  Fault detection is vital in ensuring AC microgrids' reliable and resilient
operation. Its importance lies in swiftly identifying and isolating faults,
preventing cascading failures, and enabling rapid power restoration. This paper
proposes a strategy based on observers and residuals for detecting internal
faults in grid-forming inverters with power-sharing coordination. The dynamics
of the inverters are captured through a nonlinear state space model. The design
of our observers and residuals considers $H_{-}/H_{\infty}$ conditions to
ensure robustness against disturbances and responsiveness to faults. The
proposed design is less restrictive than existing observer-based fault
detection schemes by leveraging the properties of quadratic inner-boundedness
and one-sided Lipschitz conditions. The internal faults considered in this
paper include actuator faults, busbar faults, and inverter bridge faults, which
are modeled using vector-matrix representations that modify the state space
model of the inverters. One significant advantage of the proposed approach is
its cost-effectiveness, as it does not require additional sensors. Experiments
are conducted on an islanded AC microgrid with three inductive lines, four
inductive loads, and four grid-forming inverters to validate the merits of the
proposed fault detection strategy. The results demonstrate that our design
outperforms existing methods in the field.
