Empirical approach to determine open-circuit voltage of a vanadium-redox-flow battery for models, based on published data for anion-exchange and cation-exchange membranes and temperature dependency
B.Kleinsteinberg, S.Klick and Dirk Uwe Sauer, Journal of Energy Storage, April 2020, Vol. 28
Vanadium-redox-flow batteries (VRFB) are the most commercialized flow batteries. Many models are designed to improve several parameters and setups to increase the efficiency or decrease costs. The open circuit voltage (OCV) inside VRFB models is either modelled based on state of charge (SOC) or the vanadium ion concentrations. In both cases a form of the Nernst equation is used to approximate the OCV and feeding the Nernst equation with results from measurements or theory. Measurements to approximate the OCV at a SOC are state of the art. The theoretical input for the Nernst equation still lacks of precision and approaches to increase the precision, were studied in the last decade. Here an empirical approach shows possible improvements to link the measured OCV with the theoretical SOC. The improvements are performed by fitting mathematical functions to the differences between the theoretical and measured data with leas square. This is performed for anion exchange membranes (AEM) with great success. The mean error for the approach of Zlotorowicz et al. is below 1% with a maximum error of 3%. The fitting functions is interpreted as effects influencing the energy conversion processes, like crossover, changes in material characteristics and further side reactions. Fitting the cation exchange membrane (CEM), using the same approach, proves to be more challenging. The mean error is 1.9 to 2.8% with a maximum error of 23%, which shows different approaches might improve CEM based VRFBs. The processes inside a stack with a CEM follow different processes than for AEMs and slight connection to other energy conversion systems with flow cells could be drawn. The temperature dependency shows further influences than defined in by the Nernst equation, for a VRFB. Depending on the approach the temperature shifts the OCV curve along the SOC range or changes all four fitting parameters. The results show possibilities and helps to choose from different approaches of modelling the correlation between ion concentration and SOC for AEM and CEM with temperature influences.
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