Grid-connected power inverters can be operated as virtual synchronous machines to mimic the characteristics of synchronous generators. In this manner

the inverter can participate in the frequency regulation and add virtual inertia to power systems. However

there is no index to describe the frequency response characteristics of power systems with virtual inertia provided so far

which results in the difficulty in optimizing the allocation of virtual inertia among virtual synchronous machines as well as evaluating the influence of virtual inertia on the frequency response characteristics of power systems. To deal with this problem

the H2 and H∞norms of the closed-loop transfer function(from angle perturbation input to frequency output)are utilized to describe the frequency response characteristics of the system. On this basis

the frequency response characteristics of conventional synchronous generator and virtual synchronous machine are analyzed. Furthermore

time-domain waveforms of frequency response verify the effectiveness of the method.