A Simplified Equivalent Model for the Analysis of Low-Frequency Stability of Multi-Bus DC Microgrids

In this paper, a simplified equivalent model is proposed to investigate low-frequency (LF) stability of dc microgrids. This is done by using an impedance-based approach considering exact models of microgrid components. In order to apply the impedance-based stability criterion, a multi-bus dc microgrid is first categorized as multiple interconnected single-bus dc microgrids. Then, each single-bus system is classified into two subsystems: subsystem#1 which only includes voltage-controlled (VC) DGs and subsystem#2 which includes the rest of the dc microgrid components. It is shown that due to the absence of LF interaction between subsystems, the dominant LF modes of a single-bus dc microgrid are mainly determined by the droop controllers of VC-DGs. The studies also show that the droop controller of each VC-DG accounts for the LF complex conjugate zeros at the output impedance of each VC-DG; and the internal interaction among these zeros can result in LF poles, which are the origin of LF current/power oscillations in dc microgrids. Through further analyses, it is shown that our findings for single-bus dc microgrids can be extended to any multi-bus dc microgrid as well. Owing to this fact, a simplified equivalent model, which can lead to the order reduction of the overall system, is proposed for the analysis of LF stability of dc microgrids. Thanks to the simplicity and generality of the proposed equivalent model, the effect of different parameters, such as number of VC-DGs, internal voltage controller of VC-DGs, and the microgrid line impedances on the LF stability of dc microgrids is comprehensively investigated. The studies also show that the LF stability of a dc microgrid is approximately independent of droop types (current or power). A complete set of simulation studies are provided which further supports the effectiveness of the proposed model.