WO2024087237A1 - 一种电网谐波与间谐波的检测方法 - Google Patents

一种电网谐波与间谐波的检测方法 Download PDF

Info

Publication number
WO2024087237A1
WO2024087237A1 PCT/CN2022/128583 CN2022128583W WO2024087237A1 WO 2024087237 A1 WO2024087237 A1 WO 2024087237A1 CN 2022128583 W CN2022128583 W CN 2022128583W WO 2024087237 A1 WO2024087237 A1 WO 2024087237A1
Authority
WO
WIPO (PCT)
Prior art keywords
frequency
harmonic
signal
blackman
harris
Prior art date
Application number
PCT/CN2022/128583
Other languages
English (en)
French (fr)
Inventor
陈蓉
杨勇
王铀程
Original Assignee
苏州大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 苏州大学 filed Critical 苏州大学
Publication of WO2024087237A1 publication Critical patent/WO2024087237A1/zh

Links

Images

Classifications

    • 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
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

Definitions

  • the present application relates to the technical field of power grid harmonic detection, and in particular to a method for detecting power grid harmonics and interharmonics, and more specifically to a method for detecting harmonics and interharmonics based on improved TLS-ESPRIT and a self-convolution window.
  • Parametric algorithms include Kalman filtering, Prony algorithm, neural network algorithm, Hilbert-Huang Transform (HHT), etc.
  • HHT Hilbert-Huang Transform
  • parameter-based algorithms rely on a certain high-order model and have a high computational load. They are usually used for offline analysis and are difficult to implement on embedded systems.
  • Non-parametric algorithms are mainly based on Fast Fourier Transform (FFT), which has developed into one of the most widely used algorithms in industry. It should be noted that the FFT-based detection algorithm also has its inherent defects.
  • FFT Fast Fourier Transform
  • the existing technology proposed the Hanning self-convolution window, but the sidelobe characteristics of the Hanning window itself are poor, and the improvement effect is not obvious enough; the existing technology proposed the Blackman self-multiplication-convolution window, which achieved the expected effect, but the computational load was large and interharmonics could not be detected.
  • the above methods may not be able to detect interharmonics or the detection results are not ideal.
  • Existing technologies have proposed variational mode decomposition (VMD), but when the harmonic content is large, the algorithm iteration cycle is too long; existing technologies have proposed an interharmonic detection method based on the least squares method-rotational invariance method (Total Least Squares-estimation of Signal Parameters via Rotational Invariance Technique, TLS-ESPRIT), which is a high-resolution algorithm based on eigendecomposition, which can accurately identify the frequency components in the signal.
  • VMD variational mode decomposition
  • TLS-ESPRIT Total Least Squares-estimation of Signal Parameters via Rotational Invariance Technique
  • this application improves the fast TLS-ESPRIT algorithm, accurately extracts the real harmonic and interharmonic components in complex signals through a simplified K-means cluster analysis method; at the same time, based on the Blackman-Harris window with better performance and lower sidelobe, a new second-order Blackman-Harris self-convolution window with faster sidelobe level attenuation rate is constructed, and its amplitude and phase correction formulas are derived. Finally, the algorithm is simulated and verified under multiple working conditions and tested on the experimental platform.
  • the present application proposes a method for detecting harmonics and interharmonics in a power grid, comprising:
  • the sampled data of the signal to be measured is subjected to windowing and interpolation calculation in combination with a second-order Blackman-Harris self-convolution window to estimate the amplitude and phase information of each harmonic of the signal to be measured.
  • the method of sampling the signal to be tested multiple times and detecting the frequency using a fast TLS-ESPRIT algorithm includes:
  • the signal is sampled three times and the frequency is detected using the TLS-ESPRIT algorithm to obtain three sets of initial frequency sets.
  • the detected frequency is analyzed based on a simplified K-means clustering algorithm to extract the real harmonic components, including:
  • the second-order Blackman-Harris self-convolution window is a five-term cosine combination window.
  • the method includes:
  • a polling method is used to perform harmonic analysis on the voltage and current of each phase.
  • the windowed interpolation calculation is a bispectral line interpolation of a second-order Blackman-Harris self-convolution window, and the formula is as follows:
  • a 0 (y 1 +y 2 )(2.102 03 + 0.363 12 ⁇ 2 + 0.035 61 ⁇ 4 - 0.006 698 ⁇ 6 )/N
  • , y 2
  • , ⁇ n 0 -n 1 -0.5, X(n i ) is the signal, ⁇ is the proportional coefficient, N is the number of sampling points, A 0 is the amplitude, and ⁇ i is the phase.
  • w B (n) is the Blackman-Harris window.
  • the present invention has the following beneficial effects: simulation and experimental results show that the proposed method has better harmonic and interharmonic detection accuracy and anti-interference ability.
  • the method of the present application can better extract the frequency components of the signal and can also accurately detect the amplitude and phase information of the signal in practical application.
  • FIG1 is a schematic diagram showing the ⁇ i distribution of the present application.
  • FIG. 2 is a schematic diagram showing three frequency detection results under noise interference according to an embodiment of the present application.
  • FIG3 is a schematic diagram showing the results of frequency point clustering analysis.
  • FIG. 4 shows a comparison diagram of amplitude-frequency response curves of three window functions according to an embodiment of the present application.
  • FIG5 is a schematic diagram showing the amplitude and phase detection errors under noise interference of the present application.
  • FIG6 shows a schematic diagram of the output current harmonic parameters of the photovoltaic grid-connected inverter measured in the present application.
  • FIG. 7 shows a flow chart of the algorithm of the present application.
  • FIG8 shows a schematic diagram of a simulated grid-connected current waveform of the present application.
  • FIG. 9 is a schematic diagram showing an amplitude spectrum of the amplitude detection result of the present application.
  • FIG. 10 is a schematic diagram showing a phase spectrum of a phase detection result of the present application.
  • FIG. 11 shows a schematic structural diagram of an electronic device provided in an embodiment of the present application.
  • FIG. 12 shows a schematic diagram of a storage medium provided in an embodiment of the present application.
  • the present application provides a detection method for power grid harmonics and interharmonics, which is a detection method based on the combination of an improved fast TLS-ESPRIT algorithm and a second-order Blackman-Harris self-convolution window.
  • the signal to be tested is sampled multiple times and the frequency is detected using a fast TLS-ESPRIT algorithm; then, the detection results are analyzed based on a simplified K-means clustering algorithm to extract the true harmonic components; finally, the signal is windowed and interpolated in combination with a second-order Blackman-Harris self-convolution window to accurately estimate its amplitude and phase information, thereby achieving high-precision detection of harmonics and interharmonics.
  • N is the number of samples
  • fs , fi , Ai are the sampling frequency, harmonic amplitude, frequency and phase respectively.
  • s(n) is the noise signal.
  • R is an L-dimensional left singular matrix
  • ⁇ is an L3M-dimensional diagonal matrix
  • V is an M-dimensional right singular matrix.
  • ⁇ of the matrix X Arrange the singular values ⁇ of the matrix X in descending order: ⁇ 1 ⁇ 2 ⁇ 3 ⁇ -> ⁇ k ⁇ k+1 ⁇ « ⁇ n ⁇ 0.
  • the size of the singular value reflects the content of a certain frequency component in the signal. Therefore, according to the size of the singular value, k larger singular values can be extracted to divide the matrix V into the signal subspace VS and the noise subspace VN . Then VS is the right singular matrix corresponding to k larger singular values.
  • V 1 and V 2 are obtained by removing the first and last rows of the signal subspace V S , respectively.
  • a (M-1)32k-order matrix ⁇ TLS is constructed from V 1 and V 2 :
  • each real frequency fi corresponds to an amplitude Ai .
  • the amplitude Ai is large, white noise has no obvious interference on the amplitude of the real frequency signal.
  • (a) in Figure 1 is the singular value decomposition result of a signal containing 13 frequencies and corresponding to a large amplitude. It can be seen from the figure that under different noise levels, there is an obvious truncation between the signal and the noise, and the size of the singular value of the real frequency does not change significantly. Therefore, the number of frequencies in the signal can be accurately determined.
  • the present application first presets a relatively large k * , then samples three different test signals for frequency detection, and then analyzes the frequency information obtained by the three calculations based on a simplified K-means clustering algorithm to determine the real frequency components.
  • the K-means algorithm is a clustering algorithm based on distance division. First, determine the number of clusters K, randomly select K data objects as the initial cluster centers; then calculate the square of the Euclidean distance from the data point to the K cluster centers and assign it to the nearest center point; then calculate the updated cluster center; repeat the above steps until the cluster center no longer changes.
  • this application regards each point of the first set of data as a cluster center and determines a fixed cluster radius ⁇ .
  • the cluster center is recalculated and the new cluster center is classified as a real frequency point, otherwise it is classified as a noise point and deleted.
  • the three-frequency detection result can be expressed as:
  • each frequency in formula (7) is regarded as a point in space, and its horizontal and vertical coordinates can be expressed as the corresponding frequency value.
  • the square of the Euclidean distance from each point in the second and third groups of data to the cluster midpoint can be defined as:
  • the cluster center is recalculated and classified as a real frequency point.
  • the new cluster center can be expressed as:
  • fget is the true frequency measured by the algorithm
  • f1Ci , f2Ci , and f3Ci represent the three frequency components in the i-th category.
  • FIG2 shows the results of three frequency detections when white noise with a signal-to-noise ratio of 40 dB is added to the signal without clustering, where the number of preset frequency components is 50 and the number of real frequency components is 13.
  • the algorithm of the present application can well extract the 13 real harmonic components. From the local amplification results, there are frequency points whose distance from the cluster center in the second and third frequency detections is less than ⁇ within the cluster range with the cluster center as the center and a radius of 0.5 Hz, which meets the conditions.
