A Family of Fundamental Positive Sequence Detectors Based on Repetitive Schemes

In electrical power systems, the extraction of the fundamental positive sequence (FPS) is paramount for synchronization, power calculation, and a wide variety of metering and control tasks. This work shows that a moving average filter (MAF) used in the synchronous reference frame to extract the FPS from electrical systems is equivalent to the cascade connection of a comb filter (CF) with a second-order harmonic oscillator (SOHO), with all its variables expressed in fixed reference frame coordinates. On the one hand, the CF introduces an infinite number of notches tuned at all integer harmonics of the fundamental frequency ${\omega }_0$, thus suppressing harmonic distortion in the incoming signal and acting as a repetitive-based pre-filter (RPF). On the other hand, the SOHO is responsible for delivering the fundamental component of the input signal with a unitary gain, while additionally reducing the effect of harmonic distortion. Then, it is shown that other RPFs built from previously reported repetitive schemes (all-harmonics, odd-harmonics, and the $6\ell \pm 1$ harmonics) can be placed instead of the CF, giving rise to a family of FPS detectors. In particular, this work also shows that the CF-SOHO is a special case of the FPS detector based on the all-harmonics RPF. This work provides the mathematical derivation of the FPS detector structure, tuning rules for the SOHO gain associated with each FPS detector, as well as experimental results under a reference signal subject to perturbations such as unbalance, harmonic distortion, phase, and amplitude jumps, exhibiting convergence in only half the fundamental period in most carried out tests.