In this work we have provided a detailed analysis of the
quadratic droop controller, a tractable modification of conventional
droop control for application in islanded microgrids.
The special structure of quadratic droop control allows for
rigorous circuit-theoretic analysis methods to be applied to the
closed-loop system. A detailed analysis of system stability was
provided for several load models, along with an optimization
interpretation of the resulting decentralized controller. The
power sharing characteristics of the controller were analyzed,
showing that the controller interpolates between proportional
power sharing (in the low-gain regime) and power sharing
based on electrical distance (in the high-gain regime). Our
analysis results provide easily verifiable certificates for system
stability, and the proof techniques developed should prove quite
useful for related microgrid control problems.
The approach and techniques reported in this paper should
serve as a guidepost for further work on the following key
technical problems. While our results apply to microgrids
with uniform R=X ratios under a decoupling assumption, the
coordinate transformation used herein to treat uniform R=X
ratio microgrids (see Remark 1) has the side-effect of mixing
active and reactive power, making true active/reactive power
sharing difficult to implement. Relaxing these assumptions
may prove possible using recently developed analysis tools
such as power flow linearizations. The design of a simple,
decentralized, and provably stable droop-like controller for
voltage stabilization and power sharing in microgrids with nonuniform
R=X ratios remains an open problem.
While here we have addressed the problem of primary
control, the authors view secondary control for islanded microgrids
[6] as an area requiring new problem formulations
and increased theoretical attention. In particular, it is not clear
to what extent standard secondary control formulations such
as voltage regulation and reactive power sharing (adopted
from high-voltage systems and power supply backup systems,
respectively) are important in sub-distribution sized microgrids.