Effects of Virtual Inertia on Stability and Power Sharing in Inverter-Based Power Systems

The emulation of inertia in inverter control has been shown to be structurally equivalent to the application of droop control with a first-order lag element as primary control strategy for inverters. Usually, the implementation of virtual inertia is motivated by the desire to improve the stability of frequency after a change in loads or the occurrence of a fault. But keeping the frequency inside its boundaries is only one of multiple control objectives the primary control level has to accomplish, besides voltage stability and power sharing in order to avoid overloading. Therefore, the effects of the inertia constant in inverter-based power systems-which can be represented by a combination of droop and time constant- on different control objectives are investigated. The design of the inverter controllers is carried out centrally via the minimization of the $H_{\infty}$-norm. It can be shown that implementing higher virtual inertia does not have a positive effect on all three control objectives simultaneously. As a result, a compromise between the objectives is sought, leading to specific inertia and damping constants.