Lagrangian method for deriving electrically dual power converters applicable to nonplanar circuit topologies

This paper proposes a novel method for deriving dual converters, namely deriving current-source converters from voltage-source counterparts, and vice versa. The conventional derivation method is based on the transformation of circuit topology, in which series connections are converted into parallel connections, and vice versa. However, this method cannot be directly applied to nonplanar circuits because they do not allow perfect topological transformation, although many of them are known to have duals. Lagrangian dynamics does not depend on the topological relation to transform a system into another equivalent system; therefore, it possibly avoids problems related to topological transformation and may provide a universal and systematic method that can be consistently applied to nonplanar circuits. This paper discusses the derivation of duals using Lagrangian dynamics. Along with the theory, this paper presents two examples of Lagrangian derivation of duals. One derives a dual of a planar circuit, to which the topological transformation is applicable. The other derives two duals of a nonplanar circuit. Consequently, these examples suggest that the proposed method is a prospective candidate for universal and systematic derivation of duals.