*4.6. Wavelet-Based Methods*

In this subsection, the wavelet-based methods are reviewed. A summary of the method contributions presented in the literature is shown in Table 6.

The authors in [111] proposed a system that was designed and tested at various load currents, DC source voltages, and arc lengths to analyze the impact of each parameter on the DC arc, with the goal of providing a thorough understanding of arc behavior that could occur in DC networks. Based on the findings, a detection technique that uses both the time domain and time frequency domain characteristics to distinguish between the DC arc fault and normal conditions has been presented. A simple calculation approach for the arc current variation is utilized to portray the chaotic and dynamic nature of the DC arc physical process. The current variation can indicate different stages of arcing and is used to recognize DC arc faults. Moreover, wavelet decomposition is applied to the arc current signal. The normalized RMS value of wavelet decomposition coefficients demonstrates the ability to detect the arc fault. Finally, a comprehensive DC arc detection algorithm is created using the current change from the time domain analysis and the normalized RMS value from the wavelet analysis. A Texas Instrument's Digital Signal Processors (TI DSP) chip, which has a clock frequency of 150 MHz and has gained popularity in power electronic applications, is used to implement the detection method in the hardware. In the proposed method, the maximum and minimum currents are updated every time new data is inputted at each timer cycle, and the difference in the current is registered at the *n*th cycle. The value of *n* is determined by the length of the time window and sampling frequency. Detection accuracy is enhanced if a longer time window is achieved, as it makes the RMS versus time waveform smoother. A long time window, however, leads to a longer time response. When the amount of data points is excessive, the actual implementation must be adjusted to ensure that the calculation load is within the capabilities of the available microprocessor. The wavelet coefficients are calculated by sending a signal through lowpass and high-pass filters, as well as down sampling it by two. The filters are dependent on the used wavelet and are consistent throughout the entire level decomposition. As a result, the detection algorithm can be implemented on a microprocessor in the time domain using convolution and down sampling. The filtering procedure for the first-level DWT to obtain *Coefl*1 is carried out every two timer intervals, for which two new data points are available at this time. The second-level DWT coefficients (*Coefl*2 and *Coefh*2) are calculated whenever two new coefficients from the first-level DWT are received. As the filtering operation was performed for every timer interval instead, this method cuts the calculation load by half. In the main function, the ultimate decision is taken. The main function's flag changes to 1 at the conclusion of each time window. Only two square roots, one division, and two comparisons are performed in the main function, which takes 80 clock cycles in total, according to the benchmarks of the C28x floating point unit fast RTS library. With a clock frequency of 150 MHz, the main function's computation time at the conclusion of each *Tsw* = 25 ms is less than 1 μs, which is negligible. As a result, the detection time is mostly determined by the length of the time window. The results of the studies reveal that the detection algorithm is capable of delivering an alarm in a timely manner following the initiation of an arc fault. Typical operations, such as load changes, can also generate nuisance tripping, which can be reduced with this detection system. In [112], a modified wavelet-based technique termed the wavelet packet transform (WPT) was developed for the detection of diverse disturbances caused by faults in grid-connected solar PV systems. The study continued to evaluate the proposed WPT approach to methods based on the ordinary wavelet transform (WT) under various operating settings. In addition, qualitative and quantitative evaluations suggest that the WPT outperforms WT in terms of detection performance. The WPT uses a set of low-pass and high-pass filters to breakdown the signal retrieved at PCC. It gives both approximate and precise coefficients. Moreover, it extensively decomposes both components in order to determine the signal's frequency agreements. The breakdown procedure carried out in both components is what gives them their value. Wavelet transforms, on the other hand, do only a one-sided decomposition, segmenting only the low-pass frequency components and not the high-pass frequency components. When WT is subjected to noisy or transitory environments, this feature can compromise its performance. In [113], wavelet transformations were used to offer an online

