Conventional voltage transformers (CVTs) are still widely used as transducers in power networks, thanks to their high reliability, insulation capability, low drift over time and temperature. Their rugged construction is very often used as justification for skipping periodical tests and calibrations, that require putting them off-line, thus avoiding a time-consuming and expensive procedure. For this reason, in the last years, a growing interest has been addressed towards the study of online diagnostic and calibration procedures. The typical approach is based on the frequency response analysis that permits, under sinusoidal excitation, to detect possible deterioration of the behavior of CVT. Anyway, the real interest is to check the CVT fleet already installed and operating on the grid without requiring their disconnection from the grid. As well known, distribution grid voltage features a non negligible harmonic distortion, which may allow the online evaluation of the frequency response of the transformer, by simply connecting a reference transducer. Unfortunately, being the harmonics much lower than the fundamental, this approach cannot be employed in a straightforward way because of the nonlinear behavior of the CVT. This paper proposes an innovative condition monitoring technique of CVTs based on a simplified Volterra model. This opens the way to a new approach to the on-site characterization of CVTs, exploiting the actual voltage of the grid and thus not requiring its disconnection