  Microgrids are increasingly recognized as a key technology for the
integration of distributed energy resources into the power network, allowing
local clusters of load and distributed energy resources to operate
autonomously. However, microgrid operation brings new challenges, especially in
islanded operation as frequency and voltage control are no longer provided by
large rotating machines. Instead, the power converters in the microgrid must
coordinate to regulate the frequency and voltage and ensure stability. We
consider the problem of designing controllers to achieve these objectives.
Using passivity theory to derive decentralized stability conditions for the
microgrid, we propose a control design method for grid-forming inverters. For
the analysis we use higher-order models for the inverters and also advanced
dynamic models for the lines with an arbitrarily large number of states. By
satisfying the decentralized condition formulated, plug-and-play operation can
be achieved with guaranteed stability, and performance can also be improved by
incorporating this condition as a constraint in corresponding optimization
problems formulated. In addition, our control design can improve the power
sharing properties of the microgrid compared to previous non-droop approaches.
Finally, realistic simulations confirm that the controller design improves the
stability and performance of the power network.
