Application of low-pass filter in harmonic detection of instantaneous reactive power theory

0 Introduction
With the development of power electronics technology, the harmonic problems caused by power electronics devices have had a great impact on the safety, stability and economic operation of power grids. People are in urgent need of real-time and accurate detection and analysis of all harmonic parameters in the power grid. Since power grid harmonics are affected by factors such as nonlinearity, randomness, distribution, non-stationarity and complexity, accurate and real-time detection of harmonics is very important and not easy. At present, people are constantly exploring more effective real-time harmonic detection methods and implementation technologies.
At present, power grid harmonic detection is mainly achieved through the detection of harmonic currents. There are mainly the following methods for harmonic detection: (1) Detection using analog bandpass or bandstop filters, (2) Harmonic detection based on generalized instantaneous reactive power, like instantaneous reactive power theory, has great advantages in solving the real-time detection of total harmonics and has been widely used in the field of real-time harmonic monitoring. This article mainly refers to this method for real-time harmonic detection. (3) Harmonic detection based on Fourier transform is the most widely used method today, but its disadvantage is that the real-time detection is poor. In the detection of steady-state harmonics, most of them use fast Fourier transform and its improved algorithm, while for fluctuating harmonics or rapidly changing harmonics, other methods need to be found. (4) Harmonic detection method based on neural network, which has three main applications: ① harmonic source identification; ② power system harmonic prediction; ③ harmonic detection. (5) Harmonic detection method based on wavelet transform. Wavelet transform is a local transformation of time and frequency. It has great advantages in the detection of fluctuating harmonics and rapidly changing harmonics, but it also has inherent defects, such as the window energy is not concentrated, the frequency aliasing phenomenon occurs, and the optimal wavelet basis selection method lacks system specifications.
The algorithm based on generalized instantaneous reactive power theory is used to detect harmonic current in real time. The corresponding simulation circuit is built using MATLAB software. The influence of the low-pass filter in the detection circuit on the real-time detection effect is simulated and analyzed. The type, cutoff frequency fc and order n of the low-pass filter LPF are analyzed, which have an important influence on the dynamic response process of the harmonic real-time detection circuit based on generalized instantaneous reactive power theory.

The linear transformation matrix from the abc coordinate system to the dq0 coordinate system is

Decompose the current vector idq0 in the dq0 coordinate system into two mutually orthogonal components:

Among them, the current vector ipdq0 and the voltage vector Udqo are on the same coordinate axis.
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Assume that the current in the three-phase four-wire circuit contains positive sequence components, negative sequence components, fundamental waves and zero sequence components of each harmonic, as shown in the following formula:

In the above formula, subscript 1m is the mth positive sequence current, subscript 2m is the mth negative sequence current, and subscript 0m is the mth zero sequence current.

Among them, id and id are the DC component and AC component of id respectively, and iq and iq are the DC component and AC component of iq respectively, as shown in the following formula:

After id and iq are filtered through a low-pass filter,

the DC components id and iq are obtained. After i0 is filtered through a band-pass filter, the load fundamental current i0\' is extracted: It can be seen that the d-axis current DC component id corresponds to the load fundamental positive-sequence active component, the q-axis current DC component iq corresponds to the load fundamental positive-sequence reactive component, and the d-axis current AC component id and the q-axis current AC component id correspond to the active component and reactive component of the higher-order harmonics, respectively. Therefore, after id and i0 are filtered through LPF, the positive-sequence active component and positive-sequence reactive component corresponding to the fundamental are obtained. After the 0-axis component is filtered through a band-pass filter, it corresponds to the load fundamental asymmetric component. Therefore, the fundamental current expression can be obtained as follows:

Then the system harmonic current can be detected:

Based on the instantaneous reactive power theory harmonic detection theory, the harmonic real-time detection circuit frame used in this paper is shown in Figure 1:

2 Application of low-pass filter in real-time detection of harmonics
Low-pass filter is used in all detection methods of harmonics and fundamental reactive power based on instantaneous reactive power theory. Low-pass filter is used to obtain the DC current component from the total active current and reactive current, and then obtain the fundamental current from the DC component through PARK inverse transformation, and then obtain the harmonic current to be detected. Obviously, the direct detection of the performance of low-pass filter plays an important role in the dynamic tracking speed of system detection, and ultimately affects the real-time performance of harmonic detection of active power filter. It can be seen that the design of low-pass filter is a very important link. [page]

In view of the real-time requirements of harmonic detection, this paper uses digital low-pass filters to replace traditional analog low-pass filters in the detection method. Compared with analog filters, digital low-pass filters are easier to perform mathematical operations on, and can effectively overcome the problems of voltage drift, temperature drift and time drift that analog filters cannot overcome, achieve approximate ideal response and linear phase, and better meet the real-time requirements of harmonic detection. Through
theoretical analysis and simulation comparison, a second-order Butterworth low-pass digital filter is used to establish a Simuliuk simulation model for harmonic detection.
1) Design of ButterWorth low-pass filter
The transfer function of ButterWorth low-pass filter can be expressed as (digital filter)

n is the order of the filter. A second-order Butterworth low-pass filter is designed in the SignalProcessing Toolbox of MATLAB. The SignalProcessing Toolbox of MATLAB provides the functions buttap, buttord, and butter related to Butterworth filters. By calling the butter design function, a Butterworth filter that meets the performance indicators can be designed.

Theoretical analysis shows that the smaller the cutoff frequency, the higher the harmonic current detection accuracy and the slower the dynamic response process. The larger the cutoff frequency, the faster the dynamic response time of the detection circuit. However, some low-order harmonics cannot be attenuated by the LPF, and the harmonic current detection accuracy is poor. Therefore, in the actual harmonic current detection circuit, the cutoff frequency cannot be selected too small or too large. In the real-time harmonic detection circuit, special attention should be paid to the dynamic response of the harmonic current detection circuit. This time, the low-pass filter designed uses a second-order Butterworth low-pass filter, and the cutoff frequency is selected as f=30Hz.
The Butterworth filter has the advantages of balanced characteristics in terms of linear phase attenuation slope and loading characteristics. Therefore, in actual use, the Butterworth filter has been listed as the first choice. Through theoretical analysis and simulation comparison, a second-order Butterworth low-pass digital filter is used to establish a Simuliuk simulation model for harmonic detection. Obviously, when a digital low-pass filter is used, the dynamic response process is better in real time than that of an analog low-pass filter, and the detection result is more accurate. The circuit
simulation curves of the designed digital low-pass filter are shown in Figures 2 and 3.

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4 Conclusion
This paper uses the harmonic current detection method based on instantaneous reactive power theory, with the help of the SIMULIMK toolbox in the MATLAB software package, to build a harmonic real-time detection circuit simulation model, and designs a reasonable second-order butterwortn low-pass filter. The influence of the low-pass filter used in the detection circuit on the harmonic current detection effect is simulated and studied. In particular, the design parameters of the low-pass filter that should be paid attention to in the application of the low-pass filter in the real-time detection of harmonics, such as the influence of the cut-off frequency and order on the real-time detection, are studied in practice, which provides a useful reference for the future design of the harmonic real-time detection circuit.