Currently the analysis of sympathetic inrush mechanism is usually based on no-load operating transformers. The complex sympathetic inrush when a transformer operates with load is studied less often. The analytical expressions for the transformers flux linkages

the source and load current

when one no-load transformer is energized and the other is operating with load

are derived to obtain the influencing factors and key characteristics of the complex sympathetic inrush. Besides

the impact of sympathetic inrush on the current differential protection for generators is analyzed. Digital simulation

dynamic simulation test

and the on-site recorded data have proved the validity.