Based on the design principle of SCR series dry-type transformer insulation structure, this paper collects PD data information online during its operation and conducts on-site anatomy of the equipment [9]. Meanwhile, one-to-one correspondence related the geometric configuration of the PD fault location to the corresponding PD information characteristics is analyzed and summarized in details. Therefore, five types of PD models are designed to provide experimental and theoretical basis for establishing standard database of PD fault diagnosis, location, classification and life prediction of SCR series dry-type transformer in service, and the aim is to realize finally the intelligent monitoring and warning for the equipment operating status [10].

For artificially simulating the unevenness of the electric field distribution, five pairs of experimental models are designed and made from the industry standard brass material, they are needle-needle, needle-plate, needle-sphere, sphere-plate and sphere-sphere electrode system respectively, the clearance distances of needle-needle, needle-plate and needle-sphere are all 12 mm, while gaps of the sphere-plate and sphere-sphere equals to 10 mm. The needle electrodes are all copper cylindrical with a diameter of 4 mm, and the tip angle is 30˚. Then the plate electrodes are made from copper circular plate, diameter is of 100 mm, surface polishing and edge chamfering, and two sphere electrodes are all solid copper ball, and their diameters are of 10 mm and 20 mm respectively while the sphere surface polished. These five pairs of PD model are shown as in Figure 1.

The discharge chamber is a cylinder made of plexiglass material with a diameter of 450 mm, a height of 600 mm, and a wall thickness of 15 mm, as shown in Figure 2. Moreover, the chamber must be cleaned, dried and evacuated before the experiment, and then injected with clean and dry air. The experiment is carried out under the conditions of IEC and GB, and the standard specifies that the atmospheric pressure equals to 0.1013 MPa, temperature is T= 20˚C and absolute humidity 11 g/m³. In the field of electrical insulation technology, the four parameters that describe the insulating properties of gas dielectrics respectively are relative permittivity ε r , electrical conductivity γ , dielectric loss angle tangent

tg     δ and breakdown field strength E → . Under IEC and GB conditions, the relative permittivity of air is ε r ≈ 1 , and the electrical conductivity is γ ≈ 1.8 × 10 − 17 S / m , the dielectric loss angle tangent under power frequency is tg     δ = 10 − 9 , and the electric field strength of air is E → = 30   kV / cm .

The pressure of the gas in the chamber depends on the needs of the experiment, and the temperature is always maintained at 20 degrees Celsius. According to the requirements of the experiment, five pairs of PD electrode are fixed in sequence on the base of the chamber, not only the electrode gap can be adjusted free, but the electrode itself should also be easy to install and remove.

The experiment work is carried out in an electromagnetic shielded laboratory, and the experimental principle is shown in Figure 3. The acquisition of the PD signals is performed by the Hipotronics DDX-7000 digital PD detector. In order to meet the needs of signal analysis, processing and PD identification classification, PD signals are quickly acquired, stored and intercepted in integer multiple cycle lengths. In the whole experiment process of this project, 1000 original PD data are collected, that is to say 200 basic data were collected for each PD model, and the length of each data was 100 complete cycles.

Therefore, the original PD data, corresponding to the five electrode structures described herein, are illustrated in Figure 4, which are triggered by power frequency AC voltage.

For the registration of basic quantities, the momentary values of the experimental voltage and the discharge signal were processed [11]. It is known that using conventional detection methods and the electrical activity of PD is represented by three independent quantities only: the discharge magnitude q i , the ignition voltage u i and the position of the discharge related to the phase angle φ i of the test voltage. If during one half cycle of the test voltage more discharges occur, on the basis of q i , u i and φ i several quantities can be calculated [12]. In this study, the following basic quantities were measured and processed as shown in Figure5: the inception voltage U i n c as a voltage at the sample at which discharge pattern in a half cycle of the test voltage starts, and N q as the number of discharges for each halve period of the voltage cycle. Therefore, finally PD φ − q − n maps generated by the corresponding electrode have been gained shown in FigureA1 (See Appendix to this article).

