  Inadequate frequency response can arise due to a high penetration of wind
turbine generators (WTGs) and requires a frequency support function to be
integrated in the WTG. The appropriate design for these controllers to ensure
adequate response has not been investigated thoroughly. In this paper, a safety
supervisory control (SSC) is proposed to synthesize the supportive modes in
WTGs to guarantee performance. The concept, region of safety (ROS), is stated
for safe switching synthesis. An optimization formula is proposed to calculate
the largest ROS. By assuming a polynomial structure, the problem can be solved
by a sum of squares program. A feasible result will generate a polynomial, the
zero sublevel set of which represents the ROS and is employed as the safety
supervisor. A decentralized communication architecture is proposed for
small-scale systems. Moreover, a scheduling loop is suggested so that the
supervisor updates its boundary with respect to the renewable penetration level
to be robust with respect to variations in system inertia. The proposed
controller is first verified on a single-machine three-phase nonlinear
microgrid, and then implemented on the IEEE 39-bus system. Both results
indicate that the proposed framework and control configuration can guarantee
adequate response without excessive conservativeness.
