# Algorithms for Simulation of Shunt Currents in a Vanadium Redox Flow Battery
## 2 Related Work  
This section is dedicated to a brief review of recently published articles related to shunt currents models for VRFB.  
In [16], an analysis of the current distribution in a 10-cell VRFB with a single 10-cell stack was performed. This analysis consists of the comparison of a computational model with experimental data. The model presented is the equivalent electrical circuit of the 10-cell battery. The Kirchhoff equations of the electrical circuit are presented with the simplification that the current flowing in the upper channels is equivalent to the current flowing in the respective lower channels. In this way, the number of variables and equations is reduced by almost half. In the experimental part, the manufacture of a 10-cell laboratory scale VRFB is described, giving information about the materials used for it. Finally, the results of the experiment are shown and a comparison with the exposed model is made.  
A lot of information is given regarding the manufacture of the battery, which is useful for replicating the experiment. In the part of the computational model, although the battery has only one stack and simplifications have been made to reduce the number of equations and variables, no information is shown on how the implementation has been carried out.  
In [6], the mathematical model of the equivalent electrical circuit to a multistack VRFB is shown. The configuration of the connections between stacks seems to follow a U-type configuration which, according to the literature, is inferior to a Z-type configuration in terms of reduction in shunt currents as stated in [12]. The methodology to obtain the model equations is the same as in [16], being that [PERSON]'s laws of nodes and meshes are applied. These simplifications are also applied at the inter-stack level, making the current flowing through the lower trunk the same as that of the respective upper trunk. Although the equations are ordered by differentiating cases, no further details are shown, such as how the matrices are generated and how they have been implemented.  
Ref. [12] is a widely cited article in which a study of a number of designs of VRFB was carried out in order to obtain the best design in terms of efficiency, taking into account pressure losses and shunt currents. The article is useful in obtaining data on parameters related to electrolytes, electrodes, pipe measurements, etc. It is shown how the pressure losses have been modeled, but as far as the shunt currents are concerned, it is limited to only show the equivalent circuit.  
Ref. [17] shows the battery electrical model and the mass and energy balance model of a VRFB, comparing the models with experimental data. Regarding the electrical model in which the shunt currents are calculated, not much detail is given. Two articles by the same author are indicated for further details of the electric model [10; 18] in which equivalent electrical circuits of the batteries are shown. However, no details of the equations related to the equivalent electrical model are shown, at least as far as [PERSON]'s equations are concerned, nor are there details shown about the implementation of the electrical model in any of the three, limiting themselves to commenting that the implementation has been carried out in MATLAB.  
A model of the equivalent electrical circuit formulated by [PERSON]'s laws is shown in [8]. This model is applied for a case of a single stack with 19 cells; therefore, no consideration is given to the equations related to the nodes and meshes of the stacks, since they have only one stack. The model is simplified in the same way as in [16]. The article proceeds to show comparisons of the values obtained by applying this model with values obtained experimentally. No details of how the model has been implemented are shown or given.