# A State Observer Design for Simultaneous Estimation of Charge State and Crossover in Self-Discharging Disproportionation Redox Flow Batteries

## TL;DR

This paper introduces an augmented state observer for redox flow batteries that accurately estimates charge state and crossover flux, ensuring exponential convergence and robustness against model uncertainties.

## Contribution

It proposes a novel observer design combining a parametric crossover flux model with Lyapunov stability, optimized via convex programming for improved battery state estimation.

## Key findings

- Observer achieves exponential error convergence.
- Robust estimation of crossover flux in laboratory tests.
- Enhanced battery management through accurate state monitoring.

## Abstract

This paper presents an augmented state observer design for the simultaneous estimation of charge state and crossover flux in disproportionation redox flow batteries, which exhibits exponential estimation error convergence to a bounded residual set. The crossover flux of vanadium through the porous separator is considered as an unknown function of the battery states, model-approximated as the output of a persistently excited linear system. This parametric model and the simple isothermal lumped parameter model of the battery are combined to form an augmented space state representation suitable for the observer design, which is carried out via Lyapunov stability theory including the error-uncertainty involved in the approximation of the crossover flux. The observer gain is calculated by solving a polytopic linear matrix inequality problem via convex optimization. The performance of this design is evaluated with a laboratory flow battery prototype undergoing self-discharge.