César García-Veloso

arXiv2026

Instantaneous Complex Phase and Frequency: Conceptual Clarification and Equivalence between Formulations

This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive sequence operation, sole presence of electro-mechanical transient dynamics and absence of harmonics and interharmonics. To achieve this, the two fundamental definitions, i.e., those based on either the use of (i) analytic signals or (ii) space vectors, together with the premises used for their formulation, are presented and their relationship shown. Lastly, a unified notation and terminology to avoid confusion is proposed.

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arXiv2025

A Synchrophasor Estimator Characterized by Attenuated Self-Interference and Robustness Against DC Offsets: the DCSOGI Interpolated DFT

The second-order generalized integrator (SOGI), which can be used to attenuate the self-interference of the fundamental tone, is unable to reject DC offsets on the input signal. Consequently, the performance of any SOGI based synchrophasor estimation (SE) technique might be compromised in the presence of such DC components. The current work presents a SE algorithm which adopts and enhanced SOGI formulation, robust against DC, combined with a three-point IpDFT and a Hanning window. Two alternative formulations relying respectively on the use of two and three nominal fundamental period observation windows are proposed and assessed for simultaneous compliance with both phasor measurement unit (PMU) P and M performance classes. This is done by means of a simulated environment where all the operating conditions defined by the IEC/IEEE Std. 60255-118-1-2018 are evaluated simultaneously combined with a $10\%$ static DC and under two different noise levels. Furthermore, both formulations adopt a dedicated mechanism for the detection and correction of low amplitude $2^{nd}$ harmonic tones to ensure their compliance with the standard can be maintained in the presence of such disturbances even under off-nominal frequency conditions. Finally the resilience of both methods against multiple simultaneous harmonic interferences is also analyzed.

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