Solid-oxide electrolyzer (SOE) based power-to-methane (PtM) system can efficiently store surplus renewable power into synthesis natural gas by electrolysis and methanation. The system performance depends on the operating point of the electrolyzer and system design, particularly the heat exchanger network. In this paper, we investigate a SOE based PtM plant with a fixed-bed catalytic methanator and a membrane module for methane upgrading. A top-down approach is first employed to derive optimal system designs step by step from the system concept, to optimal conceptual designs with the trade-off between system efficiency and methane yield, to design-point selection and heat exchanger network design. Then, exergy evaluation with the exergy calculated into thermal - mechanical - non-reactive - reactive parts is applied to the derived four specific system designs to understand how exergy dissipation and performance of the overall system and each component vary from one to another. The results show that the system efficiency can reach between 80 and 85% (HHV) or 75-80% (LHV) when operating SOE with an inlet temperature of 700 degrees C and a utilization factor over 60%, above which electrical steam generation can be avoided and the steam can be generated by the heat from methanation reaction (around 80-85%) and anode outlet (15-18%). The system's exergy efficiency can achieve around 75-80% with the input exergy mainly destructed within the SOE (25-35%), methanator (25-35%) and heat exchangers (10-17%). However, exergy efficiencies of the SOE and methanator are high, over 90%. Depending on the temperature level of the cold stream and the temperature difference, heat exchangers generally have an exergy efficiency of over 50-80%. The electrical steam generator can only achieve an efficiency of around 20% and leads to a significant drop of system efficiency if employed; however, small electrical heating to reach the desired SOE inlet temperature, although bad, is acceptable. Therefore, one preliminary design guideline for such systems should be the avoidance of electrical steam generation. (C) 2018 The Authors. Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.