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31850 Paths tSouSsutastianianbalbeleEEnneergrgyy But a change in the flowrate Q also modifies the vanadium concentrations ccells within the cells according to (18), and in consequence the stack voltage Ustack and power Pstack according to (2) and (3). This phenomenon is illustrated in Fig. 15 where the equilibrium voltage E at Qmax and Qmin is shown: an increase of the flowrate has always a beneficial effect on E. Furthermore, the equivalent state of charge SoCeq which represents the SoC of the electrolyte within the cells is also illustrated as a function of Q. Clearly, SoCeq tends toward the battery SoC at high Q. Therefore, the change in ccells is maximal at Qmin; and consequently a large variation of Ustack and Pstack is expected between the operations at Qmin and Qmax as it can be observed in Fig. 16. From the strict point of view of Pstack, it is more interesting to operate the battery at Qmax; indeed, more power is delivered during the discharge and less is consumed during the charge. But it will be shown in the next sections that the mechanical power greatly deteriorates the performance and that the energy efficiency at Qmax is unacceptable. 1.8 1.6 1.4 1.2 1 0.8 Equilibrium voltage 0 0.2 0.4 0.6 0.8 1 state of charge [-] Discharge, input concentration cin: 1 mol/l I = 50 A Q min Discharge Charge Fig. 15. Effect of the flowrate Q on the equilibrium voltage E. On the right, the variation of the equivalent state of charge SoC as a function of Q during the discharge and the charge. In this example, the battery SoC is 0.5, i.e. the input concentrations are 1 M for each vanadium species. 400 200 0 −200 −400 1 Fig. 16. The difference between the stack power Pstack,Qmax P at Q . at Qmax and the stack power stack,Qmin min 8. Optimal operating point at constant current 0.5 State of Charge [−] 50 Q max Q min |P |−|P | stack,Q max stack,Q min 0.6 0.4 0.2 00 0.02 0.04 0.06 flowrate Q [l/s] Charge, input concentration c 0.08 0.1 : 1 mol/l 0.08 0.1 1 0.8 0.6 0.4 0 0.02 0.04 0.06 in I = -50 A flowrate Q [l/s] −50 0−100 In the previous sections, the advantages and disadvantages of operating the battery at either Qmax and Qmin were discussed. At Qmax, the stack power Pstack has the highest possible value but the mechanical power Pmech is also very large and consequently deteriorates the performance. At Qmin, Pmech is reduced to the minimum, but Pstack is negatively affected. 0 Current [A] 100 Difference [W] Equivalent SoC [-] Equivalent SoC [-] voltage [V]PDF Image | Understanding the Vanadium Redox Flow Batteries
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