Small-Signal Stability Analysis of Power Systems by Implicit Multilinear Models

This paper proposes a new approach to perform small-signal stability analysis based on linearization of implicit multilinear models. Multilinear models describe the system dynamics by multilinear functions of state, input, and algebraic variables. Using suitable transformations of variables, they can also represent trigonometric functions, which often occur in power systems modeling. This allows tensor representations of grid-following and grid-forming power converters. This paper introduces small-signal stability analysis of equilibrium points based on implicit multilinear models using generalized eigenvalues. The generalized eigenvalues are computed from linear descriptor models of the linearized implicit multilinear model. The proposed approach is tested using a 3-bus network example, first by comparing time-domain simulations of the implicit multilinear model with those of the nonlinear model, and second by comparing the generalized eigenvalues with those of the linearized nonlinear model. The results show that the decomposed tensor representation of the implicit multilinear model allows for a faster linearization compared to conventional methods in MATLAB Simulink.