Electric energy spectrum analysis method based on combined sparse transformation

Abstract

The invention discloses an electric energy spectrum analysis method based on combined sparse transformation. The method comprises the following steps: monitoring and preprocessing an electric energy signal in a power system in real time, obtaining frequency-domain wavelet coefficients of different scales by using fast Fourier transform, optimizing the frequency-domain wavelet coefficients by using a time-frequency coupling method, reconstructing to obtain a time-domain signal, and converting the time-domain signal back to a frequency domain by using integer discrete Fourier transform to obtain a time-domain signal; and then frequency spectrum self-adaptive adjustment is carried out on the frequency domain signal, frequency distribution is optimized, and finally frequency spectrum analysis is carried out based on the adjusted frequency domain signal. According to the invention, through combination of fast Fourier transform and integer discrete Fourier transform and adoption of multi-scale analysis and time-frequency coupling optimization technologies, the spectrum resolution of the electric energy signal is improved, high-precision spectrum analysis and interference suppression are realized, and the method has the advantages of resisting dynamic current interference, adaptively enhancing the key frequency band, improving the signal-to-noise ratio and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric energy spectrum analysis, and in particular relates to an electric energy spectrum analysis method based on combined sparse transformation. Background Art

[0002] As power systems continue to expand in size and complexity, power quality issues are receiving increasing attention, particularly in the area of power signal analysis within these systems. During actual power system operation, current and voltage signals may be subject to interference from a variety of factors, including but not limited to rapid changes in dynamic loads, sudden failures of power equipment, and complex environmental noise. These interferences typically manifest as transient current and voltage fluctuations, significantly impacting the stable operation and safety of power systems. Therefore, achieving accurate and stable power signal spectrum analysis has become a crucial research topic in power system monitoring and fault detection.

[0003] Currently commonly used spectrum analysis methods, such as Fourier transform and wavelet transform, can provide effective spectrum information in specific application scenarios. However, they often have difficulty achieving sufficiently high spectrum resolution and analysis stability when faced with complex dynamic current interference and non-stationary signals. Specifically, these methods have the following drawbacks:

[0004] 1. While traditional Fourier transforms can provide basic spectral information, they are significantly inadequate for processing non-stationary signals and transient interference. This method cannot accurately capture subtle variations in power signals, nor can it effectively address the complex transient variations and non-stationary characteristics common in power systems.

[0005] 2. While traditional wavelet transforms offer the advantages of multi-scale analysis, their spectrum analysis resolution and stability are poor in operating environments with strong dynamic current interference. This method is also ineffective in noise suppression and can easily lead to fuzzy spectrum distributions, making it difficult to achieve the accuracy required for engineering applications.

[0006] 3. Existing technical solutions generally lack effective mechanisms for adaptively adjusting spectral resolution and dynamically optimizing frequency ranges. This deficiency makes it difficult to efficiently optimize signal characteristics during time-frequency domain analysis, which in turn affects the system's ability to accurately identify abnormal operating conditions. Summary of the Invention

[0007] The present invention proposes an electric energy spectrum analysis method based on combined sparse transformation, which aims to solve the problems of existing methods in terms of insufficient ability to handle non-stationary signals and transient interference, poor resolution and stability, and lack of a mechanism for adaptively adjusting spectrum resolution and dynamically optimizing frequency range.

[0008] The technical solutions of the present invention are as follows:

[0009] A power spectrum analysis method based on combined sparse transformation, the method comprising:

[0010] Step 1: Real-time monitoring of electric energy signals in the power system and pre-processing of the collected electric energy signals;

[0011] Step 2: Perform multi-scale analysis on the pre-processed electric energy signal data in time and frequency using a fast Fourier transform algorithm for processing real-valued data to obtain frequency domain wavelet coefficients of different scales;

[0012] Step 3: Optimize the frequency domain wavelet coefficients of different scales using time-frequency coupling to obtain optimized frequency domain wavelet coefficients;

[0013] Step 4: Based on the optimized frequency domain wavelet coefficients, the reconstructed time domain signal is obtained by inverse wavelet transform;

[0014] Step 5: Use integer discrete Fourier transform to convert the reconstructed time domain signal into a frequency domain signal;

[0015] Step 6: Perform spectrum adaptive adjustment on the frequency domain signal to obtain an adjusted frequency domain signal;

[0016] Step 7: Perform spectrum analysis based on the adjusted frequency domain signal.

