阅读说明：本技术 一种基于dft迭代法的谐波参数估计方法 (Harmonic parameter estimation method based on DFT iteration method ) 是由 王开 任肖屹 王兰兰 刘珊 于 2020-12-03 设计创作，主要内容包括：本发明公开了一种基于DFT迭代法的谐波参数估计方法,首先对信号进行采集和预处理,然后构造频率估计的代价函数,通过DFT迭代法对谐波的真实频率进行搜索迭代运算,以代价函数最小化为目标进行优化,最终迭代出精确的谐波参数估计值。该方法能应用于包含多个阶次谐波的复杂信号,考虑并计算了偶次谐波的影响,能得到逼近真实值的估计结果。(The invention discloses a harmonic parameter estimation method based on a DFT iteration method. The method can be applied to complex signals containing multiple order harmonics, the influence of even order harmonics is considered and calculated, and an estimation result approaching a true value can be obtained.)

1. A harmonic parameter estimation method based on DFT iteration method is characterized in that the method comprises the following steps:

A. in a measurement period, sampling to obtain a harmonic signal, performing discrete Fourier transform on the harmonic signal to obtain a frequency spectrum of the signal, and positioning a peak value of the frequency spectrum to obtain a frequency estimation value of frequency;

B. constructing a frequency estimation cost function;

C. taking cost function minimization as a target, taking the frequency estimation value obtained in the step A as an initial value, and solving the frequency estimation value through a DFT iteration method;

D. and C, constructing a DFT expression column matrix equation, substituting the estimated value of the frequency obtained in the step C into the DFT expression column matrix equation, and calculating the amplitude and the phase of the harmonic wave.

2. The harmonic parameter estimation method based on DFT iteration method as claimed in claim 1, wherein the specific step of step B includes:

processing three-phase voltage signals with clark transformation to generate input phasor signals

Wherein V₊、V_{_}Andis the amplitude and initial phase, ω, of the sequence₀＝2πf₀/f_s，f₀Is the frequency of the input signal, f_sIs the sampling frequency;

when V is₊＝V_-And isWhen the signal v (n) is a real-valued sinusoidal signal, takeDefinition of S_cos(n) ═ v (n) + v (n), and this gives

Wherein

Rewriting normalized angular frequency as ω₀＝2πl₀/N＝2π(k₀+δ₀)/N，l₀Representing the number of periods, k, of the resulting sinusoidal signal₀And delta₀Is the integer and fractional part of the normalized frequency, k₀Is estimated as

Thereby will s_cosThe N-point DFT of (N) is expressed as

Order to

When two different DFT sequences S (k) are known₁) And S (k)₂) Then, the following matrix equation can be constructed:

mu and v are reference variables, their values are independent of k, when ω is₀When the value of [ mu ] is known, the value of [ mu ] can be determined by the above equation, and the calculation is described as

Similarly, another process for calculating v is described as

Since mu is v^*By elimination of a reference variableThen, ω₀Is calculated from the cost function of

3. The harmonic parameter estimation method based on the DFT iterative method as claimed in claim 1, wherein the specific step of step C includes:

setting iteration times M, a jump-out condition TOL, a stepping distance oa and an iteration result lower limit δ_aAnd an upper limit δ_b；

In each iteration loop, δ is set_c＝(δ_a+δ_b) /2, orderWhen f is<At TOL, the cycle is finished;

when f is not less than TOL, set

When f is₁＜f₂When is delta_b＝δ_c(ii) a Else δ_a＝δ_c；

Obtaining an estimate of the frequency after the iteration is complete

4. The harmonic parameter estimation method based on DFT iteration method as claimed in claim 1, wherein the specific step of step D includes:

DFT expression from sinusoidal signals

The matrix equation is listed:

wherein A is_iIs the amplitude of the i-th order harmonic,is the phase of the ith harmonic; the amplitude and phase of each harmonic are determined by the above equation.

Technical Field

The invention relates to a harmonic signal frequency estimation method based on discrete Fourier transform, which uses a DFT iteration method.

Background

With the increasing popularization of renewable energy sources and the wide application of nonlinear loads, the power quality of a power system faces a plurality of challenges, and the wide application of power electronic equipment can cause serious harmonic pollution and threaten the safe and stable operation of the power system. Harmonic analysis is therefore a research focus in recent years.

