A mathematical model of a multi-phase power conversion system composed of modified bridge-elements (B-system) capable for parallel computation has been developed. Experimental validation on the example of a power system including a synchronous generator and an AC-DC rectifier has been performed. A mathematical algorithm for B-system assembly and steps to obtain mathematical model of the B-system have been developed. Integration of mathematical models of conversion system into the complete model of a multi-phase power system has been explained and evaluation of computational efficiency of parallel computation techniques for the developed model of an AC-DC-AC converter has been performed. The presented modelling method can be employed in the design phase of smart grids, for power quality and conducted emission analysis.