Abstract
In this work, we present a simple algorithm to calculate automatically the Fourier spectrum of a Sinusoidal Pulse Width Modulation Signal (SPWM). Modulated voltage signals of this kind are used in industry by speed drives to vary the speed of alternating current motors while maintaining a smooth torque. Nevertheless, the SPWM technique produces undesired harmonics, which yield stator heating and power losses. By monitoring these signals without human interaction, it is possible to identify the harmonic content of SPWM signals in a fast and continuous manner. The algorithm is based in the autocorrelation function, commonly used in radar and voice signal processing. Taking advantage of the symmetry properties of the autocorrelation, the algorithm is capable of estimating half of the period of the fundamental frequency; thus, allowing one to estimate the necessary number of samples to produce an accurate Fourier spectrum. To deal with the loss of samples, i.e., the scan backlog, the algorithm iteratively acquires and trims the discrete sequence of samples until the required number of samples reaches a stable value. The simulation shows that the algorithm is not affected by either the magnitude of the switching pulses or the acquisition noise.
Highlights
In a normal Alternating Current (AC) power system, the voltage varies sinusoidally at a specific frequency; usually 50 Hz or 60 Hz [1]
We propose a frequency detection algorithm to deal with the problem of capturing a single Sinusoidal Pulse Width Modulation (SPWM) signal cycle in a fast, automated and reliable manner
It is important to represent a single SPWM signal period in the Fourier analysis; otherwise, the amplitude non-existing harmonics could lead to a poor electrical diagnosis
Summary
In a normal Alternating Current (AC) power system, the voltage varies sinusoidally at a specific frequency; usually 50 Hz or 60 Hz [1]. By knowing the fundamental frequency, the number of samples and sampling frequency can be adjusted exactly; otherwise, they need to be adjusted by trial and error If these parameters are not adjusted correctly, the Fourier transform will not contain the actual spectrum of the original signal; resulting in discontinuities and spectral leakage; i.e., the spilling of energy centered at one frequency into the surrounding spectral regions [2,3]. To address this problem, the windowing technique is employed to reduce the amplitude of the discontinuities at the boundaries of each period, reducing spectral leakage [3]. In Appendix B, the autocorrelation for periodic functions is defined
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