Efficient Online Estimation of Electromechanical Modes in Large Power Systems F. J. De Marco, J. A. Apolin´ ario Jr. and P. C. Pellanda Instituto Militar de Engenharia Prac ¸a General Tib´ urcio, 80, Praia Vermelha, 22290-270 Rio de Janeiro, RJ, Brazil Emails: fernandojdemarco@gmail.com, apolin@ime.eb.br, pcpellanda@ieee.org N. Martins CEPEL P.O. Box 68007, 20001-970 Rio de Janeiro, RJ, Brazil Email: nelson@cepel.br Abstract—This paper investigates the performance of a fast converging adaptive filter, the Recursive Least Squares algorithm based on the Inverse QR Decomposition (IQRD-RLS), with an exact initialization procedure, for the online estimation of low- damped electromechanical modes in a power system. In this approach, the modes are tracked from ambient data, once it is assumed that load variations constantly excite the electrome- chanical dynamics as a nearly white noise input. Monte Carlo linear simulations are run on the full Brazilian Interconnected Power System model to generate power system ambient data. The performance of the IQRD-RLS algorithm is compared to that of the Least Mean Squares (LMS) algorithm when estimating the slowest interarea mode in the system. I. I NTRODUCTION Power systems exhibit electromechanical modes of differ- ent nature (from intraplant to interarea), whose frequencies typically range from 0.2 to 2.5 Hz. Some of these modes may show insufficient damping and their accurate online estimation constitutes a critical element in the development of situational awareness tools regarding oscillations to empower modern control centers [1]. Power system modal analysis can be accomplished by using two basic approaches: applying eigenanalysis to a small-signal model or optimally fitting a linear model to a measured system response [2]. Different measurement-based methods have been applied to the three types of measured data: ambient data, ringdown signals and probing responses. The adaptive filtering approach allows having a near real-time estimate of the dominant system mode characteristics based on measured ambient data, which can be collected from synchrophasor measurements captured by existing monitors that have been strategically placed in the power system. The basic assumption for this approach is that there are practically continuous random changes in the system loads that excite slightly the electromechanical dynamics of the system causing ripple-like disturbances which are known as ambient noise, in the measurements of voltage, current, and power signals. Assuming the random variations are white, the electromechanical modal frequencies and damping are estimated from the spectral content of the ambient noise [3]. This work was motivated by the IEEE Task Force Report on Identification of Electromechanical Modes in Power Systems released in June 2012 [4], which describes only a very simple adaptive filtering method to estimate electromechanical modes from ambient data, which is the Least Mean Squares (LMS) algorithm. The use of the standard LMS algorithm, the LMS with adaptive step-size, and a combination of them have been investigated in [5]-[9]. Although the LMS technique offers computational simplicity, its performance, apart from experiencing initialization problems, strongly depends on the correlation of the input signal. This paper investigates the implementation of an adaptive filter using the Recursive Least Squares algorithm based on the Inverse QR Decomposition (IQRD-RLS). RLS algorithms are known to have fast conver- gence even when the eigenvalue spread of the input signal correlation matrix is large. In [10], the application of the conventional RLS algorithm to the identification of power system modes based on measure- ment data is studied. To make the estimation less sensitive to the large deviation from the assumed noise models (due to outliers or ringdown data) than the conventional quadratic criterion, [10] proposes to change the loss function when large prediction errors are detected, and then use a Newton- Raphson-type method to solve recursively the Least Squares (LS) problem. This paper utilizes an improved RLS algo- rithm employing the QR decomposition to triangularize the input data matrix, leading to better numerical behavior [11]. Also, the Inverse QRD-RLS algorithm (IQRD-RLS) [12] pro- vides the filter’s coefficient vector at every iteration, allowing a direct mode estimation instead of an additional (back- substitution) routine to compute these weights (as needed by the conventional QRD-RLS algorithm). Aiming at a faster convergence without the odds of a soft initialization, we have employed an exact initialization scheme. We note that the numerical robustness comes with no extra computational com- plexity when compared to the conventional RLS algorithm, i.e., O[N 2 ] multiplications, where N is the order of the filter. To generate power system ambient data, Monte Carlo lin- ear simulations, assuming a random step disturbance vector applied to a set of load buses, are run on the full Brazilian Interconnected Power System (BIPS) model, released by the Brazilian System Operator (ONS) in June 2011 [13]. The 978-1-4673-4900-0/13/$31.00 c  2013 IEEE