Correlation between uncertainties in system model parameters and distribution of critical electromechanical modes

Numerous studies conducted in the past broadly assume that normally distributed parameters of a power system, load parameter values in particular, within a given range would lead to normally distributed critical eigenvalues of the system, i.e., electromechanical modes. Normal distribution of input parameters however does not necessarily assure a Gaussian distribution of the output parameters due to various nonlinearities inherent to power systems. The uncertainties in input parameters will result in uncertainties in values of elements of reduced system state matrix from which the eigenvalues of the system are calculated. The relationship between model parameters and elements of reduced state matrix is non-linear as well as the relationship between state matrix elements and eigenvalues. This paper first shows that normally distributed system load bears no systematic distribution of electromechanical modes and then carries on to establish correlation, if any, between uncertainties in other parameters and critical modes.