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3146 Paths tSouSsutastianianbalbeleEEnneergrgyy 5.3 Mechanical model Finally, the sum of the pressure drop in the pipes Δppipe and the pressure drop in the stack Δpstack determines the hydraulic circuit pressure drop Δpsystem: Δpsystem = Δppipe + Δpstack [Pa] (32) The pump power Ppump, a determinant variable that influences the battery performance is related the head rise hp supplied by the pump, to the fluid density γ and to the flowrate Q; we can also relate it to the pressure drop Δp (Wilkes, 2005): Ppump = γhpQ = Δp Q [W] (33) The efficiency of the pump ηpump is affected by the hydraulic losses in the pump, the mechanical losses in the bearings and seals and the volumetric losses due to leakages inside the pump. Although ηpump is not constant in reality, it is assume in this work. Therefore, the effective power required by the pump Pmech is given by: Pmech = Ppump [W] (34) ηpump Thus, the relations introduced in this section can be combined to form the mechanical model of the VRB as illustrated in Fig. 10. Remember that the VRB needs two pumps to operate. ~ Δp R stack Stack hydraulic resistance μ hydraulic circuit characteristics Q P mech,stack + Pressure drop & power P mech,pipes QΣ ρ Δppipes + μ P mech Analytical model of the pipes, bends, valve and tank Fig. 10. Flowchart of the VRB mechanical model. 6. Multiphysics model and energetic considerations The combination of the electrochemical model and the mechanical model leads to the multiphysics VRB system model. The functions that determine the vanadium concentrations in the tank ctank and the state of charge SoC have been separated from the electrochemical model in order to be incorporated into a new model named reservoir and electrolyte model. A system control has also been added to supervise the battery operation; this system controls the flowrate Q and the stack current Istack. This multiphysics system model, illustrated in Fig. 11, is a powerful means to understand the behaviour of the VRB, identify and quantify the sources of losses in this storage system; thus this multiphysics model is a good means to enhance the overall VRB efficiency. 6.1 Power flow In order to optimize the performance of the VRB, it is important to understand the power flows within the VRB storage system. The power converters represented in Fig. 12 are necessary to adapt the stack voltage Ustack to the power source Ugrid or to the load voltage Uload and to supply the mechanical power required to operate the pumps. Since powerPDF Image | Understanding the Vanadium Redox Flow Batteries
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