96 grand marquis turns off and on

I have a 96 grand marquis 4.6L. Cranks fine but when i start going all the power turn off and on off and and car jerks etc. If i hit the gas real slow it won't do it too bad. Once i get a little speed it stops doing it it's only on my take off the radio, headlights, instrument cluster all loose power. I had the alternator tested its fine i just bought a brand new battery last week any ideas?