Statistical Properties of Voltage Unbalance Factor in Three-Phase Power Systems

Three-phase power systems under sinusoidal steady-state condition are commonly analyzed by means of the wellknown symmetrical component transformation. The main assumption underlying such a transformation is symmetry of the phases of a power system. In modern power systems, however, phase symmetry cannot be guaranteed for several reasons, e.g., large single-phase loads including high-speed railway systems. Nonsymmetrical phase condition results in negative-sequence voltages even if the three-phase source is balanced. This phenomenon is called voltage unbalance emission. Therefore, the ratio between the negative-sequence voltage and the positive-sequence voltage (i.e., the so called voltage unbalance factor, VUF) is defined to provide a quantitative measure of phase asymmetry effects. VUF usually takes small values (e.g., 1-2%) and therefore its measurement can be significantly affected by additive noise. In this work, the statistical properties of VUF are derived in closed form as functions of input noise level in a measurement system based on analog-to-digital conversion of voltage waveforms and spectrum evaluation through the discrete Fourier transform. In particular, it is shown that the magnitude of VUF can be regarded as a random variable with Rician distribution. Numerical simulations are performed in order to validate the probability density function, the cumulative distribution function, the mean and the standard deviation of VUF.