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32254 Paths tSouSsutastianianbalbeleEEnneergrgyy at Qmax because of its positive effect on the stack voltage Ustack highlighted in section 7.2; consequently, the worst voltage efficiencies occur at Qmin. Moreover, the voltage efficiencies at Qopt are very close to the maximal efficiencies obtained at Qmax. In fact, the stack voltages Ustack,Qmax and Ustack,Qopt are very close as it can be observed in Fig. 19. 35 30 25 20 15 4000 2000 0 −2000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Stack voltage U stack at 100 A Ustack,Qmax [V] Ustack,Qmin [V] Ustac k,Qopt [V] time [h] Stack power P stack at 100 A P stack,Qmax Pstack,Qmin [V] P [V] stack,Qopt [V] −4000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time [h] Battery power PVRB at 100 A 4000 2000 0 −2000 −4000 −6000 Fig. 19. Stack voltage Ustack, stack power Pstack and battery power PVRB during a charge and discharge cycle at 100 A. Obviously, operating the battery at Qmax is a problematic strategy as ηenergy,Qmax is very small or even negative: at small currents, the battery does not deliver any power to the load but consumes more power to operate the pumps than the stack is furnishing. When Pmech is minimized, the energy efficiencies already become interesting at Qmin, but they are increased by a further 10% when the battery is operating at Qopt. In order to compare the model with experimental data, the stack characteristics were defined to match the stack presented in section 3.7. The experimental results of M. Skyllas-Kazacos and al. are summarized in Tab. 4 (Skyllas-Kazacos & Menictas, 1997); note that they do not take into account the mechanical power required to operate the pumps and that the flowrate was constant (2 l/s which correspond to Qmax). The losses in coulombic efficiency ηcoulombic can be caused by side reactions or cross mixing of electrolyte through the membrane which are not taken into account in the model; but ηcoulombic improves as the battery becomes conditioned. In that case, the energy efficiency ηenergy,Qopt at optimal flowrate is very close to the maximal electrochemical energy efficiency. Finally, a very good concordance is observed between the voltage efficiencies at Qmax and the experimental results. P VRB, [V] Qmax PVRB, PVRB, Qmin [V] Qopt [V] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time [h] power [W] power [W] voltage [V]PDF Image | Understanding the Vanadium Redox Flow Batteries
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