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UnderstandininggththeeVVaannaaddiuimumRRedeodxoFxloFwlowBaBttaetrtiesries 31479 c max 0.8 0.6 0.4 0.2 0 1 x 10−3 State of Charge [−] 0 −100 (a) Current [A] State of Charge [−] 0 −50 Current [A] −100 (b) 0 V2+and V5+ V3+and V4+ Limiting operating conditions 0 SoC 1 Fig. 13. Operating range and limiting operating conditions. The arrows represent the direction of the vanadium concentrations change as a function of the battery operating mode. The critical operating regions are highlighted in red; they represent the regions where the vanadium concentration cvanadium tends to its limiting concentrations (cmax or cmin). being depleted (↓) or augmented (↑). Qmin can be derived from (17): Qmin,↓(t) = bNcelli(t) [l/s] (37) 0.5 100 Operating range c min F(cout,min − cin,↓(t)) Qmin,↑(t) = bNcelli(t) [l/s] (38) F(cout,max − cin,↑(t)) where cout,min and cout,max are constant minimal and maximal output concentrations. The limiting species depends on the operating mode (charge or discharge); thus Qmin is given by the maximal value of (37) and (38): Qmin(t) = max Qmin,↓(t),Qmin,↑(t) [l/s] (39) Qmin is illustrated in Fig. 14 for a wide spectrum of operating points; clearly, Qmin is larger in the critical regions that were highlighted in Fig. 13. Moreover, Qmin is, in comparison, very small in the other operating regions; therefore, there must be a large benefit to operate the battery at Qmin. η battery −50 0 0.5 50 0 100 50 2 1.5 1 0.5 0 1 Fig. 14. (a) The battery efficiency ηbattery at constant flowrate Qmax as a function of the state of charge SoC and current I. (b) Minimal flowrate Qmin as a function of the stack current Istack and the state of charge SoC. Q min η [−] battery 3 Minimal flowrate [m /s] concentration charge dischargePDF Image | Understanding the Vanadium Redox Flow Batteries
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