阅读说明：本技术 一种间谐波分析方法 (Inter-harmonic analysis method ) 是由 郭成 尹轲 李文云 于 2020-11-25 设计创作，主要内容包括：本申请公开一种间谐波分析方法,方法包括：对电力系统的电压和电流信号进行离散傅里叶变换DFT分析,获得间谐波信号频谱图；根据所述间谐波信号频谱图,确定间谐波频率分析范围；对所述间谐波频率分析范围进行频段划分,根据采样原则,对划分后的频段设置采样参数；根据所述采样参数,对所述电压和电流信号进行数据采样,对所述电压和电流信号进行重构,得到所述间谐波的幅值、频率、初相角和衰减因子；根据所述衰减因子,进行数据筛选。本申请可以精确分析出间谐波的幅值、频率、初相角和衰减因子等信息,测量精度满足标准要求,具有良好的动态特性,对高次间谐波进行准确地测量。(The application discloses an inter-harmonic analysis method, which comprises the following steps: performing Discrete Fourier Transform (DFT) analysis on voltage and current signals of the power system to obtain an inter-harmonic signal spectrogram; determining an inter-harmonic frequency analysis range according to the inter-harmonic signal spectrogram; dividing the frequency band of the inter-harmonic frequency analysis range, and setting sampling parameters for the divided frequency band according to a sampling principle; according to the sampling parameters, carrying out data sampling on the voltage and current signals, and reconstructing the voltage and current signals to obtain the amplitude, the frequency, the initial phase angle and the attenuation factor of the inter-harmonic; and screening data according to the attenuation factor. The method and the device can accurately analyze information such as amplitude, frequency, initial phase angle and attenuation factor of inter-harmonics, the measurement precision meets standard requirements, and the method and the device have good dynamic characteristics and accurately measure higher inter-harmonics.)

1. A method of inter-harmonic analysis, the method comprising:

performing Discrete Fourier Transform (DFT) analysis on voltage and current signals of the power system to obtain an inter-harmonic signal spectrogram;

determining an inter-harmonic frequency analysis range according to the inter-harmonic signal spectrogram;

dividing the frequency band of the inter-harmonic frequency analysis range, and setting sampling parameters for the divided frequency band according to a sampling principle;

according to the sampling parameters, carrying out data sampling on the voltage and current signals, and reconstructing the voltage and current signals by utilizing linear combination of exponential functions to obtain the amplitude, frequency, initial phase angle and attenuation factor of the inter-harmonic;

and screening data according to the attenuation factor to obtain a screening result.

2. The inter-harmonic analysis method of claim 1, wherein the discrete fourier transform DFT analysis is:

wherein, N is the number of sampling points, and x (N) is the voltage and current signals of the power system.

3. The inter-harmonic analysis method according to claim 1, wherein the frequency-dividing the inter-harmonic frequency analysis range is dividing the inter-harmonic frequency analysis range into a limited number of frequency bands.

4. The inter-harmonic analysis method according to claim 1, wherein the sampling principle is specifically: the sampling frequency is 4 times of the divided frequency band maximum frequency, and the sampling time is more than 2 times of the divided frequency band minimum frequency corresponding period.

5. The inter-harmonic analysis method of claim 1 wherein the step of data sampling the voltage and current signals according to the sampling parameters and reconstructing the voltage and current signals using a linear combination of exponential functions to obtain the amplitude, frequency, initial phase angle and attenuation factor of the inter-harmonics comprises the steps of:

step 1: sampling the voltage and current signals x (t), recording the sampling data as x (0), x (1), … and x (N-1), and enabling the sampling data to be x (0), x (1), … and x (N-1)

In the formula, N is the number of sampling data, P is the order of the algorithm model, and N is more than or equal to 2 k; a. the_kIs amplitude, α_kAs attenuation factor, f_kIn order to be the frequency of the radio,is the phase, Δ t is the sampling interval;

to make the error of the fitted signal smaller, the objective function is constructed as:

step 2: constructing a difference equation, the solution of which is:

the difference equation is as follows:

at this time, the signal error is e (n), as follows:

according to the aboveThe expressions for the difference equation and e (n) yield the signal x (n), as follows:

in the formula:

and step 3: considering x (n) as noise u (n) to excite the output generated by a P-order autoregressive model, solving the regular equation of the model can obtain a parameter a_kA is to_kThe following characteristic polynomials are introduced:

by rooting the characteristic polynomial, the parameter z can be determined_k；

And 4, step 4: according to the formula

Available matrix equation

Wherein

Least squares solution of matrix equations to

Thereby obtaining a parameter b_k；

And 5: from the found z_k、b_kThe following can be obtained:

