Synchronize multi level square wave signal to AC grid ?

Hi, I built a simple DC to AC inverter. The output of that inverter is about 11 levels voltage. Adding an Low Pass filter to it, smooth the shape of the output signal an it becomes more likely as a sinusoidal.

My question is: How to synchronize that signal with the grid signal ? - for example Fgrid = 50 Hz or 60 Hz.

I understand than I need to do V_out*sin(W*t + Phi) which is: V_out = 11 level voltages. W*t = frequency grid, letsay 100*PI. Phi = 0, 120, 240 - for tree phase.

Thanks for help, Henry