PD features for pattern recognition

To apply the above artificial neural networks to partial discharge pattern recognition, the ANN data input is important. The input data should be able to fully represent different patterns in an effective way.

ƒ Two-dimensional statistical patterns

PD phenomena that occur in a dielectric medium is an inherently complex stochastic process, it is therefore very helpful in analysis to take the statistical characteristics into account. By measuring pulse distribution as a function of the phase angle, it is possible to obtain information about the phenomena that cause the pulse distributions. The following phase-position quantities need to be studied: the pulse count distribution Hn(ϕ), which represents the number of

observed discharges in each phase window as a function of the phase angle; Hqmax(ϕ), which represents the maximal discharge amplitude in each phase

window; the mean pulse height distribution Hqn(ϕ), which represents the average

discharge amplitude in each phase window as a function of the phase angle. Hqn(ϕ) is derived from the total discharge quantity in each phase window divided

by the total number of discharges in the same phase window.[40]

The time dependence of the pulse count phase distribution Hn(ϕ) and the mean

discharge patterns. The Hn(ϕ) quantity contains information of the intensity of

discharges as a function of their phase angle. The Hqn(ϕ) quantity allows noise

reduction due to the difference between the statistical characteristics of the discharge pulses and that of noise pulses as a function of phase angle. The resolution on the phase angle axis is determined by the number of phase windows. This number should be as large as possible to give higher precision, but this would decrease data processing speed and increase the computer memory required. It has been found that 200 phase windows can give reasonable and sufficient resolution. The number of magnitude windows is selected in the same way and 50 is found to be a reasonable quantity to give sufficient resolution.[40] Figure 43 shows the two-dimensional statistical pattern Hqmax(ϕ), Hn(ϕ) and Hqn(ϕ), for discharge signals from XLP cables under test, collected over 500 continuous power cycles.[45]

Fig 43 PD two-dimensional patterns

ƒ Three-dimensional ϕ-q-n patterns

In addition to the two-dimensional phase-related patterns, three-dimensional Phase-Charge-Number (ϕ-q-n) patterns may be used to analyse discharge signals.

Chapter 3 – Background Approach 61 This is the characterization of the partial discharges by their angular position on the AC cycle (ϕ), their relative magnitude (q) and their frequency per unit time (n). These three parameters may be used to construct a three-dimensional surface from which important features may be extracted.[45] Rather than the accumulative signal numbers and average signal amplitudes in each phase window, for PD measurement, ϕ-q-n represents the number of PD signals nij

having both phase position ϕi and amplitude qj. ϕ-q-n and is considered to be the

most complete form of graphical PD presentation.[45] Figure 44 shows the three- dimensional ϕ-q-n patterns for discharge signals obtained over 500 power frequency cycle.

Fig 43 PD three-dimensional ϕ-q-n pattern

The downside to this approach is the number of phase and magnitude windows required to give reasonable and sufficient resolution. The number of windows needs to be limited so that the calculation times for the ANN are not unreasonably long.

ƒ Statistical operators

In reality, 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, equal discharge patterns may be expected. Therefore the Hn(ϕ) and Hqn(ϕ) quantities

are characterised by two distributions: for the positive half of the voltage cycle Hqn+(ϕ), Hn+(ϕ) and for the negative half of the voltage cycle Hqn-(ϕ), Hn-(ϕ).

[45] To study the difference between the distributions Hqn+(ϕ) and Hqn-(ϕ) in

both halves of the voltage cycle the following statistical operators may be used: Discharge asymmetry is the quotient of the mean discharge level of the Hqn(ϕ)

distribution in the positive and in the negative half of voltage cycle:

Phase asymmetry is used to study the difference in inception voltage of the Hqn(ϕ) distribution in the positive and negative half of the voltage cycle:

Cross-correlation factor is used to evaluate the difference in shape of distribution Hqn+(ϕ) and Hqn-(ϕ).

Thus, the differences between the distributions Hqn+(ϕ) and Hqn-(ϕ) are described

by three independent parameters: phase asymmetry, discharge asymmetry and cross-correlation factor. A cross correlation CC=1 means 100% shape symmetry and a value of 0 indicates total asymmetry. However, CC tells nothing about the height of the distribution. For that purpose the discharge asymmetry or phase asymmetry are used. Both these variables are defined in such a way that they are equal to 1 in the case of fully symmetric distributions and smaller than one in the case of asymmetric ones. Thus several asymmetry factors can be easily combined by multiplication. Therefore the operator MCC is introduced as follows:

The modified cross-correlation factor is used to evaluate the differences between discharge patterns in the positive and the negative voltage cycle. This is defined as the product of phase asymmetry, discharge asymmetry and cross-correlation factor. It is known that in the case of a single defect, discharge parameters can be fairly well described by a normal distribution process. Therefore to get a better evaluation of Hn(ϕ) and Hqn(ϕ) quantities, several statistical parameters typical

for normal distribution can be used:

Skewness (Sk) is an indicator for the asymmetry of a distribution with respect to a normal distribution. Sk is zero for a symmetric distribution, positive when the distribution is asymmetric to the left, and negative when the distribution is asymmetric to the right.

Chapter 3 – Background Approach 63 Kurtosis (Ku) is an indicator for the sharpness of the normal distribution. Ku is zero for a normal distribution. For a sharper than normal distribution it is positive, and if the distribution is flatter than the normal distribution Ku is negative.

Figure 44 shows an example for the above relationship. If the above statistical operators are used as the ANN input parameters, the scale of the input data for pattern recognition reduced to a few values. In a practical application, a number of tests for each defect would have to be carried out and several observations made for the same type of PD source to estimate the statistical operators. For each of the statistical operator the mean value would then be calculated and used for pattern recognition. The effectiveness of using statistical operators for PD pattern recognition needs further proof. [45]

Fig. 44 Distribution with different Skewness and Kurtosis

x_i f(x_i) Sk=0.68 Ku=0.1 x_i f(x_i) Sk=0 Ku=-0.95 Sk=-0.68 Ku=0.1 x_i f(x_i) Sk=0 Ku=0.95 x_i f(x_i)

Chapter 4