Static and dynamic analyses of three-phase rectifier with LC input filter by laplace phasor transformation

The phasor transformation applicable only to the static analysis of linear AC converters so far has been extended to the dynamic analysis in this paper. A complex LT (Laplace transformation) is newly adopted for the dynamic analysis of phasor transformed circuits. It is verified in general that any linear AC converter can be completely analyzed of closed form by the proposed transformation. A pseudo real Laplacian concept is proposed to deal with the delicate real part operation that appears in the phasor circuits of inverters or rectifiers, where conventional LT cannot be applied. The system stability of a time-varying AC converter in time domain is proved to be the same as that in complex frequency domain. A 7th order three-phase rectifier, degenerated to a 3rd order system, was fully analyzed and verified by simulations with great simplicity compared with the conventional D-Q transformation.