Fractal-based autonomous partial discharge pattern recognition method for MV motors

On-line partial discharge (PD) monitoring is being increasingly adopted to improve the asset management and maintenance of medium-voltage (MV) motors. This study presents a novel method for autonomous analysis and classification of motor PD patterns in situations where a phase-reference voltage waveform is not available. The main contributions include a polar PD (PPD) pattern and a fractal theory-based autonomous PD recognition method. PPD pattern that is applied to convert the traditional phase-resolved PD pattern into a circular form addresses the lack of phase information in on-line PD monitoring system. The fractal theory is then presented in detail to address the task of discrimination of 6 kinds of single source and 15 kinds of multi-source PD patterns related to motors, as outlined in IEC 60034. The classification of known and unknown defects is calculated by a method known as centre score. Validation of the proposed method is demonstrated using data from laboratory experiments on three typical PD geometries. This study also discusses the application of the proposed techniques with 24 sets of on-site PD measurement data from 4 motors in 2 nuclear power stations. The results show that the proposed method performs effectively in recognising not only the single-source PD but also multi-source PDs.


Introduction
Partial discharge (PD) activity within a rotating machine is not only an indication of an insulation defect but also a causative mechanism of further insulation deterioration. Standard patterns of PD activity have been developed to allow identification of a fault. Automatic PD detection and source classification is becoming increasingly important in on-line insulation condition assessment of motors [1,2]. Monitoring a motor in service and diagnosing the insulation condition by using recognition approaches from acquired PD is desirable [3,4]. However, different sources of PD could be detected under on-line measurement. Different sources of PD are of different risks and complex conditions, such as slot type PD would be high risk with low-to-medium PD magnitude, but surface type PD would be a medium risk with high PD magnitude. There is high demand in the industry to distinguish multiple PD sources. However, there are several challenges to achieve the recognition of motor PD patterns automatically.
It has been identified that different PD types generate different PD patterns [5]. The PD pattern is represented by a set of characteristic attributes, which are extracted from measured PD raw data. According to different attributes, PD pattern is commonly classified into two types for analysis and classification: phaseresolved data and time-domain data [6]. Currently, the most widely used method is based on the analysis of phase-resolved PD (PRPD) data, which has three parameters φ, q, n. Here φ is the voltage phase angle at which the PD occur (normally assigned as 5° or 10°w indows), q is the measured PD magnitude and n is the number of PDs which occur in the phase window over a defined number of measurements. PRPD patterns are considered to be a reliable indication of the root cause of an insulation fault. Recognition of multiple PD sources was introduced in [7,8], it was found that high recognition rate only occurs with multi-source PDs with highly different PRPD patterns, in terms of shapes and polarities, whereas, multiple PDs with similar PRPD patterns were found to be more difficult to distinguish [9][10][11][12]. However, the reference voltage waveform is hard to obtain in on-line monitoring condition. The loss of φ makes it impossible to use PRPD pattern in PD recognition in motors.
Pattern recognition technology has been studied and applied in PD pattern recognition in the last few decades [13,14]. Various artificial intelligence (AI) techniques such as artificial neural network, knowledge-based system, and support vector machines have been applied to PRPD pattern classification [15,16]. AI approaches require a large number of data for training and learning, and training data should be 'healthy' to ensure a good result. Other techniques, such as distance classification technique and fuzzy logic, are also used for PD source classification [17,18]. Most of the techniques introduced above provide promising fault recognition results when only one PD type exists but perform less well when multiple sources are considered. Moreover, most of these approaches, which required a massive amount of data for training and testing, were tested and validated on one specific motor under laboratory conditions. Their general application to practical on-line situations has not yet been investigated.
In a practical on-line situation, the three challenges in this paper when attempting autonomous PD pattern classification in motor condition assessment could be summarised as follows: (i) processing PD pattern without voltage phase information [19]; (ii) establishing a general pattern classification reference suitable for practical applications; (iii) recognising multiple PD sources, which may occur in a medium-voltage (MV) motor simultaneously. This paper investigates autonomous pattern recognition techniques for motor PD classification. To address the key challenges mentioned above, a novel pattern recognition framework is presented in the paper. Polar PD (PPD) representation, which converts a PRPD to a circular format, is applied to address the loss of voltage phase information. Moreover, the phase shift often causes a cluster of PD pulses, of which the integrity is essential for many established PRPD pattern recognition techniques, into two halves, one at the beginning of the PRPD pattern, and the other at the end [19]. For this reason, the PRPD patterns will be converted to PPD pattern which connects the beginning of a 50 Hz, alternating current (AC) cycle of PD data with the end of the dataset. PPD pattern images form the standard defects reference converted from PRPD images of the six PD types from IEC 60034-27 [20]. Fractal theory is applied to extract proper fractal features of both single-source and multi-source PD types. Centre score (CS) algorithm [3], a conventional PD source classification method which performs high recognition rate without data training, is implemented for PD source classification. Extensive laboratory experiments and on-site tests are conducted using artificial PD geometries to verify the feasibility of the developed system.
In the next section of this paper, it reviews the fractal theorybased PPD pattern recognition framework for PD source classification. In Section 3, PRPD-to-PPD conversion is introduced. Then the box-counting method (BCM)-based fractal analysis is introduced to extract the fractal features from threedimensional (3D) PPD pattern images in Section 4. Section 5 presents the fractal map based on IEC standard PRPD patterns. The CS algorithm for PD source classification is introduced for evaluating the possibility of PD sources in Section 6. Section 7 describes the experimental setup for validating the proposed method. Finally, Section 8 presents the application of the proposed method to practical on-site test data before the conclusions are provided in Section 9.

