CN103592514A - Novel harmonic high-precision detection method - Google Patents

Abstract

The invention discloses a novel harmonic high-precision detection method. The method comprises: constructing a novel time-frequency filter, using Hilbert transform to suppress the negative half-axis frequency, and detecting each harmonic of the signal with high precision through the time-domain convolution method. Frequency, amplitude and phase of harmonics and interharmonics. The theoretical analysis basis and calculation formula derivation of the invention, the method avoids Fourier (FFT) domain spectrum leakage, fence effect and non-integral wave phenomena. The experimental simulation results show that the time-frequency filter convolution method is flexible in design and easy in real-time engineering, which overcomes the influence of fundamental frequency fluctuations on harmonic analysis, and is effective for frequencies and amplitudes of signals containing multiple harmonics and inter-harmonics. Value, initial phase detection accuracy is high. From this signal conversion equation, the frequency, amplitude and phase of the voltage flicker signal can be obtained. For flicker signals polluted by interharmonics, the detection results will not be affected.

Description

A New Harmonic High-precision Detection Method

technical field

The invention belongs to the technical field of signal processing, in particular to a novel harmonic high-precision detection method.

Background technique

With the rapid development of my country's industrialization process, the installed capacity of the power grid continues to increase, and the use of power electronic components in the power grid is also increasing, resulting in a large number of harmonic currents injected into the power grid, resulting in sine wave distortion and a decline in power quality. Some important equipment of the system have had a major impact; it has also caused serious harm to the majority of users; at present, harmonics, electromagnetic interference, and power factor reduction are listed as the three major public hazards of the power system; harmonic hazards of the power system:

(1) Harmonics will cause additional losses to power equipment in the public grid, reducing the efficiency of power generation, transmission and power consumption equipment. A large number of third harmonics flowing through the neutral line will overheat the line, and may even cause a fire if it is serious;

(2) Harmonics will affect the normal operation of electrical equipment, causing mechanical vibration and noise failures in the motor, severe local overheating of transformers, overheating of capacitors, cables and other equipment, aging and deterioration of insulation parts, shortened equipment life, and eventually damage;

(3) Harmonics will cause grid resonance, which may amplify the harmonic current several times or even dozens of times, which will pose a major threat to the system, especially for capacitors and reactors connected in series, grid resonance often burns them out;

(4) Harmonics will cause relay protection and automatic device malfunction, resulting in unnecessary interruption and loss of power supply;

(5) Harmonics will make the measurement of electrical measuring instruments inaccurate, produce measurement errors, and bring direct economic losses to power supply departments or power users;

(6) Harmonics will interfere with the communication system near the equipment, which may cause noise and reduce the quality of communication, or lead to information loss and make the communication system unable to work normally;

(7) Harmonics will interfere with the normal operation of electronic equipment such as computer systems, resulting in data loss or crashes;

(8) Harmonics will affect the performance of radio transmission systems, radar systems, nuclear magnetic resonance and other equipment, causing noise interference and image disorder.

The high-precision analysis of power harmonics is of great significance to electric energy metering, harmonic power flow calculation, equipment network detection, power system harmonic compensation and suppression, etc.; due to asynchronous sampling and data truncation, fast Fourier transform (FFT) The algorithm for harmonic analysis produces spectrum leakage and fence effects, which affect the accuracy of harmonic analysis;

In order to reduce this kind of error, scholars at home and abroad have proposed signal window interpolation FFT analysis algorithms based on rectangular window, Hanning window, Hamming window ^] , Blackman window, Blackman-Harris window, Kaiser window and various improved windows ^] , which can Alleviate the spectrum leakage and fence effect problems encountered when FFT is applied alone, and improve the detection accuracy of harmonic parameters, but cannot detect inter-harmonics near integer harmonics; using bispectral lines based on high-order cosine combination windows ^] When the multi-spectral interpolation FFT algorithm is used to estimate the fundamental wave and harmonic parameters, it needs to solve high-order equations, and the calculation is complicated; continuous wavelet transform can realize the detection of inter/sub-harmonics, but wavelet functions of different scales exist in the frequency domain Mutual interference, when the detected signal contains harmonic components with similar frequencies, the detection method will fail; the Prony method is an effective method for harmonic and interharmonic analysis and modeling, and can accurately estimate the frequency and amplitude of each sinusoidal component and phase angle, but it needs to solve two sets of odd-order equations and first-degree polynomials, which has high computational complexity and is sensitive to noise; there are other methods, or the frequency resolution is limited, or the amount of calculation is large, and there are limitations in specific applications.

