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31648 Name number of cells Ncells Rcharge Rdischarge flow resistance R electrolyte vanadium concentration tank size Vtank initial concentration of vanadium species Table 7. the parameters of the simulation. Paths tSouSsutastianianbalbeleEEnneergrgyy Value 19 0.037 Ω 0.039 Ω 14186843 Pa/m3 2 M 83 l 1 M while minimizing the losses; there is no point to have a battery that consumes more power than necessary. To illustrate this discussion, we will use a 2.5 kW, 6 kWh VRB in the rest of this chapter; its characteristics are summarized in Tab. 7. 7.1 Maximal flowrate The simplest control strategy operates the battery at a constant flowrate set to provide enough electroactive species to sustain the chemical reaction under any operating conditions. Therefore, this flowrate Qmax is determined by the worst operating conditions: low state of charge SoC during the discharge and high SoC during the charge at high current in both cases. For the battery described in Tab. 7, Qmax is around 1.97 l/s: in that case, the mechanical power Pmech is 1720 W. In order to assess the performance, an instantaneous battery efficiency ηbattery is defined as follow: ηbattery = |Pstack| [−] (36) |Pstack | + Pmech Clearly, the battery performance is poor as it can be observed in Fig. 14 where ηbattery is illustrated as a function of the stack current Istack and the state of charge SoC. Indeed, the battery often consumes more power than necessary; therefore, constantly operating the battery at Qmax is not a wise strategy. Nevertheless, it is possible to improve this efficiency by limiting the operating range of the battery (smaller current and/or narrower state of charge); thus the flowrate Qmax and the mechanical power Pmech are reduced. But this also reduces the power rating and/or the energetic capacity while it increases the cost. 7.2 Minimal flowrate The low efficiency at constant flowrate Qmax is due to the large mechanical losses Pmech; therefore, a second control strategy is proposed to minimize Pmech. In that case, the battery is operating at a minimal flowrate Qmin that is constantly adapted to the actual operating conditions (SoC and Istack) in order to supply just enough electroactive materials to fuel the electrochemical reactions. Since the vanadium concentrations cV change proportionally to Istack, there are critical operating points where cV is close to its boundary. In some cases, the variations of vanadium concentrations tend toward the limit values (Fig. 13). In these critical regions, the electrolyte flowrate Q must be larger to palliate the scarcity of electroactive vanadium ions. Hence, the minimal flowrate Qmin depends on the required amount of electroactive species, and in consequence on Istack, and on the input vanadium concentrations cin that are eitherPDF Image | Understanding the Vanadium Redox Flow Batteries
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