Estimation of Electrical Power Quantities by Means of Kalman Filtering

The presence of non-linear loads and the increasing number of distributed generation power systems (DGPS) in electrical grids contribute to change the characteristics of voltage and current waveforms in power systems, which differ from pure sinusoidal constant amplitude signals. Under these conditions advanced signal processing techniques are required for accurate measurement of electrical power quantities. The impact of non-linear loads in electrical power systems has been increasing during the last decades. Such electrical loads, which introduce non-sinusoidal current consumption patterns (current harmonics), can be found in rectification front-ends in motor drives, electronic ballasts for discharge lamps, personal computers or electrical appliances. Current harmonics reduce the efficiency of low and medium voltage electrical grids (Dugan et al., 2003). It must be also considered that renewable energy sources in electrical grids can also deteriorate the electrical power quality. For instance, wind turbines can introduce flickering (Larson, 2000) and PV systems, due to solar radiance variations, generate variable output power. Moreover, such resources, especially in low-voltage systems, change their status (grid connection or disconnection) continuously, contributing to the electrical system instability. Diverse approaches can be applied to characterize electrical signal waveforms in real-time: windowed or recursive Fourier transforms, wavelets, artificial neural networks (ANN) (Bollen & Gu, 2006). Kalman filtering can be applied to estimate electrical quantities in power systems, such as voltage and/or current magnitude, grid balance and/or frequency. The obtained signal measurements can be employed for revenue purposes, electrical grid characterization and/or active compensation of power system disturbances. This chapter is focused on Kalman filtering based approaches for estimation of electrical power quantities, such as voltage amplitude, current harmonics amplitude or grid frequency, under sinusoidal, non-sinusoidal, balanced or unbalanced conditions. Moreover, steady-state signals and transients in power systems are also analysed. The second section in this chapter describes the characteristics of power quality disturbances in electrical grids, considering time and frequency domains. The following section reviews the applications of Kalman filters in electrical power systems. The fundamentals of Kalman and extended Kalman filtering techniques for estimation of power system signal waveforms are given in the fourth section. The implementations of Kalman filtering loops in MatLab/Simulink, as well as a new signal model for frequency estimation, are also given in this section. Section five will give the obtained simulation results under diverse conditions of the electrical grid. Finally, the conclusions of this chapter are shown. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg