Research on Harmonic Detection in Power System Based on Wavelet Transform

The harmfulness of power harmonics has promoted the development of its detection. Among them, the successful practice of wavelet transform theory has provided a new research method for harmonic detection. Under the application requirements of improving the real-time and accuracy of detection, it is necessary to have an in-depth understanding of wavelet theory. Combined with the analysis of signal characteristics, the implementation of wavelet transform in harmonic detection is studied.

1 Harmonic characteristics of power system
1.1 Harmonic problem and its impact on power system
In the power system, harmonics refer to the part of the current expression with a frequency that is an integer multiple of the fundamental wave. It is mainly due to the large-scale application of nonlinear loads in the power grid, which causes voltage and current distortion, bringing serious harm to electrical equipment, manifested in: loss of power grid energy; data sampling errors; equipment misoperation; reduced equipment service life; resonance, noise and vibration of power equipment, causing equipment failure or even damage. Harmonics can also cause serious interference to communication equipment and electronic devices. Therefore, the harm caused by harmonics to the power system has attracted widespread attention, causing "harmonic pollution".
1.2 Power harmonic detection method
Harmonic detection is the primary issue of harmonic control. In the development of harmonic detection theory, a variety of detection methods have been formed, such as analog filtering, Fourier transform, wavelet transform, instantaneous reactive power theory, neural network, etc. Among them, Fourier transform is the basic theoretical basis widely used in harmonic monitoring devices; instantaneous reactive power theory is often used for instantaneous detection of harmonics, and can also be used in harmonic governance fields such as reactive compensation; artificial neural network and wavelet transform theory are applied to harmonic detection, which is a new method currently under research. It can improve the real-time and accuracy of harmonic measurement and has a wide range of applications in the field of harmonic detection.
Wavelet transform is a kind of time-frequency analysis. At present, it is mainly used in the detection of discontinuities and singular points of voltage and current signals in power harmonic detection; separation and identification of signal components; signal noise processing; estimation of signal development trends, etc. Its successful practice of signal analysis provides a solution to the problem of power harmonic suppression.

2 Application Principle of Wavelet Transform in Power Harmonic Detection
2.1 Time-frequency Analysis Principle of Wavelet Transform
Wavelet analysis can select the accuracy of time or frequency according to needs. Generally speaking, the low-frequency signal is relatively flat and contains more frequency components, so the time resolution can be reduced to improve the frequency resolution. In the high-frequency part, there are many transient transformation features, and the relative frequency change has little effect on the signal. We can focus on the transient characteristics of the signal at a higher time resolution and reduce the frequency resolution. In other words, wavelet transform can decompose the signal at multiple resolutions.
2.2 Harmonic Detection Principle of Wavelet Analysis
Harmonic detection is to have a higher resolution and a wider frequency band in high-order harmonics and distinguish them. The wavelet transform has the ability to characterize the local characteristics of the signal in both the time and frequency domains, which lays a theoretical foundation for its application in harmonic detection. In power systems, signals often contain multiple harmonic components, and the content of high-order harmonics is relatively low. To effectively distinguish high-frequency signals, in actual detection, it is hoped that the frequency window of the low-frequency part is narrower and the frequency window of the high-frequency part is wider. Under this application requirement, wavelet theory has been developed in power harmonic detection. It provides a variable time-frequency window structure that can improve the performance of harmonic analysis and achieve the purpose of real-time and accurate detection of harmonics.
Wavelet transform has the characteristics of multi-resolution analysis. It continuously filters out components in the frequency band with relatively high frequencies, while saving these components for signal reconstruction. Multi-resolution analysis based on wavelet transform can decompose the current signal containing harmonics into block signals of different frequencies, regard the results in the low-frequency band as the fundamental component, and the high-frequency band as each harmonic component, so as to obtain harmonic information. In other words, the wavelet transform of the signal is equivalent to the signal passing through a finite-length bandpass filter, and different scale factors determine its bandpass characteristics. If harmonics of different frequencies are located in different frequency bands, they can be separated.
2.3 Characteristics of wavelet transform application in power harmonic analysis
Wavelet analysis is a time-frequency localization analysis method in which both the time window and the frequency window can be changed. It has the following characteristics: 1) It has a high time resolution in the high frequency range and a high frequency resolution in the low frequency range; it can analyze both stationary signals and non-stationary signals, especially for transient signals, it can achieve good analysis results. 2) The power signal can be decomposed into various scales by using discrete wavelet transform, and its mathematical principles can be referred to in the literature.

