Minimal Behavioral Contracts for Compositional Stability of Multi-Vendor Converter-Dominated Power Systems

Large converter-dominated power systems combine grid-following (GFL) converters, grid-forming (GFM) converters, and modular multilevel converters (MMCs) from different manufacturers, while complete control models are rarely available to any single operator. This paper asks which terminal information is sufficient for converting separately verified device behavior into a system-level stability statement and shows that this information is irreducible relative to the stated theorems, not in an absolute sense. A minimal behavioral contract is formulated from four constituents: an electrical port convention, a declared operating and frequency domain, an admissible multivariable terminal-dynamic set, and an internal-stability statement; analytical counterexamples show that none of these can be omitted. A network-strength homotopy and a port-level winding number give the exact number of unstable poles, and local integral-quadratic constraints or a structured robust condition then yield a three-way decision (robustly stable, robustly unstable, or undetermined) that accounts for sideband truncation, operating domains, and network uncertainty; exact Schur complements of a sparse bus-level matrix extend it to the complete system, and continuous-frequency covers with closed-form cell bounds replace frequency sampling. With contracts identified from noisy port records of protected models, no frozen decision contradicts the complete-model reference in 2592 compositions of a 49-state benchmark, 244 changed operating conditions, or 171 scenarios of a three-phase electromagnetic-transient benchmark with switching converters. The evidence is model-based and does not replace manufacturer, hardware, or field validation.