A Generalized Computational Method to Determine Stability of a Multi-inverter Microgrid

Microgrid-containing parallel-connected inverters, where each inverter is controlled by decentralized active power/voltage frequency and reactive power/voltage magnitude droop control laws results in flexible and expandable systems. These systems have been known to have stability problems for large values of active power/voltage frequency droop control gain. However, so far the stability analysis of multi-inverter systems has always been performed in a computationally intensive manner by considering the entire microgrid. In a practical microgrid, where the number of inverters may be large or the capacity of the units may differ, it becomes essential to develop a method by which stability can be examined without much computational burden. The system of differential algebraic equations has been simplified using justifiable assumptions to result in a final expression that allows the stability of the microgrid to be examined separately with respect to the droop control laws of each inverter transformed into an equivalent network. Moreover, the procedure allows taking into consideration the R/X ratio of the interconnecting cables. Analysis of final expressions validate the stability results reported in literature. Experimental results on hardware show the stable operation of the microgrid.