Probabilistic Modeling of Negative-Sequence Current in Three-Phase Power Systems with Statistically Unbalanced Phases

In this work the parameters of an unbalanced three-phase component, such as a load or a transmission line, are described as random variables with known statistical properties. It is well-known that phase unbalancing leads to injected current in the negative-sequence circuit producing propagation of voltage unbalance and malfunctioning of power system components. In this paper, the injected current is described in probabilistic terms as a function of the statistical properties of the component unbalancing. In particular, approximate expressions for the probability density function, the mean value, and the variance of the injected current are derived in closed form and numerically validated.