Dynamic system eigenvalue extraction using a linear echo state network for small-signal stability analysis - a novel application

A large nonlinear dynamic system usually has complex dynamic modes corresponding to the system´s eigenvalues. These eigenvalues govern the system´s local behavior and thus are critical information for designing system operation and control strategies. Without the availability of the system´s analytical model, which is often the case for large nonlinear systems, the system´s eigenvalues need to be estimated. A linear echo state network (ESN) based method for extracting observable eigenvalues of a dynamic system together with the participation factors of these eigenvalues in the accessible system states is presented in this paper. A linear ESN is first trained to track the dynamic system´s local responses under injected small perturbation signals. The dynamic system´s eigenvalues are then extracted from the ESN´s weight matrices. Given the merit of fast training of ESNs, the ESN can be quickly retrained once the system operating point changes, and the system eigenvalues can be reestimated. Application of the proposed eigenvalue extraction method in the power system small-signal analysis is presented to demonstrate the effectiveness of the proposed method.