Can i connect to nrf51 without advertising

[makouda]

I wonder if I can connect to my device without advertising in order to save energy just by knowing the device address

[xtting]

If you go detail into the BLE protocol. The connetion event can only do from the central device side, when & immediately after it recieve the broadcast package.

So, what you want is not under the BLE protocol. You can't.