  • the algorithm proposed in this application can effectively and accurately extract the true frequency component in the detection result under strong anti-interference conditions.
  • the main criteria for measuring the characteristics of window functions are the main lobe width (MLW) and the maximum side lobe level (MSLL).
  • Table 1 shows the comparison of the main lobe and side lobe characteristics of common window functions.
  • the Blackman-Harris window has a lower sidelobe peak level, indicating that it has the best suppression effect on spectrum leakage.
  • the window function can be self-convolved.
  • the expression for defining the q-order Blackman-Harris self-convolution window is:
  • the second-order Blackman-Harris self-convolution window constructed in the present application is obtained as a new five-term cosine combination window.
  • WR (w) is the spectrum function of the rectangular window.
  • Figure 4 shows the comparison of the amplitude-frequency characteristics of the window function of the present application with the original window function and the Hanning self-convolution window.
  • the main lobe width of the window function proposed in the present application is 20 ⁇ /N, and its spectral resolution is reduced, while the maximum sidelobe level reaches -184.1dB, which is significantly lower than the -92dB of the original window function and the -62dB of the Hanning self-convolution window, so it can better suppress spectrum leakage.
  • n 0 is not an integer.
  • , y 2
  • the window function w B-2 (n) is a real coefficient
  • its amplitude-frequency response W B-2 (n) is an even function
  • the equivalent function g -1 (2) is an odd function, which can be derived by the Chebyshev polynomial approximation method.
  • the amplitude correction formula can be further derived.
  • the amplitude correction can be used to perform weighted averaging on the two spectral lines n1 and n2 , which can be expressed as:
  • equation (18) can be simplified as:
  • h( ⁇ ) is an even function. Similarly, it can be derived by using the polynomial approximation method.
  • a signal containing 5 frequency components is used as a model for simulation, and the amplitude is set to 0.2% of the fundamental frequency respectively, and compared with the adaptive algorithm proposed in the prior art.
  • the sampling frequency is set to 4kHz, the number of sampling points is set to 1024, and the base frequency is set to 50Hz.
  • Gaussian white noise with a signal-to-noise ratio (SNR) of 40 to 70dB is added to the signal. The simulation results are shown in Table 2.
  • the present application sets the simulation parameters shown in Table 3.
  • the Blackman-Harris window, Hanning self-convolution window, Blackman self-multiplication-convolution window, and second-order Blackman-Harris self-convolution window are used for windowing and interpolation processing.
  • the other parameters are the same as 3.1.
  • the relative errors of amplitude and phase are shown in Tables 4 and 5.
  • the second-order Blackman-Harris self-convolution window proposed in this application has the lowest sidelobe level and the best spectrum leakage suppression effect, so it has the highest detection accuracy and the smallest relative error.
  • the relative error of amplitude detection is reduced to 10-11 % to 10-12 %; the relative error of phase detection is reduced to 10-10 % to 10-11 %.
  • the detection accuracy is significantly improved in the steady state.
  • the accuracy of each algorithm is reduced, while the detection accuracy of the algorithm in this application is still the highest.
  • the minimum amplitude error reaches 10-5 %, and the minimum phase error reaches 10-4 %, which is 10-3 higher than the Blackman self-scaling-convolution window, and 10-3 to 10-1 higher than the traditional Blackman-Harris window and Hanning self-convolution window.
  • the algorithm is implemented using a digital signal processor (DSP) TMS320F28335 with a crystal oscillator frequency of 150 MHz.
  • DSP digital signal processor
  • the analog waveform is output through a TFG6800 arbitrary signal generator, and the detection data is observed by a host computer.
  • the algorithm flow of the present application is shown in FIG7 : (1) First, the DSP completes the algorithm initialization: a fixed sampling frequency and sampling points are preset and a second-order Blackman-Harris self-convolution window is generated; (2) Then, the sampling is triggered by the EPWM interrupt, and the data is collected and saved; (3) After the A/D sampling is completed, a fast TLS-ESPRIT calculation is performed on the sampled data to extract the harmonic frequency, and the above steps are repeated until three detections are completed; (4) The frequency detection results are clustered to extract the real harmonic components and calculate the spectrum point n 0 of each harmonic; (5) Finally, the sampled data is windowed and interpolated to obtain the amplitude and phase information of each harmonic to complete the detection.
  • a polling method is required to perform harmonic analysis on the voltage and current of each phase.
  • the sampling frequency fs is set to 2kHz, the number of sampling points N is set to 1024, and the harmonic list shown in Figure 6 is used as the experimental data. Since the power analyzer cannot detect the harmonic phase information, the phase is randomly set by the arbitrary signal generator during the experiment. The detection results are observed by the host computer, and the waveform of the simulated grid-connected current output by the arbitrary signal generator is shown in Figure 8.
  • the proposed method has high accuracy in both amplitude and phase detection under actual working conditions: the maximum error of amplitude detection accuracy is only 0.04%; the maximum error of phase detection is only 0.177°.
  • the total harmonic distortion (THD) of the input signal in Table 6 is 1.438%, and the detection result of the algorithm of the application is 1.419%, with an error of 0.019%.
  • the experimental results prove the effectiveness and practicality of the algorithm of the application.
  • This application proposes a method for detecting harmonics in the output current of a photovoltaic grid-connected inverter based on a combination of an improved fast TLS-ESPRIT algorithm and a second-order Blackman-Harris self-convolution window.
  • the fast TLS-ESPRIT algorithm is used to accurately identify the frequency components in the signal, multiple detections are performed, and the detection results are analyzed based on a simplified K-means clustering algorithm.
  • a second-order Blackman-Harris self-convolution window is constructed by the self-convolution method, and an amplitude and phase correction algorithm is proposed, which verifies that the method of this application can better extract the frequency components of the signal and can also accurately detect the amplitude and phase information of the signal during actual application.
  • the electronic device 20 includes: a processor 200, a memory 201, a bus 202 and a communication interface 203, the processor 200, the communication interface 203 and the memory 201 are connected via the bus 202; the memory 201 stores a computer program that can be run on the processor 200, and the processor 200 executes the harmonic and interharmonic detection method provided by any of the aforementioned embodiments of the present application when running the computer program.
  • the memory 201 may include a high-speed random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), such as at least one disk storage.
  • RAM random access memory
  • non-volatile memory such as at least one disk storage.
  • the communication connection between the system network element and at least one other network element is realized through at least one communication interface 203 (which may be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. may be used.
  • the bus 202 may be an ISA bus, a PCI bus, or an EISA bus, etc.
  • the bus may be divided into an address bus, a data bus, a control bus, etc.
  • the memory 201 is used to store a program, and the processor 200 executes the program after receiving an execution instruction.
  • the harmonic and interharmonic detection method disclosed in any implementation of the embodiment of the present application may be applied to the processor 200, or implemented by the processor 200.
  • the processor 200 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the hardware integrated logic circuit in the processor 200 or the instruction in the form of software.
  • the above processor 200 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components.
  • DSP digital signal processor
  • ASIC application-specific integrated circuit
  • FPGA field-programmable gate array
  • the methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed.
  • the general-purpose processor can be a microprocessor or the processor can also be any conventional processor.
  • the steps of the method disclosed in the embodiments of the present application can be directly embodied as a hardware decoding processor to execute, or the hardware and software modules in the decoding processor can be executed.
  • the software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc.
  • the storage medium is located in the memory 201, and the processor 200 reads the information in the memory 201 and completes the steps of the above method in combination with its hardware.
  • the electronic device provided in the embodiment of the present application and the harmonic and interharmonic detection method provided in the embodiment of the present application are based on the same inventive concept and have the same beneficial effects as the methods adopted, operated or implemented therein.
  • the embodiments of the present application also provide a computer-readable storage medium corresponding to the harmonic and interharmonic detection method provided in the aforementioned embodiments.
  • the computer-readable storage medium is a CD 30 on which a computer program (i.e., a program product) is stored.
  • a computer program i.e., a program product
  • the computer program When the computer program is run by the processor, it will execute the harmonic and interharmonic detection method provided in any of the aforementioned embodiments.
  • examples of the computer-readable storage medium may also include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other optical or magnetic storage media, which are not listed here one by one.
  • PRAM phase change memory
  • SRAM static random access memory
  • DRAM dynamic random access memory
  • RAM random access memory
  • ROM read-only memory
  • EEPROM electrically erasable programmable read-only memory
  • flash memory or other optical or magnetic storage media, which are not listed here one by one.
  • the computer-readable storage medium provided in the above-mentioned embodiments of the present application and the harmonic and interharmonic detection method provided in the embodiments of the present application are based on the same inventive concept and have the same beneficial effects as the method adopted, run or implemented by the application program stored therein.