[0017] As a further improvement of the electric energy spectrum analysis method based on combined sparse transformation: the preprocessing in step 1 includes removing the DC component and high-pass filtering.

[0018] As a further improvement of the power spectrum analysis method based on combined sparse transformation, step 2 specifically includes:

[0019] Step 2-1, perform wavelet transform on the signal to obtain coefficients of different scales;

[0020] Step 2-2: Perform frequency domain analysis on the coefficients of each scale to obtain frequency domain wavelet coefficients of different scales.

[0021] As a further improvement of the power spectrum analysis method based on combined sparse transform, the calculation formula for coefficients of different scales obtained by wavelet transform in step 2-1 is:

[0022] ;

[0023] in, It is the coefficient of the time domain signal under wavelet transform, which is expressed in scale and displacement The signal characteristics of the following: is a time domain signal, that is Pre-processed electric energy signal data corresponding to the moment; It is the normalization coefficient of the wavelet function, which is used to ensure that the wavelet function can maintain the normalization of its energy when the scale changes; is the scale factor, is the translation factor, which controls the movement of the wavelet function on the time axis; is the original wavelet mother function, which is determined by the selected wavelet basis function.

[0024] As a further improvement of the power spectrum analysis method based on combined sparse transformation, the calculation formula of the frequency domain analysis in step 2-2 is:

[0025] ;

[0026] in, is the coefficient of the time domain signal under wavelet transform, is the coefficient The representation in the frequency domain is the corresponding frequency domain wavelet coefficient; is the frequency variable in the Fourier transform.

[0027] As a further improvement of the power spectrum analysis method based on combined sparse transformation, the formula for time-frequency coupling optimization in step 3 is as follows:

[0028] ;

[0029] in, It's a scale and displacement The frequency domain wavelet coefficients under is the optimized frequency domain wavelet coefficient; is the adaptive coefficient used to control the scale of the time-frequency coupling optimization process The effect on frequency adjustment is obtained through experiments; It's a scale The corresponding frequency range is expressed in The estimated range of signal frequency under the scale is determined by the characteristics of the wavelet basis function and is estimated by calculating the frequency distribution of the wavelet basis function.

[0030] As a further improvement of the power spectrum analysis method based on combined sparse transformation, the reconstructed time domain signal obtained in step 4 is The method is: first Perform inverse Fourier transform to get , then Perform inverse wavelet transform to obtain .

[0031] As a further improvement of the power spectrum analysis method based on combined sparse transformation, the integer discrete Fourier transform calculation formula in step 5 is as follows:

[0032] ;

[0033] in, It represents the frequency domain signal after an integer number of discrete Fourier transforms. It is the representation of the reconstructed time domain signal in the frequency domain. Spectrum information at The reconstructed time domain signal In the time domain The value of the sampling point; Represents frequency variables in the frequency domain; is the total number of sampling points of the signal; It is the kernel function of the integer discrete Fourier transform, which is used to map the time domain signal to the frequency domain and represents the contribution of each frequency variable to the time domain signal. Is an imaginary unit.

[0034] As a further improvement of the power spectrum analysis method based on combined sparse transformation, the formula for adaptive spectrum adjustment in step 6 is:

[0035] ;

[0036] in, is the frequency domain signal obtained in step 5, Represents the adjusted frequency domain signal, which is obtained by adjusting the frequency domain signal The frequency obtained after adaptive adjustment Spectrum information at Each scale The weighting coefficient of ; Represents the optimized wavelet coefficients The absolute value of .

