Battery Draining when Excellerating

I own a 2000 GMC Sonoma. When I hit the gas the battery drains but never shuts off, when at a regular speed the battery volts are normal. I have gotten a new battery and have had the alternator checked. I have replaced fuses and battery cables. Does anyone know what to check next or what the problem may be?

How do you know its draining?

Are the lights dimming?

Have you checked the actual voltage when this happens?