Time-delay stability switching boundary determination for DC microgrid clusters with the distributed control framework

In a DC microgrid cluster, distributed DC microgrids are integrated to manage diverse and distributed energy resources. Without the reliance on a management center, the distributed control framework is capable of the cluster deployment by only adjacent collaborations. However, the communication among microgrids and the formation of dispatch signals inevitably lead to time delays, which might cause the system disorder and multiple delay couplings. Considering these unstable effects, the lack of time-delay study challenges the cluster stability and burdens the energy application. The key contributions of this paper are the definition and detection of the time-delay stability switching boundary for the DC microgrid cluster with the distributed control framework, which reveals time delays switching the system stability and proves the delay-induced oscillation. Through the established time-delay model and the proposed method based on the cluster treatment of characteristic roots, the explicit time-delay stability switching boundary is detected in the delay space, which forms a determination flow of five stages: (1) system initialization: according to the cluster parameter values, the established time-delay model is initialized; (2) space transformation: applying the space mapping and the rationalization, the Sylvester resultant is constructed in the spectral delay space; (3) spectral boundary sketch: in uniformly divided blocks, spectral boundaries are found from the resultant; (4) crossing root calculation: with the spectral boundaries, crossing roots are calculated solving the characteristic equation; (5) boundary determination: back-mapping the spectral boundaries with the crossing roots, the overall boundary is presented. Comprehensive case studies are performed to study the time-delay stability switching boundary and to validate the proposed approach. The boundary existence and feature demonstrate the time-delay effect. Furthermore, the classified stable areas are revealed as well as the relevant strategies for the stability enhancement.