[0037] As a further improvement of the power spectrum analysis method based on combined sparse transformation, the spectrum analysis in step 7 includes:

[0038] (1) Extract the frequency corresponding to the maximum amplitude from the adjusted frequency domain signal, that is, the spectrum peak;

[0039] (2) The total energy is calculated by summing the squares of the frequency domain signals at different frequencies after adjustment.

[0040] Compared with the prior art, the present invention has the following positive effects:

[0041] 1. This invention effectively improves the spectral resolution of power signals under dynamic current interference by combining the fast Fourier transform algorithm (WFTA) and the integer discrete Fourier transform (IDFT), and employing multi-scale analysis and time-frequency coupling optimization techniques. This combined sparse transform method provides high-precision spectral analysis in complex power system environments, effectively reducing the impact of interference signals on analysis results, thereby improving the stability and accuracy of power data in the power system.

[0042] 2. The present invention uses an adaptive wavelet transform optimization method to dynamically adjust the amplitude of the spectrum according to the actual frequency characteristics of the electric energy signal, so that important frequency components are enhanced, while noise and interference components are effectively suppressed. This not only improves the spectral accuracy of the signal, but also maintains a high signal-to-noise ratio in complex power systems, significantly improving the recognition ability of electric energy signals, especially in environments with strong current interference, and can more accurately capture the effective information of the signal.

[0043] 3. This invention introduces an adaptive spectrum adjustment mechanism. Based on optimized wavelet coefficients, it enhances key frequency bands in the spectrum and suppresses interference signals, providing more reliable support for fault diagnosis and abnormal operating condition identification in power systems. Furthermore, by extracting key information such as spectral peaks and total energy, this invention further quantifies signal characteristics, helping to identify abnormal fluctuations in power signals and thus improving the effectiveness of power system monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0045] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the embodiments described are only a part of the embodiments of the present invention, rather than all the embodiments.

[0046] like Figure 1 , a power spectrum analysis method based on combined sparse transformation, comprising:

[0047] Step 1: Monitor the electric energy signals in the power system in real time and pre-process the collected electric energy signals.

[0048] The electric energy signals in the power system are monitored in real time through current and voltage transformers, and then the current signals and / or voltage signals are converted into digital signals through a high-speed analog-to-digital converter (ADC).

[0049] During the acquisition process, to reduce interference from external environmental noise, the acquired signal undergoes preprocessing, including DC removal and high-pass filtering. DC removal involves calculating the signal's mean as the DC component and then removing it to eliminate any low-frequency interference. High-pass filtering removes low-frequency noise components, preserving the signal portion useful for spectral analysis.

[0050] Step 2: Perform multi-scale analysis on the pre-processed electric energy signal data in time and frequency using a fast Fourier transform algorithm for processing real-valued data to obtain frequency domain wavelet coefficients of different scales.

[0051] This embodiment designs a combined sparse transform model based on a combination of an improved WFTA algorithm and an improved integer discrete Fourier transform algorithm to improve the resolution and stability of spectrum analysis.

[0052] Step 2-1: Perform wavelet transform on the signal to obtain coefficients of different scales.

[0053] The goal of the wavelet transform is to decompose the time domain signal (i.e., pre-processed electrical energy signal data) into details and approximate components in different frequency ranges, thereby enabling multi-scale analysis of the signal in time and frequency. The wavelet function localizes the frequency components of the signal by adjusting the scale and position of the wavelet mother function.

[0054] The calculation formula for coefficients of different scales obtained by wavelet transform is:

[0055] ;

[0056] in, It is the coefficient of the time domain signal under wavelet transform, which is expressed in scale and displacement The signal characteristics of the following: is a time domain signal, that is Pre-processed electric energy signal data corresponding to the moment; It is the normalization coefficient of the wavelet function, which ensures that the wavelet function can maintain the normalization of its energy when the scale changes; is the scale factor, is the translation factor, which controls the movement of the wavelet function on the time axis; is the original wavelet mother function, which is determined by the selected wavelet basis function.

