During voltage dips continuous power delivery from distributed generation systems to the grid is desirable for the purpose of grid support. In order to facilitate the control of inverter-based distributed power generation adapted to the expected change of grid requirements, generalized power control strategies based on symmetric-sequence components are proposed in this paper, aiming to manipulate the delivered instantaneous power under unbalanced voltage dips. It is shown that active and reactive power can be independently controlled with two individually adaptable parameters. By changing these parameters, the relative amplitudes of oscillating power can be smoothly regulated, as well as the peak values of three-phase grid currents. As a result, the power control of grid-interactive inverters becomes quite flexible and adaptable to various grid requirements or design constraints. Furthermore, two strategies for simultaneous active and reactive power control are proposed that preserve flexible controllability; an application example is given to illustrate the simplicity and adaptability of the proposed strategies for online optimization control. Finally, experimental results are provided that verify the proposed power control.