WO2024109031A1 - 一种基于hht变换的电压质量扰动检测方法 - Google Patents

一种基于hht变换的电压质量扰动检测方法 Download PDF

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WO2024109031A1
WO2024109031A1 PCT/CN2023/103020 CN2023103020W WO2024109031A1 WO 2024109031 A1 WO2024109031 A1 WO 2024109031A1 CN 2023103020 W CN2023103020 W CN 2023103020W WO 2024109031 A1 WO2024109031 A1 WO 2024109031A1
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signal
voltage signal
singular value
decomposition
frequency
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French (fr)
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张冲标
何勇
陈金威
杨柳
赵彦旻
钱辰雯
冯晓真
陆阳
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国网浙江省电力有限公司嘉善县供电公司
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Publication of WO2024109031A1 publication Critical patent/WO2024109031A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods

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  • the present invention relates to the technical field of power quality, and in particular to a voltage quality disturbance detection method based on HHT conversion.
  • Hilbert-Huang Transform is a disturbance detection technology that is currently used more frequently. Compared with S transform, it has a faster calculation speed and is more suitable for the detection of complex disturbances. At the same time, compared with analysis methods such as Fourier and wavelet transforms that require a priori function basis, it is more suitable for the detection of non-stationary signals.
  • the HHT method consists of empirical mode decomposition (EMD) and Hilbert transform. Specifically, this method first uses EMD to convert the initial signal into a set of modal functions of different scales, and then uses Hilbert transform to obtain the instantaneous amplitude-frequency characteristics corresponding to each modal function, so as to obtain the specific changes of the signal.
  • the existing HHT will encounter the problem of modal aliasing in the disturbance detection of power quality. Its specific manifestation is that after the original signal is decomposed by EMD, different intrinsic mode functions (IMF) are specifically distributed on the same time scale, making it impossible for IMF to accurately obtain the time-frequency characteristics of the signal and difficult to accurately detect voltage quality disturbances.
  • IMF intrinsic mode functions
  • the "A method for locating and detecting harmonic sources in power grids" disclosed in Chinese patent documents has a publication number of CN113092931A and a publication date of 2021-07-09, which includes the following steps: Step 1, using the window function method to design an FIR digital low-pass filter to filter out-of-band high-frequency electromagnetic interference; Step 2, detecting the transmission harmonic interference in the power grid system through the HHT algorithm.
  • the method of the present invention filters out high-frequency electromagnetic interference outside the power grid band, and performs harmonic detection and positioning according to the HHT algorithm.
  • the processing method has low computational complexity, simple system structure, high frequency resolution, and low cost.
  • the method uses the HHT method to realize the detection of harmonic frequency and amplitude, as well as the detection of disturbance time, frequency and amplitude of power quality disturbance signals (voltage sag, voltage bulge, voltage discontinuity, transient oscillation, transient pulse, etc.).
  • this method does not solve the modal aliasing problem encountered in the process of Hilbert-Huang transform, which makes it impossible for IMF to accurately obtain the time-frequency characteristics of the signal and it is difficult to accurately detect voltage quality disturbances.
  • the present invention aims to overcome the problem in the prior art that when the Hilbert-Huang transform is used for disturbance detection, there is a modal aliasing situation, which makes it difficult for the intrinsic mode function to accurately obtain the time-frequency characteristics of the signal and it is difficult to accurately detect the voltage quality disturbance.
  • a voltage quality disturbance detection method based on HHT transformation is provided. The original voltage signal is converted into a Hankel matrix form and then subjected to singular value decomposition and reconstruction to remove the interference signal. At the same time, the signal is subjected to frequency modulation processing and then empirical mode decomposition is performed. The modal aliasing problem existing in the HHT transformation process can be avoided, and the accuracy of voltage quality disturbance detection can be improved.
  • a voltage quality disturbance detection method based on HHT transformation comprising:
  • the original voltage signal is obtained for spectrum analysis to determine the spectrum information of the original voltage signal and judge whether it is a dense modal signal; the original voltage signal is subjected to singular value decomposition according to the spectrum information and reconstructed to obtain a reconstructed voltage signal after removing the interference signal; if the original voltage signal is a dense modal signal, the reconstructed voltage signal is first subjected to frequency modulation processing and then subjected to empirical mode decomposition; each intrinsic mode function after the empirical mode decomposition is subjected to Hilbert transform to obtain the amplitude and frequency information of the corresponding intrinsic mode function, thereby completing the detection of voltage signal disturbance.
  • the original voltage signal is firstly subjected to spectrum analysis to determine the frequency and amplitude of each mode contained in the acquired signal, and whether the signal is a dense modal signal is determined based on the result of the spectrum analysis.