[0057] By scaling the wavelet mother function and time shift , obtain local features of different scales and different time positions, and then extract multi-scale information of the signal.

[0058] Step 2-2: Perform frequency domain analysis on the coefficients of each scale to obtain frequency domain wavelet coefficients of different scales to obtain accurate information of frequency components.

[0059] For a certain scale , its wavelet coefficients is expressed in the time domain, and can be converted to the frequency domain through Fourier transform to reveal the characteristics of its frequency components. Therefore, the formula is:

[0060] ;

[0061] in, is the coefficient The representation in the frequency domain is the corresponding frequency domain wavelet coefficient; is the frequency variable in the Fourier transform.

[0062] This calculation can extract the frequency components of the signal in the frequency domain, thereby enhancing the ability of spectrum analysis.

[0063] Step 3: Utilize time-frequency coupling to optimize the frequency domain wavelet coefficients of different scales to obtain optimized frequency domain wavelet coefficients.

[0064] The wavelet transform result is combined with the Fourier transform result to generate a joint spectrum information, and the signal characteristics are obtained in both time domain and frequency domain. , optimization is performed in the frequency domain, and the optimized spectrum of each scale is obtained by weighted averaging the wavelet coefficients after Fourier transformation.

[0065] The formula for time-frequency coupling optimization is as follows:

[0066] ;

[0067] in, is the optimized frequency domain wavelet coefficient; is the adaptive coefficient used to control the scale of the time-frequency coupling optimization process The effect on frequency adjustment is obtained through experiments; It's a scale The corresponding frequency range is expressed in The estimated range of signal frequency under the scale is determined by the characteristics of the wavelet basis function and is estimated by calculating the frequency distribution of the wavelet basis function.

[0068] Time-frequency coupling optimization enables wavelet transform to effectively decompose signals in the environment of dynamic current interference and optimize the information extraction of each frequency band.

[0069] Step 4: Based on the optimized frequency domain wavelet coefficients, the reconstructed time domain signal is obtained through inverse wavelet transform.

[0070] The wavelet coefficients after time-frequency coupling optimization represent the characteristics of the signal in the frequency domain. This step restores it to the time domain signal through inverse wavelet transform, thus providing a basis for subsequent spectrum analysis.

[0071] The process of inverse wavelet transform is to multiply the optimized wavelet coefficients at each scale with the corresponding wavelet basis function and sum them to obtain the reconstructed time domain signal. :First Perform inverse Fourier transform to get , then Perform inverse wavelet transform to obtain .

[0072] Step 5: Use integer discrete Fourier transform to convert the reconstructed time domain signal into a frequency domain signal.

[0073] Reconstructed time domain signal obtained using inverse wavelet transform To perform spectrum analysis, the signal must be converted to the frequency domain using an integer discrete Fourier transform (IDFT). The purpose of the IDFT is to extract the frequency components of the signal and provide a basis for subsequent spectrum analysis. The IDFT converts the reconstructed time-domain signal into a frequency-domain representation.

[0074] The integer discrete Fourier transform calculation formula is as follows:

[0075] ;

[0076] in, It represents the frequency domain signal after an integer number of discrete Fourier transforms. It is the representation of the reconstructed time domain signal in the frequency domain. Spectrum information at The reconstructed time domain signal In the time domain The value of the sampling point; Represents frequency variables in the frequency domain; is the total number of sampling points of the signal; It is the kernel function of the integer discrete Fourier transform, which is used to map the time domain signal to the frequency domain and represents the contribution of each frequency variable to the time domain signal. Is an imaginary unit.

