Adaptive Regularized Numerical Differentiation of Noisy Signals with Application to RoCoF Estimation in Power Systems

The total variation regularization (TVR) is one of the methods widely used for numerical differentiation of noisy signals. In this method, an appropriate value must be assigned to the regularization parameter. Although various approaches have been proposed for this purpose, their practical application may still depend on problem characteristics, prior knowledge, or additional tuning. Consequently, reliable automatic selection of the regularization parameter remains an important issue. The goal of this study is to develop a new adaptive method for estimating the derivative of a discrete-time noisy signal based on the TVR. In this method, at any moment of time, first the optimal value of the regularization parameter is calculated for a fixed-length sliding window over the most recent samples. Subsequently, for the obtained optimal regularization parameter, the numerical derivative of the samples in the sliding window are computed. The main contribution of the proposed method is in the adaptive strategy developed for automatic selection of the regularization parameter from the data which assigns small values to the regularization parameter when the signal changes rapidly, and vice versa. The proposed method is used for accurate and effective rate of change of frequency (RoCoF) estimation in power systems under different circumstances.