阅读说明：本技术 基于无迹卡尔曼滤波的频率与谐波检测方法 (Frequency and harmonic detection method based on unscented Kalman filter ) 是由 吕广强 安路 蒋海峰 王宝华 于 2020-04-29 设计创作，主要内容包括：本发明公开了一种基于无迹卡尔曼滤波的频率与谐波检测方法,在观测状态变量中定义了一个基波频率分量,可以直接测得基波频率,不再需要单独的测频算法,避免了遇到现有测频方法如过零点法在谐波严重时过零点检测不准确和插值周期法采样不同步导致线性化误差的问题。本发明直接选取各次谐波的幅值和相位作为状态变量的分量,可以直接测得各次谐波幅值和相位信息,无需再进一步计算；通过使用无迹卡尔曼滤波,避免了傅里叶变换法在测频率或测谐波时采样不同步导致的频谱泄露和栅栏效应的问题。(The invention discloses a frequency and harmonic detection method based on unscented Kalman filtering, which defines a fundamental frequency component in an observation state variable, can directly measure the fundamental frequency without a separate frequency measurement algorithm, and solves the problems of inaccurate zero crossing point detection when the harmonic is serious and asynchronous interpolation period method sampling in the existing frequency measurement method, such as a zero crossing point method, which cause linearization error. The amplitude and the phase of each harmonic are directly selected as the components of the state variables, so that the amplitude and the phase information of each harmonic can be directly measured without further calculation; by using unscented Kalman filtering, the problems of frequency spectrum leakage and barrier effect caused by sampling asynchrony of a Fourier transform method during frequency measurement or harmonic measurement are avoided.)

1. A frequency and harmonic detection method based on unscented Kalman filtering is characterized by comprising the following steps:

step 1, establishing a signal model containing harmonic waves:

where y is the observed signal, r is the harmonic order, M is the total harmonic order, f is the fundamental frequency, A_rIs the amplitude of the order r of the harmonic,is the R harmonic phase, e is zero mean gaussian white noise with covariance R;

step 2, selecting observation state variables:

wherein A is_r,kIs the magnitude of the order r harmonic at time k,is the phase of the subharmonic of time k, f_kIs the fundamental frequency at time k;

step 3, establishing a system dynamic equation and a measurement equation:

wherein the content of the first and second substances,

η_kand e_kIs process noise and observation noise, the variance is Q_kAnd R_k，T_sIs the sampling interval;

step 4, performing unscented Kalman filtering to obtain an estimated value of the state variable:

wherein the content of the first and second substances,is k times obtained by algorithmThe amplitude of the order r harmonic is carved,the phase of the r-th harmonic at time k, obtained by the algorithm, is 1,2, …, M,is the fundamental frequency at time k obtained by the algorithm.

2. The unscented kalman filter-based frequency and harmonic detection method according to claim 1, wherein in the observation state variables selected in step 2, the amplitude and phase of each specific subharmonic correspond to two components, and the fundamental frequency corresponds to one component.

Technical Field

The invention relates to the field of power quality detection of power systems, in particular to a frequency and harmonic detection method based on unscented Kalman filtering.

Background

The measurement of frequency in the power system is the basis for the measurement of other parameters of the quality of electric energy. Taking harmonic measurement as an example, the frequency of each harmonic is a multiple of the frequency of the fundamental wave, and if the amplitude and phase of each harmonic are to be measured accurately, the fundamental frequency must be known, i.e., it needs to be measured in advance.

The frequency measurement method comprises a zero crossing point method, wherein the frequency is calculated by detecting the time interval between two zero crossing points of a waveform, but the frequency measurement is inaccurate due to inaccurate zero crossing point detection when harmonic waves are serious, and meanwhile, the problem of zero drift of a device can bring errors to the measurement. The interpolation period method carries out interpolation processing near the zero crossing point, reduces the difficulty of zero crossing point detection, but the sampling is asynchronous, which can cause linearization error. The fourier transform method can be used for measuring frequency and harmonic wave, but the method needs to obtain data of one period before calculation, has poor real-time performance, and has the problems of frequency spectrum leakage and barrier effect caused by the fact that the sampling period and the waveform period are not strictly synchronous. In the traditional algorithm for measuring harmonic waves by Kalman filtering, most state variables are selected asThe amplitude and phase cannot be derived directly from the state variables and further calculations are required.