The Discrete Fourier Transform (DFT) algorithm has a good application value under a static condition, has the advantage of intuitive and clear physical significance, and has been widely applied to harmonic measurement.

The DFT algorithm has many limitations and drawbacks such as spectral leakage, fence effects. The signal is sampled before signal processing, which is equivalent to passing the signal through a finite rectangular window function, and the multiplication in the time domain appears as a convolution of the spectrum in the frequency domain. The magnitude spectrum of a rectangular window is a sampling function with a large number of side lobes. During coherent sampling, the DFT spectrum of the real sinusoidal signal only has two mirror spectral lines, and the spectrum leakage does not exist. In practice, however, coherent sampling is almost non-existent, and in the case of non-coherent sampling, a side lobe in the spectrum of the window function causes spectral leakage. The fence effect results from the fact that the DFT transform is a discrete transform, and the content between every two spectral lines in the spectrum is unknown, so that there is an error in frequency estimation directly from the spectral peaks due to limitations in spectral resolution. The classical DFT-based algorithm ignores the negative frequency component for convenient analysis, the influence of long-range spectral leakage is not fully considered, the improved algorithm ignores the negative frequency component more or less, but in actual situations, the influence of the negative frequency spectral leakage is very considerable, and particularly when the positive and negative frequency spectral lines are close to each other, the performance of the algorithm is degraded. The harmonic wave measurement can cause inaccurate harmonic wave positioning and bring difficulty to harmonic wave interference treatment.

Disclosure of Invention

Aiming at the problems, the invention provides a harmonic parameter estimation method based on a DFT iteration method, which considers and calculates the spectrum superposition of positive and negative frequencies and improves the estimation performance.

In order to solve the technical problem, the invention adopts the technical scheme that: a harmonic parameter estimation method based on DFT iteration method includes the steps:

a harmonic parameter estimation method based on DFT iteration method includes the steps:

A. in a measurement period, sampling to obtain a harmonic signal, performing discrete Fourier transform on the harmonic signal to obtain a frequency spectrum of the signal, and positioning a peak value of the frequency spectrum to obtain a frequency estimation value of frequency;

B. constructing a frequency estimation cost function;

C. taking cost function minimization as a target, taking the frequency estimation value obtained in the step A as an initial value, and solving the frequency estimation value through a DFT iteration method;

D. and C, constructing a DFT expression column matrix equation, substituting the estimated value of the frequency obtained in the step C into the DFT expression column matrix equation, and calculating the amplitude and the phase of the harmonic wave.

Preferably, the specific steps of step B include:

processing three-phase voltage signals with clark transformation to generate input phasor signals

Wherein V₊、V_-Andis the amplitude and initial phase, ω, of the sequence₀＝2πf₀/f_s，f₀Is the frequency of the input signal, f_sIs the sampling frequency;

when V is₊＝V_{_}And isWhen the signal v (n) is a real-valued sinusoidal signal, takeDefinition of S_cos(n) ═ v (n) + v (n), and this gives

Wherein

Rewriting normalized angular frequency as ω₀＝2πl₀/N＝2π(k₀+δ₀)/N，l₀Representing the number of periods, k, of the resulting sinusoidal signal₀And delta₀Is the integer and fractional part of the normalized frequency, k₀Is estimated as

Thereby will s_cosThe N-point DFT of (N) is expressed as

Order to

When two different DFT sequences S (k) are known₁) And S (k)₂) Then, the following matrix equation can be constructed:

mu and v are reference variables, their values are independent of k, when ω is₀When the value of [ mu ] is known, the value of [ mu ] can be determined by the above equation, and the calculation is described as

Similarly, another process for calculating v is described as

Since mu is v^*By elimination of a reference variableThen, ω₀Is calculated from the cost function of

Preferably, the specific steps of step C include:

setting iteration times M, a jump-out condition TOL, a stepping distance oa and an iteration result lower limit δ_aAnd an upper limit δ_b；

In each iteration loop, δ is set_c＝(δ_a+δ_b) /2, orderWhen f is<At TOL, the cycle is finished;

when f is not less than TOL, set

When f is₁＜f₂When is delta_b＝δ_c(ii) a Else δ_a＝δ_c；

Obtaining an estimate of the frequency after the iteration is complete

Preferably, the specific steps of step D include:

DFT expression from sinusoidal signals

The matrix equation is listed:

wherein A is_iIs the amplitude of the i-th order harmonic,is the phase of the ith harmonic; the amplitude and phase of each harmonic are determined by the above equation.

