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32052 Paths tSouSsutastianianbalbeleEEnneergrgyy when the sum of Pstack and Pmech is simultaneously minimal. This condition is expressed by the following relation3: min( |PVRB| f(Ustack,IVRB) ) = min( |Pstack| + Pmech ) (41) f(Istack,Q,SoC) f(Q,μ,ρ) The optimal flowrate Qopt is illustrated in Fig. 18 where PVRB is shown as a function of Q and SoC. At very high SoC, Qopt is equal to Qmin because the electrolyte carries a very small amount of electroactive vanadium ions. Again, the shape of the curves can be generalized to other charge currents Istack < 0. 5000 4500 4000 3500 3000 SoC = 0.025 SoC = 0.05 SoC = 0.1 SoC = 0.2 SoC = 0.3 SoC = 0.4 SoC = 0.5 SoC = 0.6 SoC = 0.7 SoC = 0.8 SoC = 0.9 SoC = 0.95 SoC = 0.955 SoC = 0.96 SoC = 0.965 SoC = 0.97 SoC = 0.975 Minimal Power |P VRB | = |P Stack | + P mech , I = −100 A P VRB [W] 2500 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Q [l/s] Fig. 18. Optimal flowrate Qopt as a function of the flowrate Q and the state of charge SoC. Note that when SoC is high, Qopt is equal to the minimal flowrate Q, and that the charge current Istack is equal to -100 A. 8.3 Charge and discharge cycles It is always difficult to assess the performance of a battery because it often depends on the operating conditions. In this section, a series of charge and discharge at constant current is performed at minimal flowrate Qmin, at maximal flowrate Qmax and at optimal flowrate Qopt in order to assess the performance of this new control strategy. The voltage ηvoltage and energy ηenergy efficiencies are summarized in Tab. 8 and 9; the coulombic efficiency ηcoulombic is in all cases equal to 100% because the model does not take into account any side reactions such as oxygen or hydrogen evolution nor any cross mixing of the electrolyte. Both ηvoltage and ηenergy decrease when the current increase; this is mainly due to the internal losses Ulosses that are proportional to the current Istack, although the flowrates Qmin and Qopt increases to supply enough electroactive species. The highest voltage efficiencies occur 3A close look at this relation reveals that it is the same as (40), but (41) is more intuitive for the charge.PDF Image | Understanding the Vanadium Redox Flow Batteries
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