  The paper discusses the relationships between electrical quantities, namely
voltages and frequency, and affine differential geometry ones, namely affine
arc length and curvature. Moreover, it establishes a link between frequency and
time derivatives of voltage, through the utilization of affine differential
geometry invariants. Based on this link, a new instantaneous frequency
estimation formula is proposed, which is particularly suited for unbalanced
systems. An application of the proposed formula to single-phase systems is also
provided. Several numerical examples based on balanced, unbalanced, as well as
single-phase systems illustrate the findings of the paper.