Pattern recognition framework for PD source classification
This paper focuses on the establishment of a pattern recognition method which can recognise the standard motor PD patterns as given in IEC 60034. As shown in Fig. 1, the proposed PD pattern recognition consists of four main stages.
Stage 1 is the establishment of PD pattern recognition reference. At this stage, firstly, six standard types of motor PDs from IEC 60034-27 are converted from 3D PRPD patterns to 3D PPD patterns. Then, a fractal map (lacunarity versus fractal dimension) based on the 3D PPD patterns is generated using the BCM-based fractal theory.
In Stage 2, raw data is detected either in laboratory or field through high-frequency current transformers (HFCTs) and highpass filters. These raw data are then pre-processed before the extraction of fractal features. In the pre-processing procedure, denoising is carried out before a 3D PRPD image is generated for a PD dataset. The de-noising technique applied in the present work can be referred to in [21,22].
In Stage 3, the pre-processed PD data in 3D PRPD patterns is converted to 3D PPD patterns, which consists of PD pulse magnitude and pulse number distribution with respect to time within the sampling period. Then two fractal features (fractal dimension D and lacunarity Λ) are determined from the 3D PPD pattern using the BCM-based fractal theory.
In Stage 4, CSs of the set of fractal features (D, Λ) from Stage 3 are calculated based on the fractal map to recognise motor PD sources to estimate the probability of motor PD sources.