6. the inter-harmonic analysis method according to claim 1, wherein the data screening is performed according to the attenuation factor, specifically:

energy S of each frequency component_kThe expression of (a) is:

in the formula, S_kIs the energy of each frequency component, A_kIs the amplitude of each frequency component, z_kRepresenting the poles of each frequency component, wherein N is the number of sampling points, and P is the order of the model;

wherein z is_kAnd alpha_kCorrelation, α_kThe larger the modulus, S_kThe smaller the numerical value is, the faster the signal attenuation speed is;

will S_kSorting by numerical value from large to small when S_kWhen the numerical value rapidly decreases, the rapidly decreasing S is judged_kNumerical value and S following it_kThe values are caused by noise components and spurious components whose associated parameters are filtered out.

Technical Field

The application relates to the technical field of power system harmonic measurement, in particular to an inter-harmonic analysis method.

Background

With the rapid development of power electronic devices and renewable energy sources, a large number of distributed power supplies such as wind energy and photovoltaic power supplies and nonlinear loads are connected into a power system, so that the problems of harmonic waves and inter-harmonic waves are increasingly serious.

For an electric power system, harmonic and inter-harmonic currents can cause additional losses to electric power equipment and transmission and distribution lines, thereby reducing the utilization rate of electric energy and the efficiency of the system; in addition, the harmonic waves and the inter-harmonic waves can interfere relay protection and automatic control in the power system, so that hysteresis or misoperation of equipment is easily caused, and the power supply reliability of the power system is seriously influenced; for users, harmonic and inter-harmonic problems cause distortion of voltage and current waveforms on the user side, the requirements of the users on the electric energy quality of electric equipment cannot be met, the daily life and production of the users are affected, certain economic losses are caused, and the personal safety is endangered in severe cases.

In an electric power system, the inter-harmonic content is low, but the inter-harmonic has no predictability, so that the harmonic damage is caused, and the more serious damage such as voltage fluctuation and flicker is easily caused.

Aiming at the problems, a series of standards about harmonic waves and inter-harmonic waves are established at home and abroad, and the limit value of the inter-harmonic waves is established more strictly than the limit values of the inter-harmonic waves. The harmonic measurement technology can quickly measure harmonic and inter-harmonic parameters in the power system, and plays an important role in solving the problems of harmonic and inter-harmonic. However, because the content of the inter-harmonic wave changes constantly, the inter-harmonic wave measurement is more difficult than the harmonic wave, and research on the inter-harmonic wave measurement technology is relatively less.

Fast Fourier Transform (FFT) is the most widely applied method for measuring harmonic waves and inter-harmonic waves at present, and has the advantages of high calculation speed, simple algorithm, easiness in microcomputer realization and the like. However, this method is prone to spectral leakage and a fence effect, resulting in increased error; in addition, the measurement spectrum range of the inter-harmonic is too large, so that the analysis degree is not high, and the specific information such as the amplitude, the frequency and the like of the inter-harmonic cannot be accurately measured.

The Hilbert-Huang transform (HHT) is a method capable of processing unsteady nonlinear signals, comprises two processes of Empirical Mode Decomposition (EMD) and Hilbert Transform (HT), and has the advantages of high adaptability, high precision and the like, but the EMD process can generate mode mixing and end point effects, and the accuracy of an analysis result is seriously influenced.

Disclosure of Invention

The application provides an inter-harmonic analysis method which can accurately analyze information such as amplitude, frequency, initial phase angle and attenuation factor of inter-harmonic.

A method of inter-harmonic analysis, the method comprising:

performing Discrete Fourier Transform (DFT) analysis on voltage and current signals of the power system to obtain an inter-harmonic signal spectrogram;

determining an inter-harmonic frequency analysis range according to the inter-harmonic signal spectrogram;

dividing the frequency band of the inter-harmonic frequency analysis range, and setting sampling parameters for the divided frequency band according to a sampling principle;

according to the sampling parameters, carrying out data sampling on the voltage and current signals, and reconstructing the voltage and current signals by utilizing linear combination of exponential functions to obtain the amplitude, frequency, initial phase angle and attenuation factor of the inter-harmonic;

and screening data according to the attenuation factor to obtain a screening result.

Preferably, the discrete fourier transform DFT analysis is:

wherein, N is the number of sampling points, and x (N) is the voltage and current signals of the power system.

Preferably, the frequency band division of the inter-harmonic frequency analysis range refers to dividing the inter-harmonic frequency analysis range into a limited number of frequency bands.

