Estimating electromechanical modes and mode shapes using the multichannel ARMAX model

A method of estimating the electromechanical modes and mode shapes from multiple synchrophasors is presented in this paper. The approach is based upon identifying the transfer function representation of the state space model of the linearized power system through the estimation of a multichannel AutoRegressive Moving Average eXogenous (ARMAX) model. The relationship between the transfer function and the ARMAX model, which is fully derived here, is shown to be general enough that virtually any multichannel ARMAX estimation algorithm may be applied to this approach. The two-stage least squares (2SLS) algorithm is used here for illustrative purposes. The proposed method is validated with the Monte Carlo procedure using simulated data from a reduced-order model of the Western Electricity Coordinating Council (WECC) system. The performance of the new method is compared with existing multichannel mode and mode shape estimation techniques and is seen to provide increased estimation accuracy with a decrease in computation time. The proposed method is further validated with measured data from the WECC system.