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)

Abstract

一种电网谐波与间谐波的检测方法，首先对待测信号进行多次采样并利用快速TLS-ESPRIT算法检测频率；随后对检测结果基于简化K-means 聚类算法进行分析，提取出真实的谐波分量；最后结合2阶Blackman-Harris自卷积窗对信号进行加窗插值计算，准确估算出其幅值、相位信息，实现了谐波、间谐波的高精度检测。仿真和实验结果表明，本方法相较于传统方法具有更高的谐波、间谐波检测精度且抗干扰能力更强。

Description

一种电网谐波与间谐波的检测方法 技术领域
本申请涉及电网谐波检测技术领域，尤其涉及一种电网谐波与间谐波的检测方法，更具体的是一种基于改进TLS-ESPRIT与自卷积窗的谐波与间谐波检测方法。
背景技术
近年来，随着“双碳”目标的提出，以光伏为代表的分布式发电系统高比例接入电网，导致谐波污染问题日益严重，对电网以及用电设备造成恶劣影响。同时，由于光能本身易受外界因素影响，光伏并网系统输出电流谐波呈现波动性、随机性等特点，对谐波治理提出了更高的要求。
准确快速的谐波监测是谐波治理的前提，传统的离线数据分析已无法适应日益复杂的电网工况。因此，为了提升谐波治理的有效性，进而保证光伏并网系统能够安全地接入电网，提供高质量电能，探索一种新的准确的谐波检测算法具有重要意义。
常见的谐波检测方法可以分为参数算法和非参数算法两类。参数算法包括卡尔曼滤波、Prony算法、神经网络算法、希尔伯特-黄变换法(Hilbert-Huang Transform,HHT)等。然而，基于参数的算法依赖于确定的高阶模型，且有较高的计算负荷，通常应用于离线分析，难以在嵌入式系统上实现。非参数算法主要基于快速傅里叶变换(Fast Fourier Transform,FFT)，其已发展为工业上应用最为广泛的算法之一。需要注意的是，基于FFT的检测算法也有其固有的缺陷，在实际应用过程中由于电网频率存在波动，往往不能对待测信号进行整周期截断，即同步采样，容易造成频谱泄露和栅栏效应，进而影响检测精度。为了改善这一问题，最常见的方法是加窗插值法，国内外学者提出了很多窗函数用于基于插值的检测算法，如Hanning窗、Blackman窗、Nuttall窗等。可是由于经典窗函数的旁瓣特性不佳，其检测精度不能满足要求且偶次谐波检测结果误差相对较高。于是有学者将自卷积引入到经典窗中，通过对窗函数自卷积的方法进一步改善旁瓣特性，已有技术提出了Hanning自卷积窗，可是Hanning窗本身旁瓣特性较差，提升效果不够明显；已有技术提出了Blackman自乘-卷积窗，达到了预计的效果，但是计算负荷大且无法检测出间谐波。
同时，受限于频谱分辨率和处理器资源，上述方法或无法实现间谐波检测或检测结果不理想。已有技术提出了变分模态分解(VMD)，然而当谐波含量较多时，该算法迭代周期过长；已有技术提出基于最小二乘法-旋转不变法(Total Least Squares-estimation  of SignalParameters via Rotational Invariance Technique，TLS-ESPRIT)的间谐波检测方法，该算法是一种基于特征分解的高分辨算法，可以精确的识别信号中的频率分量。
已有技术针对TLS-ESPRIT算法需要提前输入谐波数量k的弊端提出了相应的自适应算法，通过对奇异值的相邻增长比和对应阶次的累计比例进行分析，进而确定谐波数量k，但该方法计算k值的过程复杂且容易受到系统不稳定的影响，鲁棒性较差，同时，当部分谐波含量很少(<0.1％)时，奇异值的增长比变化不明显，该方法会出现漏判问题。
发明内容
有鉴于此，针对上述问题，本申请对快速TLS-ESPRIT算法进行改进，通过基于简化K-means聚类分析的方法准确提取复杂信号中的真实的谐波、间谐波分量；同时，基于性能更好、旁瓣更低的Blackman-Harris窗构造出一种新的旁瓣电平衰减速率更快的2阶Blackman-Harris自卷积窗，并推导得到其幅值和相位修正公式。最后对算法进行多工况下的仿真验证并在实验平台上进行测试。
基于上述目的，本申请提出了一种电网谐波与间谐波的检测方法，包括：
对待测信号进行多次采样并利用快速TLS-ESPRIT算法检测频率；
对所述检测的频率基于简化K-means聚类算法进行分析，提取出真实的谐波分量并计算得到每一次谐波的频谱点n 0；
结合2阶Blackman-Harris自卷积窗对所述待测信号的采样数据进行加窗插值计算，估算所述待测信号的每一次谐波的幅值、相位信息。
进一步地，所述对待测信号进行多次采样并利用快速TLS-ESPRIT算法检测频率，包括：
对信号进行3次采样并利用TLS-ESPRIT算法检测频率，得到三组初始频率集合。
进一步地，所述对所述检测的频率基于简化K-means聚类算法进行分析，提取出真实的谐波分量，包括：
将每一个频率看作空间中的点，并将第一组初始频率集合的频率点作为第一个聚类中心；
计算第二组和第三组初始频率集合中的点到第一个聚类中心的距离，判断是否满足真实频率点的条件，若是，则重新计算聚类中心并作为真实频率，反之则归类为噪声点并将其删除；
重复以上步骤，对其余频率分量进行聚类。
进一步地，所述2阶Blackman-Harris自卷积窗为五项余弦组合窗。
进一步地，在所述对待测信号进行多次采样之前，包括：
(1)预设固定的采样频率和采样点数并生成2阶Blackman-Harris自卷积窗；
(2)随后通过EPWM中断触发采样。
进一步地，对于三相系统，采用轮询的方法对每一相电压、电流进行谐波分析。
进一步地，所述加窗插值计算为2阶Blackman-Harris自卷积窗的双谱线插值，公式如下：
γ＝5.271 023 8β+1.093 029 36β 3+0.746 302 3β 5+0.392 204 7β 7
A 0＝(y 1+y 2)(2.102 03+0.363 12γ 2+0.035 61γ 4-0.006 698γ 6)/N
Figure PCTCN2022128583-appb-000001
其中，定义左右两条谱线分别为n 1、n 2且存在n 1<n 0<n 2；0≤n 0-n 1≤1；这两条谱线的幅值分别为：y 1＝|X(n 1)|，y 2＝|X(n 2)|，γ＝n 0-n 1-0.5，X(n i)为信号，β为比例系数，N为采样点个数，A 0为幅值，θ i为相位。
进一步地，所述2阶Blackman-Harris自卷积窗的表达式为：
w B-2(n)＝w B(n)*w B(n)
其中w B(n)为Blackman-Harris窗。
相对于现有技术，本发明具有以下有益效果：仿真和实验结果表明所提方法具有更好的谐波、间谐波检测精度以及抗干扰能力。本申请方法可以更好的提取出信号的频率分量且实际应用过程中也可以准确的检测信号的幅值和相位信息。
附图说明
在附图中，除非另外规定，否则贯穿多个附图相同的附图标记表示相同或相似的部件或元素。这些附图不一定是按照比例绘制的。应该理解，这些附图仅描绘了根据本申请公开的一些实施方式，而不应将其视为是对本申请范围的限制。
