Bi-directional solid oxide cell systems (Bi-SOC) are being increasingly considered as an electrical energy storage method and consequently as a means to boost the penetration of renewable energy (RE) and to improve the grid flexibility by power-to-gas electrochemical conversion. A major advantage of these systems is that the same SOC stack operates as both energy storage device (SOEC) and energy producing device (SOFC), based on the energy demand and production. SOEC and SOFC systems are now well-optimised as individual systems; this work studies the effect of using the bi-directionality of the SOC at a system level. Since the system performance is highly dependent on the cell-stack operating conditions, this study improves the stack parameters for both operation modes. Moreover, the year-round cumulative exergy method (CE) is introduced in the solid oxide cell (SOC) context for estimating the system exergy efficiencies. This method is an attempt to obtain more insightful exergy assessments since it takes into account the operational hours of the SOC system in both modes. The CE method therefore helps to predict more accurately the most efficient configuration and operating parameters based on the power production and consumption curves in a year. Variation of operating conditions, configurations and SOC parameters show a variation of Bi-SOC system year-round cumulative exergy efficiency from 33% to 73%. The obtained thermodynamic performance shows that the Bi-SOC when feasible can prove to be a highly efficient flexible power plant, as well as an energy storage system.