Contents of the invention

(1) Technical problems to be solved

In view of this, the main purpose of the present invention is to propose a new harmonic high-precision detection method, 1) effective time-frequency filter design ; 2) Hilbert transform to suppress the negative half-axis frequency ; 3) design time-domain convolution algorithm with high precision The frequency, amplitude and phase of each harmonic and inter-harmonic of the signal can be accurately detected; 3) Theoretical proof that the algorithm is effective .

the

(2) Technical solutions

In order to achieve the above object, the present invention provides a novel harmonic high-precision detection method, the method comprising:

 A time-frequency filter is designed, using Hilbert transform to suppress the negative half-axis frequency, and the frequency, amplitude and phase of each harmonic and inter-harmonic of the signal can be detected with high precision through time-domain convolution; theoretical analysis is carried out in the invention Compared with computational derivation, this method avoids Fourier (FFT) domain spectrum leakage, fence effect and non-integral wave phenomenon.

Preferably, the extracted time-frequency filter:

   （1）

(1)

为阶跃函数，

为滤波器中心参数，系数B用来调整滤波器带宽（如取B=1），ω₀中心频率；其频域表达式为： in

is a step function,

It is the center parameter of the filter, the coefficient B is used to adjust the filter bandwidth (for example, take B=1), _ω0 is the center frequency; its frequency domain expression is:

（2）

(2)

；图2给出这时频滤波器特征趋势，（a）图时域趋势，(b)频域趋势；他们都随中心频率ω₀而变化；由（2）式及图1(b)可见G（ω，ω₀）只在ω₀为中心的窄频带幅值显著，其它几乎为零。 in

; Figure 2 shows the characteristic trend of this time-frequency filter, (a) the trend in the time domain, (b) the trend in the frequency domain; they all change with the center frequency ω ₀ ; it can be seen from the formula (2) and Figure 1(b) G(ω,ω ₀ ) is significant only in the narrow frequency band with ω ₀ as the center, and the others are almost zero.

Preferably, the Hilbert transform of the extraction:

的HT定义为 real signal

The HT is defined as

     (3)

(3)

为求卷积,的傅里叶变换为

,则

傅里叶变换为 in

For convolution, The Fourier transform of

,but

Fourier transform to

             (4)

(4)

为符号函数；信号f(t)通过Hilbert变换和它的复信号联系起来，可以构成解析信号          

                 （5）

is a symbolic function; the signal f(t) is connected with its complex signal through the Hilbert transform, and an analytical signal can be formed

(5)

的负频率部分；即 An important property of parsing signals is that they preserve The positive frequency part of , rejecting

The negative frequency part of ; that is

      （6）。

(6).

the

Preferably, the continuous theoretical analysis of the extraction:

There are harmonic signals with frequency ω ₁ >0 in a narrow frequency band centered on ω ₀ :

  (7)

(7)

Its frequency domain expression:

   (8)

(8)

的解析信号

的傅里叶变换为(由（6）、（8）式得)

Analysis signal of

The Fourier transform of is (obtained from (6), (8) formula)

         （9）

(9)

   （10）

(10)

(11)

but:

        （12）

(12)

                                         （13）

(13)

  （14）。

(14).

Preferably, the extracted parameters are initialized: the sampling frequency is fs, then the sampling period DT=1/fs,

The number of sampling points is N; take N ₁ =[0.9N], N ₂ =[0.94N].

Preferably, the implementation process of the invention is shown in FIG. 1 , and the time/frequency characteristic of the time-frequency filter is shown in FIG. 2 . the

(3) Beneficial effects

1. This novel harmonic high-precision detection method provided by the present invention avoids Fourier (FFT) domain spectrum leakage, fence effect and non-integer wave phenomenon; the design of time-frequency filter convolution method is flexible and efficient. The engineering real-time realization is convenient, and the influence of the fundamental frequency fluctuation on the harmonic analysis is overcome, and the detection accuracy of the frequency, amplitude and initial phase of the signal containing multiple harmonics and inter-harmonics is high;

2. Advantages and features of the novel harmonic high-precision detection method provided by the present invention:

1) Avoid the Fourier (FFT) domain spectrum leakage, fence effect and non-integral wave phenomenon;

2) The design and implementation of time-frequency filter convolution method is flexible, and the engineering real-time implementation is convenient;

3) The invention can detect harmonics in the signal, and can also be used to detect voltage flicker;

4) The algorithm has low complexity, wide application range and strong real-time performance.

