A model to describe the behavior of the probe of an atomic force microscope (AFM) operated in frequency modulation (FM) dynamic mode with constant excitation (CE) is developed, with the aim of describing recent experiments after the introduction of a noncontact piezoresponse force microscopy (PFM) method based on such an operation mode, named CE-FM-PFM (Labardi et al 2020 Nanotechnology 31, 075707). The model provides insight into improving the accuracy of converse piezoelectric coefficient (d 33) measurements on the local scale in this PFM mode. Its rather general applicability helps to quantify the residual electrostatic contribution in local piezoresponse measurements by AFM, which is anticipated to be strongly mitigated in the CE-FM-PFM compared to the more standard contact-mode PFM.