Connecting device for connecting two n-phase AC voltage grids (1, 3) of the same frequency, comprising n susceptance elements with continuously variable susceptance values in each case, wherein, by means of each susceptance element, two connecting conductors, that are associated with one another, of the AC voltage grids (1, 3) can be connected to one another and the exchange of active power between the AC voltage grids can be controlled by means of targeted variation of the susceptance values, characterized in that the connecting device comprises a transformer having - a first primary winding that is connected to a first connecting conductor of a first AC voltage grid, - a second primary winding that is connected to a second connecting conductor of the first AC voltage grid, - a third primary winding that is connected to a third connecting conductor of the first AC voltage grid, - a first secondary winding that is connected to a first connecting conductor of a second AC voltage grid by means of a first susceptance element, - a second secondary winding that is connected to a second connecting conductor of the second AC voltage grid by means of a second susceptance element, - a third secondary winding that is connected to a third connecting conductor of the second AC voltage grid by means of a third susceptance element, - a first tertiary winding that is connected to the first connecting conductor of the second AC voltage grid by means of a fourth susceptance element, - a second tertiary winding that is connected to the second connecting conductor of the second AC voltage grid by means of a fifth susceptance element, - a third tertiary winding that is connected to the third connecting conductor of the second AC voltage grid by means of a sixth susceptance element, wherein the secondary windings and the tertiary windings are each interconnected in star connections that generate a phase offset of pi/3 relative to one another and respectively pi/6 relative to the primary windings. the connecting device comprises a transformer having - a first primary winding that is connected to a first connecting conductor of a first AC voltage grid, - a second primary winding that is connected to a second connecting conductor of the first AC voltage grid, - a third primary winding that is connected to a third connecting conductor of the first AC voltage grid, - a first secondary winding that is connected to a first connecting conductor of a second AC voltage grid by means of a first susceptance element, - a second secondary winding that is connected to a second connecting conductor of the second AC voltage grid by means of a second susceptance element, - a third secondary winding that is connected to a third connecting conductor of the second AC voltage grid by means of a third susceptance element, - a first tertiary winding that is connected to the first connecting conductor of the second AC voltage grid by means of a fourth susceptance element, - a second tertiary winding that is connected to the second connecting conductor of the second AC voltage grid by means of a fifth susceptance element, - a third tertiary winding that is connected to the third connecting conductor of the second AC voltage grid by means of a sixth susceptance element, - a first primary winding that is connected to a first connecting conductor of a first AC voltage grid, - a second primary winding that is connected to a second connecting conductor of the first AC voltage grid, - a third primary winding that is connected to a third connecting conductor of the first AC voltage grid, - a first secondary winding that is connected to a first connecting conductor of a second AC voltage grid by means of a first susceptance element, - a second secondary winding that is connected to a second connecting conductor of the second AC voltage grid by means of a second susceptance element, - a third secondary winding that is connected to a third connecting conductor of the second AC voltage grid by means of a third susceptance element, - a first tertiary winding that is connected to the first connecting conductor of the second AC voltage grid by means of a fourth susceptance element, - a second tertiary winding that is connected to the second connecting conductor of the second AC voltage grid by means of a fifth susceptance element, - a third tertiary winding that is connected to the third connecting conductor of the second AC voltage grid by means of a sixth susceptance element, wherein the secondary windings and the tertiary windings are each interconnected in star connections that generate a phase offset of pi/3 relative to one another and respectively pi/6 relative to the primary windings.