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VII. Appendix A – Supporting information for Chapter V 1. Correlation plot of relevant variables for Fe-Cr RFB cell operation To assess the correlation between parameters relevant for RFB cell operation, an analysis using the Kendall tau (τ) coefficient [239] was performed for the set of variables including the electrode thickness (Thick), electrode geometric area (Area), geometric current density (Rate), coulombic efficiency (CE), voltaic efficiency (VE), energy efficiency (EE), and decay rate (DR). The Kendall rank correlation was chosen for this analysis, as it is a non-parametric measure that determines the strength of association based on concordance and discordance in the data and does not assume a relationship between the variables being assessed. For any pair of indices 1 ≤ i < j ≤ n where n is the total number of observations for variables x and y, a pair of observation is concordant if (xi – xj) and (yi – yj) have the same sign, discordant if they have opposite signs, and neither if either xi = xj or yi = yj. Kendall’s τ is defined as the difference between the number of concordant and discordant pairs divided by the number of ways to select two data points from n. Mathematically, τ can be defined by EquationVII-1 [239]: 2K n-1n t=n(n-1); K=ååx(xa,i,xa,j,yb,i,yb,j) i=1 j=i+1 Where ξ is the conditional given by Equation VII-2: Figure VII-1 shows the correlation plot of all seven variables. The number in each subplot corresponds to τ, while the magenta line is the best linear fit to the data. The numbers highlighted in red font are determined to be statistically significant based on a p-value of less than 0.05. The electrode geometric area and thickness, voltaic efficiency, energy efficiency, coulombic efficiency, and decay rate are all shown to be statistically significant. All computation and plotting were performed using the MATLAB® function corrplot. ï x(xa,i,xa,j,yb,i,yb,j )=íï 0 if ì1 if (xa,i -xa,j)(yb,i -yb,j)>0 (VII-1) (VII-2) (xa,i -xa,j )(yb,i -yb,j )=0 ïî-1 if (x -x y -y <0 a,i a, j )( b,i b, j ) 111PDF Image | Bringing Redox Flow Batteries to the Grid
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