PRPD-to-PPD pattern conversion
Before extracting the fractal features of a PD pattern, the preprocessed PD data is firstly converted to a 3D PRPD pattern. In IEC 60034, the given PRPD pattern is 3D where phase information φis in abscissa and PD amplitude is in ordinate. The information of n, the number of PDs, is indicated by different colours.
To avoid the influence of the loss of reference voltage phase, 3D PPD pattern is considered in the on-site test data. In the previous study as introduced in [19], it is hard to acquire a reference voltage signal in on-line monitoring. The only applicable voltage is the low-voltage (LV) power supply as a reference, with data acquisition being triggered at the 0° (positive zero-crossing) point of the LV power supply. The present authors have carried out PD measurements in six power stations. The experience is that the phase shift between the motor working voltage and the LV power supply varies in different power stations. Although this LV zerocrossing provides a synchronised reference for data capture, an unknown phase shift exists relative to the waveform of the motor working voltage.
The relative phase information is kept in a circular format. The number of PDs occurring in each pixel position is added over the number of records taken during a test and a φ-q-n pattern becomes an x-y-n pattern.
The conversion from 3D PRPD patterns to 3D PPD patterns is as follows. The data point in a 3D PPD pattern image is calculated from where θ represents the phase information of a PD pulse, which is extracted from the time instant of each pulse in the 20 ms data record gathered; r represents the normalised PD pulse in the polar coordinate system; n represents the count or number of PDs which occurs in the phase window over a defined number of measurements; x, y represent the pixelated positions of each PD; c is a constant value which makes all the values of x and y equal or greater than zero. In a PPD image of a resolution of 128 × 128, c equals to 128 for the convenience of observation that the polar origin is in the centre of the image; the z-axis represents the PD count n.

Brief overview of fractal theory
Fractal theory is an image processing technique. Mandelbrot in [23] first developed the concept of fractal geometry which was applied to the model and describe natural shapes and phenomena with a brand new dimension known as 'self-similarity' [24,25]. Fractal dimension (FD) measures the geometrical complexity of images. However, it has been observed that FD alone is insufficient for purposes of discrimination since the two surfaces of different appearance could have the same value of FD. So, Lacunarity, Λ, was introduced as a measure of spatial heterogeneity. Beyond being an intuitive measure of gaps, lacunarity can quantify additional features of patterns such as 'rotational invariance' and more generally, heterogeneity [26,27].
PD activity is also considered as a natural phenomenon occurring in electrical insulation system due to inhomogeneity in the insulation material and gives rise to a variety of complex shapes in its PRPD patterns [28]. According to IEC 60034-27, motor PD sources have different PRPD pattern shapes and this provides a way to distinguish PD sources by comparing their PRPD pattern shapes. The complexity of the shape of a 3D PRPD or a 3D PPD pattern image can be represented by fractal geometry [29]. It shows the possibility to apply the proposed fractal analysis with fractal dimension and lacunarity to recognise the PD patterns in motors automatically [30][31][32].
The BCM is adopted for computing the fractal features of 3D images [33]. BCM is a method of gathering data for analysing complex patterns by breaking a dataset or image into smaller and smaller pieces, typically 'box'-shaped, and analysing the pieces at each smaller scale. The advantage of BCM is that it considers both the number of empty boxes and filled boxes. Besides, the size of the filled box is taken into consideration as well and the inhomogeneous character of the fractal image is well represented. In this paper, the BCM-based fractal analysis is applied to extract FD and lacunarity from 3D PPD pattern images.

Calculation of fractal features using the BCM
The basic procedure of BCM is to systematically lay a series of grids of decreasing the box sizes over an image and record data (the counting) for each successive size. In order to extract fractal features from 3D PPD pattern images, the steps are listed below: • Step 1: To scale the box size, L. L is the side size of a 3D box in BCM to cover a fractal object [25]. With the decreasing of L, the measurements obtained become increasingly sensitive and lend to infinity if the L approaches 0. Here the determination of the value of L is based on the consideration of accuracy and the required computational effort, both of which increase with the maximum value of L. Theoretically, it is beneficial to examine as large a range of L (L = 0, ..., L max ) as possible until L max reaches the image dimension. In this work, L max has been chosen as 128, the size of the pixel map of the PPD patterns. where N is the number of possible points within the box. N (L) is defined as the expected total number of boxes needed to cover the whole image, as shown in where S is the number of image points of PPD pattern. • Step 3: To calculate FD. The actual size of the contents N(L) is proportional to L −D [26], as shown in where L max is the max value of L.
Their 3D PRPD patterns, shown in the left-hand column of Fig. 2, form the pattern recognition standard in this work. Moreover, the 3D PRPD format is converted to 3D PPD patterns, as shown in the right-hand column of Fig. 2.
The individual 3D PPD pattern images, with a resolution of 128 × 128. x and y axes denote the polarised phase and normalised amplitude, respectively. z-axis denotes the pulse count data. The number of PD events at each x/y location is uniquely mapped to one of the 16 colours available.
In the proposed method in Section 4, 3D PPD pattern images are divided by box size, L = 2 n (n = 0, 1, …, 7). A total of eight groups of boxes are calculated. Then the fractal-based feature extraction is made to extract fractal dimension and lacunarity features from converted 3D PPD patterns.

