  We propose a framework to engineer synthetic-inertia and droop-control
parameters for distributed energy resources (DERs) so that the system frequency
in a network composed of DERs and synchronous generators conforms to prescribed
transient and steady-state performance specifications. Our approach is grounded
in a second-order lumped-parameter model that captures the dynamics of
synchronous generators and frequency-responsive DERs endowed with inertial and
droop control. A key feature of this reduced-order model is that its parameters
can be related to those of the originating higher-order dynamical model. This
allows one to systematically design the DER inertial and droop-control
coefficients leveraging classical frequency-domain response characteristics of
second-order systems. Time-domain simulations validate the accuracy of the
model-reduction method and demonstrate how DER controllers can be designed to
meet steady-state-regulation and transient-performance specifications.
