Analysis of the resonance phenomenon in unmatched power cables with the resonance surface response

Power converters are an essential part of modern power systems, giving flexibility to the power transportation and allowing the insertion of a wide range of different energy sources. One drawback of the converters is that the supraharmonic conducted emissions introduced by them can compromise the stability of these systems through electromagnetic interference (EMI). Electromagnetic compatibility (EMC) filters are used to prevent such problems. Nevertheless, these filters are designed to respect standards based on measurements in conditions considerably different from real applications. Particularly, if a converter is connected to electrically long cables its conducted emissions may be amplified by the resonance phenomenon. The method described in this paper allows the definition of a range for the filters input impedances where the conducted emissions in a long cable will not be amplified beyond established levels. In some cases the method allows the visualization of three-dimensional surfaces indicating the magnitude, frequency and position of the resonance phenomenon. In the general case these surfaces are defined on higher dimensions and can be analyzed with deterministic optimization algorithms. The originality of this paper resides in the generalized analysis of the resonance phenomenon, that it is based on frequency-dependent cable parameters and applies to unbalanced systems.