Disclosure of Invention

The invention aims to provide a frequency and harmonic detection method based on unscented Kalman filtering.

The technical scheme for realizing the purpose of the invention is as follows: a frequency and harmonic detection method based on unscented Kalman filtering comprises the following steps:

step 1, establishing a signal model containing harmonic waves:

where y is the observed signal, r is the harmonic order, M is the total harmonic order, f is the fundamental frequency, A_rIs the amplitude of the order r of the harmonic,is the R harmonic phase, e is zero mean gaussian white noise with covariance R;

step 2, selecting observation state variables:

wherein A is_r,kIs the magnitude of the order r harmonic at time k,is the phase of the subharmonic of time k, f_kIs the fundamental frequency at time k;

step 3, establishing a system dynamic equation and a measurement equation:

wherein the content of the first and second substances,

η_kand e_kIs process noise and observation noise, the variance is Q_kAnd R_k，T_sIs the sampling interval;

step 4, performing unscented Kalman filtering to obtain an estimated value of the state variable:

wherein the content of the first and second substances,is the amplitude of the r-th harmonic at time k obtained by the algorithm,the phase of the r-th harmonic at time k, obtained by the algorithm, is 1,2, …, M,is obtained by an algorithmThe fundamental frequency at time k.

Compared with the prior art, the invention has the following remarkable advantages: the detection method of the invention gives consideration to the frequency detection problem when establishing the harmonic detection model, does not need a separate frequency measurement algorithm any more, and avoids some problems existing in the existing frequency measurement method; the detection method can directly measure the amplitude and phase information of each harmonic without further calculation; the detection method of the invention avoids the problems of frequency spectrum leakage and barrier effect caused by asynchronous sampling of the Fourier transform method.

Drawings

FIG. 1 is a flow chart of an algorithm used by the present invention.

Fig. 2 is a diagram showing the detection result of the fundamental frequency in the embodiment of the present invention.

FIG. 3 is a diagram illustrating the detection result of each harmonic amplitude in the embodiment of the present invention.

Fig. 4 is a diagram illustrating the detection result of each harmonic phase in the embodiment of the present invention.

Detailed Description

As shown in fig. 1, a frequency and harmonic detection method based on unscented kalman filter includes the following steps:

step 1, establishing a signal model containing harmonic waves:

where y is the observed signal, r is the harmonic order, M is the total harmonic order, f is the fundamental frequency, A_rIs the amplitude of the order r of the harmonic,is the R harmonic phase, e is zero mean gaussian white noise with covariance R;

step 2, selecting observation state variables:

each specific subharmonic has its amplitude and phase in pairTwo components, the fundamental frequency corresponds to one component, where A_r,kIs the magnitude of the order r harmonic at time k,is the phase of the subharmonic of time k, f_kIs the fundamental frequency at time k;

step 3, establishing a system dynamic equation and a measurement equation:

wherein the content of the first and second substances,

η_kand e_kIs process noise and observation noise, the variance is Q_kAnd R_k，T_sIs the sampling interval;

step 4, performing unscented Kalman filtering to obtain an estimated value of the state variable:

wherein the content of the first and second substances,is the amplitude of the r-th harmonic at time k obtained by the algorithm,the phase of the r-th harmonic at time k, obtained by the algorithm, is 1,2, …, M,is the fundamental frequency at time k obtained by the algorithm. These amplitude, phase and frequency information are the final result of the detection method.

The invention selects the state variableThe frequency and the amplitude and the phase of each harmonic can be directly measured at one time, a separate frequency measurement algorithm is not needed, the amplitude and the phase are not needed to be further calculated, and the problems of the frequency and harmonic detection method are solved. The unscented Kalman filtering does not need to strictly control the number of sampling points in each waveform period, namely, the problems of frequency spectrum leakage and barrier effect caused by asynchronous sampling of the Fourier transform method do not exist.

The present invention will be described in detail with reference to examples.