  • the frequencies of each mode in the signal are too close, which will make the HHT transform unable to separate correctly and thus produce modal aliasing. Therefore, it is necessary to perform an improvement based on singular value decomposition reconstruction-signal frequency modulation on the original voltage signal and then perform Hilbert-Huang transform to avoid the occurrence of modal aliasing problems and improve the accuracy of voltage quality disturbance detection.
  • the original voltage signal belongs to a dense modal signal, where a 1 and a 2 are the amplitudes of the corresponding signals, f 1 and f 2 are the frequencies of the corresponding signals and f 1 >f 2 , and is the initial phase angle of the corresponding signal, and ⁇ is the frequency ratio set to be greater than 1.
  • the signal frequencies when they are similar, they can be regarded as some special amplitude modulation signals, and they satisfy the condition that the mean of the extreme value envelope is zero and the number of zero crossing points is the same as or one less than the number of extreme value points. Therefore, modal aliasing will occur when HHT decomposition is directly used. Therefore, it is necessary to perform spectrum analysis on the original voltage signal to determine whether modal aliasing will occur.
  • the signal with a larger value among the signal frequencies f1 and f2 is divided by the signal with a smaller value to obtain the frequency ratio ⁇ .
  • the larger the frequency ratio the greater the difference in the frequencies of the two signals, and the less likely it is to cause modal aliasing.
  • a frequency ratio of 2 can be selected as the judgment standard for dense modal signals.
  • the steps of performing singular value decomposition and reconstructing to obtain a reconstructed voltage signal are:
  • the number of rows m of the matrix in the Hankel matrix is half of the length N of the original voltage signal; the voltage signal can be regarded as consisting of a disturbance signal and an interference signal.
  • the singular values in the singular value matrix are arranged in descending order, which reflects the specific energy concentration of the signal, the signal is decomposed according to the specific size of the singular value, and the smaller singular value is set to 0, so that the interference signal in the original voltage signal can be removed.
  • the number of effective singular values is the main frequency of the original voltage signal multiplied by a set multiple; for the singular values of the previous effective singular value number, when a singular value is less than 1/p of the previous singular value, the singular value and subsequent singular values are set to zero, and p is a preset value greater than 1.
  • the present invention realizes the judgment of setting some singular values in the singular value matrix to zero by setting the singular values after the effective singular value number to zero, and then processes the singular values of the previous effective singular value number. If the numerical difference between the two adjacent preceding and following singular values is too large, it means that the latter singular value and the following singular values are interference signals, so the zeroing operation is also required.
  • the step of performing frequency modulation processing on the reconstructed voltage signal is:
  • Z r (t) is the real signal after transformation
  • jZ j (t) is the imaginary signal after transformation
  • the reconstructed voltage signal needs to be frequency modulated.
  • Signal frequency modulation can indirectly achieve dense mode separation and avoid the modal aliasing problem caused by the interaction of dense modes.
  • the core idea is to subtract the frequency of the adjacent mode from the appropriate frequency of the frequency modulation through signal frequency modulation, amplify the frequency ratio, make the frequency modulated signal a non-dense modal signal, and then perform empirical mode decomposition on the frequency modulated signal.
  • the real signal and the imaginary signal of the frequency modulation signal Z(t) are subjected to empirical mode decomposition respectively, and the decomposition expression of the frequency modulation signal Z(t) is obtained after combining them;
  • the frequency modulated signal is subjected to empirical mode decomposition to obtain the sum of several intrinsic mode functions IMF and residuals; then
  • the real intrinsic mode function IMF of the reconstructed voltage signal is obtained by inverse frequency transformation of the intrinsic mode function IMF; the real and imaginary parts of the frequency modulated signal constructed from the reconstructed voltage signal are subjected to empirical mode decomposition respectively to avoid the problem of mode aliasing caused by directly performing empirical mode decomposition on the voltage signal.
  • the selection of the frequency modulation frequency ⁇ 0 needs to satisfy
  • the selection of the frequency modulation frequency in the present invention needs to make the frequency ratio after frequency modulation greater than the set ⁇ , so as to change the original voltage signal from a dense modal signal to a non-dense modal signal.
  • a suitable frequency modulation frequency ⁇ 0 is subtracted from both the numerator and the denominator to achieve a downward shift of the signal frequency and amplify the signal frequency ratio to be greater than ⁇ , thereby completing the frequency modulation processing.
  • the present invention has the following beneficial effects: by converting the original voltage signal into a Hankel matrix form and then performing singular value decomposition and reconstruction to remove interference signals, and at the same time performing frequency modulation processing on the signal and then performing empirical mode decomposition, the modal aliasing problem existing in the HHT transformation process can be avoided, and the accuracy of voltage quality disturbance detection can be improved.
  • FIG1 is a flow chart of a voltage quality disturbance detection method according to the present invention.
  • FIG2 is a time domain diagram of a voltage signal in an embodiment of the present invention.
