  Modern safety-critical energy infrastructures are increasingly operated in a
hierarchical and modular control framework which allows for limited data
exchange between the modules. In this context, it is important for each module
to synthesize and communicate constraints on the values of exchanged
information in order to assure system-wide safety. To ensure transient safety
in inverter-based microgrids, we develop a set invariance-based distributed
safety verification algorithm for each inverter module. Applying Nagumo's
invariance condition, we construct a robust polynomial optimization problem to
jointly search for safety-admissible set of control set-points and design
parameters, under allowable disturbances from neighbors. We use sum-of-squares
(SOS) programming to solve the verification problem and we perform numerical
simulations using grid-forming inverters to illustrate the algorithm.
