Dynamic System Strength as Structured Stress Radii with Complete Contribution Allocation for Converter-Dominated Multiport Grids

Short-circuit-ratio-type indices describe the static fault level of a connection point but not how much network weakening, dispatch growth, or control-parameter drift a heterogeneous multiport system can absorb before a damping threshold or a stability limit is reached. This paper defines a dynamic system strength for systems with grid-following, grid-forming, modular multilevel converter, and synchronous-machine ports. The device–network return-difference matrix is normalized based on a power metric built from rated powers and port bases, which makes its frequency-band margin invariant to port units, base values, and power-preserving coordinate transformations. Network, dispatch, control, and model-uncertainty stresses form structured blocks, and dynamic strength is the largest multiplier of a task-specific stress set inside a safe set defined jointly by stability, performance thresholds, and an applicability flag. A first-boundary tracking algorithm with candidate-band refinement from eigenvalues or from frequency data alone reports radius bounds, the critical frequency, and the active failure mechanism, and radius changes are allocated completely to continuous and discrete resources based on Aumann–Shapley and Shapley values. On a three-port benchmark, three support resources raise the performance radius from 0.4884 to 1.4012 at an unchanged static proxy, and the normalized margin is unchanged under base changes with condition numbers up to 1000, whereas the raw singular value drifts by up to two orders of magnitude. On a converter-level test system with converters rated 1000, 100, and 10 MVA, the first boundaries are a return-difference threshold in the PLL–network band and the transfer limit of the weakened network, the allocation credits the PLL retuning of the large plant with 87% of the radius change and a non-binding damping resource with zero, and the applicability flag withholds the small-signal statement when the current limiters engage.