Kalman filter is used widely in harmonics detection in power system, where, the quality of the Kalman filter depends on having accurate predicting values based on a mathematical model of the harmonics in power system. It required an exact knowledge of the harmonics’ orders, and this is difficult especially that in some of power system apparatus the order of harmonics may change during their operation. For that reason an adaptive Kalman filter combined with Fast Fourier Transform FFT is proposed to determine the orders of harmonics that should be modelled in Kalman filter, in order to reduce the error in the estimated signal.
Słowa kluczowe: Kalman filter, FFT, Harmonics, Power System.
Filtr Kalmana może być wykorzystywany do określania harmonicznych w systemie energetycznym. Dokładność określania harmonicznych zależy od dokładności predykcji. W celu poprawy dokładności adaptacyjny filtr Kalmana jest wspomagany szybką transformatą Fouriera.
Keywords: filtr Kalmana, harmoniczne w systemie energetycznym, FFT
Harmonics are existed in power system due to the power electronics devices, nonlinear loads and Photo Voltaic PV plants.. etc , where the Total Harmonics Distortion THD is not fixed, and it may increase rapidly under certain operating conditions, such as low radiation in PV system . The increment of THD may be due to the increment of the harmonics amplitude or the increment of the numbers of the harmonics’ components in the signals. Many of passive and active filters have been used to estimate the fundamental component in distorted input signal, where exact value of the fundamental signal is necessary for the protection devices to work probably. Kalman filter is one of the most of filters that have been used in power system and power system apparatus for different purposes - especially for harmonic signal estimation in power system- and it showed a better performance compared to other filters , but it is required to model the system exactly which means that all the harmonics in the signal must be modelled. It has been discussed in details the effect of harmonic modelling in the Kalman filter in , and it was concluded that the best performance of Kalman filter achieved, when all the harmonics in the input signal are modelled, and it was also concluded that, estimating extra harmonics, which are not existed in the measured signal, doesn’t affect the Kalman filter output. The error signal (difference between the input signal and the estimated output by the Kalman filter), becomes zero only when all the harmonics of the input signal are included in the Kalman model. The problem here, when the order of harmonics are changed, while the modelled harmonics are unchanged this will cause the error signal to exceed an acceptable limit, and the order of the estimated harmonics must be modified to reduce that error, for that reason an adaptive Kalman filter is proposed in this paper to model t [...]
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