3.1. Acoustic Signal Measurements
Acoustic signal measurements can be utilised to diagnose PD. Acoustic sensors are located on the transformer tank to detect the acoustic waves generated by PD activity [
32]. These sensors can be placed in different locations on the tank, depending on the type of partial discharge activity being detected. Once the acoustic signal is detected, it is recorded and analysed using various signal processing techniques to extract features that indicate PD activity [
32,
33,
34]. Some common features that are extracted from the acoustic signal include the amplitude, time, frequency, and phase of the signal [
33]. The acoustic wave equation is given by:
where
p is the acoustic pressure,
ρ is the density of the medium,
c is the speed of sound in the medium, and
is the acoustic potential. The existence of partial discharge in power transformers can be diagnosed by analysing the acoustic signals produced by the discharge [
34]. The amplitude of the acoustic signal can be related to the severity of PD and can be expressed as:
where A is the amplitude of the acoustic signal, K is a constant, Q is the charge produced by the partial discharge, L is the length of the discharge, and r is the distance from the source to the receiver.
3.3. Convolution Neural Networks (CNNs)
Convolution neural networks (CNNs) are used to enhance the accuracy of PD diagnoses in power transformers by utilising acoustic signals [
37]. A CNN is a type of artificial neural network that is intended to process data with a grid-like structure, such as images or acoustic signals [
38]. To use a CNN for PD diagnosis in power transformers, the acoustic signal is first pre-processed by applying filters to remove noise and enhance features that are relevant to PD activity [
37,
38,
39]. The pre-processed signal is then fed into the CNN as input, and the network learns to automatically extract features that indicate PD activity. The architecture of a CNN for PD diagnosis in power transformers typically consists of multiple convolutional layers, followed by pooling layers and fully connected layers [
40]. The convolutional layers apply filters to the input signals, which are learned during the training process. The pooling layers extract the output of convolutional layers to reduce computational costs and avoid overfitting [
39,
40]. The fully connected layers map the output of the pooling layers to a probability distribution over a set of possible PD locations.
Figure 1 showcase the structure of CNN [
41].
The output of the CNN can be further analysed to identify the severity of PD activity in each location. The severity can be quantified using metrics such as the amplitude and frequency content of the acoustic signal in each location. The performance of the CNN can be evaluated using metrics such as the F1 score, recall, precision, and accuracy. Accuracy is normally a straightforward metric that represents the ratio of correctly predicted instances to the total instances, and it is showcased in Equation (4). Equation (5) presents the precision, which is the ratio of correctly predicted positive observations to the total predicted positives. Precision is particularly important when the cost of false positives is high. This is followed by recall, which is the ratio of correctly predicted positive observations to all observations in the actual class. This metric is crucial when the cost of false negatives is high. Lastly, The F1 score is the harmonic mean of precision and recall. It provides a balance between precision and recall. These metrics provide a measure of how well the CNN is able to detect and locate PD activity within the transformer. The calculation of these metrics is performed by using the equations:
3.5. Conventional Machine Learning-Based PD Diagnosis Approaches
The literature on conventional Machine Learning (ML)-based partial discharge (PD) diagnostic approaches power transformers with rich studies aiming to enhance the reliability and efficiency of PD detection and classification. Power transformers are critical components in electrical systems, and the timely identification of PD events is essential in ensuring their safety and reliability while operating. Conventional ML techniques have been widely explored in this context, focusing on the extraction of relevant features from PD signals, signal processing methods, and the application of various classification algorithms. the summary of the evolutional literature of PD detection in power transformer from 2000 to 2023 is outlined below, showcasing the state-of-the-art of conventional techniques based on PD diagnosis approaches.
R. Braunlich et al. [
38] investigated the PD diagnosis in power transformers using a spectrum analyser and a phase-resolving PD analyser for offline electrical PD detection and found that it is possible to detect PD faults, and the development of sensitivity is greater than 50 pC. X. Wang et al. [
39] conducted a similar research study by placing piezoelectric and fibre optic sensors with an acoustic frequency response of 5 MHz. They found that the localisation of PD signal and detecting PD signals is difficult when there was environmental noise. R. M. Sharkawy et al. [
40] created circuits to measure PD using electrical and acoustic signals and concluded that their method can effectively measure PD recognition online. J. Rubio-Serrano et al. [
41] performed a study using electro-acoustic detection and found that different PD sources can be recognised using energy ratio and cross-correlation, and statistical analysis to find the source of PD. S. Coenen and S. Tenbohlen [
42] performed a similar study using piezoelectric sensors at the outer tank and three UHF probes installed in three oil valves. They found that the technique is efficient for triggering the PD signal with a low-frequency electric or UHF signal and denoising the signal with an acoustic signal. J. Li et al. [
43] conducted another study using an antenna with a UHF Hilbert fractal for online PD detection. They noted that the method can be successfully used for recognising PDs and for the online UHF PD monitoring of transformers.
In the same year, R. A. Hooshmand [
44] conducted some experiments modifying the binary of partial swarm optimisation (PSO) algorithm combined with an acoustic emission approach. The authors validated their results with the genetic algorithm method and found that the techniques can localise and detect two PD sources with a small margin of error. S. Zheng et al. [
45] performed a study using UHF detection and found that the PDs near 500 pC inside the transformer windings could be located and detected. H. H. Sinaga et al. [
46] conducted some tests utilising UHF detection and recorded by spectrum analyser and oscilloscope and found the classification and recognition of single and multiple PD phenomena with good accuracy. L. Cui et al. [
47] performed similar experiments at constant voltage testing on the model in the laboratory, analysing surface discharge in oilpaper insulation. They found that this clustering method shows the “hold together” characteristic for wavelet moment. T. Boczar et al. [
48] conducted some studies using the acoustic emission method and found that implementing the method is effective but expensive for computer-based experts to analyse the transformer’s technical condition. I. Búa-Núñez et al. [
49] performed the tests by combining piezoelectric (PZT) and fibre optic sensors with acoustic emissions. It was found that acoustic emission produced by PDs can be found and located with a 1 cm accuracy. M.K. Chen et al. [
50] performed a similar study using three radio-frequency coils for PD detection connected to the transformer tank. They found that the technique provided reliable early stage detection for online PD detection.
