Synthesis of sinusoidal waveform references synchronized with periodic signals

This paper proposes a novel method to generate a sinusoidal waveform synchronized with any measurable periodic signal whose frequency is within a given neighborhood. The synthesized sinusoidal signal could be used as a reference current for certain applications of parallel active power filters or any other where such synchronization would be necessary (e.g., ac/dc converters for renewable energy resources, power factor correctors, power supplies, UPS, etc.) The method is based on the behavior of a dynamical system and avoids employing the usual combination of phase-locked loop (PLL) and lookup table found in most parallel active filters synthesizing a sinusoidal source current (a table also means using significant storage memory). The novel method produces two high-quality sinusoidal waveforms that are in quadrature and is applicable to those parallel active filters whose control methodology is in the alpha beta reference frame, or alternatively, it produces three sinusoidal waveforms shifted 120 degrees for designs that work in the abc frame. Here, a (2n + 1)th order implementation is described, including a proof of convergence. For its most simple implementation (n = 1), simulated and experimental results are included.