  • FIG3 is a schematic diagram of performing empirical mode decomposition using the detection method of the present invention in an embodiment of the present invention
  • FIG. 4 is a schematic diagram of directly performing empirical mode decomposition in an embodiment of the present invention.
  • a voltage quality disturbance detection method based on HHT transformation includes:
  • the original voltage signal is subjected to singular value decomposition according to the spectrum information and reconstructed to obtain a reconstructed voltage signal after the interference signal is removed;
  • the reconstructed voltage signal is first subjected to frequency modulation processing and then subjected to empirical mode decomposition; if the original voltage signal is a non-dense modal signal, the reconstructed voltage signal can be directly subjected to empirical mode decomposition, or it can be subjected to frequency modulation processing and then subjected to empirical mode decomposition;
  • the original voltage signal belongs to a dense modal signal, where a 1 and a 2 are the amplitudes of the corresponding signals, f 1 and f 2 are the frequencies of the corresponding signals and f 1 >f 2 , and is the initial phase angle of the corresponding signal, and ⁇ is the frequency ratio set to be greater than 1.
  • the length of the original voltage signal is N, the number of rows of the matrix is m, and half of the signal length N is selected.
  • N is an odd number
  • half of N+1 is selected
  • the number of columns n N-m+1.
  • U and d are orthogonal matrices of m ⁇ m and n ⁇ n dimensions respectively, thus obtaining the singular value matrix
  • ⁇ diag( ⁇ 1 , ⁇ 2 ,..., ⁇ r )
  • the rank of the matrix H is r.
  • the singular values of the previous valid singular value number in the singular value matrix are retained, and other singular values are set to zero to obtain an updated singular value matrix;
  • the valid singular value number is the main frequency number of the original voltage signal multiplied by a set multiple; among the singular values of the previous valid singular value number, when a singular value is less than 1/p of the previous singular value, the singular value and the subsequent singular values are all set to zero, p is a preset value greater than 1, the multiple is set to 2 in the present invention, and the value of p is selected to be 5, that is, the valid singular value number is twice the main frequency number of the original voltage signal, and when a singular value is less than one-fifth of the previous singular value, the singular value and the subsequent singular values are all set to zero.
  • the updated singular value matrix is then inversely decomposed to obtain the updated Hankel matrix and the reconstructed voltage signal x(i) after removing the interference signal.
  • Both x(i) and x(t) are reconstructed voltage signals, the former focuses on the sequence of the reconstructed voltage signal, and the latter focuses on the change of the reconstructed voltage signal over time.
  • Z r (t) is the real signal after transformation
  • jZ j (t) is the imaginary signal after transformation
  • j is the imaginary unit.
  • the real and imaginary signals of the frequency modulation signal Z(t) are subjected to empirical mode decomposition respectively to obtain
  • C rk (t) is the intrinsic mode function IMF obtained by decomposing the real signal
  • C jk (t) is the intrinsic mode function IMF obtained by decomposing the imaginary signal
  • r nr and r nj are the corresponding residuals after decomposition.
  • the original voltage signal is firstly subjected to spectrum analysis to determine the frequency and amplitude of each mode contained in the acquired signal, and whether the signal is a dense modal signal is determined based on the result of the spectrum analysis.
  • the frequencies of each mode in the signal are too close, which will make the HHT transform unable to separate correctly and thus produce modal aliasing. Therefore, it is necessary to perform an improvement based on singular value decomposition reconstruction-signal frequency modulation on the original voltage signal and then perform Hilbert-Huang transform to avoid the occurrence of modal aliasing problems and improve the accuracy of voltage quality disturbance detection.
  • the modal aliasing phenomenon is specifically manifested in that the same time scale components are distributed in different eigenmode functions, making the eigenmode functions It cannot accurately reflect the time-frequency characteristics of the signal; generally, when there are high-frequency discontinuous signals in the signal and when the decomposed signal is a dense modal signal, when using HHT transformation, modal aliasing is easy to occur. Therefore, the present invention removes interference signals and discontinuous signals through singular value decomposition and reconstruction, and adjusts the dense modal signal to a non-dense modal signal through signal frequency modulation processing, thereby avoiding the occurrence of modal aliasing.
  • the signal frequencies when the signal frequencies are similar, assuming that the amplitudes of the signals are the same and the initial phases are also the same, they can be regarded as some special amplitude modulation signals, and they satisfy the condition that the mean of the extreme value envelope is zero and the number of zero crossing points is the same as or one less than the number of extreme value points. Therefore, modal aliasing will occur when HHT decomposition is directly used. Therefore, it is necessary to perform spectrum analysis on the original voltage signal to determine whether modal aliasing will occur.
  • the signal with a larger value among the signal frequencies f1 and f2 is divided by the signal with a smaller value to obtain the frequency ratio ⁇ .
  • the larger the frequency ratio the greater the difference in the frequencies of the two signals, and the less likely it is to cause modal aliasing.
  • a frequency ratio of 2 can be selected as the judgment standard for dense modal signals.
