Statistical Analysis of Voltage Unbalance Emission Due to Asymmetrical Loads in Three-Phase Power Systems

This paper investigates the statistical properties of the voltage unbalance factor in a three-phase system due to an asymmetrical three-phase load with uncertain parameters. The parameters of the three-phase load are treated as random variables with Gaussian distribution. Random asymmetry in the three-phase load results in random values of the voltage unbalance factor. The probability density function, the cumulative distribution function, the mean value and the variance of the voltage unbalance factor are derived in closed form and numerically validated. The obtained results are useful to provide a quantitative description of possible effects of asymmetry in a three-phase load such as the connection of a large single-phase load.