Vol.5 No.4 2013

Research paper : Evaluating Uncertainty for the Standardization of Single Cell/Stack Power Generation Performance Tests for SOFC (A. Momma et al.)−258−Synthesiology - English edition Vol.5 No.4 (2013) input quantities around the rated values. As an example, figure 4 shows the measurement data taken to calculate the sensitivity coefficient of the voltage to the unit temperature. When the rated value is 750 ºC and the fuel utilization rate is 70 %, the slope obtained at that particular point in the plot is the sensitivity coefficient. Generally speaking concerning the variation in the experiment for obtaining sensitivity coefficients, SOFC manufacturers make the measurements by varying input quantities, such as temperature and gas flow rate, around the rated values. For unit temperature, a variation of 50 ºC is normally used. Thus, we recommended in the draft standard that the range of the unit temperature for calculating the sensitivity coefficient be approximately ±50 ºC. The data in figure 4 can be obtained by measuring the I-V characteristics at a rated temperature and at ±50 ºC. We took this approach so that this measurement of the sensitivity coefficient would not pose an undue burden on the manufacturers. In some cases, it is simply not possible to measure the sensitivity coefficient, and thus it is not possible to evaluate uncertainty. Table 1 shows how to obtain the sensitivity coefficient for each input quantity in the SOFC test and whether it is possible to evaluate uncertainty. However, it may not be possible to evaluate uncertainty originating from fuel and oxidizing gas compositions. When gas is supplied using a mixture gas cylinder, for example, it is virtually impossible to independently change the concentration of one component gas of the gas mixture to measure its sensitivity coefficient, thus making it impossible to evaluate the impact of the uncertainty of a component gas on the voltage.5 An example of uncertainty analysis for the SOFC performance testTable 2 shows an example of uncertainty analysis (uncertainty budget table) conducted on the results of the Uf = 70 %Uf = 80 %slope at rated pointCell temperature / ℃Uf = 50 %Cell voltage / V8007507000.70.750.80.850.9Uf = 60 %Uf = 40 %Fig. 4 An experiment to calculate the sensitivity coefficient of the cell voltage to the temperatureThe variation range of the input quantity was set at about ±50 ºC.2.58E-018.60E-03expanded uncertainty ( k = 2 )1.29E-014.30E-03combined standard uncertaintyB9.31E-041.61E-03 V±(0.05 % of rdg+12digits)digital recorderB5.34E-049.25E-04 V±(0.1 % of rdg + 0.1 mV)isolation amplifier29A6.26E-053.22E-021.07E-03V/V1.00E+001.07E-03 Vcell voltage5.02E-010.87 Nml/min±(0.05 % of rdg+12digits)digital recorderBB2.89E+0150 Nml/min±1 % of full rangeMFC29A5.09E-012.88E-049.59E-06Vmin/Nml3.32E-07Nml/min2.89E+01air flow rateB4.05E-01MFC (calibrated by Dry cal)instrument29A8.68E-02variation5.26E-031.75E-04Vmin/Nml4.23E-04Nml/min4.14E-01fuel flow rateB7.80E-020.135 A ±(0.05 % of rdg+12digits)digital recorderB8.70E-030.015 A ±0.05 % of rdgshunt resistorinstrument29A1.83E-03variation1.64E-025.45E-04V/A6.95E-037.85E-02 AcurrentB1.01E+001.751 ℃ ±(0.15 % of rdg + 0.7 ℃)digital recorderB3.03E+005.253 ℃ ±0.75 % of rdg in degree Cthermo-couple (K, class 2)instrument29A4.90E-03variation1.24E-014.13E-03V/℃1.29E-033.20E+00 ℃cell temperaturestandard uncertainty in power (W)standard uncertainty in voltage (V)sensitivity coefficientdegree of freedomtype of uncertaintystandard uncertaintymaximum error boundaccuracyunceratinty factorinput and measurement parameterinstrumentvariationinstrumentvariation---------------Table 2. An example of an uncertainty budget table on the current-regulated rated power test using an SOFC single cell


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