Application of set-theoretic method to assess the locational impacts of virtual inertia services on the primary frequency responses

Due to the increasing utilization of lightweight gas turbine units and renewable energy resources, the power grid is shifting towards a situation with less inertia, which results in the decline in system primary frequency responses and threatens the grid reliability. However, the capability of fast-acting storage devices to provide frequency response brings the operational flexibility into system dynamic performances. Therefore, it is of need to design a control algorithm to mimic the inertial responses using the fast-acting storage devices and to develop an appropriate tool to study the location-dependent impacts of the provided virtual inertia on the power system dynamic behaviors. This work explicitly applies the set-theoretic method to represent the effects of uncertain but bounded wind energy outputs and demand levels. The application of the set-theoretic methods significantly reduces the computational complexity by avoiding repeatedly running full transient stability simulations. Several illustrative simulation results are presented to verify the effectiveness of the proposed method and to demonstrate the locational dependence of the impacts of the inertia services on the system dynamic behaviors.