arXiv:2611.09796v1 Announce Type: new Abstract: The small-signal stability of a power system model with arbitrary loads is investigated, with a focus on locally constant power loads in lossless networks. A central element of the proposed analysis is the matrix H, which represents the partial derivatives of generator powers with respect to their relative angles. The local stability of any equilibrium point is determined by the properties of H if the loads consume locally constant power. Specifically, an equilibrium point is asymptotically stable if H is positive definite and unstable if H is full-rank and not positive definite, while several quantitative relationships between the eigenvalues of H and the system Jacobian matrix are also established. The main contribution is that loads are allowed to be arbitrarily located within the transmission network, thereby generalizing the existing H matrix stability criterion which is valid only if loads are located at the same buses as the generators. The advantage of the proposed criterion is demonstrated through case studies involving systems with up to 2869 buses. Accurate stability assessments are maintained, where alternative methods, such as the NRPS model, are found to be overly conservative. Additionally, a computational acceleration by a factor of 340 relative to Jacobian-based methods is achieved.