Adaline-based approaches for time-varying frequency estimation in power systems Damien Halbwachs * Patrice Wira * Jean Merckl´ e * * Laboratoire Mod´ elisation, Intelligence, Processus et Syst` emes (MIPS), Universit´ e de Haute Alsace, 4 rue des Fr` eres Lumi` ere, 68093 Mulhouse, France (e-mails: damien.halbwachs@uha.fr, patrice.wira@uha.fr, jean.merckle@uha.fr) Abstract: Two new neural approaches for on-line frequency estimation of a sinusoidal signal perturbed by harmonic distortions and random noise are presented in this paper. These approaches are based on an iterative formulation of the signal which is learned by Adaline neural networks. Adalines are very simple and efficient artificial neural networks, they can be easily implemented on a digital signal processor. The proposed approaches are therefore suitable for real-time implementations and their performance and robustness are evaluated by numerical simulations and experimentally under different severe operating conditions. The proposed neural estimators are favorably compared to the classical zero-crossing method, to an active notch filter method, and to a previous Adaline based-method. Furthermore, all these methods are also evaluated in terms of computational costs. Keywords: frequency estimation, frequency tracking, Adaline, artificial neural networks, power distribution network. 1. INTRODUCTION On-line frequency estimation of sinusoidal signals is a classical problem and has many practical applications. Frequency of power system voltages and currents is for example a key parameter in supervising and controlling the quality of the delivered power (Arrillaga and Watson, 2003). In this application, it is imperative to precisely know the fundamental frequency and the harmonics pa- rameters such as their magnitude and phase. Efficient filters can thus be designed for compensating for the har- monic distortions (Ould Abdeslam et al., 2007). Many algorithms have been proposed to evaluate the fre- quency content from discrete time samples of a measured signal. Most of them are frequency domain harmonic anal- ysis algorithms and are based on the Discrete Fourier Transform (DFT) or on the Fast Fourier Transform (FFT). These methods however suffer from three main drawbacks, aliasing, leakage and picket-fence effect (Joorabian et al., 2009). To overcome them, the Fourier algorithm can be associated to a Zero-Crossing (ZC) technique (Djuric and Djuriic, 2008). Combining both methods allows to provide the fundamental frequency of a measured signal corrupted by higher-order harmonics. The ZC-technique is a simple and well-known method which can be used as a standalone frequency estimator. Its principle relies on calculating the number of cycles within a predetermined time interval. However, this method is sen- sitive to noise and is often combined with other methods like least squares algorithms (Sadler and Casey, 2000). Kalman or extended Kalman filters are other important alternatives for frequency estimation. In (Dash et al., 1999), an extended Kalman filter is based on a state space formulation of a three-phased voltage vector obtained with the well-known αβ-transform. Nevertheless, Kalman filtering for frequency estimation is really efficient only with three-phase signals. Phase-Locked Loops (PLLs) are also well-known signal processing techniques used for frequency measurement. In (Akagi et al., 2007) for example, a PLL has been developed for three-phase signals. This PLL is based on a fictitious instantaneous active power expression and allows frequency estimation, under distorted and unbalanced voltage waveforms. It determines automatically the system frequency and the phase angle of the fundamental positive- sequence component of a three-phase generic signal even under highly distorted and perturbed system voltages. Frequency estimation can also be achieved through an Adaptive Notch Filter(ANF). An ANF is a second-order notch filter that is further furnished with a nonlinear differential equation to update the frequency. In (Karimi- Ghartemani et al., 2005), an ANF is adapted and inserted in the context of power systems. The proposed ANF is used for estimation of power system frequency and its performance is compared with that of a PLL approach. Recently, Artificial Neural Networks (ANNs) approaches have been developed for on-line frequency estimation. Hopfield neural networks, i.e., a type of recurrent ANN, have been successfully employed in (Lai et al., 1999). Adaline-based approaches have also been proposed (Dash et al., 1997; Ai et al., 2007). Whatever the architecture, ANNs have to be appropriate for a real-time frequency evaluation. The neural network implementation, but also the computational costs of the learning algorithm, must be compliant with the real-time constraint of this application. D. Halbwachs, P. Wira, and J. Mercklé, "Adaline-based approaches for time-varying frequency estimation in power systems" 2nd IFAC International Conference on Intelligent Control Systems and Signal Processing (ICONS 2009), Istanbul, Turkey, September 21-23, 2009.