Vector space representation of signals for transient signal analysis in transformers and shunt reactor

Abstract

During the impulse testing of power apparatus, there were failures which are better visible in time domain spectrum of the measured transient signals (applied impulse voltage and responses of the apparatus) while others in frequency domain. Hence, testing engineer needs to utilize time or frequency domain spectrum or combination of both to make a final decision about the power apparatus. In this paper, the principles of vector space representation of signals are effectively adopted in the measured transient signals during the impulse testing of transformers and shunt reactor. It provides a better way to visualize the mutual computation between the measured transient signals through proper adoption of projection theorem, normalization and orthogonal matrix principles.In this context, the normalized transient signal due to reduced impulse voltage is considered to be first basis function. The next successive impulse sequences of the transient signals due to rated impulse test voltage are made mutually orthogonal to previous transient signals through projection theorem. The constructed orthogonal signal is normalized for formulation of orthonormalized basis signal. If the surge characteristic of the winding is changed due to faults during the rated impulse test voltage, then the mutual effective coefficient needs to identify the deviation based on ‘best mutual matches’ between orthonormalized basis signal and first basis function. The mutual effective coefficient makes a ‘best mutual matches’ through appropriate mathematical formulation to provide the occurrence or non-occurrence of faults. To express the performance of the mutual effective coefficient, 5 MVA, 7.5 MVA, 150 MVA transformers, 80 Mvar shunt reactor and 22kV interleaved disc winding are considered.