Performance Simulation of Tubular Segmented-in-Series SOFC Using Simplified Equivalent Circuit

Abstract

In previous researches on SOFCs, various kinds of cell shapes have been proposed and many experimental and numerical studies have been carried out. Among them, tubular segmented-in-series SOFCs have an advantage that they can obtain high output voltage since a lot of single cells are connected in series along the cell tube. However, the majority of the numerical studies on SOFCs have been selected planer type as analysis target. In contrast, numerical works on tubular segmented-in-series SOFCs are relatively few. In the case of tubular segmented-in-series SOFC, the current flows along series-connected single cells. Hence, the current path in tubular segmented-in-series SOFC is relatively complicated in comparison with that in planar-type SOFCs. For this reason, a lot of resistance elements are required to make a highly accurate equivalent circuit applicable to simulations of tubular segmented-in-series SOFCs and, therefore, calculation load is very heavy in case no simplification is applied to the equivalent circuit. Hence, in order to simulate performance of tubular segmented-in-series SOFCs, the calculation load per single cell should be alleviated. Considering the above, a method to simplify the equivalent circuit used for the simulation of tubular segmented-in-series SOFCs is proposed in this study. As for the simplified equivalent circuit, a single cell is composed of an electromotive force, anodic and cathodic overvoltages and nine resistance elements. In order to reduce the resistance elements down to nine, the term of correction coefficient is introduced into the simple theoretical expression formula for resistance of each element. The reason of the above correction is to avoid overestimation of power loss due to limitation of current path caused by the rough area division of resistance elements used in the simplified equivalent circuit. With respect to the determination of the correction coefficients, before starting whole simulation of the SOFC tube, circuit simulations of a single cell are carried out for both of the simplified equivalent circuit with nine resistance elements and the detailed equivalent circuit with fine area division and current distributions are calculated for conceivable operating conditions. Based on the numerical results, the power loss of each resistance element is evaluated for both the simplified and detailed equivalent circuit cases. Finally, the correction coefficient of each resistance element contained in the simplified equivalent circuit is determined so as to equalize its power loss obtained through the simplified simulation with the total power loss of the resistances contained in the corresponding area obtained through the detailed simulation. Since the current distribution in the single cell changes depending on both operating temperature and output current, the correction coefficients of nine resistances are determined for various operating conditions. In order to incorporate the correction coefficients in the simulation program for whole tubular segmented-in-series SOFC, their interpolation equations in terms of the temperature and output current are created. By using the correction coefficients for nine resistance elements, the power loss attributed to the detailed current path inside the cell can be taken into account by the simplified equivalent circuit that uses only nine resistance elements. Based on the above proposed simulation method, the authors developed a simulation code for tubular segmented-in-series SOFCs. At first, to confirm the effect of the consideration of detailed current path on the results of the numerical simulation, the temperature distribution obtained through the simulation considering the correction coefficients is compared with that neglecting the correction coefficients. From this comparison, no significant impact of the consideration of the correction coefficients was observed concerning the temperature distribution. Next, the output voltage obtained by the simulation considering the correction coefficients was compared with that neglecting the correction coefficient. As a result, it was found that the output voltage considering the correction coefficients is higher than that neglecting the correction coefficient. The voltage difference was about 20 mV per single cell. In other words, the difference of the output voltage related to the complicate current path inside the cell becomes larger as single cells connected in series increase. This means the need to use some kind of equivalent circuit that can take detailed current distribution into consideration. Although the preprocessing is required to determine the correction coefficients of nine resistance elements, the equivalent circuit proposed in this study is simple but can practically calculate the influence of the detailed current path inside tubular segmented-in-series SOFC, indicating the effectiveness and usefulness of the proposed method.