  • the number of rows m of the matrix in the Hankel matrix is half of the length N of the original voltage signal; the voltage signal can be regarded as consisting of a disturbance signal and an interference signal.
  • the singular values in the singular value matrix are arranged in descending order, which reflects the specific energy concentration of the signal, the signal is decomposed according to the specific size of the singular value, and the smaller singular value is set to 0, so that the interference signal in the original voltage signal can be removed.
  • the present invention realizes the judgment of setting some singular values in the singular value matrix to zero by setting the singular values after the effective singular value number to zero, and then processes the singular values of the previous effective singular value number. If the numerical difference between the two adjacent preceding and following singular values is too large, it means that the latter singular value and the following singular values are interference signals, so the zeroing operation is also required.
  • the reconstructed voltage signal needs to be frequency modulated.
  • Signal frequency modulation can indirectly achieve dense mode separation and avoid the modal aliasing problem caused by the interaction of dense modes.
  • the core idea is to subtract the frequency of the adjacent mode from the appropriate frequency of the frequency modulation through signal frequency modulation, amplify the frequency ratio, make the frequency modulated signal a non-dense modal signal, and then perform empirical mode decomposition on the frequency modulated signal.
  • an empirical mode decomposition is performed on the frequency modulated signal to obtain the sum of several intrinsic mode functions IMF and residuals; then, the intrinsic mode function IMF of the real reconstructed voltage signal is obtained by inverse frequency transformation of the intrinsic mode function IMF; the real part and imaginary part of the frequency modulated signal constructed from the reconstructed voltage signal are subjected to empirical mode decomposition respectively, so as to avoid the problem of mode aliasing caused by directly performing empirical mode decomposition on the voltage signal.
