A multi-stack simulation of shunt currents in vanadium redox flow batteries
Introduction
Redox flow batteries are electrochemical energy storage devices that combine qualities of batteries and fuel cells [1]. The storage medium is an electrolyte solution which, for most redox flow battery types, does not undergo a phase change during the electrochemical reaction. The reaction takes place in stacks of cells whereas the main part of the electrolyte solution is stored in external tanks; the electrolyte solution is constantly pumped in a closed loop between the tanks and the stack. Storage capacity and power conversion can thus be designed separately [2]. This battery type is, amongst others, suitable for large-scale applications like temporary storage of electrical energy generated from wind or photovoltaic farms [3], [4], [5], [6]. The focus of this work is the all-vanadium redox flow battery type which was pioneered by Skyllas-Kazacos et al. [7].
Both the feed and removal of electrolyte solution to and from the stacks and the individual cells is implemented using shared pipe works. This creates two additional ionic connections between the cells and stacks in addition to the electrical connections via the bipolar plates. During charge and discharge of the battery additional currents, called leakage currents or shunt currents, will form along the ionic connections. The shunt current pathways in a redox flow battery with two cells are depicted in Fig. 1.
The occurrence of shunt currents is also reported in bipolar electrolyzers [8], [9] and liquid fuel cells [10]. For redox flow batteries, shunt currents were originally investigated by NASA [11], [12], [13]. The models to evaluate the magnitude and effects of the shunt currents combine two sets of properties. These are the properties of the redox flow battery stack and the transient properties for charge and discharge operations. These are incorporated into an equivalent circuit of the stack and sets of differential equations are then generated. An equivalent circuit for a redox flow battery is shown in Fig. 2; the resistor designations are explained in Section 3.1.
The charge and discharge properties can be static to allow an analytical approach in solving for the effects of single parameters or sets of parameters [11], [14]. More common is a numerical approach in solving the equations of the model [15], [16], [17], [18], [19], [10], [20] for a combination of static battery properties and time-dependent charge and discharge operation properties. Codina and Aldaz [15] used their model to evaluate the effects of shunt currents between three stacks of an iron chromium redox flow battery. Tang et al. [21] have proposed a fully dynamic model for both the properties of battery operation and properties of the electrolyte solutions of the vanadium redox flow battery. For the latter, they introduce the effects of vanadium crossover, i.e. the diffusion of vanadium ions across the separating membrane and the ensuring side reactions [22].
This work is part of preliminary studies for the construction of a vanadium redox flow battery to buffer the electricity generated by a 2 MW wind turbine at the site of the Fraunhofer Institute for Chemical Technology. The battery specification calls for a peak power performance of 2 MW and a storage capacity of 20 MWh. At least 600 m3 of a 1.6 M vanadium electrolyte solution will be needed to realize this capacity. Computer aided process engineering (CAPE) is used in order to speed up the development process of the vanadium redox flow battery system and its electrical connection to the wind turbine [23]. CAPE will also be used to optimize the operating parameters, this is important to make the battery economically viable [24].
The aim of this work is to develop a first model for shunt currents which occur in sets of vanadium redox flow battery stacks that are electrically connected in series and share a common electrolyte feed and removal pipe network. The electric series connection is needed to realize the operational voltage of the rectifiers and the inverters of a large redox flow battery installation. Shunt currents between the stacks could be avoided by providing a separate pipe network for each stack; however, this increases the needed pumping power and decreases the overall energy efficiency [25]. The proposed model in this report also features dynamic properties for both anolyte and catholyte solutions depending on the state-of-charge of the system.
Section snippets
Experimental details
The starting electrolyte for both vanadium half-cells was an aqueous solution of 0.8 mol l−1 vanadyl sulphate VOSO4, 0.4 mol l−1 di-vanadium tri-sulphate V2(SO4)3, 2 mol l−1 sulfuric acid H2SO4 and 0.05 mol l−1 phosphoric acid H3PO4 were used (GfE Metalle und Materialien GmbH, Germany). A vanadium redox flow battery with an anion exchange membrane (FAP-0, FumaTech GmbH, Germany) was used to prepare the anolyte and catholyte solutions. The starting electrolyte underwent electrodialysis at a
Analog circuit method
The stack is described as a network of electrical elements, shown in Fig. 2 for a single stack. The network is made up from resistors for the internal cell resistances and the shunt current path resistances, voltage sources for cell potentials and a current source that provides the constant charge respective discharge current. Current balances can be setup by applying Kirchhoff's law to each cell. The formulation of these balances, the resulting sets of linear equations and one approach of
Conductivity measurements
The conductivities of Vanadium anolyte (V2+/V3+) and catholyte (V(IV)O2+/V(V)O2+) solutions were measured for different state-of-charges at different temperatures. The values for the state-of-charges of 0 and 1 are shown in Table 1. Comparing our results for a solution of 1.6 M Vanadium and 2 M sulfuric acid to the results of [27] for a solution of 1.5 M Vanadium and 2 M sulfuric acid, our values deviate 6%, −17%, 20% and 7% from the reported values reported for the V(II), V(III), V(IV) and
Summary and future development
A model for the shunt currents in all-vanadium redox flow battery consisting of three stacks which are electrically connected in series has been developed. The model uses an equivalent circuit to represent the ionic connections between the cells and the stacks which make up the pathways of the shunt currents. The model considers the dependence of the electrolyte conductivities at different state-of-charges, which have been measured. It has been validated using a single stack and static
Acknowledgments
The authors gratefully acknowledge the financial support of the Ministry of Finance of the German Federal State of Baden-Württemberg and the German Federal Ministry of Education and Research.
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