Vector SDE Based Stochastic Analysis of Transformer
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Abstract
In this research, the stochastic behaviours of
transformer have been analysed by using the stochastic
differential equation approach where both noise in the
voltage source applied to the transformer and the random
variations in elements and parameters of transformers have
been considered. The resulting vector stochastic
differential equations of the transformer have been both
analytically and numerically solved in the Ito sense where
the Euler-Maruyama scheme has been adopted for
determining the numerical solutions which have been their
sample means have been used for verification. With the
obtained analytical and numerical solutions, the stochastic
properties of the transformer’s electrical quantities have
been studied and the influences of noise in the voltage
source and random variations in elements and parameters
of transformers to those electrical quantities have been
analysed. The causes of high and low frequency stochastic
variations of such electrical quantities in both transient and
steady state have been pointed out. Moreover, further
extension of our stochastic differential equations and the
related mathematical formulations has also been given.
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