M. Tucci, A. Floriduz, S. Riverso, and G. Ferrari-Trecate. Kron reduction methods for plug-and-play control of AC islanded microgrids with arbitrary topology. Technical report, Dipartimento di Ingegneria Industriale e dell'Informazione, Universit\`a degli Studi di Pavia, Pavia, Italy, 2015. arXiv:1510.07873
In this paper, we provide an extension of the scalable algorithm proposed in (Riverso et al., 2015) for the design of Plug-and-Play (PnP) controllers for AC Islanded microGrids (ImGs). The method in (Riverso et al., 2015) assumes DGUs are arranged in a load-connected topology, i.e. loads can appear only at the output terminals of inverters. For handling totally general interconnections of DGUs and loads, we describe an approach based on Kron Reduction (KR), a network reduction method giving an equivalent load-connected model of the original ImG. However, existing KR approaches can fail in preserving the structure of transfer functions representing transmission lines. To avoid this drawback, we introduce an approximate KR algorithm, still capable to represent exactly the asymptotic periodic behavior of electric signals even if they are unbalanced. Our results are backed up with simulations illustrating features of the new KR approach as well as its use for designing PnP controllers in a 21-bus ImG derived from an IEEE test feeder.