My controler sync with cable but with battery it blink

Got a weird trouble with my Wireless controler. If i try to power the console with the controler it doesn't work. when everything is on i push the sync button on both (console and controler) they both spin, flash like if they where sync but on the console the light power of and on the controler the whole circle blink green. If i take out the battery and just plug the usb charging cable, the controler sync right away and work like a charm. As soon i take out the cable and put back battery pack the same thing appen. look like sync but controler blink.

Any idea for that little trouble ?

Thanks