[0077] The integer discrete Fourier transform converts the optimized time domain signal into a frequency domain representation through Fourier transform, which can analyze the frequency components of the signal from the frequency domain, thereby conducting in-depth research on the characteristics of the electric energy signal and further enhancing the accuracy of the spectrum.

[0078] Step 6: Perform spectrum adaptive adjustment on the frequency domain signal to obtain an adjusted frequency domain signal.

[0079] Adaptively adjust the spectrum to enhance key signal components and suppress interference. The adjusted frequency-domain signal not only represents the optimized spectrum information obtained through time-frequency coupling, but also further enhances key signal components and suppresses interference through the adaptive spectrum adjustment process. By adjusting the spectrum amplitude based on the optimized wavelet coefficients at each scale, the system enhances key frequency components while effectively suppressing noise and interference components under dynamic current interference.

[0080] The formula for spectrum adaptive adjustment is:

[0081] ;

[0082] in, Represents the adjusted frequency domain signal, which is obtained by adjusting the frequency domain signal The frequency obtained after adaptive adjustment Spectrum information at Each scale The weighting coefficient of , determined by experiments; Represents the optimized wavelet coefficients The absolute value of .

[0083] Adaptive spectrum adjustment enhances low-SNR spectrum portions while suppressing interference bands, improving the signal-to-noise ratio of the analysis. This approach preserves signal characteristics while reducing the impact of interference signals, thereby improving spectrum accuracy and stability. This enhances the reliability of power spectrum analysis, especially in situations with strong dynamic current interference.

[0084] Step 7: Perform spectrum analysis based on the adjusted frequency domain signal.

[0085] The peak value and total energy of the spectrum are extracted to identify the main frequency components of the signal and its abnormal changes, providing a basis for power system diagnosis. Therefore, spectrum analysis includes:

[0086] (1) Extract the frequency corresponding to the maximum amplitude from the adjusted frequency domain signal, i.e., the spectrum peak. This frequency represents the main component or frequency peak in the signal and accurately reflects the most significant frequency component in the power signal. Especially in an environment with complex dynamic current interference, it can effectively avoid the influence of noise and capture the true frequency characteristics.

[0087] (2) The total energy is calculated by summing the squares of the frequency domain signals at different frequencies after adjustment.

[0088] By further quantifying the total energy of a signal, we can assess its overall strength and the concentration of its frequency distribution. Total energy is a key indicator of the signal's energy distribution within the spectrum, helping to identify unusual fluctuations or changes in the signal. Abnormal energy levels in certain frequency bands within the spectrum indicate prominent characteristics or abnormal operating conditions within the signal.

[0089] Spectrum analysis includes but is not limited to obtaining spectrum peaks and total energy.

[0090] This method improves the spectral resolution and recognition accuracy of power spectrum analysis, particularly in environments with dynamic current interference. It can better capture signal details and optimize their spectral representation. The adaptively adjusted spectral information can provide more accurate and stable support for power system monitoring and fault diagnosis, effectively improving power system reliability and fault detection capabilities.

[0091] It should be noted that it is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. The scope of the present invention is defined by the claims rather than the foregoing description.

Claims

1. A power spectrum analysis method based on combined sparse transformation, characterized in that: The method includes: Step 1: Real-time monitoring of electric energy signals in the power system and pre-processing of the collected electric energy signals; Step 2: Perform multi-scale analysis on the pre-processed electric energy signal data in time and frequency using a fast Fourier transform algorithm for processing real-valued data to obtain frequency domain wavelet coefficients of different scales; Step 3: Optimize the frequency domain wavelet coefficients of different scales using time-frequency coupling to obtain optimized frequency domain wavelet coefficients; Step 4: Based on the optimized frequency domain wavelet coefficients, the reconstructed time domain signal is obtained by inverse wavelet transform; Step 5: Use integer discrete Fourier transform to convert the reconstructed time domain signal into a frequency domain signal; Step 6: Perform spectrum adaptive adjustment on the frequency domain signal to obtain an adjusted frequency domain signal; Step 7: Perform spectrum analysis based on the adjusted frequency domain signal.

