The paper offers an approach to the investigation of the dynamics of nonlinear non-stationary processes with the focus on the risk of dynamic system stability loss. The risk is assessed on the basis of the accumulated knowledge about power supply system operation. New methods for power supply modes analysis are developed and applied as follows: linear discrete point knowledge-based models are developed for nonlinear non-stationary objects; wavelet analysis is used for non-stationary processes; stability loss risks are analyzed through the investigation of spectral decompositions of Gramians of these linear predictive models. Case studies are included