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Section 4.2 Validation methodology A low RMSE value does not necessarily imply a good match of the end-of-charge and the end-of-discharge voltage. This is because the RMSE is dominated by the comparatively long period of time within the cycle, in which the voltage does not change significantly. Therefore, it is possible for a model to obtain a low RMSE, but still to have a significant deviation in the end-of-charge and/or end-of-discharge voltages. The deviation between the measured and the simulated end-of-charge and end-of- discharge voltage is defined as shown in Eq. (4-3). The maximum deviation over all cycles is taken as the deviation for the particular experiment. ∆ECharge,k,l EExperimenttCharge,k,l ESimulationtCharge,k,l ·100 % EExperiment tCharge,k,l (4-3) Wherein: k Counting index for experiments (-) l Counting index for cycles within an experiment (-) tCharge,k,l Time when the lth charging process of the kth experiment is finished (s) tDischarge,k,l Time when the lth discharging process of the kth experiment is finished (s) Combined quality criterion The criteria RMSEk, ΔECharge,k and ΔEDischarge,k can each serve as an individual quality criterion for the match of model and reality. However, it is preferable to obtain low values for all three criteria. Hence, a combined quality criterion taking into account the values of RMSEk, ΔECharge,k and ΔEDischarge,k is proposed, as shown in Eq. (4-4). Therein, the arithmetic mean of all three quantities is computed, with a double weight on RMSEk. ∆EDischarge,k,l EExperimenttDischarge,k,l ESimulationtDischarge,k,l ·100 % EExperiment tDischarge,k,l qk 14 2 RMSEk ∆ECharge,k ∆EDischarge,k (4-4) In two cases, the manufacturer deployed a constant voltage phase during the charging process. In these cases, only the discharging process shows the aforementioned distinct minimum in the stack voltage. The combined quality criterion is then defined as shown in Eq. (4-5). qk 13 2 RMSEk ∆EDischarge,k (4-5) The combined quality criterion is derived for each experiment. The largest value for all experiments of one particular manufacturer states on the overall match between model and stack of this manufacturer. 67PDF Image | Model-based Design Vanadium Redox Flow Batteries
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