fault detection method for power conditioning systems (PCS). Switch open faults and over harmonics are detected using a multi-level decomposition wavelet transform approach. Using the normalized standard deviation of the wavelet coefficient, a quick and accurate diagnostic function is also achievable, allowing the suggested method to detect islanding conditions. Simple calculations (a time correlation generated by sequential multiplication and addition) and exact diagnostic capabilities of fault identification with good simulation outputs to check and evaluate its claims characterize the method's algorithm. The multilevel decomposition wavelet transform provides the method's straightforward calculation characteristic. At each wavelet tree level, the algorithm extracts wavelet coefficients from the measured signal, and errors are discovered and categorized using the wavelet coefficient changes. Using a three-level MLD tree, the fault detection technique was created for PCS fault scenarios. Switch open and over harmonic are the two scenarios considered. The PCS uses a semiconductor switch, such as a field effect transistor (FET) or an IGBT, to convert DC solar voltage to AC grid current. The switch open can be attributed to a switching device failure, whereas the over harmonic can be attributed to a controller or sensor failure. The cases of switch short faults are not taken into account here. The system is protected by the over-current limiting function or melting fuse when the switches are in short fault, and the PCS ceases running. The PCS current has a distorted waveform when the switches are open faulted, and it continues to provide high order harmonics to the grid. An UP and DOWN switch failure in the inverter bridge might be categorized as an open switch problem. The authors of [114] used the discrete wavelet transform (DWT) to analyze the traced I-V curve of a residential PV system and define these coordinated points in the related diagnosis effort. The DWT was utilized to implement the fault diagnosis of residential PV systems as a preprocessing tool. It enables feature extraction through signal decomposition and noise reduction. The reduced short-circuiting current of partially shaded cells is represented by the vertical height or current in a PV string identified by the DWT method, whilst the horizontal or voltage distance from the VOC to the inflex is connected to the number of bypassed modules. The approach is divided into two sections, namely passive and active. In the passive diagnosis section, a residue signal is generated by comparing the measured PV power signal and simulated model in real time to monitor the alarm signal and abnormal condition in the system, using the model base fault diagnosis technique. After the manifest and certainty error signals have been determined, the flash test is used as the active and second portion of the test procedure. During this phase, the step load is separated from the PV and power generation, and the MPPT mode of the inverter is interrupted. The I-V curve of the PV array is tracked and logged by modifying the inverter switching pattern for a deeper inspection and interpretation. The model provided in [115] for the defect diagnosis of PV arrays was improved using improved wavelet neural networks, wavelet neural networks, and back propagation neural networks. The training technique now includes a Gaussian function, which is utilized as an activation function, an additional momentum mechanism, and an adaptive learning rate method. The conclusion is taken from simulation findings that the proposed technique in this study is capable of efficiently diagnosing the PV array problem with good performance accuracy, convergence time, and stability under the identical conditions of the network input and desired output. The proposed fault diagnosis algorithm is summarized in Figure 9. Four PV system fault types are diagnosed using the model, namely short-circuit, open-circuit, abnormal degradation, and partial shading. There are five network output layer variables since the system requires the precise diagnosis of four types of problems and no fault condition. The selection of the number of hidden layer nodes in a neural network is a difficult topic with no theoretical foundation to follow. The number of hidden layer nodes is critical to the network's success. If the number is too little, we may not acquire a network from training, implying that the network's robustness is poor and its anti-noise ability is weak, making it unable to recognize models that have never been seen before. If the hidden layer's node number is too big, the learning time will be too long, and the error will not be minimal. Furthermore, there could be an issue with overfitting. As a result, based on

an empirical equation, the trial and error method is commonly employed to identify the appropriate number of concealed nodes.

**Figure 9.** Proposed fault diagnosis method based on the wavelet neural network [115].

In [116], a wavelet optimized exponentially weighted moving average (WOEWMA) monitoring technique based on the principal component analysis (PCA) was created. The presented monitoring approach combines the advantages of exponentially weighted moving averages, MOO, and wavelet representation. MOO is used to tackle the challenge of determining the best strategy for minimizing both the missed detection rate (MDR) and the false alarm rate (FAR). Apart from the decorrelation of auto-correlated observations, the wavelet representation increases the monitoring performance by lowering MDR and FAR, as well as obtaining the exact deterministic features. The proposed method is appropriate for real-time implementation due to its quick calculation time. This approach is robust in a range of faulty conditions, including single and multiple (cascade and simultaneous) occurrences, and can detect faults in both the DC and AC conversion sections. The proposed method has several advantages, including dynamic multiscale representation to extract accurate features and de-correlate auto-correlated measurements; the PCA technique to model PV systems; the EWMA of two parameters in OEWMA are optimized using the multi-objective optimization; and the WOEWMA chart can detect smaller fault shifts, thereby improving the PV model monitoring.


**Table 6.** Summary of wavelet-based methods.
