  Virtual inertia is an effective control approach to attenuate sudden voltage
changes during transient events in low-inertia DC grids. While methods have
been proposed to implement virtual inertia, its impact on DC grid stability in
the presence of constant power loads (CPLs) remains unclear. In this paper, we
perform a rigorous stability analysis for DC grids with CPLs powered by
virtual-inertia-enhanced converters. We derive a closed-form stability
criterion that can be used to evaluate the impact of virtual inertia on the
system stability, and demonstrate that, given a set of system parameters, the
stability of a DC grid powering CPLs can be improved for a range of virtual
inertia designs. We provide analytical expressions for the optimal virtual
inertia that improves stability and for the maximum virtual inertia that does
not deteriorate stability. In addition, we present a step-by-step guideline to
design a stable DC grid with virtual inertia. Test results are presented to
validate the analysis.
