Truncation Number Selection of Harmonic State-Space Model Based on the Floquet Characteristic Exponent

Abstract

Harmonic state-space (HSS) theory has been an effective method for studying system stability with time-periodic characteristics, such as modular multilevel converters (MMCs) and renewable power generation under unbalanced grid conditions. However, the original state-space formulation of the HSS model comprises infinite-dimensional matrices. Truncation is necessary before practical computing application. Therefore, this letter proposes a truncation number selection method for the HSS model. The theoretical basis of the proposed method is based on the Floquet characteristic exponent of the linear time-periodic model, which has a straightforward physical meaning. Finally, a case study of an MMC grid-tied system with tests in RT-LAB illustrates the validity of the proposed method.