  • the selection of the frequency modulation frequency in the present invention needs to make the frequency ratio after frequency modulation greater than the set ⁇ , so as to change the original voltage signal from a dense mode signal to a non-dense mode signal.
  • a suitable frequency modulation frequency ⁇ 0 is subtracted from the numerator and denominator at the same time to achieve the downward shift of the signal frequency and amplify the frequency ratio of the signal to be greater than ⁇ , thereby completing FM processing.
  • a voltage signal x(t) as shown in FIG2 is selected, which can be divided into four parts, namely, a dense modal signal x1 (t), which contains a fundamental voltage of 220V, 50Hz and a harmonic with an amplitude of 100V and a frequency of 70Hz; a third harmonic x2 (t) with an amplitude of 100V; a high-frequency intermittent harmonic x3 (t) with an amplitude of 80V and a frequency of 450Hz, whose amplitude and phase remain unchanged during the detection time; and finally, an intermittent Gaussian white noise x4 (t) of 10dB:
  • the voltage quality disturbance detection method of the present invention can solve the modal aliasing problem existing in the voltage signal, thereby improving the accuracy of voltage quality disturbance detection.

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Abstract

一种基于HHT变换的电压质量扰动检测方法，包括获取原始电压信号进行频谱分析，确定原始电压信号频谱信息并判断是否为密集模态信号；根据频谱信息对原始电压信号进行奇异值分解并重构得到去除干扰信号后的重构电压信号；若原始电压信号为密集模态信号，则先对重构电压信号进行调频处理再进行经验模态分解；对经验模态分解后的本征模函数进行希尔伯特变换，获取对应本征模函数的幅值和频率信息，完成电压信号扰动的检测。通过将原始电压信号转换为汉克尔矩阵形式后进行奇异值分解和重构去除干扰信号，同时对信号进行调频处理后再进行经验模态分解，可以避免HHT变换过程中存在的模态混叠问题，提升电压质量扰动检测的准确性。

Description

一种基于HHT变换的电压质量扰动检测方法 技术领域
本发明涉及电能质量技术领域，尤其是涉及一种基于HHT变换的电压质量扰动检测方法。
背景技术
希尔伯特黄变换(Hilbert-Huang Transform，HHT)是目前使用较多的扰动检测技术，比起S变换，它的计算速度更快，更适合复合扰动方面的检测；同时相比起需要先验函数基的傅里叶及小波变换等分析方法，它更适用于处理非平稳信号的检测。HHT方法由经验模态分解(Empirical Mode Decomposition,EMD)和Hilbert变换组成，具体来说，该方法首先利用EMD将初始信号转换为不同尺度的模态函数集合，再通过Hilbert变换求出各模态函数所对应的瞬时幅频特征，以此来获取信号的具体变化情况。现有的HHT在电能质量的扰动检测中会遇到模态混叠问题，其具体表现形式为原始信号在经过EMD分解后，在同一时间尺度下，具体分布着不同的固有模态函数(Intrinsic Mode Function，IMF)，使得IMF无法准确获得信号的时频特性，难以准确地检测电压质量扰动。
在中国专利文献上公开的“一种电网谐波源定位检测方法”，其公开号为CN113092931A，公开日期为2021-07-09，包括如下步骤：步骤一、采用窗函数法设计FIR数字低通滤波器滤除带外高频电磁干扰；步骤二、经HHT算法对电网系统内的传输谐波干扰进行检测。本发明的方法通过滤除电网带外高频电磁干扰，并依HHT算法做谐波检测及定位，处理方法运算量低，系统结构简洁，频率分辨率高，成本较低。该方法采用HHT方法实现了对谐波频率和幅值的检测，以及对电能质量扰动信号(电压凹陷、电压凸起、电压间断、暂态震荡、暂态脉冲等)的扰动时间、频率和幅值的检测。但是该方法并没有解决在进行希尔伯特黄变换过程中会遇到的模态混叠问题，使得IMF无法准确获得信号的时频特性，难以准确地检测电压质量扰动。
