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This paper presents a new methodology for optimal design of transformerless Photovoltaic (PV) inverters targeting a cost-effective deployment of grid-connected PV systems. The optimal values and types of the PV inverter components are calculated such that the PV inverter Levelized Cost Of the Electricity (LCOE) generated during the PV system lifetime period is minimized. The LCOE is calculated also considering the failure rates of the components, which affect the reliability performance and lifetime maintenance cost of the PV inverter. A design example is presented, demonstrating that compared to the non-optimized PV inverter structures, the PV inverters designed using the proposed optimization methodology exhibit lower total manufacturing and lifetime maintenance cost and inject more energy into the electric-grid and by that minimizing LCOE.