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Operating modern power grids with stability guarantees is admittedly imperative. Classic stability methods are not well-suited for these dynamic systems as they involve centralized gathering of information and computation of the system's eigenvalues, processes which are oftentimes not privacy-preserving and computationally burdensome. System operators (SOs) would nowadays have to be able to quickly and efficiently assess small-signal stability as the power grid operating conditions change more dynamically while also respect the privacy of the distributed energy resources (DERs). Motivated by all these, in this paper we introduce a framework that comprises a computationally efficient, privacy-preserving, distributed and compositional stability assessment method. Our proposed method first calls for representative agents at various buses to exchange information with their neighbors and design their local controls in order to meet some local stability conditions. Following that, the agents are required to notify the SO whether their local conditions are satisfied or not. In case the agents cannot verify their local conditions they can augment their local controls using a global control input. The SO can then warrant stability of the interconnected power grid by assembling the local stability guarantees, established by the agents, in a compositional manner. We analytically derive the local stability conditions and prove that when they are collectively satisfied stability of the interconnected system ensues. We illustrate the effectiveness of our proposed DSA method via a numerical example centered around a three-bus power grid.