A virtual synchronous generator (VSG) control has been proposed as a means to control a voltage source converter interfaced generation and storage to retain the dynamics of a conventional synchronous generator. The storage is used to provide the inertia power and droop power in the VSG control to improve the frequency stability. Since the parameters in the VSG control can be varied

it is necessary for it to be tuned to be adaptive

in order to achieve an optimal response to grid frequency changes. However

the storage cannot provide infinite power and the converter has a strict power limitation which must be observed. The adaptive VSG control should consider these limitations

which have not been considered previously. This paper proposes an adaptive VSG control aimed at obtaining the optimal grid supporting services during frequency transients

accounting for converter and storage capacity limitations. The proposed control has been validated via hardware-in-the-loop testing. It is then implemented in storage co-located with wind farms in a modified IEEE 39-bus system. The results show that the proposed control stabilizes the system faster and has better cooperation with other VSGs

considering storage and converter limits.