Whatever current sensor you are using, the current sign is easily obtained by either using a comparator or - if you are using some microcontroller - numerically.

Regarding the converter control, usually a microcontroller is involved these days. If you want to go for a controller-less implementation, virtually any FPGA should do. ("CPLD"s are rare these days.)

are there any problem of incertain current sign (when the current is in neighborhood of 0 )

There is always a problem with uncertainty around zero.

The usual approach (whether in the analog or digital domain) is to add an appropriate low-pass filter in the input signal's path plus some hysteresis.

In the digital domain one might even add some PLL or FLL as the grid's frequency is quite stable, meaning that the zero crossings are predictable with high reliability.

thank you U. Dreher