Testing a statistical package for identifying pulse height distribution for a data acquisition system for partial discharges

A 2-channel data acquisition and processing system (DAPS) for partial discharges PD has been developed. It features a fast (20 MSa/sec) digitizer and can acquire up to 16 million samples per channel, yielding an array (q/sub i/,/spl phi//sub i/), where the q/sub i/ are the pulse heights of the PDs and the /spl phi//sub i/ are the corresponding phases. The resolution of this system is 50 mV in pulse height PH and 1/spl deg/ in phase. A 3D plot of the n(q/sub i/,/spl phi//sub i/) is also generated. The statistical package generates the two parameters /spl beta//sub 1/, /spl beta//sub 2/ from the first four moments of the measured PH distributions n(q/sup i/), which depend on the total sample size N, and the size of the voltage window /spl Delta/V. A Gaussian white noise source was used to generate an artificial PH array V/sub i/ for various values of N and these arrays were input into the data processing part of the system as a test. It was found that for large N (10000) that the /spl beta//sub 1/, /spl beta//sub 2/ approach the theoretical limit of (0,3) for a normal distribution as expected. Using standard formulas, which map the parameters governing a given distribution into /spl beta//sub 1/, /spl beta//sub 2/ space; similar random PH arrays V/sub i/ have been generated for a number of other distributions which map into more extensive regions of /spl beta//sub 1/, /spl beta//sub 2/ space. These new PH arrays were fed into the data processing part of the system to generate the corresponding /spl beta//sub 1/, /spl beta//sub 2/ for various values of N and /spl Delta/V as was done for the normal distribution. The new distributions include the beta, the gamma, the log-normal, and the Weibull; convergence to the theoretical limits for /spl beta//sub 1/, /spl beta//sub 2/ was again found for large N. However there is an overlap in /spl beta//sub 1/, /spl beta//sub 2/ space for the beta and Weibull distributions; strategies to overcome the lack of uniqueness will be discussed.