Yes, active power is the transfer of power from one system to another one that will “do work”, i.e. heating or motion, as well as storing energy. Reactive power is a circulation of current in way that no “work” is done, but the exchange of power from onone that will “do work”, i.e. heating or motion, as well as storing energy. Reactive power is a circulation of current in way that no “work” is done, but the exchange of power from one system to another one will create a sustained oscillation, such as in LC tank. It is physically possible to design a single-phase inverter that will do both, you can use dq theory, or pq theory modified for single phase, or CPT, or simply PI controllers with a resonant term. However, the power electronics must always be designed to have the principles of power transference between two systems, as well as having free-wheeling path for current circulation for the power circulation.
Many thanks for your explanation can you recommend one paper in which both active and reactive power of a single-phase two-stage grid-connected PV system is controlled in alpha-beta (stationary) reference frame?