EMT-Validated Branch-and-Bound Determination of Robust Small-Signal Stability Regions for Multi-Converter Power Systems Under Joint Operating, Control, Model-Error and Topological Uncertainty

Assessing additional converter capacity requires stability analysis under operating, control, device-model and network-topology uncertainty. This paper integrates structured singular value analysis with branch and bound to assess regions in engineering coordinates, including capacity, short-circuit ratio, synchronisation bandwidth and reactive support. Each box undergoes equilibrium screening and structured uncertainty analysis; candidate instability is confirmed by reconstructing a physical scenario and applying a winding-number test. On a nine-bus, six-device system, the computation assigns 8.34% of the domain to verified robust boxes, 38.80% to undecided boxes, 18.49% to boxes containing confirmed instability witnesses and 34.37% to boxes rejected by equilibrium screening. Verification on a 44-point frequency grid reduces the initial robust share from 19.01% to 8.34%. Under a fixed stressed scenario, the critical capacity is bracketed between 477.148 and 477.178 MW. An average-value electromagnetic-transient model reproduces the candidate device’s positive-rotation admittance with deviations of approximately 0.2% in magnitude and 0.2° in phase at eight frequencies, as well as the strongly unstable system growth rate to about 2%; switching simulations corroborate selected qualitative outcomes. The contribution is the integrated planning workflow. Its reported coverage depends on refinement and identification quality and remains conditional on sampled equilibrium and residual assessments and finite-frequency evaluation.