Fractal map of single-source PD
Fractal features (D and Λ) of the converted 3D PPD images from the standard 3D PRPD patterns are calculated and shown in Table 1.
To consider the fact that PD activities and associated PD patterns rarely repeat themselves, even for the same defect site and for the same type of PD by a certain degree, 20 sets of data originated from each of the IEC standard PRPD pattern images by compressing and extending the pattern up to 30% were implemented in order to test the robustness of the proposed method. Fig. 3 plots the clusters of fractal features of the converted PPD images after extension and compression. In Fig. 3, the darker points are the fractal parameters converted from unchanged standard PRPD image, as presented in Table 1; the lighter points are the clusters of fractal parameters after compression and extension.
In Fig. 4, the proposed method can separate the groups using fractal features. As shown, clusters belonging to a particular fault type are found to lie close to each other, and more significantly, most are reasonably well separated from other fault types. It is to be noticed that the fractal features of PD 2 and PD 4 overlap to a degree. That's because the PRPD images of these two PD types have a very similar shape: both polarities of PD 2 and PD 4 are a triangle, as presented in Fig. 4. The difference between PD 2 and PD 4 is in their symmetry. The triangles of PD 2 at each polarity are symmetric. This is because it is generated between insulation layers where the conductivity and permeability are same. The triangles of PD 4 at each polarity are asymmetric. This is because it is generated between the insulation layer and stator core where the conductivity and permeability are different. Since the risk associated with PD 2 and PD 4 is at a high level [34], it is highly recommended that a more detailed inspection of the motor is carried out once a PD fault with these fractal features is detected.

Fractal map of multiple-source PD
The double-source PDs are formed by various combinations of the six single-source PDs. The number of double-source PD sources formed is 15. The procedure of setting up the criteria for distinguishing double-source PD is similar to that described in the previous sections. Fig. 5 shows the 15 clusters of fractal features of the converted double-source PPD images after extension and compression.
In practical PD measurements, the multi-source PD problem is very common [15]. To investigate the ability of the proposed PD recognition techniques to recognise multi-source PDs, these 21 PD types form a fractal map shown in Fig. 5 to distinguish multisource PD detected from the on-site test.
In Figs. 3 and 5, the clusters of fractal features of different PPD images are well separated but the boundary is very close to one  another, making it difficult to discriminate among double-source PDs. It is impossible to provide a reliable PD type classification method to specify the PD type(s) to one unidentified PD fault. In this paper, CS-based PD source classification is introduced to list the possibilities of each potential PD type to provide probability estimation.

CS algorithms for PD source classification
In order to determine whether a data set fits well with predefined fault information, the CS is developed. The CS is defined as the percentile rank of the distance between the fractal point of unknown defects and the centre of the defined fractal clusters. The fractal features of the defined PD patterns are displayed in a 2D space (D and Λ), as shown in Figs. 3-5. Taking Fig. 4 as an example, six clusters of defined single-source PD patterns are displayed in one map. The mathematical centre of each cluster is determined and the position of an unknown defect can be compared with this centre. The CS can vary from 0 to 100%. It reflects the probability of an unknown defect recognised as a defined PD pattern in the fractal map. The value of CS higher than 0 indicates a possible defined PD pattern in the fractal map; the value of CS equals to 0 indicates an unknown PD pattern. The first step is to measure the distance between the fractal features of unknown defects and the average values of the fractal features of defined fractal clusters in the fractal map. The distance is calculated as where u is the fractal feature (D and Λ) of the unknown defect; μ is the average value of all defined fractal clusters; σ k is the standard deviation of a defined fractal cluster; k is the number of the PD types, k = 1, …, 21.
The standard deviation of a defined fractal cluster is given as where N is the total number of fractal clusters, in this case, N = 21; μ i is the average value of a defined fractal cluster. The covariance matrix can be considered to be a multidimensional generalisation of the 1D standard deviation. Finally, the CS is defined as where PR is the percentile rank of d k 2 as given as where c l is the count of all scores less than the score of interest, f i is the frequency of the score of interest, and N is the number of examinees in the samples. The recognition rate is calculated based on the ratio between the recognised test sample and the sum of all test samples.

