Electrogravitic drives are usually solid state (electronic) devices that claim to produce authentic antigravity and "warp drive" capabilities.
These drives begin to enter the realm of complex physics at this point, which I am virtually helpless to explain or even understand myself without several years of college. But there is one electrogravitic drive that I can comprehend.
It is the Alcubierre Warp Drive. Its theory of operation is based on the somewhat far-fetched existance of "Negative Matter", matter which repels all normal matter, just as normal matter attracts all other normal matter.
The concept is, assuming that negative matter exists, you take a hunk of normal matter, and bolt it to a hunk of negative matter via a strong, solid object. The normal matter will attract all matter, and the negative matter will repel all matter. This causes a gravitational imbalance favoring the normal side of the drive, causing the entire system to freefall towards the normal matter side of the drive, dragging whatever is attached to it along for the ride.
This would be the ultimate space drive. You have no moving parts, no ejection of matter, and most astounding of all, no expenditure of energy. This would appear do disobey the laws of thermodynamics. But remember, we're talking about natural gravity, which does not need to expend energy to accelerate objects. Drop a brick on your toe from two meters and see if the Earth breaks a sweat before you do.
If you want to experiment with this type of spacedrive at home, good luck. Even if negative matter is a common occurence in the universe, you'll need the resources of the entire planet to attempt to stockpile it from outer space.