By simplifying a substation, a third-order non-autonomous ferromagnetic circuit with single-phase potential transformer has been obtained. Since the voltage is a sine function, by adding a time dimension to the circuit, it becomes a fourth-order autonomous circuit, and some simulation analysis is carried out on it. Studies show the existence of chaotic dynamical behavior in the circuit system, so that we can draw the conclusion that the excitation characteristic of the core has an important influence on the chaotic dynamical behavior of the circuit.