Online Parameter Estimation of the Polarization Curve of a Fuel Cell With Guaranteed Convergence Properties: Theoretical and Experimental Results

In this article, the problem of online parameter estimation of a proton exchange membrane fuel cell (PEMFC) polarization curve, that is, the static relation between the voltage and the current of the PEMFC is addressed and solved. The task of designing this estimator—even off-line—is complicated by the fact that the uncertain parameters enter the curve in a highly nonlinear fashion, namely in the form of nonseparable nonlinearities. We consider several scenarios for the model of the polarization curve, starting from the standard full model and including several popular simplifications to this complicated mathematical function. In all cases, separable regression equations are derived—either linearly or nonlinearly parameterized—which are instrumental for the implementation of the parameter estimators. We concentrate our attention on online estimation schemes for which, under suitable excitation conditions, global parameter convergence is ensured. Due to these global convergence properties, the estimators are robust to unavoidable additive noise and structural uncertainty. Moreover, since the schemes are online, they are able to track (slow) parameter variations, that occur during the operation of the PEMFC. These two features—unavailable in time-consuming offline data-fitting procedures—make the proposed estimators helpful for online time-saving characterization of a given PEMFC, and the implementation of fault-detection procedures and model-based adaptive control strategies. Simulation and experimental results that validate the theoretical claims are presented.

I. Introduction

In This article, a solution to the problem of deriving a globally convergent online parameter estimator for the polarization curve of proton exchange membrane fuel cells (PEMFCs) is reported. The practical motivation to address this problem is well-known and it includes the determination of the PEMFCs state of health, the optimization of their operating conditions, and their energy management [1]. PEMFCs have emerged as a promising and scalable energy conversion and sustainable power generation technology. As a subset of fuel cell technology, PEMFCs offer a variety of unique features that make them suitable for diverse applications. These features include energy efficiency, rapid start-up, compact size and weight, low noise, low emission, and modularity characteristics that have widespread this type of fuel cells [2], [3]. Monitoring the suitable operation of PEMFCs requires complicated experiments and instrumentation that cannot be applied in field operations; therefore, time-consuming offline data-fitting procedures are employed [4]. In recent years, mathematical models that describe the operation of PEMFC under different operating conditions have been developed. Due to the complexity of the behavior of the PEMFC, these models involve highly nonlinear relations that depend, again in a nonlinear way, on uncertain parameters. The values of these parameters, which reflect the actual PEMFC performance, inevitably affect the effectiveness of the developed models in simulation, design, optimal operation, and control. Therefore, it is indispensable to investigate the problem of parameter estimation of these models. Several unwanted phenomena, such as catalyst poisoning, flooding or drying of the membrane, etc., can be monitored, and the working parameters of a PEMFC can be quickly regulated with the help of real-time parameter estimation [5]—hence our interest in online parameter estimators. Also, to ensure good performance in the face of uncertainty and noise, our attention is concentrated on schemes for which global convergence properties under some suitable excitation conditions are proven.