Description of drawings

Fig. 1 flow chart of a novel harmonic high-precision detection method provided by the present invention;

Fig. 2 is the time/frequency diagram of the time-frequency filter provided by the present invention;

Fig. 3 compares the true value and detected value of each harmonic characteristic parameter provided by the present invention;

Fig. 4 is the subharmonic frequency f=350.7Hz result provided by the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be described in further detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

The core content of the present invention is to realize a new type of time-frequency filter, use Hilbert transform to suppress the negative half-axis frequency, and detect the frequency, amplitude and Phase; the invention requires theoretical analysis and calculation derivation in parallel, and the method avoids Fourier (FFT) domain spectrum leakage, fence effect and non-integral wave phenomenon. the

As shown in Figure 1, accompanying drawing 1 is a kind of novel harmonic high-precision detection method flowchart provided by the present invention, and this method comprises the following steps:

Step 101: Select a time-frequency filter function;

Step 102: Parameter initialization: the sampling frequency is fs, then the sampling period DT=1/fs, and the number of sampling points is N; take N ₁ =[0.9N], N ₂ =[0.94N];

Step 103: calculating discrete convolution;

Step 104: Calculate harmonic frequency f (Hz), amplitude A;

Step 105: Calculate the harmonic initial phase φ (°C).

The discrete convolution calculation steps described in the above step 103 include:

，采样数为N；取N₁=[0.9N]，N₂=[0.94N]，计算离散卷积： Let the discrete sampling frequency be fs, then the sampling period DT=

, the number of samples is N; take N ₁ =[0.9N], N ₂ =[0.94N], and calculate the discrete convolution:

       （15）

(15)

 （16）。

(16).

the

Harmonic frequency f (Hz) described in above-mentioned step 104, amplitude A calculating step comprises:

         （17）

(17)

                     (18)

(18)

(19).

the

The harmonic initial phase φ (℃) calculation steps described in the above step 105 include:

   （21）。

(twenty one).

Based on the flowchart of a new harmonic high-precision detection method shown in Figure 1, Figure 2 further shows the time/frequency diagram of the time-frequency filter. the

the

Below in conjunction with specific embodiment, this novel harmonic high precision detection method provided by the present invention is further described in detail; Experiment: signal contains fundamental wave, direct current, 2 interharmonics and 3 subharmonics, and their parameters are shown in the table 1, its expression:

  （22）

(twenty two)

Its sampling frequency is fs=2kHz, and the number of samples is N=5000; the detection results of the method in this paper are also in the right part of Table 1; the real values and detection values of each harmonic frequency, amplitude, and initial phase are drawn on the same coordinate in Figure 2, and the results are very good. precise;

The detection operation near the sub-harmonic frequency f=350.7Hz in Table 1 is shown in Figure 4. The abscissas of Figures (a), (b) and (c) are the number of sample points; Figure (a) is the amplitude of formula (15) , Figure (c) shows the magnitude of the inverse Fourier transform (IFFT) after frequency domain filtering of the signal, the two are consistent after 500 points; Figure (b) is the instantaneous frequency of formula (16), and Figure (d) horizontal The coordinates are frequency (Hz), and the Hilbert transform of the signal is an analytical signal frequency domain amplitude.

The specific embodiments described above have further described the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention. the

Claims (3)

1. A novel harmonic high-precision detection method is characterized in that the method comprises: designing a novel time-frequency filter, suppressing the negative half-axis frequency with the Hilbert transform, and detecting each signal of the signal with high precision by the time-domain convolution method. The frequency, amplitude and phase of sub-harmonic and inter-harmonic; the theoretical analysis basis and calculation formula derivation of the invention, this method avoids the Fourier (FFT) domain spectrum leakage, fence effect and non-integral wave phenomenon; time-frequency filtering The convolution method is flexible in design and easy in real-time engineering, overcomes the influence of fundamental frequency fluctuations on harmonic analysis, and has high detection accuracy for frequency, amplitude, and initial phase of signals containing multiple harmonics and inter-harmonics; And thus can detect voltage flicker. 2. novel harmonic high-precision detection method according to claim 1, is characterized in that, described novel time-frequency filter: 1) in

is a step function,

is the filter center parameter, coefficient B is used to adjust the filter bandwidth (for example, take B=1), ω ₀ center frequency; 2)

in

It is the center parameter of the filter, the coefficient B is used to adjust the filter bandwidth (for example, take B=0.04), and ω is the center frequency of ₀ . 3. novel harmonic high-precision detection method according to claim 1, is characterized in that, described time-domain convolution harmonic high-precision detection algorithm: if discrete sampling frequency is fs, then sampling period DT= , the number of samples is N; take N ₁ =[0.9N], N ₂ =[0.94N], and calculate the discrete convolution:

       

  Then the harmonic frequency f (Hz), amplitude A, and initial phase φ (°C) are respectively: , ,

   

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