发明内容
本发明是为了克服现有技术中采用希尔伯特黄变换进行扰动检测时，存在模态混叠情况使得本征模态函数无法准确获得信号的时频特性，难以准确检测电压质量扰动的问题，提供了一种基于HHT变换的电压质量扰动检测方法，通过将原始电压信号转换为汉克尔矩阵形式后进行奇异值分解和重构去除干扰信号，同时对信号进行调频处理后再进行经验模态分解，可以避免HHT变换过程中存在的模态混叠问题，提升电压质量扰动检测的准确性。
为了实现上述目的，本发明采用以下技术方案：
一种基于HHT变换的电压质量扰动检测方法，包括：
获取原始电压信号进行频谱分析，确定原始电压信号的频谱信息并判断是否为密集模态信号；根据频谱信息对原始电压信号进行奇异值分解并重构得到去除干扰信号后的重构电压信号；若原始电压信号为密集模态信号，则先对重构电压信号进行调频处理后再进行经验模态分解；对经验模态分解后的各本征模函数进行希尔伯特变换，获取对应本征模函数的幅值和频率信息，完成电压信号扰动的检测。
本发明中首先对原始电压信号进行频谱分析，判断获取信号中所包含的各阶模态的频率和幅值，并根据频谱分析的结果来判断信号是否是密集模态信号，当属于密集模态信号时信号中的各阶模态频率过于接近会使HHT变换无法正确分离从而产生模态混叠；因此需要对原始电压信号进行基于奇异值分解重构-信号调频的改进后再进行希尔伯特黄变换，以避免模态混叠问题的出现，提高电压质量扰动检测的准确性；最后根据分解得到的本征模函数进行希尔伯特变换获取幅值和频率信息进行电压扰动的判断是现有常见的技术，因此不进行详细说明。
作为优选，对于经过频谱分析的原始电压信号当不满足f1/f2＞α且a1f1＞a2f2时原始电压信号属于密集模态信号，其中a1和a2为对应信号的幅值，f1和f2为对应信号的频率且f1＞f2，和为对应信号的初相角，α为设定的大于1的频率比。
本发明中当信号频率相近时，可以将其视作某种特殊的调幅信号，而其又满足极值包络的均值为零同时过零点数目与极值点数目相同或差一个，所以在直接采用HHT分解时就会产生模态混叠，因此需要对原始电压信号进行频谱分析判断是否会产生模态混叠，选择信号频率f1和f2中数值较大的信号除以数值较小的信号得到频率比α，频率比越大说明两信号频率差异越大不容易产生模态混叠，可以选择频率比为2作为密集模态信号的判断标准。
作为优选，进行奇异值分解并重构得到重构电压信号的步骤为：
根据原始电压信号x0(i),(i＝1,2,…,N)构造对应的汉克尔矩阵H，矩阵的行数为m，列数n＝N-m+1；
对汉克尔矩阵H进行奇异值分解，得到奇异值矩阵其中∑＝diag(σ1,σ2,…,σr)，奇异值σ1＞σ2＞…＞σr＞0，矩阵H的秩为r；
保留奇异值矩阵中前有效奇异值数的奇异值，将其他奇异值置零得到更新后的奇异值矩阵；更新后的奇异值矩阵再由奇异值分解的逆运算得到更新后的汉克尔矩阵和去除干扰信号后的 重构电压信号x(i)。
本发明中汉克尔矩阵中矩阵的行数m取原始电压信号长度N的一半；可以将电压信号看做扰动信号与干扰信号两部分组成，同时由于奇异值矩阵中的奇异值是以递减顺序排列的，其反映了信号的具体能量集中情况，所以根据具体的奇异值大小来对信号进行分解，将较小的奇异值置0，就可以去除原始电压信号中的干扰信号。
作为优选，所述有效奇异值数为原始电压信号主频数乘以设定倍数；对于前有效奇异值数的奇异值，当某一奇异值小于前一奇异值的1/p时，将该奇异值以及之后的奇异值都置零，p为预设的大于1的值。
本发明中对奇异值矩阵中的部分奇异值置零的判断实现将有效奇异值数以后的奇异值置零后，在对前有效奇异值数的奇异值进行处理，若相邻的前后两个奇异值的数值差异过大则说明后一个奇异值及其以后的奇异值是干扰信号，因此也要进行置零操作；本发明中有效奇异值数根据频谱信息中的主频数确定，可以选择为主频数的两倍；而对于相邻两奇异值的差异可以选择p＝5作为阈值。
作为优选，所述对重构电压信号进行调频处理的步骤为：
对重构电压信号x(t)进行希尔伯特变换得到其解析信号
其中ω1＝2πf1，ω2＝2πf2；
选择调频频率ω0对解析信号X(t)进行调频变换，得到调频信号
其中Zr(t)为变换后的实部信号，jZj(t)为变换后的虚部信号。
本发明中判断出原始电压信号为密集模态信号，则需要对重构电压信号进行调频处理，信号频率调制可以间接实现密集模分离，避免密集模相互作用引起的模态混叠问题，其核心思想是通过信号调频从调频的适当频率中减去相邻模态的频率，放大频率比，使调频后的信号成为非密集模态信号，然后对调频后的信号进行经验模态分解。
作为优选，完成调频处理后，对调频信号Z(t)的实部信号和虚部信号分别进行经验模态分解，并组合后得到调频信号Z(t)的分解表达式；
将调频信号Z(t)的分解表达式乘以得到解析信号X(t)的分解表达式，取解析信号X(t)的分解表达式的实部作为重构电压信号x(t)的分解表达式，完成重构电压信号的经验模态分解。
本发明中对调频信号进行经验模态分解，得到若干个本征模函数IMF和残差之和；然后 通过对本征模函数IMF的调频逆变换得到真实的重构电压信号的本征模函数IMF；从重构电压信号构造出的调频信号的实部和虚部分别进行经验模态分解，避免直接对电压信号进行经验模态分解造成的模态混叠的问题。
作为优选，所述调频频率ω0的选择需要需要满足
且ω1-ω0＞0，ω2-ω0＞0。
本发明中对于调频频率的选取需要使得调频后的频率比大于设定的α，从而将原始电压信号从密集模态信号变为非密集模态信号，对于频率比小于α的两个频率，在分子和分母上同时减去一个合适的调频频率ω0，实现信号频率的下移并放大信号的频率比至大于α，从而完成调频处理。