图1示出本申请的σ i分布情况示意图。
图2示出根据本申请实施例的噪声干扰下的三次频率检测结果示意图。
图3示出频率点聚类分析结果示意图。
图4示出根据本申请实施例的三种窗函数的幅频响应曲线对比图。
图5示出了本申请噪声干扰下的幅值、相位检测误差示意图。
图6示出了本申请实测光伏并网逆变器输出电流谐波参数示意图。
图7示出了本申请算法流程图。
图8示出了本申请模拟并网电流波形示意图。
图9示出了本申请幅值检测结果振幅谱示意图。
图10示出了本申请相位检测结果相位谱示意图。
图11示出了本申请一实施例所提供的一种电子设备的结构示意图。
图12示出了本申请一实施例所提供的一种存储介质的示意图。
具体实施方式
下面结合附图和实施例对本申请作进一步的详细说明。
本申请提供一种电网谐波与间谐波的检测方法，属于基于改进快速TLS-ESPRIT算法与2阶Blackman-Harris自卷积窗相结合的检测方法。首先对待测信号进行多次采样并利用快速TLS-ESPRIT算法检测频率；随后对检测结果基于简化K-means聚类算法进行分析，提取出真实的谐波分量；最后结合2阶Blackman-Harris自卷积窗对信号进行加窗插值计算，准确估算出其幅值、相位信息，实现了谐波、间谐波的高精度检测。
1改进快速TLS-ESPRIT算法
快速TLS-ESPRIT算法原理
设复杂信号x(n)由m个谐波、间谐波叠加噪声构成，其表达式可以定义为：
Figure PCTCN2022128583-appb-000002
式中，n＝0,1,2,3……N-1；N为采样个数；f s、f i、A i、
Figure PCTCN2022128583-appb-000003
分别为采样频率、各次谐波幅值、频率和相位。s(n)为噪声信号。
对信号x(n)构造Hankel矩阵X：
Figure PCTCN2022128583-appb-000004
其中L为快拍数；M为阵元数，对Hankel矩阵进行奇异值分解，可得：
Figure PCTCN2022128583-appb-000005
式中，R为L维左奇异矩阵，∑为L3M维对角矩阵，V为M维右奇异矩阵。对矩阵X的 奇异值σ进行降序排列：σ 1≥σ 2≥σ 3≥……σ k≥σ k+1≥……σ n≈0，奇异值大小反映了某一频率分量在信号中的含量，因此根据奇异值的大小可以提取出其中k个较大的奇异值将矩阵V划分为信号子空间V S和噪声子空间V N，则V S为对应k个较大的奇异值的右奇异矩阵。
将信号子空间V S分解为两个交叉的子空间：
Figure PCTCN2022128583-appb-000006
V 1、V 2分别为信号子空间V S除去第一行和最后一行获得，由V 1和V 2构造(M-1)32k阶矩阵ψ TLS：
Ψ TLS＝V 1 +V 2     (5)
式中，(·) +表示伪逆。
对式(5)进行特征值分解，得到λ i(i＝1,2,3…k),则频率估计值
Figure PCTCN2022128583-appb-000007
可以表示为：
Figure PCTCN2022128583-appb-000008
改进快速TLS-ESPRIT算法
由上述分析可知，进行快速TLS-ESPRIT计算时首先需要得到谐波分量个数k，然而在实际过程中，k值往往是未知的。倘若k值设置的过小，则会存在频率信息遗漏的问题；反之k值设置的过大，则会引入虚假的频率分量。
由公式(1)可知，每一个真实存在的频率f i对应着一个幅值A i，当幅值A i较大时，白噪声对真实频率信号的幅值无明显干扰，图1中的(a)为含13种频率且对应幅值较大的信号的奇异值分解结果，从图中可以看出，在不同噪声等级下，信号与噪声的分界存在明显截断，且真实频率的奇异值大小无明显变化，因此可以准确的确定信号中的频率个数。
然而，当幅值A i较小时，白噪声对真实频率信号的幅值存在较大干扰，图1中的(b)为含13种频率且对应幅值较小的信号的奇异值分解结果，从图中可以看出，当噪声较大时，信号与噪声的分界无明显截断，因此无法准确得到信号中的频率个数。
为了解决这个问题，本申请首先预设一个相对较大的k *，随后采样3段不同的待测信号进行频率检测，再对三次计算得出的频率信息基于简化K-means聚类算法进行分析，从而确定其中真实的频率分量。
K-means算法是一种根据距离划分的聚类算法。首先确定聚类数目K，随机选择K个数据对象作为初始聚类中心；随后计算数据点到这K个聚类中心的欧式距离平方并划分给距离最近的中心点；然后计算更新后的聚类中心；重复以上步骤直至聚类中心不再发生变化。
本申请为了简化算法，将第一组数据的每一个点看作聚类中心，确定一个固定的聚类半 径ε，当第二组和第三组数据中均存在数据点满足到某一聚类中心的距离小于ε，则重新计算聚类中心，并将新的聚类中心归类为真实的频率点，反之则归类为噪声点并将其删除。
定义复杂信号中真实的频率分量个数为k，预设信号中的频率分量个数为k *，则三次频率检测结果可以表示为：
Figure PCTCN2022128583-appb-000009
式中，
Figure PCTCN2022128583-appb-000010
为三次频率检测结果的合集，将公式(7)中的每一个频率看作空间的一个点，其横纵坐标均可以表示为对应的频率值，则第二组和第三组数据中的每一个点到聚类中点的欧式距离平方可以定义为：
Figure PCTCN2022128583-appb-000011
当第二组和第三组中同时存在频率分量满足dist(·)<ε，本申请将ε定义为0.5Hz，则重新计算聚类中心，并将其归类为真实存在的频率点，新的聚类中心可以表示为：
Figure PCTCN2022128583-appb-000012
式中，f get为算法所测得的真实频率，f 1Ci、f 2Ci、f 3Ci表示在第i类中的三个频率分量。
因此改进TLS-ESPRIT算法执行流程为：
1)对信号进行3次采样并利用TLS-ESPRIT算法检测频率，得到三组初始频率集合。
2)将每一个频率看作空间中的点，并将第一组的频率点作为聚类中心。
3)计算第二组和第三组中的点到第一个聚类中心的距离，判断是否满足真实频率点的条件，若是，则重新计算聚类中心并作为真实频率，反之将其删除。
4)重复步骤2和步骤3，对其余频率分量进行聚类。
图2展示了未聚类时，在信号中添加信噪比为40dB白噪声情况下，三次频率检测结果，其中，预设频率分量个数为50，真实频率分量个数为13。
从图2中可以看出三次频率检测结果存在较大差异，对数据点空间化处理并进行聚类，删除噪声点后得到如图3所示的聚类结果。
从图3中可以看出，本申请算法可以很好的提取出真实存在的13种谐波分量，从局部放大结果来看，在以聚类中心为圆心，0.5Hz为半径的聚类范围内同时存在第二次和第三次频率检测中与聚类中心的距离小于ε的频率点，满足条件。
综上所述，本申请所提算法可以有效地在较强抗干扰下准确提取检测结果中的真实频率分量。
2基于2阶Blackman-Harris自卷积窗幅值、相位检测算法
构造2阶Blackman-Harris自卷积窗