Experimental setup
The experimental work completed aims to test the performance of the proposed algorithms including PD data pre-processing procedures, PRPD-to-PPD pattern conversion, fractal theory-based PPD pattern feature extraction, and CS-based classification. Because it is hard to generate and control the same PD types in a real motor, the experiment is carried on the simplified geometry to present the similar fault type inside a motor. The experiment setup for validation is depicted in Fig. 6. Function generator was used to generate 50 Hz sine wave, which was used as the input signal to a power amplifier to be amplified as power supply. A HFCT, with frequency response 50 kHz-20 MHz, is clamped around the ground wire to measure PD signal (as in on-site tests). Artificial faults are designed to simulate three types of PD sources, namely internal void discharge (denoted as PD 1), delamination between conductor and insulation discharge (denoted as PD 3), surface discharge (denoted as PD 5).
During the data acquisition, Channel 1 recorded the outputs from the HFCT while Channel 2 recorded the applied voltage as the phase reference. For each of the modelled faults, measurements were conducted for 20 times with each four times under one level of voltage supply. The lowest voltage supply is the PD inception voltage, and the higher-level voltage is 0.2 kV higher than lower level. At one acquisition, PD pulses are recorded over 500 power cycles. For each of three faults, 20 acquisitions are recorded and thus total 60 sets of discharge signal samples are used as test data for evaluating the algorithms presented in this paper. Fig. 7 shows the single-source PD recognition results when applying the introduced experiment setup and data pre-processing procedures to the experimental data. The fractal map as shown in Fig. 4 in Section 5.1 is applied to the CS-based pattern classification algorithm for the probability estimation of PD source type. The fractal features are extracted from the 3D PPD patterns shown in Fig. 7 and are displayed in the fractal map in Fig. 8.

Single-source PD pattern recognition:
The fractal analysis results for the single-source PDs are shown in Fig. 8. It is clearly that the PD type in experiment 1 was correctly recognised as PD 1 (internal void discharge); the PD type in experiment 2 was correctly recognised as PD 3 (delamination between conductor and insulation); the PD type in experiment 3 was correctly recognised as PD 5 (surface discharge).
The recognition results based on the CS method are in Table 2. It shows 3 sets of experiments, each with 20 sets of data. In experiment 1, due to the fractal clusters PD 1 and PDs 1 & 4 are close in fractal map shown in Fig. 5, the CS results of PDs 1 and 4 are also demonstrated in Table 2. In considering the fact that 19 sets of CS results of PD 1 are above 0, the recognition rate of PD 1 in experiment 1 is 95%. This is applicable in other PD type recognition. The recognition rates of single-source PD in these three experiments are not <90%. However, due to the overlap between clusters in multi-source fractal map in Fig. 5, the CS results are able to provide the probabilities for all possible defined PD types. The higher CS is, the more likely this PD pattern is.