本发明具有如下有益效果：通过将原始电压信号转换为汉克尔矩阵形式后进行奇异值分解和重构去除干扰信号，同时对信号进行调频处理后再进行经验模态分解，可以避免HHT变换过程中存在的模态混叠问题，提升电压质量扰动检测的准确性。
附图说明
图1是本发明电压质量扰动检测方法的流程图；
图2是本发明实施例中某一电压信号的是时域图；
图3是本发明实施例中采用本发明检测方法进行经验模态分解的示意图；
图4是本发明实施例中直接进行经验模态分解的示意图。
具体实施方式
下面结合附图与具体实施方式对本发明做进一步的描述。
如图1所示，一种基于HHT变换的电压质量扰动检测方法，包括：
获取原始电压信号进行频谱分析，确定原始电压信号的频谱信息并判断是否为密集模态信号；
根据频谱信息对原始电压信号进行奇异值分解并重构得到去除干扰信号后的重构电压信号；
若原始电压信号为密集模态信号，则先对重构电压信号进行调频处理后再进行经验模态分解；若原始电压信号为非密集模态信号时，可以直接对重构电压信号进行经验模态分解，也可以进行调频处理后再进行经验模态分解；
对经验模态分解后的各本征模函数进行希尔伯特变换，获取对应本征模函数的幅值和频 率信息，完成电压信号扰动的检测。
对于经过频谱分析的原始电压信号当不满足f1/f2＞α且a1f1＞a2f2时原始电压信号属于密集模态信号，其中a1和a2为对应信号的幅值，f1和f2为对应信号的频率且f1＞f2，和为对应信号的初相角，α为设定的大于1的频率比。
进行奇异值分解并重构得到重构电压信号的步骤为：
根据原始电压信号x0(i),(i＝1,2,…,N)构造对应的汉克尔矩阵H
原始电压信号的长度为N，矩阵的行数为m选取信号长度N的一半，当N为奇数时选取N+1的一半，列数n＝N-m+1。
对汉克尔矩阵H进行奇异值分解，则有
H＝UDVT
U和d分别为m×m维和n×n维的正交矩阵，从而得到奇异值矩阵其中∑＝diag(σ1,σ2,…,σr)，奇异值σ1＞σ2＞…＞σr＞0，矩阵H的秩为r。
保留奇异值矩阵中前有效奇异值数的奇异值，将其他奇异值置零得到更新后的奇异值矩阵；有效奇异值数为原始电压信号主频数乘以设定倍数；在前有效奇异值数的奇异值中，当某一奇异值小于前一奇异值的1/p时，将该奇异值以及之后的奇异值都置零，p为预设的大于1的值，本发明中设定倍数为2，p的值选择为5，即有效奇异值数为原始电压信号主频数的两倍，当某一奇异值小于前一奇异值的五分之一时，将该奇异值及之后的奇异值都置零。
更新后的奇异值矩阵再由奇异值分解的逆运算得到更新后的汉克尔矩阵和去除干扰信号后的重构电压信号x(i)。x(i)和x(t)都为重构电压信号，前者重点表示重构电压信号的序列，后者重点表示重构电压信号关于时间的变化。
对重构电压信号进行调频处理的步骤为：
对重构电压信号x(t)进行希尔伯特变换得到其解析信号
其中ω1＝2πf1，ω2＝2πf2；
选择合适的调频频率ω0对解析信号X(t)进行调频变换，即乘以得到调频信号
其中Zr(t)为变换后的实部信号，jZj(t)为变换后的虚部信号，j为虚数单位。
调频频率ω0的选择需要需要满足
且ω1-ω0＞0，ω2-ω0＞0。
完成调频处理后，对调频信号Z(t)的实部信号和虚部信号分别进行经验模态分解得到
其中Crk(t)为实部信号分解得到的本征模函数IMF，Cjk(t)为虚部信号分解得到的本征模函数IMF；rnr和rnj分别为相对应的分解后的残差。组合后得到调频信号Z(t)的分解表达式
将调频信号Z(t)的分解表达式乘以得到解析信号X(t)的分解表达式
取解析信号X(t)的分解表达式的实部作为重构电压信号x(t)的分解表达式
x(t)＝Re(X(t))
从而完成重构电压信号的经验模态分解。
本发明中首先对原始电压信号进行频谱分析，判断获取信号中所包含的各阶模态的频率和幅值，并根据频谱分析的结果来判断信号是否是密集模态信号，当属于密集模态信号时信号中的各阶模态频率过于接近会使HHT变换无法正确分离从而产生模态混叠；因此需要对原始电压信号进行基于奇异值分解重构-信号调频的改进后再进行希尔伯特黄变换，以避免模态混叠问题的出现，提高电压质量扰动检测的准确性；最后根据分解得到的本征模函数进行希尔伯特变换获取幅值和频率信息进行电压扰动的判断是现有常见的技术，因此不进行详细说明。
模态混叠现象具体表现为在相同时间尺度成分分布在不同本征模函数中，使本征模函数 无法准确反映信号的时频特性；一般当信号中存在高频间断信号以及当被分解信号为密集模态信号时，在运用HHT变换时，都容易产生模态混叠现象。因此本发明通过奇异值分解和重构去除干扰信号和间断信号，通过信号调频处理将密集模态信号调整为非密集模态信号，从而避免模态混叠现象的产生。
本发明中当信号频率相近时，假设信号的幅值相同，初相位也相同，则可以将其视作某种特殊的调幅信号，而其又满足极值包络的均值为零同时过零点数目与极值点数目相同或差一个，所以在直接采用HHT分解时就会产生模态混叠，因此需要对原始电压信号进行频谱分析判断是否会产生模态混叠，选择信号频率f1和f2中数值较大的信号除以数值较小的信号得到频率比α，频率比越大说明两信号频率差异越大不容易产生模态混叠，可以选择频率比为2作为密集模态信号的判断标准。
本发明中汉克尔矩阵中矩阵的行数m取原始电压信号长度N的一半；可以将电压信号看做扰动信号与干扰信号两部分组成，同时由于奇异值矩阵中的奇异值是以递减顺序排列的，其反映了信号的具体能量集中情况，所以根据具体的奇异值大小来对信号进行分解，将较小的奇异值置0，就可以去除原始电压信号中的干扰信号。
