how does a single-phase, two-wire inverter connect to the split phase grid?

SPT

I have a single-phase, two-wire grid-tied inverter, can i connect it to the split-phase grid directly? One to the L1 and one to the netrual.

BB.

What brand/model of GT Inverter do you have?

In general, if you have a 240 VAC GT inverter, then you connect to the Black+Red Wires (through a double pole breaker). Some (newer) GT inverters will have a white/neutral connection too (no current flow, just to check that the AC split phase power system is properly grounded/no broken neutral connections).

If you have a 120 VAC GT Inverter--You would connect to the Hot and Neutral of your split phase power system (and single pole breaker). And everything will work fine (appliances will work normally, your utility meter will slow down/stop/run backwards based on your GT inverter's output--And if the utility meter has the capability to turn backwards, and your utility supports it in their billing plan).

For safety, in North America, you are supposed to wire your GT inverter on its own branch circuit from the main panel. You are not supposed to use a "plug and play" GT inverter plugged into a standard home outlet.

-Bill