represents the density of the discharged electrolyte, ρ j 0 ≡ ρ j 0 (c V , c S , T 0 , SoC = 0), at the reference temperature T 0 and the specified total vanadium and sulphate concentrations. These expressions assume that the electrolyte density varies linearly with T and SoC, but quadratically with the total vanadium and sulphate concentrations. As a result, ρ j T = (∂ρ j /∂T ) SoC j and ρ j SoC = (∂ρ j /∂SoC) T j denote the partial derivatives of ρ j with respect to T and SoC, A j is the density at the reference state (c V,0 , c S,0 , T 0 , SoC = 0), and B j to E j represent the linear and quadratic fitting coefficients for the density variations with the total vanadium and sulphate concentrations. Density is thus expressed as the density ρ j 0 of the discharged electrolyte at a given temperature and composition (2) plus its variations with the SoC and temperature during VRFB operation . The multivariate regression coefficients obtained from the experimental campaign are listed in Table . The regression for ρ + yielded a root mean squared error (RMSE) of 7.80 • 10 -4 g/cm 3 , while that for ρ -gave a RMSE of 9.10 • 10 -4 g/cm 3 .