According to reference [13] and reference [14], it is known that the statistical

variation in PD occurs, both in magnitude and in the temporal behavior of partial discharges. This variation in the time is partly caused by statistical variations in the discharge phenomenon itself and is also partly the result of the changes in the discharge site. Therefore, the voltage cycle is divided into phase windows representing the phase angle axis (0˚ to 360˚). If the observation takes place over several voltage cycles, four quantities can be determined in each phase window, i.e. the sum of the discharge magnitudes, the number of discharges, the average value of discharges and the maximum value of discharges. In the research process of this paper, the following phase-position quantities are processed just as reference [15]: the impulse count distribution H n ( φ ) , which represents the number of observed discharges in each phase window as a function of the phase angle; the mean impulse height distribution H q n ( φ ) , which represents the average amplitude in each phase window as a function of the phase angle. H q n ( φ ) is calculated by dividing the total discharge amount in each phase window by the impulse number of discharges in the same phase window. These quantities, observed throughout the whole angle axis, result in distributions of discharge recurrence as a function of phase angle. Based on previous research, we already know that the discharges occur during a voltage cycle in two sequences, and for each half of the voltage cycle separate discharge patterns can be measured. But in the case of similar inception conditions for each half of the voltage cycle, similar discharge patterns can be expected. Therefore, H q n ( φ ) and H n ( φ ) are characterized by two distributions, i.e. H q n + ( φ ) and H n + ( φ ) for the positive half of the voltage cycle, and H q n − ( φ ) and H n − ( φ ) for the negative half of the voltage cycle.

As mentioned above, the five different PD signal waveforms (shown in Figure 4) over a sinusoidal period are respectively divided into N phase windows, as illustrated in Figure 5. For each phase window n (pulse count), q (discharge quantity) and φ (phase angle) are calculated. Usually two distributions are determined: 1) H n ( φ ) gives the number of discharge impulses in each phase window, 2) H q n ( φ ) takes the average magnitude of the discharge pulses as a function of the phase angle. Therefore, the characteristic quantities of PD can be defined as the reference [16].

Fingerprints obtained in the experiments are shown as a set of the histograms composed of PD statistical characteristic parameters, and the shape of each histogram could present the essential nature of PD signals. Then each feature of a histogram has statistical characteristics for specified PD type. Therefore, these statistical features are used as pattern character vectors of PD classification for our research objectives. In this paper, these statistical features include skewness ( S k ), kurtosis ( k u ), asymmetry (A), cross correlation (cc) and phase factor ( P f ) that are all calculated based on the PD signals. These parameters are defined as follows:

S k = ∑ i = 1 w ( x i − μ ) 3 × p i σ 3 (1)

where, x i is the discrete value of phase window i, p i is the probability of frequency of appearance for that value x i in phase window i, μ is the mean value ∑ x i ⋅ p i , and σ is the variance σ 2 = ∑ ( x i − μ ) 2 ⋅ p i . The skewness represents the asymmetry of the distribution. If the distribution is symmetric, S k = 0 . If it is asymmetric to the left, S k > 0 , otherwise S k < 0 .

k u = ∑ i = 1 w ( x i − μ ) 4 × p i σ 4 − 3 (2)

The kurtosis represents the sharpness of the distribution. If the distribution has the same sharpness as a normal distribution, k u = 0 . If it is sharper than normal, k u > 0 , and k u < 0 means it is flatter. Examples of these two statistical parameters are demonstrated in Figure 6.

The discharge factor A describes the difference in the mean discharge level in the negative and positive distributions. It is defined as following:

A = Q s − / n − Q s + / n + (3)

where, Q s + and Q s − are the sum of discharges of the mean pulse height distribution in the positive and the negative half of the voltage cycle; n + and n − are the number of discharges of the mean pulse height distribution in the positive and the negative half of the voltage cycle.

The cross correlation factor is calculated as:

c c = ∑ q i + q j − − ∑ q i + q j − / N ′ ( ∑ ( q i + ) 2 − ∑ ( q j + ) 2 / N ′ ) ( ∑ ( q i − ) 2 − ∑ ( q j − ) 2 / N ′ ) (4)

where, q i + is the mean discharge magnitude in window i of the positive half cycle and q i − the mean discharge magnitude in the corresponding window in

the negative half cycle; N ′ is the number of phase windows per half cycle. Thus, if the shapes are the same, then c c = 1 ; if they differ completely, then c c = 0 .

