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Purpose -This paper aims to provide a complete three-phase distributed constants model of cable-induction machine systems useful for EMC and overvoltages propagation studies. Design/methodology/approach -The paper considers a three-phase distributed constants model for the supply cable and a model of the same type for the induction machine. All the magneto-electric links between phases are considered. The Clarke transform is applied in order to reduce the analytical complexity of the obtained model. A new numerical method is also proposed for the integration of the resulting whole three-phase model, very similar, in terms of methodology, to the well-known finite differences models. Findings -The whole model for the three-phase drives is used for EMC and overvoltages propagation studies. The proposed examples highlight how, thanks to the Clarke model, the dynamic analysis of the three-phase drives in case of application of a standard fault source or an equivalent pulse width modulation (PWM) impulse, become easy to implement on a standard PC and with standard software (i.e. Matlab). The obtained results, compared with those that are presented in the literature, confirm the validity of the proposed model and numerical approach. Originality/value -The developed model is of a three-phase type because it is not possible to consider a single-phase equivalent model in case of asymmetric voltage sources (i.e. asymmetric faults or PWM inverter voltage supply). The model also includes all the magneto-electric couplings between phases that play a fundamental role in the considered applications.

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We consider quasi-linear elliptic equations involving the p-Laplacian with nonlinearities which interfere asymptotically with the spectrum of the differential operator. We show that such equations have for certain forcing terms at least two solutions. Such equations are of so-called Ambrosetti-Prodi type. In particular, our theorem is a partial generalization of corresponding results for the semi-linear case by Ruf-Srikanth (1986) and de Figueiredo (1988).