For a Vienna type rectifier, unbalanced grids introduce twice the fundamental frequency ripples in dc-link voltage and input active/reactive power. To eliminate the input power ripple, the common current reference generation strategy, such as dualframe hybrid vector control, can be adopted to maintain constant input power and eliminate ripples in dc-link voltage under light unbalanced grids. However, this control method does not work when under severe unbalanced grids. The theoretical operation area of the constant power control method under unbalanced grids is analysed in this study, furthermore, a compromised control method, which injects a small amount of input power ripple and makes a compromise between the working area and the output voltage ripples, is proposed. The control method can work when the grids have severe unbalance. The experimental operating area of constant power control is presented. The performance comparison and waveforms of three control strategies under different unbalanced grids are given.