  The interaction among inverter-based resources (IBRs) and power network may
cause small-signal stability issues, especially in low short-circuit-level
grids. Besides, integrating static synchronous compensators (STATCOMs) in a
multi-IBR system for voltage support can deteriorate small-signal stability.
However, it is still challenging to fully understand the impact mechanism of
STATCOMs on IBR-induced oscillation issues and to design optimal STATCOMs'
control for dampening these oscillation issues in a multi-IBR system due to
complex system dynamics and varying operating conditions. To tackle these
challenges, this paper proposes a novel method to reveal how STATCOMs influence
IBR-induced oscillation issues in a multi-IBR system from the viewpoint of grid
strength, which can consider varying operating conditions. Based on this
proposed method, critical operating conditions are identified, wherein the
system tends to be most unstable. Moreover, we demonstrate that robust
small-signal stability issues of the multi-IBR system with STATCOMs can be
simplified as that of multiple subsystems under critical operating conditions,
which avoids exhaustive studies on many operating conditions with detailed
system models. On this basis, an adaptive control-parameter design method is
proposed for STATCOMs to ensure system robust stability under varying operating
conditions. The proposed methods are validated by a modified IEEE39-node test
system.
