CN111077370A

CN111077370A - Improved recursive discrete Fourier transform detection method

Info

Publication number: CN111077370A
Application number: CN202010000806.6A
Authority: CN
Inventors: 李莎; 朱东柏
Original assignee: Harbin University of Science and Technology
Current assignee: Harbin University of Science and Technology
Priority date: 2020-01-02
Filing date: 2020-01-02
Publication date: 2020-04-28

Abstract

The invention provides an improved recursive discrete Fourier transform detection method based on sine and cosine table lookup and zero-crossing point verification, and relates to the technical field of power electronics. Compared with a detection method based on an instantaneous reactive power theory, the improved recursive discrete Fourier transform detection method can not only extract fundamental waves of a three-phase system, but also be applied to a single-phase system, and the improved detection algorithm is added with phase-shift extraction positive sequence calculation, sliding window calculation and zero-crossing point phase-locking processes, so that the improved detection algorithm is suitable for three-phase asymmetric working conditions, the calculated amount is reduced, and complicated traditional phase-locking calculation is omitted.

Description

Improved recursive discrete Fourier transform detection method

Technical Field

The invention relates to the technical field of power electronics, in particular to an improved recursive discrete Fourier transform detection method.

Background

Aiming at the detection technology research of an active filter, the detection of harmonic waves and reactive power is firstly carried out; the fast Fourier extraction algorithm essentially extracts fundamental waves through the orthogonality of trigonometric functions, and then removes the fundamental waves from original signals to obtain the sum of components such as harmonic waves, reactive power and the like; since the fourier transform method is very computationally intensive and is limited in use, it is necessary to perform discrete processing of the fourier transform and further recursive processing.

Most signals in engineering are continuous analog signals, the signal processing needs to be processed by a digital chip, and a front-end A/D conversion chip is adopted to acquire and convert required voltage and current signals into digital signals, and then the digital signals are sent into a DSP to be processed by an algorithm. Any periodic waveform can be decomposed into the sum of a direct current component, a fundamental component and a series of harmonic components as long as the Dirichlet condition is satisfied, wherein the harmonic frequency is an integral multiple of the fundamental frequency. Harmonic analysis is the computation of the amplitude and phase of each component of a periodic waveform, the amplitude and phase of each component of any periodic waveform being a function of frequency. Thus, using a Fourier series, a waveform in the form of a time domain representation can be transformed into the frequency domain for analysis.

If the period of the fourier series tends to infinity, the fourier integral can be obtained, the fourier orthogonal transform defined by the fourier integral has wider practicability, and the traditional recursive discrete fourier transform detection method mainly has the following two disadvantages: firstly, phase locking is needed for calculating a starting point; secondly, N groups of data in the whole period need to be calculated, and the calculation amount is large.

Disclosure of Invention

The invention provides an improved recursive discrete Fourier transform detection method based on sine and cosine table lookup and zero-crossing point verification on the basis of the traditional recursive discrete Fourier transform detection method.

Compared with a detection method based on an instantaneous reactive power theory, the improved recursive discrete Fourier transform detection method can not only extract fundamental waves of a three-phase system, but also be applied to a single-phase system, and the improved detection algorithm is added with phase-shift extraction positive sequence calculation, sliding window calculation and zero-crossing point phase-locking processes, so that the improved detection algorithm is suitable for three-phase asymmetric working conditions, the calculated amount is reduced, and complicated traditional phase-locking calculation is omitted.

Drawings

FIG. 1 is a diagram of a sliding window calculation.

Detailed Description

When the three-phase system is unbalanced, the algorithm will be discussed below by taking the phase a current as an example.

If the load fundamental current is given as equation (1), the positive sequence component equation of the a-phase load fundamental current is as follows:

negative sequence component formula of A phase load fundamental current:

the zero-sequence component formula of the A-phase load fundamental current is as follows:

the phase shift is used to extract the positive sequence component of the A-phase voltage.

