is insufficient; when the sampling frequency is too high, the calculation time increases significantly.

[0077] 4. The impact of signal length:

[0078] When the signal length is 2048 points, the best balance is achieved between positioning accuracy and computation time; when the signal length is too short, the time resolution is insufficient; when the signal length is too long, the computational complexity increases significantly.

[0079] Example 4: Comprehensive comparison with traditional methods

[0080] This embodiment comprehensively compares the GASTFT method with traditional methods such as the original ST, the improved ST (IST), the dual-resolution ST (DRST), wavelet transform (WT), and empirical mode decomposition (EMD).

[0081] The test signals are composed of voltage sags, swells, harmonics, flicker, transients, and composite disturbances.

[0082] The comparison results are shown in Table 5.

[0083] Table 5 Performance Comparison of Different Methods

[0084] Temporary descent positioning error Transient positioning error Calculation time Spectral overlap Engineering Applicability ST 8.83% 8.25% 0.12s serious generally IST 11.88% 9.17% 0.35s slight good DRST 7.51% 7.50% 0.28s medium good WT 6.24% 5.89% 0.56s slight better EMD 7.21% 6.45% 1.23s slight generally GASTFT 2.58% 1.25% 0.42s none excellent

[0085] As shown in Table 5, the GASTFT method is significantly better than other methods in terms of voltage sag and transient disturbance localization. The GASTFT method can completely avoid spectral overlap, while other methods have spectral overlap problems to varying degrees. The computation time of the GASTFT method is slightly higher than that of ST and DRST, but much lower than that of WT and EMD. The GASTFT method shows excellent adaptability and stability in practical engineering applications.

[0086] Through a detailed analysis of the above four embodiments, it can be concluded that:

[0087] 1. The combination of an adaptive segmentation strategy and a composite objective function enables the GASTFT method to dynamically adjust its time-frequency resolution based on signal characteristics. This method effectively overcomes the problems of fixed resolution and insufficient adaptability in traditional STFT-like methods. The average error is 2.58% in voltage sag localization and 1.25% in transient disturbance localization, both significantly lower than existing methods.

[0088] 2. Parameter sensitivity analysis results show that the method of the present invention has controllability and stability, and the optimal configuration is as follows: , The sampling frequency is 2048Hz and the signal length is 2048 points.

[0089] 3. Comprehensive performance comparison shows that the method of this invention has significant advantages in terms of positioning accuracy, spectral overlap suppression, computational efficiency, and adaptability to engineering applications. Compared with typical methods such as STFT, IST, DRST, WT, and EMD, the GASTFT method can provide a clearer time-frequency structure and more accurate disturbance localization while maintaining lower computational cost.

[0090] 4. The method of this invention has a wide range of applications and can be used in various complex power quality scenarios. These include, but are not limited to, actual engineering conditions such as wind power grid connection, power electronic overvoltage, and resonance process analysis, and can effectively reveal the evolution law and frequency migration characteristics of disturbances.

[0091] In summary, the GASTFT method proposed in this application achieves dynamic adjustment of time-frequency resolution through a piecewise adaptive strategy and composite objective function optimization, effectively solving the problems of limited adaptability and flexibility of existing methods. Experimental results show that the GASTFT method has significant advantages in PQDs analysis and can provide reliable technical support for fault diagnosis, pattern recognition, and early warning in power systems, thus possessing important engineering application value.

[0092] The above description is merely a preferred embodiment of the GASTFT method and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A piecewise adaptive Fourier transform analysis method for power quality disturbance signals, characterized in that, Includes the following steps: S101, acquire the PQDs signal in the power system to obtain a discrete signal sequence of length N. ; S102, the above discrete signal sequence Perform a Fast Fourier Transform (FFT) to obtain the spectrum. ,in, Frequency index; S103, the maximum envelope method is used to obtain the spectrum. China satisfies The peak envelope points, where, For peak envelope, , The number of peak envelope points selected. This is the envelope threshold; S104, Select characteristic frequency points , ,in, The number of characteristic frequency points; S105, based on characteristic frequency points Calculate the spectrum segmentation points and : ; S106, Apply a composite objective function to each segment. The corresponding Gaussian window parameters are optimized, and the composite objective function integrates the energy concentration metric E. CM and 90% peak time width The expression for the above composite objective function is: , in, The weight parameter takes a value of ; S107. The optimized window function is used to perform short-time Fourier analysis on the signal to obtain time-frequency analysis results with adaptive time-frequency resolution.

2. The method according to claim 1, characterized in that, The envelope threshold mentioned in step S103 Set to 1-5% of the fundamental amplitude.

3. The method according to claim 1, characterized in that, Energy concentration measure E in step S106 CM The calculation is as follows: ， in, The normalized result of the short-time Fourier transform matrix modulus is as follows: 。 4. The method according to claim 1, characterized in that, In step S106 The calculation method is as follows: record the time sample corresponding to a 10% amplitude increment between the baseline value and the peak value. and and calculate = .

5. The method according to claim 1, characterized in that, The Gaussian window parameter optimization in step S106 satisfies: ， Its constraints are: ， in, The standard deviation factor for each segment, For frequency resolution, This represents the minimum distance to the adjacent segment point.

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