Phase asymmetry is:

P f = φ i n − φ i n + (5)

where, φ i n + and φ i n − are the inception discharge phase of the positive and the negative half of the voltage cycle. The phase asymmetry P f is used to study the difference in inception voltage of the positive and negative half of the voltage cycle.

As known from the aforementioned discussion, statistical parameters of the PD pulse sequence are useful to describe the distribution histograms of the several quantities of PD pulses. In general, it seems to be a better choice to use parameters which describe the shape of the distribution, rather than using absolute values which depend on the real data such as the mean value of the discharge magnitudes. Figure 7 shows 5 types of PD fingerprint acquired respectively, and each fingerprint contains 29 quantitative values, which is a set of unique spatial vectors that correspond to the PD events of the specified electrode configuration under periodic 50 Hz AC voltage. Therefore, these 5 types of PD fingerprint represent their intrinsic characteristics in the nature. In other words, five vector spaces are constructed and each is 29-dimension. Nevertheless, they are not directly utilized to carry out PD pattern classification. The reason is that due to the large number of data vectors, the structure of the classifier may be very complex and hence, the recognition algorithm cannot be completed successfully, then eventually the ideal classification effect may not be achieved.

As well known, the high-dimensional data space vector can be reduced to a low-dimensional space through related operations. This can not only reduce the data amount, but also convert complex problems into simple and easy-to-handle ones. There have been effective analytical methods applied in different fields of Artificial intelligence recognition for fault detection, diagnosis and prediction. Further, such methods have also been successfully applied in PD pattern recognition and fault classification [17].

One of the crucial issues in classification is the curse of dimensionality, hence, a low-dimension feature space is desired for simplifying calculation and reducing costs. Therefore, features should be carefully selected for preserving the maximum class separability. In our study, the criterion based on within and between-class scatter values is adopted as the measure of discrimination at a set of histogram values. The within-class scatter value measures the scatter of feature vectors of different classes around their respective mean values, and the between-class scatter value is defined as the scatter of the conditional mean values around the overall mean value [18] [19]. Therefore, the class separability criteria are expressed as follows:

1) Within-class scatter matrix:

S w = ∑ i = 1 M P i S i (6)

where, S i is covariance matrix of w i , which is calculated as follows:

S i = E [ ( x − μ i ) ( x − μ i ) T ] (7)

Here, P i is a prior probability of the class w i . Namely, P i ≈ n i / N , where n i is the sample number of w i in all samples N.

2) Between-class scatter matrix:

S b = ∑ i = 1 M P i ( μ i − μ 0 ) ( μ i − μ 0 ) T (8)

where, μ 0 is a global average vector μ 0 = ∑ i M P i μ i .

3) Mixed scatter matrix:

S m = S w + S b (9)

4) Distance separability criterion:

J = t r { S w − 1 S m } (10)

All in all, J presents the dispersion of vectors within the class and also the dispersion between the classes, and it is a criterion for judging the structure of vector space within a class and the separability between classes. A large value of J indicates that the space vectors within the class are reasonably constituted. The feature quantity extracted from the fingerprint of the class not only is able to completely characterize its similarity, but also can indicate that the distance between the classes is also large meaning that there is separation [20].

It is shown from Figure 7 that 29 characteristic quantities are included in fingerprint for each PD model. As evidenced by well-known theories and practices, too many characteristic quantities for recognition can make the structure of the neural network more complex and the training process more difficult and time-consuming. Therefore, it is a very important task to carefully select different combinations of feature quantities. This task not only requires a certain amount of practical experience and multiple experiments, but also it must be met principle of classification and verified by the class separability criterion. Hence, nine characteristic quantities are picked from the distribution function H q n ( φ ) in each fingerprint of PD models, which are respectively S k + , S k − , K u + , K u − , Q s + , Q s − , A, cc, P f . At the same time, the nine characteristics can be divided into 5 groups, the first group X₁ contains three quantities (A, cc, P f ), the second group X₂ has four quantities ( S k + , S k − , K u + , K u − ), the third group X₃ has five quantities ( S k + , S k − , K u + , K u − , A), the fourth group X₄ contains seven quantities ( S k + , S k − , K u + , K u − , Q s + , Q s − , A), and last group X₅ Contains all nine characteristic quantities ( S k + , S k − , K u + , K u − , Q s + , Q s − , A,cc, P f ).

