Adaptive Observer for Charge-State and Crossover Estimation in Disproportionation Redox Flow Batteries undergoing Self-Discharge

Abstract

This article considers a model formulation and an adaptive observer design for the simultaneous estimation of the state of charge and crossover flux in disproportionation redox flow batteries. This novel nonaqueous battery chemistry allows a simple isothermal lumped parameter model to be formulated. The transport of vanadium through the porous separator is a key unknown function of battery variables and it is approximated in the space of continuous functions. The state and parameter observer adaptation laws are derived using Lyapunov analysis applied to the estimation error, the stability and convergence of which are proved. Numerical values of observer gains are calculated by solving a polytopic linear matrix inequality and equality problem via convex optimization. The performance of this design is evaluated on a laboratory flow battery prototype, and it is shown that the crossover flux can be considered a linear function of state of charge for this battery configuration during self-discharge.

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

“…where k mt = 5.6142·10 −8 L/min is the mass-transfer coefficient. This value for k mt was calculated by fitting the model, (4)-(5), including (22), to the experimental data assuming an initial condition of 100% for SOC cell [32]. Figure 3: (a)-(b) and (c) depicts the battery states and crossover term, respectively (dash-dot lines) and their estimated values by the proposed observer (solid lines), alongside the estimated parameters of the model.…”

“…In this section, for clarity of explanation, the model formulated by the authors in [32] is described.…”

“…Considering that the volumetric flow rate in (4) satisfies Condition 5, the approximate augmented model ( 7) admits a polytope description so that the time-variant nature of the LMI problem (15) can be recast as a polytopic convex problem [32], [52], [47], [53], [46]:…”

“…The battery is described with a simple isothermal lumped-parameter model, which considers the state of charge in one half-cell (including the associated reservoir) and in one chamber of the reactor, alongside the crossover flux out of the half-cell through the reactor's membrane separator. This paper presents an alternative approach to previous work by the authors [32] which included a general parametric model for the crossover flux with no particular assumptions about a specific transport mechanism through the membrane. The present model instead considers time varying parameters generated by a persistently excited linear system, whose states are included as additional states in the original nonlinear DRFB model, and whose space-state representation is suitable for observer design based on the standard Lyapunov second method of stability.…”

Redox Flow Batteries: A Literature Review Oriented to Automatic Control

“…Adaptive estimation techniques have also been used to estimated with precision the SOC, using similar models. In [138] an adaptive observer design for simultaneous estimation of SOC and crossover flux is presented; the work assumes a nonaqueous RFB that is simply modelled with a isothermal lumped parameter model, measuring the temperature and the flow rate. Another adaptive technique is proposed in [139], which consists on a novel joint real time estimator based on the EKF, which estimates the SOC using the recursive least squares (RLS) method, measuring the OCV and the current.…”