Frequency Evolution and Halving Behavior of Gas Bubble Deformation in Oil Under Power-Frequency AC Electric Fields

Bubbles generated in the oil-paper insulation reduce the dielectric strength and lead to insulation failure in power transformers. Previous studies have shown that under AC electric fields, bubbles typically deform at twice the power frequency, resulting in distortion of the electric field distribution in the oil gap. To explore bubble deformation characteristics during the AC pre-breakdown process, an observation platform with an 8-mm oil gap is developed to investigate a single air bubble with an initial diameter of approximately 2.5 mm. The periodic deformation of an air bubble under a stepwise-increasing 50 Hz AC voltage is systematically investigated via high-speed photography. A distinct frequency-halving phenomenon is observed, in which the dominant deformation frequency shifts from 100 Hz to 50 Hz with increasing voltage. At sufficiently high voltages, the deformation response becomes dominated by the 50 Hz component. Upon further increasing the voltage to 26.5 kV, the bubble enters a dynamically unstable state in the tested configuration, which can result in uncontrollable expansion and eventual gap breakdown. To elucidate the underlying physical mechanism, an asymmetric Duffing equation is formulated. The analysis reveals that this phenomenon arises from two distinct effects. First, the DC component of the electric force produces a static offset, which breaks the deformation symmetry and generates the 50 Hz component. Second, the nonlinear restoring force associated with surface tension induces a hardening effect, driving the shift of the deformation frequency from 100 Hz to 50 Hz. Compared with partial discharge monitoring, the observed change in bubble deformation frequency can also serve as an effective early-warning indicator of insulation failure.