Fault Diagnosis of a Direct Drive Wind Turbine Using a Bank of Goertzel Filters

Low-Cost Diagnosis of Rotor Asymmetries of Induction Machines at Very Low Slip With the Goertzel Algorithm Applied to the Rectified Current

“…The first step of the proposed approach consists in fixing the position of a narrow diagnostic frequency band that covers the whole load range, and halving its width. This solves the problem of missing the fault harmonics in case of frequency deviations, when their frequencies are the only ones computed, as in [26]- [28], and also eliminates the need of analysing disjoint narrow frequency bands that may contain the fault harmonics, whose position and width is load dependent, as in [30]. This step is done by rectifying the current signal before spectral analysis, either by using a hardware rectifier or by changing the sign of the negative current samples, as in [31].…”

“…Nevertheless, for diagnostic purposes, only the modulus squared of the Goertzel algorithm output is needed, according to (9), which can be calculated from (19) as [26] |…”

“…If this set is very small, its computational cost is much lower than the FFT of the whole current signal. The Goertzel algorithm has been used for obtaining only the fault harmonics of a permanent magnet synchronous generator in [26], using a bank of filters with a sampling frequency of 1 MHz, of an IM with bearing faults in [27] and with broken bars in [28]. Nevertheless, in these works, the exact position of the fault harmonics must be known before applying the Goertzel algorithm, which may result in misdiagnosis in case of small frequency deviations.…”

“…On the one hand, the use of the rectified current signal, as in [31], which allows to define a single diagnostic band that covers the whole load range, to halve its width, and to translate its lower frequency to zero frequency. On the other hand, the use of the Goertzel algorithm, implemented using real number arithmetic as in [26], but applied only to the frequency bins of the diagnostic band with minimum leakage, what eliminates the need of storing and windowing the full current signal. The combined use of the rectified current signal and the optimized implementation of the Goertzel algorithm produces a high resolution current spectrum in the full load range of the IM, with a negligible memory and code footprint and a reduced computational burden, what enables its implementation in online low-cost embedded devices, such as FPGAs and DSPs, or in modern smart sensors, mounted on the machine framework.…”