Abstract
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.
Highlights
THREE-phase power systems under steady-state sinusoidal conditions are usually analyzed by resorting to the wellknown symmetrical component transformation (SCT) [1]-[3]
A thorough statistical analysis foresees assigning a probabilistic distribution to the load deviations δZa, δZb, δZc, and deriving the corresponding statistical properties of Voltage Unbalance Factor (VUF) in (18) where δZp is a function of δZa, δZb, δZc according to (12)
An approximate model for the voltage unbalance emission based on the weak coupling assumption for the positive and negative sequence circuits in a three-phase power system with asymmetrical load has been derived
Summary
THREE-phase power systems under steady-state sinusoidal conditions are usually analyzed by resorting to the wellknown symmetrical component transformation (SCT) [1]-[3]. The lack of symmetry in a three-phase load results in a mutual coupling between the sequence circuits after the symmetrical component transformation. Since in many cases of practical interest the asymmetry level in a three-phase load can be regarded as a small perturbation with respect to the ideal symmetrical condition, in this paper a weak-coupling approach between sequence circuits is proposed [18]. In case of weak coupling the emission from the positive to the negative sequence circuit can be readily evaluated through a simple and approximate equivalent circuit consisting in a current-controlled voltage source depending on the load asymmetry.
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