Preferably, the sampling principle is specifically as follows: the sampling frequency is 4 times of the divided frequency band maximum frequency, and the sampling time is more than 2 times of the divided frequency band minimum frequency corresponding period.

Preferably, the data sampling is performed on the voltage and current signals according to the sampling parameters, and the voltage and current signals are reconstructed by using a linear combination of exponential functions to obtain the amplitude, the frequency, the initial phase angle and the attenuation factor of the inter-harmonic, and the method includes the following steps:

step 1: sampling the voltage and current signals x (t), recording the sampling data as x (0), x (1), … and x (N-1), and enabling the sampling data to be x (0), x (1), … and x (N-1)

In the formula, N is the number of sampling data, P is the order of the algorithm model, and N is more than or equal to 2 k; a. the_kIs amplitude, α_kAs attenuation factor, f_kIn order to be the frequency of the radio,is the phase, Δ t is the sampling interval;

to make the error of the fitted signal smaller, the objective function is constructed as:

step 2: constructing a difference equation, the solution of which is:

the difference equation is as follows:

at this time, the signal error is e (n), as follows:

according to the aboveThe expressions for the difference equation and e (n) yield the signal x (n), as follows:

in the formula:

and step 3: considering x (n) as noise u (n) to excite the output generated by a P-order autoregressive model, solving the regular equation of the model can obtain a parameter a_kA is to_kThe following characteristic polynomials are introduced:

by rooting the characteristic polynomial, the parameter z can be determined_k；

And 4, step 4: according to the formula

Available matrix equation

Wherein

Least squares solution of matrix equations to

Thereby obtaining a parameter b_k；

And 5: from the found z_k、b_kThe following can be obtained:

preferably, the data screening is performed according to the attenuation factor, specifically:

energy S of each frequency component_kThe expression of (a) is:

in the formula, S_kIs the energy of each frequency component, A_kIs the amplitude of each frequency component, z_kRepresenting the poles of each frequency component, wherein N is the number of sampling points, and P is the order of the model;

wherein z is_kAnd alpha_kCorrelation, α_kThe larger the modulus, S_kThe smaller the numerical value is, the faster the signal attenuation speed is;

will S_kSorting by numerical value from large to small when S_kWhen the numerical value rapidly decreases, the rapidly decreasing S is judged_kNumerical value and S following it_kThe values are caused by noise components and spurious components whose associated parameters are filtered out.

Compared with the prior art, the invention has the beneficial effects that: the method has good dynamic characteristics, and can set sampling parameters according to the adjustment of frequency band division and accurately measure the higher harmonics; the frequency, amplitude, initial phase, attenuation factor and other information of the interharmonic can be accurately solved, and the measurement precision of the interharmonic meets the standard requirement.

Drawings

In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a flow chart of a method of inter-harmonic analysis of the present application;

FIG. 2 is a schematic diagram of inter-harmonic order of the present application;

fig. 3 is a schematic diagram of frequency band division and setting of sampling parameters according to an embodiment of the present application.

Detailed Description

The technical solution in the embodiments of the present invention is described in detail below with reference to the drawings of the present application.

Fig. 1 is a flow chart of an inter-harmonic analysis method according to the present invention, as shown in fig. 1, the method includes:

performing Discrete Fourier Transform (DFT) analysis on voltage and current signals of the power system to obtain an inter-harmonic signal spectrogram;

specifically, the discrete fourier transform DFT analysis is as follows:

wherein: n is the number of sampling points, and x (N) is the voltage and current signals of the power system.

Determining an inter-harmonic frequency analysis range according to the inter-harmonic signal spectrogram;

the middle harmonic frequency analysis range of this embodiment is 0-1200 Hz.

FIG. 2 is a schematic diagram of the inter-harmonic order of the present application, and as can be seen from FIG. 2, 5-45Hz is 0 th inter-harmonic, 55-95 is 1 st inter-harmonic, and so on.

