Accurate Stability Analysis of Modular Multilevel Converters Modeled as Delayed Periodic Systems

The increasing use of modular multilevel converters (MMCs) raises system stability concerns, such as instability in a wide frequency range. Accurate stability analysis of such systems thus is urgently demanded. In this regard, the small signal modeling of the system can be described by a set of linear time- periodic (LTP) differential equations involving time delays, which requires much more effort. A generalization of the ordinary differential equation (ODE)-based harmonic state space (HSS) framework to delayed differential equations (DDEs), HSS-DDE for short, has been proposed to tackle time delays and periodicity within a unified framework. However, the authors found in practical application that this model produces erroneous results when the time delay involved is not an integer multiple of the period. Therefore, this paper first intensively analyzes the limitations of the HSS-DDE model, and then introduces the time-periodic infinitesimal generator and partial discretization idea to reconstruct an improved model that is not affect by the relationship between time delays and period. Thus, the stability of delayed periodic systems can be readily studied. The results of a numerical example and the grid-connected MMC system verify the accuracy and validity of the proposed model.