An Improved Bootstrap Method for Electromechanical Mode Estimation Using Multivariate Probability Distributions

Electromechanical modes must be estimated with a high level of accuracy in order for the estimates to be useful in helping to ensure reliable power system operation. To assess the accuracy of modal estimates, one would ideally use a Monte Carlo approach where several independent experiments would be performed on an unchanging system. However, in reality a power system is constantly changing, making Monte Carlo tests impractical. Therefore, bootstrapping has been applied to the task of estimating the accuracy of mode estimators. The previously proposed bootstrapping methods involved resampling residuals obtained from various algorithms, from which resampled mode estimates were obtained using a computationally intensive method that includes filtering and the reapplication of the modal estimation algorithm for each bootstrap. This paper proposes a more efficient method of bootstrapping by directly resampling the parameter estimates of an algorithm through the estimation of a multivariate probability distribution. The proposed method is compared with the old method using both simulated and measured data and is shown to retain the accuracy of the old method while significantly reducing the computation time.