Vol.5 No.4 2013
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Research paper : Evaluating Uncertainty for the Standardization of Single Cell/Stack Power Generation Performance Tests for SOFC (A. Momma et al.)−257−Synthesiology - English edition Vol.5 No.4 (2013) used to keep the temperature high. In our experiment, we set up the SOFC cell in the laboratory system we normally work on and employed the single-point control method for temperature control. Figure 3(a) shows the temperature distribution of an electrolyte-supported cell—a type of cell of which internal reforming characteristic is not expected to be sufficient enough—when hydrogen was introduced as fuel. The hydrogen gas was supplied from the center of a disc-plate cell and then was circulated to the periphery. The graph demonstrates that, regardless of the load level, the temperature distribution remained within approximately ±2 ºC of the average cell temperature. Judging from the allowable variation of approximately ±1 % of the set value endorsed by the proposed draft standard, we believed this to be a sufficiently acceptable level. In contrast, figure 3(b) shows the temperature distribution of an anode-supported cell when partially-reformed methane was used as fuel. This type of SOFC, unlike the electrolyte-supported cell, is expected to have sufficient internal reforming characteristic, which is one of the benefits of SOFC. From the graph it is evident that a decrease in the temperature at the inlet area occurred due to the endothermic reaction from the internal reforming of methane. While the temperature distribution varied according to the load level, it nevertheless remained within about ±3 ºC of the average temperature. If we could assume this temperature distribution as a local temperature variation within the cell, we judged that this degree of variation sufficiently falls within the allowable range even when internal reforming occurs. (Actual evaluation of the impact of temperature distribution is very difficult because local impedance changes as a result of temperature distribution, resulting in a change in current distribution.)As shown above, it was verified through experiments that atmospheric pressure and temperature distribution have little impact on uncertainty, and hence it was decided that they were not to be incorporated into the equation for uncertainty evaluation. In reality their impact on uncertainty is not small enough to be completely ignored, and they should ideally be included in the equation. However, it is not realistic to expect cell manufacturers to make measurements of such parameters as pressure dependence and temperature distribution for all types of cells they produce. In fact, very few studies have been published on the measurements of pressure dependence or temperature distribution such as those conducted for this paper. Moreover, even if temperature distribution is measured, it would be very difficult to estimate its impact on uncertainty. For this reason, it was fortunate, in the end, that the impact of these factors on uncertainty was small and that it was possible to achieve the goal of uncertainty evaluation even when these factors were omitted from the uncertainty evaluation equation. In addition, the draft standard provides that if there are multiple points of temperature measurement in a test unit, the manufacturer must determine the allowable range of temperature distribution in advance and conduct the measurements within that allowable range. In other words, as long as the temperature is measured within the range, it is not necessary to take into consideration the uncertainty resulting from temperature distribution.4.2 Uncertainty equation used in the draft standardGiven the circumstances described above, we proposed the following equation in the draft standard for evaluating uncertainty when the voltage of SOFC, V, is measured while input quantity, Xj, is being controlled. where u(X) is the standard uncertainty of X; subscript I is the uncertainty of measurement instruments; subscript F is the uncertainty due to variations; and is the sensitivity coefficient of measurand V to input quantity Xj. The last was to be determined through a laboratory experiment. In addition, it was decided that the sensitivity coefficient should be used to correct the value of the measurand multiplying the difference between the average value and the set value of an input quantity. Table 1 shows the input quantities to be evaluated by the uncertainty evaluation equation based on the circumstances and the experimental results shown above. In one of the Annexes to the draft standard, we showed the method of calculating the instrument uncertainty of temperature, current, flow rate, and voltage, as well as the method of calculating the uncertainty of the measurand by combining the instrument uncertainty and the uncertainty resulting from measurement variations. We believe that this approach ensures that the evaluation of uncertainty is conducted in a consistent manner without leaving the equation open to interpretation. 4.3 Relationship between measurand and input quantity (measurement of sensitivity coefficients)We proposed that the sensitivity coefficients used in the uncertainty equation are to be obtained by actual measurements. Because it was decided that the evaluation of uncertainty was to be made only at rated values, as mentioned above, the measurements of sensitivity coefficients were to be made by measuring the voltage while varying the

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