在信号处理的过程中，通常采用余弦窗对信号进行加窗处理，其一般表达式为：
Figure PCTCN2022128583-appb-000013
式中K为余弦窗的阶数，且系数a k满足如下条件：
Figure PCTCN2022128583-appb-000014
衡量窗函数特性的主要标准是主瓣宽度(MLW)和旁瓣最高电平(MSLL)，主瓣宽度越窄则频谱分辨率越高，而旁瓣最高电平越低则越可以抑制频谱泄露现象。表1所示为常见窗函数的主瓣和旁瓣特性对比。
表1常见窗函数的主瓣和旁瓣特性
Figure PCTCN2022128583-appb-000015
从表1中可以看出，Blackman-Harris窗具有更低的旁瓣峰值电平，说明其对频谱泄露现象的抑制效果最佳，为了进一步改善旁瓣特性，可以对窗函数进行自卷积运算。定义q阶Blackman-Harris自卷积窗的表达式为：
Figure PCTCN2022128583-appb-000016
在对原窗函数进行q阶自卷积后，其序列长度变为qN-1，对末尾补零后得到长度为qN的序列窗。考虑到每进行一次自卷积运算，序列长度便会增加N个，为了方便在嵌入式系统中实现，阶数q不宜选取过大，因此本申请选取q＝2构造自卷积窗。
通过对卷积后的数据点进行拟合，得到本申请所构造的2阶Blackman-Harris自卷积窗为新的五项余弦组合窗。
2阶Blackman-Harris自卷积窗的频率特性
由傅里叶变换可知，Blackman-Harris窗的频谱函数为：
Figure PCTCN2022128583-appb-000017
式中，W R(w)为矩形窗的频谱函数。
w为连续角频率，设w＝2kπ/N，其中k＝0,1,2…N-1，由卷积定理可知，时域上的卷积即为频域上的乘积，则q阶Blackman-Harris自卷积窗的频谱函数为：
Figure PCTCN2022128583-appb-000018
图4所示为本申请窗函数与原窗函数和Hanning自卷积窗的幅频特性对比。窗函数的主瓣宽度为距离原点最近的两个零点之间的距离，即令W B-2(2kπ/N)＝0。本申请所提窗函数的主瓣宽度为20π/N，其频谱分辨率有所降低，而旁瓣最高电平达到了-184.1dB，和原窗函数的-92dB以及Hanning自卷积窗的-62dB相比有了显著降低，因此可以更好的抑制频谱泄露。基于2阶Blackman-Harris自卷积窗的插值公式
设待测信号为公式(1)，利用本申请所提出的窗对其进行时域截断，则加权样本x(n)w B-2(n)的离散时间傅里叶变换(DTFT)为：
Figure PCTCN2022128583-appb-000019
式中，S(n)为加窗噪声s(n)w B-2(n)的DTFT；采样间隔Δf＝f s/N。为了避免离散谱线之间的相互干扰，在本申请中假设谱线之间的距离大于主瓣宽度。
忽视负频点的影响，则频谱|X(n)|可以近似表示为：
Figure PCTCN2022128583-appb-000020
由于非同步采样的影响，所需要的频率点往往不能正好落在离散频谱上，即n 0不为整数，采用双谱线插值的方法可以用较少的计算量实现较高的计算精度，因此定义其左右两条谱线分别为n 1、n 2且存在n 1<n 0<n 2；0≤n 0-n 1≤1。则这两条谱线的幅值分别为：y 1＝|X(n 1)|，y 2＝|X(n 2)|。
设γ＝n 0-n 1-0.5，则可以定义比例系数β：
Figure PCTCN2022128583-appb-000021
记式(17)为β＝g(γ)，其反函数记作γ＝g -1(β)。当窗函数w B-2(n)为实系数时，其幅频响应W B-2(n)为偶函数，因此等效函数g -1(2)为奇函数，可以采用切比雪夫多项式逼近的方法进行推导，求得γ后便可以进一步推导幅值修正公式。
幅值修正可以对n 1和n 2两条谱线进行加权平均，可以表示为：
Figure PCTCN2022128583-appb-000022
当采样点N较大时，式(18)可以简化为：
A 0＝N -1(y 1+y 2)h(γ)   (19)
式中，h(γ)为偶函数。同理，可以采用多项式逼近的方法对其进行推导。
由式(16)可知，基于2阶Blackman-Harris自卷积窗的相位修正公式为：
Figure PCTCN2022128583-appb-000023
将γ从[-0.5,0.5]取一组数组，利用Matlab进行多项式逼近，得到传统Blackman-Harris窗与2阶Blackman-Harris自卷积窗的双谱线插值公式：
1)传统Blackman-Harris窗
Figure PCTCN2022128583-appb-000024
Figure PCTCN2022128583-appb-000025
Figure PCTCN2022128583-appb-000026
2)2阶Blackman-Harris自卷积窗
Figure PCTCN2022128583-appb-000027
Figure PCTCN2022128583-appb-000028
Figure PCTCN2022128583-appb-000029
3仿真分析
含多频率复杂电信号的频率检测
为了验证本申请方法可以更好的提取信号中的频率分量，以含5种频率分量的信号为模型进行仿真，分别设置幅值为基频的0.2％，并与现有技术所提出的自适应算法进行对比。
设置采样频率为4kHz，采样点数为1024，基频为50Hz，为了模拟实际过程中的干扰和采样误差，对信号加入信噪比(SNR)为40至70dB的高斯白噪声，仿真结果对比如表2所示。
表2本申请改进算法与现有技术频率检测结果对比
Figure PCTCN2022128583-appb-000030
由表2的仿真结果可知，现有技术所提出的方法在噪声较大时会出现频率遗漏的问题，而本申请所提出的算法在不同信噪比白噪声干扰下均可以检测出信号中的所有频率分量且精度更高。
稳态情况下弱谐波信号幅值、相位检测
在光伏并网系统中，各次谐波、间谐波通常幅值较小，因此本申请设置表3所示的仿真参数，在无噪声干扰的情况下，分别利用Blackman-Harris窗、Hanning自卷积窗、Blackman自乘-卷积窗、2阶Blackman-Harris自卷积窗对其进行加窗插值处理，其余参数与3.1相同，幅值和相位的相对误差如表4、表5所示。
表3弱信号各频率的幅值、相位信息
Figure PCTCN2022128583-appb-000031
Figure PCTCN2022128583-appb-000032
表4各次谐波分量的幅值检测相对误差
Figure PCTCN2022128583-appb-000033
表5各次谐波分量的相位检测相对误差
Figure PCTCN2022128583-appb-000034
由表4、表5可以看出，由于本申请提出的2阶Blackman-Harris自卷积窗拥有最低的旁瓣电平，其对频谱泄露抑制效果最佳，因此具有最高的检测精度，相对误差最小。其中，幅值检测的相对误差降低至10 -11％至10 -12％；相位检测的相对误差降低至10 -10％至10 -11％，相较于其余三种窗函数，在稳态时检测精度有了明显的提升。