Double-source PD pattern recognition:
To validate the application of the proposed method to double-source PD recognition, three artificial data sets are generated by combining the PD data from two of the experimental arrangements, as follows:  Due to the reference voltage signal was applicable in lab condition, it was possible to combine different PRPD patterns to generate a double-source PD pattern to test the feasibility of the proposed methods. Fig. 9 shows the 3D PPD patterns of the three double-source PDs.
The fractal analysis results for the double-source PDs are shown in Fig. 10. It is clearly that the PD type from the combined PRPD patterns of experiments 1 and 2 was correctly recognised as the PDs 1 and 3 (blue circle in Fig. 10); the PD type from the combined PRPD patterns of experiments 1 and 3 was correctly recognised as the PDs 1 and 5 (red circle in Fig. 10); the PD type from the combined PRPD patterns of experiments 2 and 3 was correctly recognised as the PDs 3 and 5 (yellow circle in Fig. 10).
The recognition results based on the CS method are in Table 3. It shows 3 sets of results from the combined PRPD pattern, each with 20 sets of data. In the results of combined experiments 1 and 2, due to the fractal clusters PDs 1 and 3 and PDs 1 and 2 are close in fractal map shown in Fig. 5, the CS results of the PDs 1 and 2 are also demonstrated in Table 3. In considering the fact that 16 sets of CS results of PD 1 are above 0, the recognition rate of PDs 1 and 3 is 95% in this combined experimental result. This is applicable in other PD type recognition. The recognition rates of single-source PD in these three experiments are not <80%.

Applications to practical on-site test data
The proposed method is applied to the practical situation of on-site test of three-phase industrial motors. The test data was collected at a number of nuclear power stations, using HFCTs clamped around the earth strips of the motor supply cables. The installation of the current sensor in field is illustrated in Fig. 11, where, the applied current sensors are installed at the earth strip below the switchboard. The benefit of the use of HFCT is that it, due to its good frequency bandwidth, is capable of detecting PD emanating from local switchgear, from cable and from cooling water pump motor which is usually 300-500 m away. PD was detected from four MV motors (A, B, C and D) and recorded for later analysis. Fig. 12 shows the PRPD pattern of tested motors. By visual inspection of the PRPD patterns in comparison with standard PD patterns as given in IEC60034-27, the fault in motor A might be PD 1 (internal void discharge); the PD pattern of motor B might be double-source PD 4 and 5 (slot discharge and surface discharge);  the PD pattern of motor C might be PD 1 (internal void discharge); and the PD pattern of motor D might be PD 4 (slot discharge). It is to be noted that the authors do not have photographs to show the evidential damage of the defect site (Fig. 13).
The proposed pattern recognition algorithm was applied to these four motors. The recognition results were shown in Table 4. The recognition results agree well with the visual inspection. The recognition rate for multi-source PD is not <86.7% in practical situations. The CS-based pattern classification shows all potential PD patterns with a ranked score. Take Motor D, for example the PD pattern recognition result is PD 4 with the recognition rate 100%, PDs 2 and 6 with recognition rate 83%, PD 2 with recognition rate 83%, which all have high possibilities. When considering the average CS, the average value of CS of PD 4 is much higher than the other two patterns. It indicates the tested PD pattern is more likely to be PD 4.

Conclusion
This paper described a combination of theoretical and practical study into the feasibility of using fractal theory to discriminate multiple motor PD sources. PRPD patterns were modified to create  polar PD patterns to address the problem of lack of voltage phase information. Two fractal features, fractal dimension D and lacunarity Λ, were employed to measure the shapes of PPD. The reference PPD patterns were created from the PRPD patterns in IEC 60034-27-2. The fractal maps of single-source PDs and double-source PDs showed good stability when the shapes of PPD patterns were compressed and extended. Three types of PD geometries were built and tested under laboratory conditions to validate the proposed method's pattern recognition performance for both single-source PDs and double-source PDs. Four sets of motor PD from on-site data were visually assessed and analysed in the fractal map of single-source PDs and double-source PDs. The recognition results agree well with the visual inspection. The limitation is that several clusters of PPD patterns are very close in the fractal map, which may cause incorrect identification. However, the ones close to each other have similar risk level in terms of further degradation. A risk-based diagnosis will be investigated as future work.