Based on the distance separability criteria according to Section 3.1, we derive J X 1 = 177.3 , J X 2 = 41.9 , J X 3 = 1243.8 , J X 4 = 1905.6 and J X 5 = 1589.9 respectively. The Jvalues show that 5 groups of feature combinations all satisfy the requirements of classification and have obvious separability, and moreover, X₄ is particularly distinct.

In this study, Back-Propagation Neural Network (BPNN) is used as classifier. Numerous studies show that BPNN, a rich learning algorithm, achieves good performance in the presence of memory, and is well-preforming in PD pattern recognition as well. The BPNN structure is shown in Figure 8.

The BP algorithm is a form of supervised learning for the feed-forward ANN and it consists of two steps, namely forward and backward learning. Although the back-propagation algorithm can calculate the modified weights of the hidden layer in learning, there are several problems should pay attention to in the process of learning and training of BPNN. For example, the number of neurons each hidden layer, the initial weight settings, the setting of the learning step and inertial coefficient, and the case if the learning is trapped in local minimum, etc. These issues may affect the recognition performance of BPNN, and may even cause BPNN to fail to converge in the training process [21].

Among all 200 sets of samples for each type of PD fingerprint, 75 sets are as training samples, the other 75 sets take as test samples and the last 50 sets are as verification samples. The training function is “traingdx”, and the training error curves of characteristic quantities X₁, X₂, X₃, X₄ and X₅ are shown in Figure 9. Further, the number of hidden layer neurons is 6, 8, 10, 13 and 19 respectively. The recognition results are presented in Table 1.

It should be emphasized here that the five groups of curves in Figure 9 have implied the influence of neurons on the recognition results of the neural network. For X₁, X₂, X₃, X₄ and X₅, using the network structure of Figure 8, their input the number of feature quantities is 3, 4, 5, 7, and 9, respectively. Because the number of neurons in the input layer of each neural network should match it, the number of neurons in the input layer should be 3, 4, 5, 7, and 9, respectively. On this basis, the corresponding optimized neural network structure was obtained through repeated experiments. The corresponding number of neurons in the hidden layer of the neural network were respectively 6, 8, 10, 13 and 19, and the output layer of the neural network must be the number of neurons is 5, because this paper is to identify five PD patterns, and according to the machine learning criterion described in the literature [22], the convergence criterion of the neural network learning and training in this paper is given.

Table 1 shows that selected fingerprint can be a useful and informative characteristic to identify PD modes under the condition that the hidden layer neurons are 19 except x₃, but this does not mean that the more feature quantities, the higher the recognition result. Actually, the identification rate of characteristic quantity X₄ is the highest out of 5 sets of input feature vectors, because the vector x₄ best satisfies the class separability criterion.

How to select the number of hidden layer neurons is a very complex issue, which often needs the designer’s experience and numerous experiments. There are

currently no ideal analytic formulas and rules to follow. In this paper, the number of neurons in the hidden layer is chosen according to Kolmogorov’s theorem [23]. Table 2 shows that the hidden layer structure of BPNN has an obvious effect on the recognition results, especially for a certain type of electrode model. When the number of hidden layer neurons is 6 or above, the neural network can obtain a recognition rate of 100%. However, excessive hidden layer neurons in artificial neural networks may have the following problems:

1) The structure of artificial neural networks is too complex, which not only requires more time to train, but also increases the cost.

2) Because the network structure is too complex, its convergence becomes slow or even fails to converge.

3) Due to the complex network structure, its robustness and fault tolerance rate are greatly reduced.

To sum up, the artificial neural network structure optimization is also a technical problem that cannot be ignored besides the correct acquisition of the original signal of the PD, the determination of the PD mode class and the selection of a reasonable PD feature vector. As shown in Table 2, X₅ is a reasonable set of the PD feature vector in the midst of the PD fingerprint, and when there are 6 neurons in the hidden layer, the recognition rate of the network has reached 100%, which means that the network structure and performance at this time are the best, at the same time, having the best classification effect is a matter of course.