Dividing the frequency band of the inter-harmonic frequency analysis range, and setting sampling parameters for the divided frequency band according to a sampling principle;

specifically, the frequency division of the inter-harmonic frequency analysis range refers to dividing the inter-harmonic frequency analysis range into a limited number of frequency ranges, and in this embodiment, the inter-harmonic frequency analysis range of 0-1200Hz is divided into a low frequency range (0-400Hz), a medium frequency range (350-. The sampling principle is as follows: the sampling frequency is 4 times of the highest frequency of the frequency band, and the sampling time is more than 2 times of the corresponding period of the lowest frequency of the frequency band. Fig. 3 is a schematic diagram of frequency band division and sampling parameter setting according to the embodiment of the present application, and it can be seen from fig. 3 that different frequency bands are set with different sampling frequencies and sampling times according to the sampling rule, so that the measurement accuracy is ensured, and no important information is lost. The specific sampling parameter results of each frequency band are shown in table 1:

TABLE 1 sampling parameters for each frequency band

According to the sampling parameters, carrying out data sampling on the voltage and current signals, and reconstructing the voltage and current signals by utilizing linear combination of exponential functions to obtain the amplitude, the frequency, the initial phase angle and the attenuation factor of the inter-harmonic wave, wherein the method comprises the following steps:

step 1: sampling the voltage and current signals x (t), recording the sampling data as x (0), x (1), … and x (N-1), and enabling the sampling data to be x (0), x (1), … and x (N-1)

In the formula, N is the number of sampling data, P is the order of the algorithm model, and N is more than or equal to 2 k; a. the_kIs amplitude, α_kAs attenuation factor, f_kIn order to be the frequency of the radio,is the phase, Δ t is the sampling interval;

to make the error of the fitted signal smaller, the objective function is constructed as:

step 2: constructing a difference equation, the solution of which is equation (2), as follows:

at this time, the signal error is e (n), as follows:

combining equations (6) and (7) yields a signal x (n) as follows:

in the formula (8), the reaction mixture is,

and step 3: considering x (n) as noise u (n) to excite the output generated by a P-order autoregressive model, solving the regular equation of the model can obtain a parameter a_kA is to_kThe following characteristic polynomials are introduced:

by rooting the polynomial (9), the parameter z can be determined_k；

And 4, step 4: the matrix equation can be obtained from equation (2)

Wherein

Least squares solution of matrix equations to

Thereby obtaining a parameter b_k；

And 5: from the found z_k、b_kThe following can be obtained:

and (3) performing data screening according to the attenuation factor to obtain a screening result, which specifically comprises the following steps:

energy S of each frequency component_kThe expression of (a) is:

in the formula, S_kIs the energy of each frequency component, A_kIs the amplitude of each frequency component, z_kRepresenting the poles of each frequency component, wherein N is the number of sampling points, and P is the order of the model;

wherein, according to the last α in (13)_kIs given by the expression of_kAnd alpha_kIs correlated, thereby S_kAnd alpha_kCorrelation, α_kThe larger the modulus value, z_kThe smaller the modulus value, thus S_kThe smaller the numerical value is, the faster the signal attenuation speed is;

will S_kSorting by numerical value from large to small when S_kWhen the numerical value rapidly decreases, the rapidly decreasing S is judged_kNumerical value and S following it_kThe values are caused by noise and spurious components whose associated parameters are filteredAnd (4) removing.

For example, mixing S_kSorting by numerical value from large to small when S_kWhen the value rapidly decreases to be less than the previous value 1/100, S rapidly decreasing to be less than the previous value 1/100 is determined_kNumerical value and S following it_kThe values are caused by noise components and spurious components whose associated parameters are filtered out.

According to the technical scheme, the invention provides the inter-harmonic analysis method, which comprises the steps of carrying out Discrete Fourier Transform (DFT) analysis on voltage and current signals of the power system to obtain an inter-harmonic signal spectrogram; determining an inter-harmonic frequency analysis range according to the inter-harmonic signal spectrogram; dividing the frequency band of the inter-harmonic frequency analysis range, and setting sampling parameters for the divided frequency band according to a sampling principle; according to sampling parameters, data sampling is respectively carried out on each divided frequency band, and voltage and current signals are reconstructed by utilizing linear combination of exponential functions to obtain the amplitude, the frequency, the initial phase angle and the attenuation factor of the inter-harmonic wave; and screening data according to the attenuation factor to obtain a screening result.

The method can determine the inter-harmonic frequency range to be analyzed through Discrete Fourier Transform (DFT) analysis; the inter-harmonic frequency analysis range is divided into frequency bands, and data sampling is carried out on different frequency bands according to a certain sampling rule, so that accurate measurement of inter-harmonics, particularly accurate measurement of higher inter-harmonics, can be realized; sampling the voltage and current signals according to the sampling data, and reconstructing the voltage and current signals to obtain the amplitude, the frequency, the initial phase angle and the attenuation factor of the inter-harmonic wave; and screening data according to the attenuation factor, screening out noise components and false components, and further realizing accurate measurement of inter-harmonics.

The above description is only a partial embodiment of the present invention, and is not intended to limit the technical scope of the present invention, and any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.