2. The electric energy spectrum analysis method based on combined sparse transformation according to claim 1, characterized in that: The preprocessing in step 1 includes DC component removal and high-pass filtering.

3. The electric energy spectrum analysis method based on combined sparse transformation according to claim 1, characterized in that: Step 2 specifically includes: Step 2-1, perform wavelet transform on the signal to obtain coefficients of different scales; Step 2-2: Perform frequency domain analysis on the coefficients of each scale to obtain frequency domain wavelet coefficients of different scales.

4. The electric energy spectrum analysis method based on combined sparse transformation according to claim 3, characterized in that: The calculation formula for the coefficients of different scales obtained by wavelet transform in step 2-1 is: ； in, It is the coefficient of the time domain signal under wavelet transform, which is expressed in scale and displacement The signal characteristics of the following: is a time domain signal, that is Pre-processed electric energy signal data corresponding to the moment; It is the normalization coefficient of the wavelet function, which is used to ensure that the wavelet function can maintain the normalization of its energy when the scale changes; is the scale factor, is the translation factor, which controls the movement of the wavelet function on the time axis; is the original wavelet mother function, which is determined by the selected wavelet basis function.

5. The electric energy spectrum analysis method based on combined sparse transformation according to claim 3, characterized in that: The calculation formula for frequency domain analysis in step 2-2 is: ； in, is the coefficient of the time domain signal under wavelet transform, is the coefficient The representation in the frequency domain is the corresponding frequency domain wavelet coefficient; is the frequency variable in the Fourier transform.

6. The electric energy spectrum analysis method based on combined sparse transformation according to claim 1, characterized in that: The formula for time-frequency coupling optimization in step 3 is as follows: ； in, It's a scale and displacement The frequency domain wavelet coefficients under is the optimized frequency domain wavelet coefficient; is the adaptive coefficient used to control the scale of the time-frequency coupling optimization process The effect on frequency adjustment is obtained through experiments; It's a scale The corresponding frequency range is expressed in The estimated range of signal frequency under the scale is determined by the characteristics of the wavelet basis function and is estimated by calculating the frequency distribution of the wavelet basis function.

7. The electric energy spectrum analysis method based on combined sparse transformation according to claim 1, characterized in that: The reconstructed time domain signal obtained in step 4 is The method is: first Perform inverse Fourier transform to get , then Perform inverse wavelet transform to obtain .

8. The electric energy spectrum analysis method based on combined sparse transformation according to claim 1, characterized in that: The integer discrete Fourier transform calculation formula in step 5 is as follows: ； in, It represents the frequency domain signal after an integer number of discrete Fourier transforms. It is the representation of the reconstructed time domain signal in the frequency domain. Spectrum information at The reconstructed time domain signal In the time domain The value of each sampling point; Represents frequency variables in the frequency domain; is the total number of sampling points of the signal; It is the kernel function of the integer discrete Fourier transform, which is used to map the time domain signal to the frequency domain and represents the contribution of each frequency variable to the time domain signal. Is an imaginary unit.

9. The electric energy spectrum analysis method based on combined sparse transformation according to claim 1, characterized in that: The formula for spectrum adaptive adjustment in step 6 is: ； in, is the frequency domain signal obtained in step 5, Represents the adjusted frequency domain signal, which is obtained by adjusting the frequency domain signal The frequency obtained after adaptive adjustment Spectrum information at Each scale The weighting coefficient of ; Represents the optimized wavelet coefficients The absolute value of .

10. The electric energy spectrum analysis method based on combined sparse transformation according to any one of claims 1 to 9, characterized in that: The spectrum analysis in step 7 includes: (1) Extract the frequency corresponding to the maximum amplitude from the adjusted frequency domain signal, that is, the spectrum peak; (2) The total energy is calculated by summing the squares of the frequency domain signals at different frequencies after adjustment.

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