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The transformerless photovoltaic (PV) inverters are the major functional units of modern grid-connected PV energy production systems. In this study, a new optimisation technique is presented for the calculation of the optimal types and values of the components comprising a transformerless PV inverter, such that the PV inverter levelised cost of the generated electricity is minimised. The proposed method constitutes a systematic design process, which is capable to explore the impact of the PV inverter configuration on the trade-off between the PV inverter manufacturing cost and the power losses affecting the corresponding energy production. The design optimisation results demonstrate that the optimal values of the PV inverter design variables depend on the inverter specifications, the technical and economical characteristics of the components used to build the PV inverter and the meteorological conditions prevailing at the installation area. Compared with non-optimised transformerless inverters, the PV inverter structures derived using the proposed design optimisation methodology exhibit lower manufacturing cost and simultaneously are capable of producing more energy into the electric grid system.