In this paper, the idea of operating an inverter to mimic a synchronous generator (SG) is motivated and developed. We call the inverters that are operated in this way synchronverters. Using synchronverters, the well-established theory/algorithms used to control SGs can still be used in power systems where a significant proportion of the generating capacity is inverter-based. We describe the dynamics, implementation, and operation of synchronverters. The real and reactive power delivered by synchronverters connected in parallel and operated as generators can be automatically shared using the well-known frequency- and voltage-drooping mechanisms. Synchronverters can be easily operated also in island mode, and hence, they provide an ideal solution for microgrids or smart grids. Both simulation and experimental results are given to verify the idea.

For linear systems described by $\dot x(t) = Ax(t) + Bu(t)$, where A generates a semigroup on the state space X and B is an unbounded operator, some necessary as well as some sufficient conditions are given for B to be admissible, i.e., for any t, the state $x(t)$ should be in X and should depend continuously on the input $u \in L^p $. This approach begins with an axiomatic description of such a system in terms of a functional equation. The results are applied to the wave equation on a bounded interval.