Variances in estimates of power system inter-area modes using lattice structure — initial results

Use of estimated inter-area modes as quantifiers of dynamic behavior of bulk power systems estimated is becoming widespread practice. Previously, authors proposed an order-recursive lattice algorithm to estimate an auto-regressive (AR) model, thereby the inter-area modes. The statistics of estimates are evaluated using Monte Carlo simulations. In this paper, new research for direct estimation of the variance of the mode frequency/damping for such a model is presented. It estimates the covariance of the reflection coefficients by using the matrix of all AR polynomials to diagonalize the sample correlation matrix. The covariance matrix of the reflection coefficients is related to that of the AR polynomial and then to that of frequency and damping estimates. Preliminary results using Monte Carlo simulations of power system models are presented. It is demonstrated that on an average, estimated variance compares well with the population variance and hence provides a good metric of the statistical error.