3 Application of wavelet analysis in power harmonic detection
3.1 Application of wavelet transform
Currently, wavelet analysis is used to solve the problem of power harmonic detection, and it is mainly used in the following aspects:
3.1.1 Detection of signal characteristics
1) Detection of sudden change signal
The sudden change signal belongs to the transient change characteristic of the signal and contains important characteristics of the signal. By using the analysis ability of wavelet transform in time domain and frequency domain, and the strong sensitivity of wavelet zoom characteristics to such signals, not only can its position be accurately identified, but also the frequency components can be gradually finely focused on the details of the signal, and the degree of change of the sudden change point can be effectively analyzed.
In the detection of power system harmonics, the detection of sudden change signals by wavelet transform mainly includes: detection of changes in signal discontinuity points, detection of power signal faults, detection of signal interference, etc.
2) Signal trend detection
In the power system, the influence of harmonics and noise often distorts the original signal, making it difficult to identify the trend of the real signal, which hinders the analysis results. What reflects the nature of the system itself are some slowly changing signals, that is, the lowest frequency part. Wavelet transform has the characteristics of multi-resolution analysis. From the perspective of frequency, it can filter out high-frequency components layer by layer, making the signal closer and closer to the development trend of the signal; from the perspective of time domain, as the scale of wavelet decomposition increases, the slowly changing part of the signal is also closer to the real signal, thus reflecting the overall development trend of the signal.
Therefore, through wavelet analysis, the useful signal part hidden in the interference signal of the power system can be displayed, the development trend of the signal can be identified, and reliable information can be provided for further analysis of the signal.
3) Signal frequency detection
Power harmonic detection refers to separating the higher harmonics contained in the power signal. Due to wavelet decomposition, different time and frequency resolutions can be obtained at different scales. By analyzing the information of all scales, the signals contained in different frequency intervals can be separated, and the frequency components of the entire signal can be detected.
In the detection of power harmonics, it is necessary to select appropriate wavelet functions to decompose the signal scale according to engineering practice and experience, analyze the harmonic components it contains, and take effective suppression measures for "harmonic pollution".
3.1.2 Signal processing
1) Noise reduction
Noise is the most common interference signal in the power system and the main barrier to accurate analysis of harmonics. According to the characteristics of noise, the following processing methods are usually adopted to eliminate noise using wavelet analysis:
One is forced denoising. That is, all high-frequency coefficients in the wavelet decomposition are changed to zero, and then the signal is reconstructed. This method is simple and the reconstructed signal is smoother, but it is easy to lose useful high-frequency components. The other is threshold denoising. This method uses a threshold value to process the highest frequency decomposition coefficient in the wavelet decomposition of the signal, that is, the part greater than the threshold is retained, and the coefficient below the threshold is zero. The threshold value of the high-frequency coefficients of other scales is changed. As the decomposition level increases, the threshold value can be reduced by about 2 to 1/2 times. This processing has a good effect in practical applications, but the threshold value needs to be set based on experience or some basis.
Since wavelet analysis can analyze signals in both the time domain and the frequency domain and has multi-resolution capabilities, it can effectively distinguish signal mutations and noise at different decomposition levels, thereby achieving signal denoising.
In the power system, the collected signal may contain many spikes or mutations, and the noise is not a stable white noise. To analyze this kind of signal, we must first do preprocessing, remove the noise part of the signal, extract the useful signal, and then analyze the useful signal to improve the accuracy of detection.
2) Filtering
Analyze the frequency components of the signal and use appropriate filters to separate the harmonics to achieve the purpose of harmonic detection.
Filtering means allowing signals with some frequencies to pass through and filtering out the rest of the frequency parts. Wavelets can distinguish the high-frequency and low-frequency parts of the signal, and conveniently realize the filtering function. Various common filtering implementation methods:
Low-pass filtering: refers to retaining low-frequency components and filtering out high-frequency components. Generally, the details, mutation parts and noise of the signal are mainly affected by high-frequency components. After low-pass filtering, the signal can be smoothed and denoised. Mallat algorithm and wavelet packet algorithm can be used to achieve low-frequency filtering of various requirements to meet design requirements.
High-pass filtering: refers to retaining high-frequency components and filtering out low-frequency components. High-frequency information generally reflects the detailed information of the signal. After high-pass filtering, the outline of the signal will appear particularly obvious. Orthogonal wavelet decomposition and orthogonal wavelet packet can be used to decompose the signal, retain the high-frequency components of the decomposed signal, and then replace the low-frequency components with zero to achieve high-pass filtering to meet the design requirements.
Bandpass filtering: refers to retaining data in a certain frequency band in the signal. Orthogonal wavelet packets can be used to achieve detailed and clear bandpass filtering. 3.2 Main factors affecting the effect of harmonic detection
3.2.1 Establishing a model of power grid signals
Harmonic analysis first samples the actual power grid signal and establishes a signal model. However, actual sampling requires precise instruments and equipment and a specific environment, so it is difficult to establish a reasonable harmonic signal model.
In the actual power grid, since there are both linear and nonlinear loads, the power grid harmonics contain both stable fundamental waves and harmonic components, and also contain some unstable transient change signals, such as irregular changes caused by some uncertain factors such as noise interference and system failures. Here we assume two types of analysis signals: one collected signal contains only fundamental waves and multiple harmonics, and observes the analysis of harmonic components using wavelet transform.
Function expression 1: Y1=sin(2πft)+sin(6πft)+sin(10πft), where f=50Hz.

