  With the increasing penetration of distributed energy resources (DERs), it is
of vital importance to study the dynamic stability of microgrids (MGs) with
external control inputs in the electromagnetic transient (EMT) time scale. This
requires detailed models of the underlying control structure of MGs and results
in a high-order nonlinear MG control system. Higher-level controller design and
stability analysis of such high-order systems are usually intractable and
computation-costly. To overcome these challenges, this paper proposes a
large-signal order reduction (LSOR) method for MGs with considerations of
external control inputs and the detailed dynamics of underlying control levels
based on singular perturbation theory (SPT). Specially, we innovatively
proposed and strictly proved a general stability and accuracy assessment
theorem that allows us to analyze the dynamic stability of a full-order
nonlinear system by only leveraging its corresponding reduced-order model (ROM)
and boundary layer model (BLM). Moreover, this theorem also theoretically
provides a set of conditions under which the developed ROM is accurate.
Finally, by embedding such a theorem into the SPT, we propose a novel LSOR
approach with guaranteed accuracy and stability analysis equivalence. The
proposed LSOR method is generic and can be applied to arbitrary dynamic
systems. Multiple case studies are conducted on MG systems to show the
effectiveness of the proposed approach.