M. Harbaji et al. [
51] conducted the experiments using the acoustic emission method and found the technique effective when principle component analysis (PCA) is used as the feature extractor with KNN as a classifier. H. Mirzaei et al. [
52] performed some experimental tests using UHF detection in the valves of tank model and real power transformers by installing several new UHF antennae. The performance improved the accuracy of PD localisation by increasing the distinction between potential PD locations inside the transformer. B. Sarkar et al. [
53] conducted similar studies using an optical PD sensor built on Fiber Bragg Gratings (FBG) that measures the acoustic pressure produced during PD. They concluded by confirming that the technique can be used for online monitoring and placed inside the power transformer tank. Z. Qi, [
54] investigated a similar analysis of two-dimensional linear discriminants (2DLDA) and found that the PD pattern recognition was no longer affected by the multiple factors of defect size, applied voltage, and insulation aging. J. Seo et al. [
55] performed experiments using a high-frequency current transducer (HFCT) mounted on the transformer’s grounding wire—an inductive system. They found that the proposed approach outperforms the typical wavelet transforms with a single threshold. In [
56], a study was conducted using a combination of UHF and acoustic PD detection techniques and found that the method has the ability to recognise the unique signals of the individual PD source. R. Rostaminia et al. [
57] performed experimental measurements of PD test circuits using SVM and concluded that various types of defects are classified, and that texture features display the highest degree of accuracy. H. Jahangir et al. [
58] conducted experimental tests using UHF with probes on six different drain valves on the transformer tank. They concluded that the method consists of extremely high errors, and that PD calibration using UHF probes is not practical. However, it is possible to use the maximum charge estimation method. Y.B. Wang et al. [
59] conducted similar studies using a particle-swarm-optimisation-route-searching algorithm for acoustic emissions to locate and predict the propagation time of acoustic waves. The methods produce better detection accuracy compared to other localisation detections. R. Ghosh et al. [
60] conducted a study using acoustic emission-based localisation to estimate the time of arrival by the source filter model of acoustic theory and found that the approach results are approximately 1 cm to the accuracy of PD localisation. S. Qian et al. [
61] investigated the benefit of using fibre optic sensors for PD acoustic detection, and Signac developed a fibre sensor system. They concluded that the method outperformed the piezoelectric transducer in detecting AE signals originating inside the winding. J. Du et al. [
62] conducted studies looking at transformer oil characteristics for a 30–75 °C temperature range using the AE method. They found that changes in parameters like viscosity and BDV, decreased the AE signal’s amplitude from 65 °C to 75 °C at 17 kV.
Y.B. Wang et al. [
63] performed an experimental test using a Fabry–Perot optical fibre sensor array combined with a steered response power sound-source localisation algorithm, which was used in the AE method. Their results showed higher accuracy compared to the more common piezoelectric transducer. C. Gao et al. [
64] performed a similar study using a combinational approach of a UHF probe’s tip fitted with an AE sensor. They concluded that the integrated sensor exhibits higher sensitivity than with direct acoustic wave detection. W. Si et al. [
65] conducted studies using optical fibre sensors for optical detection and found that the method fitted well with a water activity probe that works in various dielectric oils. M. A. Ansari et al. [
66] performed studies using surface, floating, and void electrodes on a discrimination algorithm and found that the multi-step discrimination method can distinguish and separate mixed signals with similar shapes, which were not feasible by the one-step method, or improve the separation capability in subclasses, which was a better selection than three or more PD sources. M. Azadifar et al. [
67] performed some tests using the time difference of arrival (TDoA). It has been found that the TDoA technique, which employs three sensors, cannot deliver precise results when the line of sight is obstructed by the presence of transformer windings.
H. Karami et al. [
68] performed a similar study using time reversal and concluded that this technique has never been performed before to locate PD sources in transformers using electromagnetic TR. More in-depth theoretical and experimental studies are required to evaluate the method’s effectiveness on a real transformer and in the presence of noise. H. Karami et al. [
69] performed experimental work using PD sources emitting both acoustic and electromagnetic (EM) waves. It was concluded that the windings’ core and layers have not been modelled in this instance. According to our analysis, the proposed acoustic TR technique can successfully locate a PD source that has been placed in various difficult locations (within a winding and between two windings). Additional work is being performed to make the suggested method 3D-capable and to conduct experimental validations to evaluate the method’s effectiveness when applied to a real power transformer. T. D. Do et al. [
70] conducted a study classifying the power transformer fault with CNN and reported that the methods can be used for PD classification both in quiet and noisy environments, and the researcher must consider using real-world data to validate the simulated results to actual transformer PD signals. H. Karami et al. [
71] conducted similar studies using time reversal and the 2D FDTD (Finite Difference Time Domain) and found that the 3-D cavity is a problem, and that the actual location is confined between the cavity walls. Lastly, it was reported that the technique is not performed on actual power transformers. H. Karami et al. [
72] conducted a similar study using time reversal and 2D finite-difference time-domain (FDTD) to 3D MATLAB toolbox (k-Wave) and found that the external acoustic environmental noise, such as the transformer’s own vibrations, could contaminate the acoustic signal. It was not performed on transformers, and no real-time data were used on the modelling, hence their test was accurate at all levels.