Summation of probabilistic harmonic vectors [power systems]

A method of determining the magnitude of the sum of random harmonic vectors of arbitrary probability characteristics is presented. Utilization of summation technique, in conjunction with harmonic load flow, to evaluate net harmonic magnitudes due to distributed sources in both deterministic and stochastic networks is discussed. It is demonstrated and stochastic networks is discussed. It is demonstrated that the widely used form of probability density function of the magnitude of the sum of random vectors arises from simplification of the general expressions developed here. To assess its validity, a comparative study between the method developed and Monte Carlo simulation is carried out, showing good agreement. However, the analytical method is a lot faster and provides closed-form expressions for the probability density characteristics of the sum of random vectors