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_i,φ_i), where the q_i are the pulse heights of the PDs and the φ_i are the corresponding phases. The resolution of this system is 50 mV in pulse height PH and 1° in phase. A 3D plot of the n(q_i,φ_i) is also generated. The statistical package generates the two parameters β₁, β₂ from the first four moments of the measured PH distributions n(qⁱ), which depend on the total sample size N, and the size of the voltage window ΔV. A Gaussian white noise source was used to generate an artificial PH array V_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 β₁, β₂ 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 β₁, β₂ space; similar random PH arrays V_i have been generated for a number of other distributions which map into more extensive regions of β₁, β₂ space. These new PH arrays were fed into the data processing part of the system to generate the corresponding β₁, β₂ for various values of N and ΔV 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 β₁, β₂ was again found for large N. However there is an overlap in β₁, β₂ space for the beta and Weibull distributions; strategies to overcome the lack of uniqueness will be discussed.