We expound a versatile analytical model to characterize redox flow batteries (RFBs) from the cell to stack scales. It is validated against measurements of our own RFB, zinc-ferricyanide, as well as against those from the literature of competitive RFBs. We also put forth a heuristic framework for optimization of capital cost and design parameters, as well as consequent findings: that modeling enables even-handed comparison of even pre-commercial RFB concepts, with zinc/ferricyanide as the most cost-effective candidate so far; and that overpotential characteristics and engineering strategies are highly RFB dependent, but readily probed by a robust model. More of the electrical grid is being powered by renewables. In particular, wind and solar photovoltaics see the fastest projected growth in the next decade.1 To realize this pace of development, however, we need a means to manage their intermittent supply. Among candidate technologies for energy storage, redox flow batteries (RFBs) stand out in durability, safety, and, most notably, flexibility of design.
2The design space for RFBs is further widened by recent innovations in chemistries 3,4 and layouts. 5,6 In this expanse, concerted experimental efforts can no longer inform the most promising paths toward cost-effectiveness; a comprehensive, high-level model is needed. Some progress has been made to characterize the performance 2,7-13 and cost 10 of, in particular, vanadium-containing RFBs. These models, however, have sought spatial resolution at the expense of computational efficiency, or used system-specific fitting factors for nominal accuracy, thereby limiting prediction scope. This work aims instead to explicate and validate a generalized analytical model for characterization with global optimization by a memetic algorithm. Put together, our model enables the even-handed assessment of new RFB designs. This model thereby integrates well with continued experimental work to bring RFBs to market.
ApproachWe seek ultimately to optimize redox flow battery (RFB) stacks for the grid; to do so on a reasonable timescale calls for an analytical formulation. We hereon make several simplifications:in which the subscript j refers to species j and the superscript k refers to compartment k (with 0 ≤ k ≤ 5), as illustrated in Figure 1. Cell dimensions are defined as L, H , and W in the x, y, and z directions, respectively. These cells may be arranged in bipolar assemblies, or modules, and then interconnected to form stacks (Figure 2). For each stack, the * Electrochemical Society Member.z E-mail: yanys@udel.edu number of cells per module is defined as N , whereas the number of modules per stack is defined as M.To elucidate the resulting system of equations, we consider noteworthy RFBs described in the literature: Zn/Fe(CN) 6 , 14 V/V 10 , Zn/Fe 3 , and S/Br 2 , 15 the first of which is measured in-house (modifications detailed in Supporting Information).Characterization.-Cell.-During discharge, an RFB cell is a source of a certain voltage, E (Equation 1). Were there no ineff...