A simplified solution for bi-dimensional random-walks and its application to power quality related problems

In this paper, the random-walk approach is applied to the vectorial sum of harmonic currents injected in a network by distorting loads. It is shown that for stochastically independent vectors the joint distribution of the orthogonal components can be analytically expressed by multinormal probability density functions. Therefore, the determination of the resultant magnitude distribution would require an infinite sum of modified Bessel functions. In order to solve this problem, an approximate analytical solution, which shows good accuracy even when the number of connected loads is not large, is derived and discussed. The expressions presented can be usefully applied to power-quality related problems, such as compensation-system design, and can provide guidance for establishing standard limits to harmonic pollution