## 1 Introduction  
In recent years, as the smart grid enters the comprehensive construction stage, more and more power electronic equipment is put into operation. Among these power electronic devices, there are devices with nonlinear impedance characteristics, such as rectifiers, inverters, and phase speed control and voltage regulation devices. The use of non-linear power electronic equipment generates a lot of harmonic pollution, which causes significant voltage and current distortions and severely affects power quality. Therefore, accurate harmonic detection is of great significance for improving power quality and ensuring the reliability and safety of a power system [1; 2]. The accuracy and response speed of harmonic detection depends on the method of harmonic detection. At present, the commonly used harmonic detection methods are as follows: analog filter method, instantaneous reactive power harmonic detection method, neural network harmonic detection method, wavelet transform harmonic detection method and Fourier transform harmonic detection method. The earliest harmonic measurements were achieved by analog filtering methods, which are very sensitive to the parameters of circuit components. Therefore, it is difficult to obtain ideal amplitude frequency and phase frequency characteristics, with large errors and poor real-time performance [3]. The harmonic detection method based on instantaneous reactive power usually uses a digital low pass filter, which has a large delay and directly affects the accuracy and speed of detection [4]. Based on the neural network harmonic detection method, the adaptive linear neural network method needs to accurately obtain the fundamental frequency to accurately extract the harmonic information in the signal [5]. The back-propagation neural network method requires a large number of sample data for training, and will have the disadvantages of training failure or slow convergence speed [6]. The harmonic detection method based on wavelet transform is suitable for the study of non-stationary signals. It has good time-frequency characteristics and is sensitive to transient signals. The analysis of different frequencies through multi-resolution improves the analysis accuracy and preserves the time domain information of the signal. However, the analysis accuracy of the harmonics in the steady state is not as good as that of the FFT, and the frequency is aliased, which will reduce the accuracy of the detection results [7,8]. The use of FFT algorithm to perform DFT solves the problem of a larger amount of calculation. However, DFT has spectrum leakage and fence effects, which will cause large errors in the analysis frequency and amplitude. The large errors and defects in the detection of non-steady-state signals limit the application of DFT in harmonic detection of power systems [9,10]. The research on the harmonic detection method based on Fourier transform is mainly focused on finding a window function with concentrated energy and rapid side lobe attenuation and an interpolation algorithm with higher performance. By analyzing the current mainstream harmonic detection methods, the most widely used discrete Fourier transform based harmonic detection methods and discrete wavelet transform based harmonic detection methods are selected. By analyzing the advantages of the DFT and DWT, some scholars have proposed a hybrid harmonic detection strategy combining two methods [11,12]. First, the original signal is decomposed into a high frequency part and low frequency part by wavelet transform (the Mallat algorithm), and the separation and extraction of low frequency steady-state harmonics and high frequency non-steady-state harmonics are realized. Because most of the steady-state harmonics exist in the low frequency part, few of the steady-state harmonics exist in the high frequency part. The non-steady-state harmonics in the high frequency part are composed of steady-state harmonics and attenuated harmonics.