Recently, small solid oxide fuel cell (SOFC) systems have been developed for various applications because of their high performance. In such small generation systems, quick and frequent start-stops are often required. However, it is generally considered that these start-stops with SOFC systems are not preferable because SOFC systems are operated at high temperature. Also, quantitative studies on the thermal behavior of small SOFC systems are limited. The purpose of this paper is to obtain insight into the possibility of using small SOFC systems with quick and frequent start-stops. A simple two-dimensional numerical model for $1kW$-class SOFC systems was fabricated to study this problem. The model consists of a cylindrical SOFC stack, a prereformer on the stack, a heat exchanger for exhaust gas, and a thermal insulator that covers the stack and the prereformer. Using this model, first, the characteristics of the power generation efficiency were estimated under various operating conditions. In addition, the validity of the modeling was verified. Next, the start-up dependence on their structure and operating conditions was investigated. Finally, for the cyclic daily start-up and shutdown (DSS) procedure, the total efficiency during a day was calculated when the energy loss during start-stops is considered. As a result of the analysis, the following points were found. First, the validity and accuracy of the modeling was established, and their efficiency under the rated condition becomes 60% (DC/HHV) at a steam-carbon $ratio=2.5$ and an oxygen $utilization=50%$. Next, the thickness of the thermal insulator $(0.03W∕m∕K)$ is required to be more than $6cm$ to reduce the heat loss from the outer surface of the thermal insulator to $<5%$ of the provided fuel energy $(2kW)$ under the rated condition. In this case, it takes ca. $150min$ to start, if the fuel (methane) flow rate is $3.02NL∕min$, which is equivalent to $2kW$ of heat flow. Finally, for the DSS operation, consisting of repetition of a $16h$ operation and an $8h$ stop in a day, the total efficiency decreases by ca. 1.5% from the rated power generation efficiency. Therefore, it is clarified that $1kW$-class SOFC systems can be quite suitable even in the case where quick and frequent start-stops are required.

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