electrical problem

Here's the scenario:
2004 Buick LeSabre with 77,000 miles.  When driving, the guages will all go to zero momentarily, then back to the operating conditions.  All lights on the dash come on, as if the car was just turned on, then off to operating condition.  The air condiitoner will also go off momentarily, then back to normal operating status.

The above only happens while the car is moving.  When in gear with brake applied (as in at stoplight) it does not happen.  It will happen if the car is moving, but in neutral.

Other electrical devices are not affected.  The radio continues to play, power windows will work properly, etc. if they are being used during this momentary blip.  The cruise control remains engaged and operating.

This happens consistently every 15 seconds when moving.

Ideas?????