Optimal Configuration and Siting Analysis of VSGs Considering Spatial Differences in Frequency Dynamics

With increasing renewable-energy penetration and power-electronic interfacing, virtual synchronous generators (VSGs) are important inertia-support resources for low-inertia power systems. Existing VSG configuration studies mainly minimize investment cost or treat frequency-security indices as constraints, rather than directly optimizing siting from the perspective of frequency stability. This paper proposes a weighted rate-of-change-of-frequency (w-RoCoF) siting index for VSG configuration. The limitations of center-of-inertia (COI) theory in representing spatial frequency distributions are first analyzed. Then, based on frequency-divider (FD) theory, nodal RoCoF in multi-machine systems is analytically derived, and the w-RoCoF index is formulated to quantify system frequency stability while preserving nodal dynamic information. A multi-objective VSG siting and sizing model considering frequency stability and configuration economy is further established. Case studies on modified IEEE 9-bus and IEEE 39-bus systems show that w-RoCoF identifies critical locations more effectively than the COI index. In the IEEE 39-bus case, the proposed configuration reduces w-RoCoF by 50.7% compared with the cost-oriented scheme and reduces required virtual inertia by 19.7% compared with the frequency-stability-oriented scheme.