Out-of-step oscillation center and its location under multi-frequency oscillation are studied based on a three machine equivalent system. In the same unstable mode

units with different angles cause the oscillation center to migrate to differently modulated sides. The more distinct the different modulations

the greater the offset. Under multi-frequency oscillation

the out-of-step oscillation center still satisfies the condition that voltage is zero. There is only one section whose minimum voltage is equal to zero because of unit oscillation at the same moment

which is the out-of-step oscillation center. When the center appears

the equivalent two machine system power angle on both sides of the line where the center is located swings 180° apart. The maximum range of oscillation center migration is determined by the system impedance parameters. With the impedance parameters determined

the oscillation center migration direction is determined by the three machine system power angle variation tendency. The traditional criteria based on local information can hardly adapt to the multi frequency oscillation scenario. The criterion that the phase difference on both sides of the line swings 180° apart is able to accurately determine the moment the out-of-step oscillation center appears and its location under multi frequency oscillation.