From the analysis of the wavelet decomposition results in Figures 2 and 3, it can be seen that the first harmonic contained in the original signal exists in a5, the third harmonic is shown in d4, and the detail coefficient d3 contains the fifth harmonic component of Y1. It can be seen that the wavelet transform can effectively analyze signals containing multiple harmonics and separate the various frequency components contained in them.
When another type of collected signal contains a sudden change signal, observe the analysis of the transient change signal by the wavelet transform.

The analysis of Figures 5 and 6 shows that the moment when the signal suddenly changes can be clearly seen from the detail signal d1. In the reconstruction of the signal, the high-frequency information starts to appear from d3, and it can be seen that the frequency of the discontinuity point is higher, while the low-frequency component is displayed in a4. Therefore, when analyzing signals containing transient transformations, wavelets can not only detect sudden changes but also effectively analyze the harmonic content. In fact, the amount of information contained in the collected power signal is relatively complex, so it is generally necessary to establish various models based on practical experience and use wavelet transform to analyze the components in the signal. 3.2.2 Selecting a suitable wavelet function in combination with the characteristics of power grid harmonics
Since the basis of wavelet analysis is not unique, any function that meets the wavelet conditions can be used as a wavelet function. In the detection of harmonics, in order to realize the time-frequency analysis and distortion-free reconstruction of the signal, it is necessary to select a suitable analysis function in combination with the signal model and the characteristics of the wavelet function itself, such as orthogonality, vanishing moment, support set, etc.
Here, the Haar wavelet is selected, and then the harmonic content of the Y1 signal is analyzed, and the analysis results are observed and compared.

Since the Haar wavelet itself is a step function, it is discontinuous in the time domain and has jumps. In addition, its frequency domain localization characteristics are poor and its attenuation speed is slow. It cannot meet the application requirements of time-frequency analysis, so it does not have a good analytical ability for power system harmonic detection. From the analysis results of the two wavelet functions: for the Y1 signal, coif3 is better than Haar, and can clearly analyze the frequency components contained in the signal. This is not only related to the analyzed signal, but mainly related to the properties of the wavelet function itself. In engineering practice, wavelet functions are often selected based on practical experience.

4 Research directions of wavelet transform in harmonic detection
4.1 Application of combined wavelets in harmonic detection
Since the frequency band of a single wavelet is narrow, if it is necessary to extract the spectrum within a certain frequency range, a single wavelet is difficult to meet the requirements. Using a combination of multiple wavelets, the spectrum of each wavelet is superimposed, and a filter with a bandpass characteristic is designed to detect the harmonic components of the power signal. Experiments have confirmed that the use of combined wavelets to detect harmonics can not only obtain better detection effects, but also effectively filter out noise interference.
4.2 Research new detection methods for specific types of harmonics
The improved wavelet algorithm and the combination of wavelet and other detection algorithms provide new ideas for existing harmonic detection. For example, a harmonic analysis of voltage flicker signals based on sub-band filtering. The low-pass filter in the traditional synchronous detector is replaced by a wavelet sub-band filter. This new synchronous detector not only has the amplitude detection function, but also has the spectrum analysis function.
For example, there are spectrum leakage and fence phenomena in the detection of interharmonics, and an interharmonic detection method combining FFT and wavelet transform is proposed. This method obtains the frequency of each spectrum by the FFT algorithm, determines the number of multi-resolution decomposition layers and frequency band range according to the obtained frequency, and finally uses wavelet transform to decompose and reconstruct the signal, extract the fundamental frequency and each interharmonic component, and track the changes of interharmonics in real time, so as to achieve the purpose of detecting interharmonics.

5 Conclusion
With the goal of developing an effective, accurate and reliable power harmonic detection method, wavelet transform is used to study the power system. Based on an in-depth analysis of the application of wavelet theory in harmonic detection, combined with typical signals of power system harmonics, simulation experiments are used to illustrate the main factors of sampling wavelet analysis of harmonics. Finally, based on the current research results, the research direction of wavelet in harmonic detection application is given.