GFCI (Ground Fault Circuit Interruptor)
A GFCI receptacle is designed to prevent electrical shock. This device constantly monitors the current flow in the hot and neutral conductors.
The current in the hot and neutral conductors should match. If the current flow doesn't match, the device disconnects itself and any receptacles it protects from the electrical source.
Because the device does not actually check the ground current, it can be installed without a ground wire. A GFCI wired in this manner, or any receptacles protected by it, is required to be marked "NO EQUIPMENT GROUND" and is an allowable method of changing two-wire ungrounded receptacles to three-wire grounding receptacles.
Change the GFCI first, then if it still is tripping inspect the cord on the transformer really well for bite marks or damage.