非稳态情况下弱谐波信号幅值、相位检测
在实际应用的过程中，由于采样误差以及电网频率的随机波动，信号中往往存在噪声干扰。
为了验证本申请算法在非稳态情况下的抗干扰能力，在上述仿真参数中加权信噪比为60dB的高斯白噪声；同时，各频率发生±0.2Hz的随机波动。分别利用3种不同的窗与本申 请方法进行比较，幅值和相位检测的相对误差如图5所示。
由图5可知，在噪声干扰和频率波动的冲击下，各算法的精度均有所降低，而本申请算法的检测精度依然最高。其中幅值最小误差达到10 -5％，相位最小误差达到了10 -4％，比Blackman自乘-卷积窗提高了10 -3，比传统的Blackman-Harris窗与Hanning自卷积窗提高了10 -3至10 -1。
由仿真结果可知，本申请算法具有最强的抗噪声能力，能够适应电力系统中复杂的环境。
4实验分析
实验平台介绍
为了验证本申请提出的方法在实际谐波检测过程中的有效性，采用数字信号处理器(DSP)TMS320F28335实现算法，其晶振频率为150MHz，通过TFG6800任意信号发生器输出模拟波形，上位机观测检测数据。
为了模拟真实的信号，采用图6所示的一组由功率分析仪实测的光伏并网逆变器输出电流谐波数据为实验参数，可以发现，在三相对称的电网中，谐波主要由低次的正序和负序谐波构成，而偶次和零序谐波分量以及高次谐波含量很少，因此本申请仅提取前15次谐波作为实验数据。
软件设计方案
本申请的算法流程如图7所示：(1)首先DSP完成算法初始化：预设固定的采样频率和采样点数并生成2阶Blackman-Harris自卷积窗；(2)随后通过EPWM中断触发采样，采集数据并保存；(3)完成A/D采样后对采样得到的数据进行快速TLS-ESPRIT计算以提取谐波频率，重复上述步骤直至完成三次检测；(4)对频率检测结果进行聚类处理，提取出真实的谐波分量并计算得到每一次谐波的频谱点n 0；(5)最后对采样数据进行加窗插值计算，得到每一次谐波的幅值、相位信息，完成检测。
对于三相系统而言，为了节约处理器资源，需要采用轮询的方法对每一相电压、电流进行谐波分析。
实验结果
设置采样频率f s为2kHz，采样点数N为1024，以图6所示的谐波清单作为实验数据，由于功率分析仪无法检测到谐波相位信息，因此实验时相位通过任意信号发生器随机设置。通过上位机观测检测结果，任意信号发生器输出模拟并网电流波形如图8所示。
从图8中可以看出，由于谐波含量较少，波形近似为正弦波，因此检测难度更大，对算法的要求也更高，利用本申请算法检测结果的振幅谱和相位谱如图9、图10所示，各次谐波检测幅值、相位相对误差如表6所示
表6幅值、相位实验检测结果对比
Figure PCTCN2022128583-appb-000035
由表6可知，本申请所提方法在实际工况中幅值和相位检测都具有很高的精度：其中幅值检测精度最大误差仅为0.04％；相位检测最大误差仅为0.177°。表6中的输入信号总谐波失真(THD)为1.438％，本申请算法检测结果为1.419％，误差为0.019％。实验结果证明了本申请算法的有效性和实用性。
本申请提出了一种基于改进快速TLS-ESPRIT算法与2阶Blackman-Harris自卷积窗相结合的光伏并网逆变器输出电流谐波检测的方法。首先利用快速TLS-ESPRIT算法准确识别信号中的频率分量，进行多次检测并对检测结果基于简化K-means聚类算法进行分析。随后通过自卷积的方法构造出2阶Blackman-Harris自卷积窗，并提出幅值和相位修正算法，验证了本申请方法可以更好的提取出信号的频率分量且实际应用过程中也可以准确的检测信号的幅值和相位信息。
请参考图11，其示出了本申请的一些实施方式所提供的一种电子设备的示意图。如图11所示，所述电子设备20包括：处理器200，存储器201，总线202和通信接口203， 所述处理器200、通信接口203和存储器201通过总线202连接；所述存储器201中存储有可在所述处理器200上运行的计算机程序，所述处理器200运行所述计算机程序时执行本申请前述任一实施方式所提供的谐波与间谐波检测方法。
其中，存储器201可能包含高速随机存取存储器(RAM：Random Access Memory)，也可能还包括非不稳定的存储器(non-volatile memory)，例如至少一个磁盘存储器。通过至少一个通信接口203(可以是有线或者无线)实现该系统网元与至少一个其他网元之间的通信连接，可以使用互联网、广域网、本地网、城域网等。
总线202可以是ISA总线、PCI总线或EISA总线等。所述总线可以分为地址总线、数据总线、控制总线等。其中，存储器201用于存储程序，所述处理器200在接收到执行指令后，执行所述程序，前述本申请实施例任一实施方式揭示的所述谐波与间谐波检测方法可以应用于处理器200中，或者由处理器200实现。
处理器200可能是一种集成电路芯片，具有信号的处理能力。在实现过程中，上述方法的各步骤可以通过处理器200中的硬件的集成逻辑电路或者软件形式的指令完成。上述的处理器200可以是通用处理器，包括中央处理器(Central Processing Unit，简称CPU)、网络处理器(Network Processor，简称NP)等；还可以是数字信号处理器(DSP)、专用集成电路(ASIC)、现成可编程门阵列(FPGA)或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件。可以实现或者执行本申请实施例中的公开的各方法、步骤及逻辑框图。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器等。结合本申请实施例所公开的方法的步骤可以直接体现为硬件译码处理器执行完成，或者用译码处理器中的硬件及软件模块组合执行完成。软件模块可以位于随机存储器，闪存、只读存储器，可编程只读存储器或者电可擦写可编程存储器、寄存器等本领域成熟的存储介质中。该存储介质位于存储器201，处理器200读取存储器201中的信息，结合其硬件完成上述方法的步骤。
本申请实施例提供的电子设备与本申请实施例提供的谐波与间谐波检测方法出于相同的发明构思，具有与其采用、运行或实现的方法相同的有益效果。
本申请实施方式还提供一种与前述实施方式所提供的谐波与间谐波检测方法对应的计算机可读存储介质，请参考图12，其示出的计算机可读存储介质为光盘30，其上存储有计算机程序(即程序产品)，所述计算机程序在被处理器运行时，会执行前述任意实施方式所提供的谐波与间谐波检测方法。
需要说明的是，所述计算机可读存储介质的例子还可以包括，但不限于相变内存(PRAM)、静态随机存取存储器(SRAM)、动态随机存取存储器(DRAM)、其他类型的随机 存取存储器(RAM)、只读存储器(ROM)、电可擦除可编程只读存储器(EEPROM)、快闪记忆体或其他光学、磁性存储介质，在此不再一一赘述。
本申请的上述实施例提供的计算机可读存储介质与本申请实施例提供的谐波与间谐波检测方法出于相同的发明构思，具有与其存储的应用程序所采用、运行或实现的方法相同的有益效果。