Has the advantages that: the method can obtain the relation between the DFT unit and the step change frequency through an equation, and eliminate the influence of symbol conversion by using six different DFT units, thereby realizing the high-precision frequency estimation of single-frequency signals with frequency step change, such as FSK. The method can be applied to complex signals containing multiple order harmonics, the influence of even order harmonics is considered and calculated, and an estimation result approaching a true value can be obtained. According to the simulation result, the method has good effect of harmonic parameter estimation, and can realize accurate harmonic processing positioning.

Drawings

FIG. 1 is a flow chart of the algorithm of the DFT iteration method employed in the present invention;

FIG. 2 is a diagram illustrating the effect of the method of the present invention on the estimation of the fundamental frequency in the case of harmonics of orders 2, 3, 4, 5, 6, 7, 9, and 11, where L is 2.14, in the case of no noise;

FIG. 3 is a graph showing the effect of the method of the present invention on the estimation of the amplitudes of the harmonics when facing 11 th harmonic in the case of no noise, where L is 2.14;

fig. 4 is a diagram showing the effect of the method of the present invention on the estimation of the phase of each harmonic in the case of no noise, where L is 2.14, for the 11 th harmonic.

Detailed Description

The present invention will be further described with reference to the following examples.

The invention discloses a harmonic parameter estimation method based on a DFT iteration method. The method comprises the following specific steps:

a data acquisition and preprocessing

In a measurement period, sampling to obtain a harmonic signal, performing discrete Fourier transform on the harmonic signal to obtain a frequency spectrum of the signal, and positioning a peak value of the frequency spectrum to obtain a rough frequency estimation value of the frequency;

b constructing a cost function

First, by the DFT expression of the harmonics:

to facilitate the analysis, let

When two different DFT sequences S (k) are known₁) And S (k)₂) Then, the following matrix equation can be constructed:

mu and v are called reference variables, their values are independent of k, when ω is₀When the value of [ mu ] is known, the value of [ mu ] can be determined by the above equation. This calculation is noted as

Similarly, another process for calculating v is described as

Since mu is v^*By eliminating the reference variableThus, ω₀Can be calculated from a cost function of the formula (#representsthe conjugate)

C evaluating frequency by DFT iteration method

Setting iteration times M, a jump-out condition TOL, a stepping distance oa and an iteration result lower limit δ_aAnd an upper limit δ_b；

In each iteration loop, δ is set_c＝(δ_a+δ_b) /2, orderWhen f is<At TOL, the cycle is finished;

when f is not less than TOL, set

When f is₁＜f₂When is delta_b＝δ_c(ii) a Else δ_a＝δ_c。

Obtaining an estimate of the frequency after the iteration is complete

D calculating the amplitude and phase of the harmonic wave by DFT method

DFT expression from sinusoidal signals

The matrix equation is listed:

wherein A is_iIs the amplitude of the i-th order harmonic,the phase of the ith harmonic.

The amplitude and phase of each harmonic can be easily determined by the above formula.

The harmonic times in the invention are usually 2, 3, 4, 5, 6, 7, 9 and 11 times, and one of the numbers is taken in each calculation;

to further illustrate the iterative method, its performance was tested by simulation experiments;

for frequency estimation simulation, setting the DFT point number as 128 and L as 2.14; the iteration times are 100 times, the jump-out condition is 10^ (-3), the stepping distance is 10^ (-5), and the figure 2 shows the estimation effect of the invention on the fundamental frequency when facing 2, 3, 4, 5, 6, 7, 9 and 11 harmonics; FIG. 3 is a diagram showing the effect of the method of the present invention on the estimation of the amplitudes of the harmonics of order 11 in the absence of noise; fig. 4 shows a diagram of the effect of the estimation of the phase of each harmonic in the case of the noise-free case when the method of the present invention faces 11 th harmonic.

According to the simulation result, the method has good effect of harmonic parameter estimation, and can realize accurate harmonic processing positioning.