Electromechanical Mode Estimation in the Presence of Periodic Forced Oscillations

Electromechanical modes are inherent to any interconnected power systems which provide a measure of the small-signal stability margin of the system. A number of algorithms have been developed for the estimation of these modes using synchrophasor measurements. However, most of these algorithms are not designed to operate in the presence of forced oscillations (FO). These FOs are results of periodic rogue input driving the system. When FOs are present, estimates of system modes can be biased depending on the frequency and the amplitude of the FOs. To tackle this problem, a new algorithm is proposed in this paper to estimate system modes in the presence of FOs. In the proposed method, the over-determined modified Yule-Walker method which is used to estimate autoregressive coefficients of an autoregressive moving average (ARMA) signal model is extended to an ARMA with exogenous input (ARMAX) model that incorporates the presence of FOs. Two versions of the proposed method are included in this paper based on the requirement of the information of the duration of FOs in the signal. Results obtained by implementing the proposed algorithm on simulated data and real-world data validate the effectiveness of both versions of the proposed method.

I. Introduction

Power systems consist of a sophisticated network of transmission lines inter-connecting different generators and loads spread over a wide area. These interconnections, while improving system reliability, increase complexity level of the system giving rise to their own set of challenges, electromechanical oscillations being one [1]. These oscillations are the natural response of power systems associated with system modes, which contain information on the small–signal stability margin of the system. Mathematically, these modes are given by the eigenvalues of the system state matrix and are characterized by frequency and damping ratio. For a system to have a reasonable small–signal stability margin, damping ratio of all the system modes must be greater than some value, typically 3–5% [2]. A system event such as a critical line or generator trip can cause a decrease in the damping ratio of a system mode indicating that the system moved toward a less stable region, as was observed in the 1996 western grid outage [3]. Thus, continuous monitoring of these modes can provide critical information on the system stability margin and can help thwart an impending system outage by enabling a timely action.