Claims (10)

  1. 一种电网谐波与间谐波的检测方法，其特征在于，包括：
    对待测信号进行多次采样并利用快速TLS-ESPRIT算法检测频率；
    对所述检测的频率基于简化K-means聚类算法进行分析，提取出真实的谐波分量并计算得到每一次谐波的频谱点n 0；
    结合2阶Blackman-Harris自卷积窗对所述待测信号的采样数据进行加窗插值计算，估算所述待测信号的每一次谐波的幅值、相位信息。
  2. 根据权利要求1所述的方法，其特征在于，
    所述对待测信号进行多次采样并利用快速TLS-ESPRIT算法检测频率，包括：
    对信号进行3次采样并利用TLS-ESPRIT算法检测频率，得到三组初始频率集合。
  3. 根据权利要求2所述的方法，其特征在于，
    所述对所述检测的频率基于简化K-means聚类算法进行分析，提取出真实的谐波分量，包括：
    将每一个频率看作空间中的点，并将第一组初始频率集合的频率点作为第一个聚类中心；
    计算第二组和第三组初始频率集合中的点到第一个聚类中心的距离，判断是否满足真实频率点的条件，若是，则重新计算聚类中心并作为真实频率，反之则归类为噪声点并将其删除；
    重复以上步骤，对其余频率分量进行聚类。
  4. 根据权利要求1所述的方法，其特征在于，
    所述2阶Blackman-Harris自卷积窗为五项余弦组合窗。
  5. 根据权利要求1-4任一项所述的方法，其特征在于，
    在所述对待测信号进行多次采样之前，包括：
    (1)预设固定的采样频率和采样点数并生成2阶Blackman-Harris自卷积窗；
    (2)随后通过EPWM中断触发采样。
  6. 根据权利要求5所述的方法，其特征在于，
    对于三相系统，采用轮询的方法对每一相电压、电流进行谐波分析。
  7. 根据权利要求1所述的方法，其特征在于，
    所述加窗插值计算为2阶Blackman-Harris自卷积窗的双谱线插值，公式如下：
    γ＝5.271 023 8β+1.093 029 36β 3+
    0.746 302 3β 5+0.392 204 7β 7
    A 0＝(y 1+y 2)(2.102 03+0.363 12γ 2+
    0.035 61γ 4-0.006 698γ 6)/N
    Figure PCTCN2022128583-appb-100001
    其中，定义左右两条谱线分别为n 1、n 2且存在n 1<n 0<n 2；0≤n 0-n 1≤1；这两条谱线的幅值分别为：y 1＝|X(n 1)|，y 2＝|X(n 2)|，γ＝n 0-n 1-0.5，X(n i)为信号，β为比例系数，N为采样点个数，A 0为幅值，θ i为相位。
  8. 根据权利要求1或7所述的方法，其特征在于，
    所述2阶Blackman-Harris自卷积窗的表达式为：
    w B-2(n)＝w B(n)*w B(n)
    其中w B(n)为Blackman-Harris窗。
  9. 一种电子设备，包括存储器、处理器及存储在所述存储器上并可在所述处理器上运行的计算机程序，其特征在于，所述处理器运行所述计算机程序以实现如权利要求1-7任一项所述的方法。
  10. 一种计算机可读存储介质，其上存储有计算机程序，其特征在于，所述程序被处理器执行实现如权利要求1-7中任一项所述的方法。
PCT/CN2022/128583 2022-10-27 2022-10-31 一种电网谐波与间谐波的检测方法 WO2024087237A1 (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202211326726.5 2022-10-27
CN202211326726.5A CN115389816B (zh) 2022-10-27 2022-10-27 一种电网谐波与间谐波的检测方法

Publications (1)

Publication Number Publication Date
WO2024087237A1 true WO2024087237A1 (zh) 2024-05-02

