Suggestion: The induction motor electrical equivalent circuit may be used to derive the Power Factor, PF, dependency on Frequency, Fs. There are various textbooks including the induction motor equivalent circuit, e.g.
Gordon R. Slemon, "Magnetoelectric Devices Transducers, Transformers, and Machines," John Wiley and Sons, Inc., 1966, Figure 5.21 on page 376 can be used to express PF=arctan[(Xe+XLr')/(Re+Rr'/s)], in per units,
Where
s is slip. It can be assumed approximately constant
Reactance Xe~Fs
(Xe is linked to Thevenin's theorem simplification of the equivalent circuit covering the stator impedance and magnetizing branch)
Re is similarly derived as Xe
Rr' is the rotor resistance transferred to the stator side
XLr'~Fs
(XLr' is rotor inductive reactance transferred to the stator side)
Hence, PF will be increasing with increasing frequency