Nonlinear observer for online concentration estimation in vanadium flow batteries based on half-cell voltage measurements

This paper presents a nonlinear observer to estimate the active species concentrations in vanadium flow batteries. To conduct the estimation, the observer relies only on current, flow rate and two half-cell voltage measurements. In contrast to previous works in the field, the proposed observer is capable to deal simultaneously with two significant and challenging conditions: (1) a not necessarily high flow rate, which results in different concentrations for tanks and cells, and (2) presence of crossover and oxidation side reactions, that result in imbalance between the electrolytes on the positive and negative sides of the system. The stability and convergence of the observer are formally demonstrated using a Lyapunov analysis and subsequently validated through comprehensive computer simulations. Finally, utilising the information provided by the observer, a strategy to independently regulate the flow rate of each electrolyte based on their individual state of charge is developed.