Excitation inrush current is generated during no-load switching of the main transformer in a nuclear power plant. This current may cause sympathetic inrush in adjacent operating transformers and increase the three-phase current imbalance in auxiliary motors. It may also lead to misoperation of three-phase unbalanced protection. To address these issues, an expression for the inrush current during no-load closing of transformers was derived, with remanence introduced as an adjustable parameter. The findings show that pre-magnetizing the main transformer in the opposite direction to the closing magnetic flux can cancel out the residual magnetism and bias magnetism. Thus, the inrush current was effectively suppressed. Based on the analysis of the sympathetic inrush current expressions, it was concluded that the system impedance value greatly influences the degree of three-phase unbalance caused by the inrush. A simulation model of the primary circuit of a nuclear power plant with six generating units was constructed using PSCAD. The magnetizing inrush current, the sympathetic inrush current, and the unbalanced state of the medium voltage motor associated with the adjacent transformer during the no-load closing process. The effects of motor load levels and system contact impedance on the motor's three-phase unbalanced were analyzed. The results demonstrate that pre-magnetization can effectively reduce the three-phase unbalance and prevent misoperation of the asynchronous motor protection. This approach offers a new solution for protecting asynchronous motors affected by no-load closing of the main transformer.