Quasi Steady-State Frequency

J. Gutiérrez-Florensa, A. Ortega, L. Sigrist, F. Milano

IEEE Transactions on Circuits and Systems I: Regular Papers Vol. 73, nº. 4, pp. 2986 - 2998

Summary:

Accurate frequency estimation is critical for the control, monitoring and protection of electrical power systems. This paper introduces the novel concept of Quasi Steady-State (QSS) frequency as a quantity that fills the gap between stationary and instantaneous frequency. QSS frequency coincides with the fundamental frequency of an AC voltage in any stationary conditions, including unbalanced and non-sinusoidal, and is able to capture the time-varying fundamental frequency in transient conditions. The paper also proposes a metric borrowed from fluid dynamics, namely, the time derivative of the circulation, to define the scope of validity of the QSS frequency. Analytical examples as well as a case study based on a fully-fledged EMT model of the IEEE 39-bus system serve to illustrate, respectively, the properties of the QSS frequency and its behavior in transient conditions.

Spanish layman's summary:

Este artículo presenta el concepto de frecuencia de Cuasi-Régimen Permanente (QSS), una nueva magnitud que cubre el vacío entre la frecuencia estacionaria y la instantánea, y que se mantiene válida incluso en condiciones desbalanceadas o no sinusoidales. También se propone una métrica basada en la derivada temporal de la circulación para delimitar su validez, ilustrando sus propiedades mediante ejemplos analíticos y simulaciones.

English layman's summary:

This paper introduces the concept of Quasi Steady-State (QSS) frequency, a novel quantity that bridges the gap between stationary and instantaneous frequency, and remains valid under unbalanced and non-sinusoidal conditions. A metric based on the time derivative of the circulation is also proposed to define its domain of validity, with analytical and simulation-based examples illustrating its behavior.

Keywords: Frequency measurement, filtering, differential geometry, instantaneous frequency, Fourier transform.

JCR-JIF Impact Factor and WoS quartile: 5,600 - Q1 (2025)

DOI reference: https://doi.org/10.1109/TCSI.2025.3612501

Published on paper: April 2026.

Published on-line: September 2025.

Citation:
J. Gutiérrez-Florensa, A. Ortega, L. Sigrist, F. Milano, "Quasi Steady-State Frequency", IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 73, nº. 4, pp. 2986 - 2998, April 2026. [Online: September 2025] doi: 10.1109/TCSI.2025.3612501