Delay Impact Kernel and Multiple Delay Coupling Mechanism during the Interaction of Coordinated DC Microgrids

With the increasing industrial usage of DC microgrids, this work concerns the time-delay issue during the microgrid interaction, which invariably takes time during operations. During the coordination of DC microgrids, time delays widely exist in the processes of information exchange. For the theoretical investigation, the time-delay model is firstly derived for such coordinated microgrid. Due to the infinite dimensionality incurred by the delays, the spectral delay space (SDS), as a preparatory step for the stability analysis tool, is employed to extract the critical delay spectra and their moving behaviors for the microgrid system. It is shown that the time-delay impact during the interaction is imposed through a closed kernel destroying the microgrid stability. To closely check the property of the delay impact kernel, especially the direction of the crossing behavior for purely imaginary roots, the concept of root tendency (RT) is profoundly analyzed and proved, which reveals the coupling mechanism of multiple delays. Over a testing system consisting of three DC microgrids, the proposed model and analysis are effectively implemented and verified. It is found that the delay impact kernel is periodical and bounded. Besides, the kernel can be divided into different areas according to the RTs, which indicates only partial kernel area will cause the unstable crossings due to the coupling of multiple delays.