Probabilistic modeling of voltage asymmetry

A new formulation is proposed regarding power network imbalance. From symmetrical component theory, a random vector of imbalance is defined having two dimensions. The probability distribution of negative phase sequence voltage is calculated and used to derive a probability distribution for current harmonics generated by a six pulse power converter. Three applications of the theory are considered, the first concerns the validation of the model and the characterisation of imbalance observed on two networks, the second concerns the interaction between voltage imbalance and harmonic current generated by a power converter and the third application concerns the overheating of an induction motor subject to a random negative phase sequence voltage. The analytical nature of the model forms a compromise between simplicity of utilisation and the representation of complex phenomena