This paper investigates the design of a Parallel Hybrid Converter topology for DC/AC applications connected using a three-winding transformer. The original Parallel Hybrid Converter (PHC) topology consists of a Silicon IGBT bridge and a partially rated Silicon Carbide MOSFET bridge with a shared DC bus. A common-mode inductor is needed in this topology to mitigate the circulating current between the two bridges. This paper introduces a novel variant of the PHC with a three-winding transformer that removes the requirement of the common-mode inductor. Component sizing optimisation for this topology is performed using a Non-Denominated Set Genetic Algorithm. A Long-Horizon Model predictive control method will be implemented into an FPGA controller that includes the MOSFET bridge's current limit constraint in the cost function. Experimental tests validate the performance of this topology and FPGA controller implementation, with an IGBT bridge frequency about 1000 Hz and grid-side output current THD below 3% achieved.