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UnderstandininggththeeVVaannaaddiuimumRRedeodxoFxloFwlowBaBttaetrtiesries 3357 Salt Charge V2+ VSO4 ↑ Discharge Electrolyte ↓ Anolyte ↑ Anolyte ↑ Catholyte ↓ Catholyte V3+ V4+ or VO2+ V5+ or VO2+ 0.5 V2(SO4)3 VOSO4 0.5 (VO2)2SO4 ↓ ↓ ↑ Table 2. The different vanadium ions with their corresponding salt, their concentration variation during the charge and discharge of the VRB, and the electrolyte where they are dissolved. 1.8 1.6 1.4 1.2 1 Cell voltage 15 1.8 1.7 1.6 10 1.5 Cell voltage Cell volt age Experimental Analytical 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 state of charge [−] Concentration 1.4 1 7.5 0.75 7 0.5 6.5 0.25 6 1.3 5 1.2 1.1 1 0.9 2+ Va 5+ nd V 3+ Va + H 4+ nd V 0 5.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 state of charge [−] State of charge [−] (a) (b) Fig. 3. (a) Top: Cell voltage versus the state of charge at 25◦C. Bottom: Protons H+ and vanadium concentrations. (b) Comparison between the Nernst equation (3) and the experimental data published in (Heintz & Illenberger, 1998). The red bars represent the difference between the analytical and experimental data. 3. Electrochemical model The main electrochemical relations governing the equilibrium voltage where introduced in the previous section. In order to have an electrochemical model of the VRB, it is now necessary to describe how the vanadium concentrations vary during the battery operation. 3.1 Concentration of vanadium ions We see clearly from (1) that during the redox reactions, the vanadium ions are transformed and that some protons H+ are either produced or consumed. Therefore, the ion concentrations must change in the electrolyte to reflect these transformations which depend on how the battery is operated. For example, when the battery is charged, V 2+ and V O2+ are produced and their concentrations increase; and V3+ and VO2+ are consumed and thus their concentrations diminish. This process is reversed when the battery is discharged. Tab. 2 summarizes the direction of the change for each species. Concentration of vanadium [mol/l] voltage [V] + Concentration of H [mol/l] Difference between experimental and analytical values [%] voltage [V]PDF Image | Understanding the Vanadium Redox Flow Batteries
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