Family

ID=84127763

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2022/128583 WO2024087237A1 (zh) 2022-10-27 2022-10-31 一种电网谐波与间谐波的检测方法

Country Status (2)

Country Link
CN (1) CN115389816B (zh)
WO (1) WO2024087237A1 (zh)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118294721A (zh) * 2024-06-06 2024-07-05 北京率为机电科技有限公司 一种用于宽频谐波测量的光纤电流互感器同步检测方法
CN118395346A (zh) * 2024-06-20 2024-07-26 广州南洋电缆集团有限公司 用于电力系统的节点运行安全性评估方法

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116735957B (zh) * 2023-06-07 2024-02-27 四川大学 计及主瓣重叠干扰的近频谐波与间谐波测量方法及系统

Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101701982A (zh) * 2009-11-16 2010-05-05 浙江大学 基于加窗插值fft的电力系统谐波检测方法
CN103308766A (zh) * 2013-05-15 2013-09-18 湖南大学 一种基于凯撒自卷积窗双谱线插值fft谐波分析方法及其装置
CN103743949A (zh) * 2014-01-06 2014-04-23 国家电网公司 一种基于单通道FastICA的谐波与间谐波的检测方法
CN105137185A (zh) * 2015-07-23 2015-12-09 河海大学 一种基于离散傅里叶变换的频域插值电力谐波分析方法
CN106872777A (zh) * 2017-02-15 2017-06-20 国网江苏省电力公司苏州供电公司 一种谐波和间谐波分离分析方法
CN109030941A (zh) * 2018-05-30 2018-12-18 上海电机学院 Hanning自乘卷积窗FFT三谱线插值谐波分析方法
CN109541306A (zh) * 2018-12-06 2019-03-29 华北电力大学 一种基于tls-esprit的谐波间谐波检测方法
CN110095650A (zh) * 2019-05-05 2019-08-06 三峡大学 基于五项Rife-Vincent(I)窗的四谱线插值FFT的复杂谐波检测分析方法
WO2020049717A1 (ja) * 2018-09-07 2020-03-12 三菱電機株式会社 信号処理回路、レーダ装置、信号処理方法及び信号処理プログラム
CN113032716A (zh) * 2019-12-24 2021-06-25 南京理工大学 基于加窗插值和Prony算法的谐波与间谐波分析方法

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108427031B (zh) * 2018-05-02 2020-08-04 三峡大学 基于多项式拟合及非干扰区域划分的间谐波检测方法
CN109142868A (zh) * 2018-08-10 2019-01-04 上海电机学院 电力谐波检测仪
CN109782063A (zh) * 2018-10-23 2019-05-21 国网安徽省电力有限公司芜湖供电公司 一种基于纳托尔自卷积窗三谱线插值fft的动态间谐波分析方法
CN111222088B (zh) * 2019-12-10 2021-07-30 国网江苏省电力有限公司扬州供电分公司 一种改进的平顶自卷积窗加权电力谐波幅值估计方法

Patent Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101701982A (zh) * 2009-11-16 2010-05-05 浙江大学 基于加窗插值fft的电力系统谐波检测方法
CN103308766A (zh) * 2013-05-15 2013-09-18 湖南大学 一种基于凯撒自卷积窗双谱线插值fft谐波分析方法及其装置
CN103743949A (zh) * 2014-01-06 2014-04-23 国家电网公司 一种基于单通道FastICA的谐波与间谐波的检测方法
CN105137185A (zh) * 2015-07-23 2015-12-09 河海大学 一种基于离散傅里叶变换的频域插值电力谐波分析方法
CN106872777A (zh) * 2017-02-15 2017-06-20 国网江苏省电力公司苏州供电公司 一种谐波和间谐波分离分析方法
CN109030941A (zh) * 2018-05-30 2018-12-18 上海电机学院 Hanning自乘卷积窗FFT三谱线插值谐波分析方法
WO2020049717A1 (ja) * 2018-09-07 2020-03-12 三菱電機株式会社 信号処理回路、レーダ装置、信号処理方法及び信号処理プログラム
CN109541306A (zh) * 2018-12-06 2019-03-29 华北电力大学 一种基于tls-esprit的谐波间谐波检测方法
CN110095650A (zh) * 2019-05-05 2019-08-06 三峡大学 基于五项Rife-Vincent(I)窗的四谱线插值FFT的复杂谐波检测分析方法
CN113032716A (zh) * 2019-12-24 2021-06-25 南京理工大学 基于加窗插值和Prony算法的谐波与间谐波分析方法

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118294721A (zh) * 2024-06-06 2024-07-05 北京率为机电科技有限公司 一种用于宽频谐波测量的光纤电流互感器同步检测方法
CN118395346A (zh) * 2024-06-20 2024-07-26 广州南洋电缆集团有限公司 用于电力系统的节点运行安全性评估方法

Also Published As

Publication number Publication date
CN115389816A (zh) 2022-11-25
CN115389816B (zh) 2023-04-07

Similar Documents

Publication Publication Date Title
WO2024087237A1 (zh) 一种电网谐波与间谐波的检测方法
CN109375060B (zh) 一种配电网故障波形相似度计算方法
CN110648088B (zh) 一种基于鸟群算法与svm的电能质量扰动源判断方法
Lin et al. Power quality detection with classification enhancible wavelet-probabilistic network in a power system
CN114781196A (zh) 一种基于稀疏采集模型的谐波检测方法
Li et al. A voltage sag detection method based on modified s transform with digital prolate spheroidal window
Ma et al. Harmonic and interharmonic analysis of mixed dense frequency signals
CN113176460A (zh) 一种基于改进经验小波变换的电能质量扰动信号检测方法
Wang et al. An adaptive filters based PMU algorithm for both steady-state and dynamic conditions in distribution networks
CN111537776A (zh) 一种行波波头标定方法、装置、终端以及介质
Mei et al. Wavelet packet transform and improved complete ensemble empirical mode decomposition with adaptive noise based power quality disturbance detection
CN110826498A (zh) 基于hht的暂态电能质量检测方法
CN104076203A (zh) 一种考虑负频率影响的超低频间谐波检测方法
Liu et al. A novel random spectral similar component decomposition method and its application to gear fault diagnosis
CN113608018A (zh) 提高谐波检测精度的自适应vmd检测方法、装置及存储介质
CN112180161A (zh) 一种非同步高采样率采样条件下谐波间谐波群测量方法
CN112069453B (zh) 一种基于小波变换的电力系统强迫振荡源时频域定位方法
Chang et al. Multi-synchrosqueezing transform-based hybrid method for frequency components detection of nonstationary voltage and current waveforms
CN114184838A (zh) 基于sn互卷积窗的电力系统谐波检测方法、系统及介质
Thomas et al. Machine learning based detection and classification of power system events
CN113866493A (zh) 一种风电引起电压波动与闪变的测量方法
Jianze et al. Time-varying transient harmonics measurement based on wavelet transform
Zhang et al. Study of harmonic analysis based on improved discrete Fourier transform
Lu et al. Subsynchronous oscillation detection using synchrosqueezing wavelet transforms and K-means clustering
CN115097206B (zh) 一种适用于静动态场景的宽频测量方法

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 22963218

Country of ref document: EP

Kind code of ref document: A1