  This paper considers the control of AC-AC inter-linking converters (ILCs) in
a multi-grid network. We overview the control schemes in the literature and
propose a passivity framework for the stabilization of multi-grid networks,
considering both AC grid-following and AC grid-forming behavior for the ILC
connections. We then analyze a range of AC/AC interlinking converter control
methods derived from the literature and propose suitable controllers for this
purpose including both AC grid-forming and grid-following behavior. The
controller we propose is partially grid-forming; in particular, it is based on
a combination of a grid-following and a grid-forming converter to improve the
stability properties of the network. Simulation results and theoretical
analysis confirm that the proposed ILC control designs are appropriate for the
multi-grid network.
