# Under what conditions does a VSC require a DC-link capacitor?

For basic, conventional converters, such as the three-phase two- and three-level converters, the use of a DC-link capacitor makes sense to me. Considering only reactive power applications, it makes sense to me that a DC-link capacitor is necessary, since $$i_{ua}+i_{ub}+i_{uc}\neq0$$ where i_ua refers to the current in the upper arm of phase a, for example.

Then, in the case of the modular multilevel converter (MMC) (if it is used for solely reactive power purposes), we see that, in fact, $$i_{ua}+i_{ub}+i_{uc}=0.$$ So, in this case, I see that a DC-link capacitor is not necessary, since there is no need for current to be supplied that isn't already supplied by the other two phases.

Now, imagine we have an MMC that is operated like a two-level converter. That is, the upper and lower legs operate turn on and off instantly, and in complement to each other. In this case, would a DC-link capacitor be necessary?