Effects of error in time-delay on AEPD source localization using newton's method: Numerical experimentation

Newton's method is one of the commonly used methods for acoustic emission partial discharge (AEPD) source localization in power transformers. The major problem in the AEPD source localization is the difficulty in accurately measuring the signal arrival time from the source to the multiple sensors. The exact instant at which the partial discharge (PD) occurs is not known. Therefore, instead of the absolute time, the time-delay in signal reception of each sensor with respect to the sensor nearest to the PD source is estimated. In the present study the effect of time-delay error on the accuracy of the PD source localization is analyzed through numerical experimentations. The solution of the Newtons's method in turn depends on the choice of the initial guess. Hence, different initial guesses are selected for Newton's method randomly. For a fixed set of coordinates for the four sensors and the PD source positions, the time-delays are theoretically calculated. The error is systematically increased in the calculated time-delay to form different groups of time-delays. The PD source is localized using each initial guess for all the groups of time-delays to analyze the effect of error in time-delay on accuracy of PD source localization. The error in time-delay greatly affects the AEPD source localization. Moreover, if Newton's method with a bad initial guess is used then the errors in AEPD source localizations are not systematic.