本发明中对奇异值矩阵中的部分奇异值置零的判断实现将有效奇异值数以后的奇异值置零后，在对前有效奇异值数的奇异值进行处理，若相邻的前后两个奇异值的数值差异过大则说明后一个奇异值及其以后的奇异值是干扰信号，因此也要进行置零操作；本发明中有效奇异值数根据频谱信息中的主频数确定，可以选择为主频数的两倍；而对于相邻两奇异值的差异可以选择p＝5作为阈值。
本发明中判断出原始电压信号为密集模态信号，则需要对重构电压信号进行调频处理，信号频率调制可以间接实现密集模分离，避免密集模相互作用引起的模态混叠问题，其核心思想是通过信号调频从调频的适当频率中减去相邻模态的频率，放大频率比，使调频后的信号成为非密集模态信号，然后对调频后的信号进行经验模态分解。
本发明中对调频信号进行经验模态分解，得到若干个本征模函数IMF和残差之和；然后通过对本征模函数IMF的调频逆变换得到真实的重构电压信号的本征模函数IMF；从重构电压信号构造出的调频信号的实部和虚部分别进行经验模态分解，避免直接对电压信号进行经验模态分解造成的模态混叠的问题。
本发明中对于调频频率的选取需要使得调频后的频率比大于设定的α，从而将原始电压信号从密集模态信号变为非密集模态信号，对于频率比小于α的两个频率，在分子和分母上同时减去一个合适的调频频率ω0，实现信号频率的下移并放大信号的频率比至大于α，从而完成 调频处理。
在本发明的实施例中选择如图2所示的电压信号x(t)，其可以分为四个部分，分别为密集模态信号x1(t)，其中含有220V，50Hz的基波电压以及幅值为100V，频率为70Hz的谐波；幅值为100V的3次谐波x2(t)；幅值为80V，频率为450Hz的高频间歇谐波x3(t)，其幅值与相位在检测时间中保持不变；最后为10dB的间歇高斯白噪声x4(t)：
在采用本发明的检测方法后进行经验模态分解得到的各个本征模函数如图3所示，而直接进行经验模态分解得到的本征模函数如图4所示，经过对比可以看出相比于直接使用经验模态分解，采用本发明的电压质量扰动检测方法可以解决电压信号中存在的模态混叠问题，从而提升对于电压质量扰动检测的准确性。
上述实施例是对本发明的进一步阐述和说明，以便于理解，并不是对本发明的任何限制，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (7)

  1. 一种基于HHT变换的电压质量扰动检测方法，其特征在于，包括：
    获取原始电压信号进行频谱分析，确定原始电压信号的频谱信息并判断是否为密集模态信号；
    根据频谱信息对原始电压信号进行奇异值分解并重构得到去除干扰信号后的重构电压信号；
    若原始电压信号为密集模态信号，则先对重构电压信号进行调频处理后再进行经验模态分解；
    对经验模态分解后的各本征模函数进行希尔伯特变换，获取对应本征模函数的幅值和频率信息，完成电压信号扰动的检测。
  2. 根据权利要求1所述的一种基于HHT变换的电压质量扰动检测方法，其特征在于，对于经过频谱分析的原始电压信号
    当不满足f1/f2>α且a1f1>a2f2时原始电压信号属于密集模态信号，其中a1和a2为对应信号的幅值，f1和f2为对应信号的频率且f1>f2，和为对应信号的初相角，α为设定的大于1的频率比。
  3. 根据权利要求1或2所述的一种基于HHT变换的电压质量扰动检测方法，其特征在于，进行奇异值分解并重构得到重构电压信号的步骤为：
    根据原始电压信号x0(i),(i＝1,2,…,N)构造对应的汉克尔矩阵H，矩阵的行数为m，列数n＝N-m+1；
    对汉克尔矩阵H进行奇异值分解，得到奇异值矩阵其中∑＝diag(σ1,σ2,…,σr)，奇异值σ1>σ2>…>σr>0，矩阵H的秩为r；
    保留奇异值矩阵中前有效奇异值数的奇异值，将其他奇异值置零得到更新后的奇异值矩阵；更新后的奇异值矩阵再由奇异值分解的逆运算得到更新后的汉克尔矩阵和去除干扰信号后的重构电压信号x(i)。
  4. 根据权利要求3所述的一种基于HHT变换的电压质量扰动检测方法，其特征在于，所述有效奇异值数为原始电压信号主频数乘以设定倍数；对于前有效奇异值数的奇异值，当某一奇异值小于前一奇异值的1/p时，将该奇异值以及之后的奇异值都置零，p为预设的大于1的值。
  5. 根据权利要求2所述的一种基于HHT变换的电压质量扰动检测方法，其特征在于，所述对重构电压信号进行调频处理的步骤为：
    对重构电压信号x(t)进行希尔伯特变换得到其解析信号
    其中ω1＝2πf1，ω2＝2πf2；
    选择调频频率ω0对解析信号X(t)进行调频变换，得到调频信号
    其中Zr(t)为变换后的实部信号，jZj(t)为变换后的虚部信号。
  6. 根据权利要求5所述的一种基于HHT变换的电压质量扰动检测方法，其特征在于，完成调频处理后，对调频信号Z(t)的实部信号和虚部信号分别进行经验模态分解，并组合后得到调频信号Z(t)的分解表达式；
    将调频信号Z(t)的分解表达式乘以得到解析信号X(t)的分解表达式，取解析信号X(t)的分解表达式的实部作为重构电压信号x(t)的分解表达式，完成重构电压信号的经验模态分解。
  7. 根据权利要求5或6所述的一种基于HHT变换的电压质量扰动检测方法，其特征在于，所述调频频率ω0的选择需要需要满足
    且ω1-ω0>0，ω2-ω0>0。
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