The following is fundamental positive-sequence active power extraction of the unbalanced grid load current i (t) containing the harmonics: in order to extract a fundamental positive sequence active component signal of a load current i (t) of a power grid, firstly, a fundamental trigonometric function sin (ω t) is multiplied by a load positive sequence current signal i (t) by utilizing an orthogonality principle of a trigonometric function, and then a result A is obtained₁Integral processing is carried out, and finally, fundamental positive sequence active current i can be obtained_1pa ⁺(t)。

The fundamental wave positive sequence reactive power extraction method for the grid load current i (t) is similar, and after the process, i needs to be finally extracted_1pa ⁺(t)、i_1qa ⁺(t) discretizing so that the digital processor can be programmed to implement the algorithm:

to A₁、A₂The integration processing is carried out in a rated period T, and the purpose is to extract the positive sequence component of the fundamental wave:

to B₁、B₂After simplification and discretization processing are carried out, fundamental wave positive sequence active current coefficients i of the load current of the power grid can be obtained respectively_1pa ⁺(t) and the fundamental positive sequence reactive current coefficient i_1qa ⁺(t)：

Through a similar process, the formula can be obtained:

above fundamental wave positive sequence active current coefficient i_1pa ⁺(t) and the fundamental positive sequence reactive current coefficient i_1qa ⁺The solution of (t) is not provided with a sliding window, the traditional RDFT algorithm is to perform discrete Fourier transform on the signal of the last cycle at each sampling point, so the data operation amount is large, the sampling frequency is limited, and in order to solve the defects, the sliding window improvement is added on the basis of the traditional RDFT algorithm.

When the signal of the current sampling point is calculated, the signal data of the previous sampling point is replaced, the problem of calculation efficiency is solved, the detected rounding error is discarded at each cycle, and the problem of iterative amplification of the rounding error is solved.

The first calculation process of the sliding window calculation is carried out at a zero crossing point, phase detection is realized at the zero crossing point, in the programming process, a zero crossing point judgment process is placed in the sliding window calculation process, and if the zero crossing point is judged, the first sliding window calculation is forced to be carried out.

After the sliding window is modified, the formula (8) and the formula (9) are changed into formulas:

through a similar process, the formula can be obtained:

the fundamental wave positive sequence signal formula of the grid load current at the kt moment can be obtained by the formula (10) and the formula (11):

so far, the superposition result of the unbalanced component, the harmonic component and the reactive component in the load current, namely the compensation quantity formula of the A-phase current required to be sent by the active filter can be obtained:

if only the unbalanced component and the harmonic component in the load current are compensated, the formula of the A-phase current compensation amount required to be sent by the active filter is as follows:

in equation (14), N is the number of sampling points of the detection algorithm in one power frequency period T (0.02 sec), where N is f_s/f₀，f₀Is the mains voltage power frequency, f_sIs the sampling frequency of the detection system. The command current for harmonic compensation is obtained by inverting equations (13) and (14).

Claims

1. An improved recursive discrete Fourier transform detection method based on sine and cosine look-up tables and zero-crossing point checks. The method is characterized in that: compared with a detection method based on an instantaneous reactive power theory, the improved recursive discrete Fourier transform detection method can not only extract fundamental waves of a three-phase system, but also be applied to a single-phase system, and the improved detection algorithm is added with phase-shift extraction positive sequence calculation, sliding window calculation and zero-crossing point phase-locking processes, so that the improved detection algorithm is suitable for three-phase asymmetric working conditions, the calculated amount is reduced, and complicated traditional phase-locking calculation is omitted.

2. The detection method according to claim 1, characterized in that: according to the invention, a sliding window improvement is added on the basis of the traditional RDFT algorithm, when the signal of the current sampling point is calculated, the signal data of the previous sampling point is replaced, the problem of calculation efficiency is solved, the detected rounding error is discarded at each cycle, and the problem of iterative amplification of the rounding error is solved.