Model-based aging tolerant control with power loss prediction of Proton Exchange Membrane Fuel Cell

doi:10.1016/j.ijhydene.2018.11.219

International Journal of Hydrogen Energy

Volume 45, Issue 19, 3 April 2020, Pages 11242-11254

https://doi.org/10.1016/j.ijhydene.2018.11.219 Get rights and content

Highlights

•
We develop a time-varying model of PEM fuel cell.
•
A model inversion method is proposed for references calculation through aging.
•
An aging tolerant control strategy is detailed based on the state of health.
•
A Maximal Power Point Tracking strategy robust to aging is proposed.
•
A RUL forecasting algorithm is developed considering the maximum power.

Abstract

Proton Exchange Membrane Fuel Cells are promising energy converters that allow powering vehicles or buildings in a clean manner. Nevertheless, their performance are affected by faults and irreversible degradation mechanisms that are far from being fully understood. Consequently, during the last decade, researches have been conducted on the diagnostic of faults of this promising converter. Nevertheless, aging was never the subject of a particular attention concerning control. As a result, this paper proposes an aging tolerant control strategy for Proton Exchange Membrane Fuel Cells. It aims at generating the load current reference taking the state of health into account. Moreover, using a model inversion of an Energetic Macroscopic Representation with time-varying parameters, the coherent references of input flows of gas can be calculated. Finally, the paper details a method to identify and predict the maximum power the fuel cell is able to provide at present time based on a Maximum Power Point Tracking algorithm. Also this algorithm aims at forecasting the Remaining Useful Life for a given power reference. This method is validated on a simulation case.

Introduction

In a context of diminishing fossil energy resources, it is imperative to start an energy transition that includes renewable sources. In order to succeed in this transition, the worldwide community needs to tackle the middle and long term energy storage issue. One of the possible methods relies on using hydrogen as an energy vector that is transformed into electricity thanks to a Proton Exchange Membrane Fuel Cell (PEMFC) [1]. Those converters are receiving a growing interest from the scientific and industrial community around the globe due to its high energy density and efficiency, what makes it a suitable solution to replace Internal Combustion Engine for transportation applications. Moreover those converters are able to provide, in a combined manner, electricity and heat to an entire building (μ-CHP) [2].

Among the bottlenecks of the diffusion of this promising technology, the lifespan of a PEMFC is still too limited (2500 h on average under transportation operating conditions), which is inferior to the prerequisite [3], [4]. Various means of research might lead to overcome this limit: material improvement, optimization of the design, and development of a smart control in order to avoid specific behaviors which degrade this converter. For the last point, it is required to estimate the degradation (i.e. the State of Health) and then to act consequently on the control.

Prognostics and Health Management (PHM) is a maintenance strategy aiming at extending the life of a device thanks to monitoring [5], diagnosis [6], [7], prognostic [8] and control [9]. As a consequence, a growing interest emerges among the fuel cell community for this maintenance philosophy [10]. Knowing the State of Health (SoH) of a PEMFC is crucial at the decision step of the PHM cycle. Indeed, it is possible to eliminate or to limit certain faults by the control. For several years the scientists develop Fault Tolerant Control (FTC) of PEMFC systems. Generally, it concerns the power converters [11], the air compressor [12], or the cooling system [13] and aim at eliminating several faults (drying/flooding [14], defect of the air compressor etc.).

However, as far as the authors knowledge, only one paper concerning the Degradation Tolerant Control (DTC) of PEMFC has been identified in the consulted literature. In Mezzi et al. [15] the authors develop an algorithm aiming at computing the triplet of references: current, temperature and stoichiometric factors in order to obtain a desired fix reference voltage for a requested power. It allows to keep the operational voltage of the fuel cell close to the nominal value, hence reducing the aging rate. Nevertheless, it should be noted that this work does not clearly study the impact of the aging on the fuel cell control performance.

Furthermore, when the PEMFC is too much degraded, it becomes impossible to supply a certain amount of required power. Whereas in the consulted literature, the PEMFC is usually considered out of use when one or several SoH indicators reach an arbitrary threshold [16], [17]. To tackle this issue, it is interesting to propose a power-based threshold for the End of Life for which an algorithm of prognostic can be applied.

Therefore, a novel model-based methodology is proposed in this paper for Degradation Tolerant Control and Prognostics applied to a PEMFC:

•
We develop a control law which takes into account the SoH
•
Based on the SoH estimation, the strategy is able to adjust the objective in order to compute the correct input references during the aging
•
An algorithm estimating the maximum power the converter can provide through aging is detailed
•
Finally, a power-based method for Remaining Useful Life prediction is proposed

The structure of this paper follows: first, the PEMFC technology is introduced with, in particular, a brief description of the degradation phenomenon in PEMFC Description and Degradation Phenomenon. Then, a time-varying model of PEMFC is presented. It is structured in the Energetic Macroscopic Representation (EMR) formalism, which allows to develop a model-inversion based control in Time Varying EMR Model for PEMFC Control. In the following section, a control strategy for aging PEMFC is detailed. It allows to regulate the provided power in spite of the loss of performance. Also, the maximum power the fuel cell can provide during its lifespan is obtained thanks to a Maximum Power Point Tracking algorithm (MPPT). Finally, an Inverse First Order Reliability Method (IFORM) is designed based on the output of the MPPT in order to predict the Remaining Useful Life (RUL) of the PEMFC for a given power reference which is considered to be the threshold of End of Life. Also, a simulation validation is carried out along this paper.

Section snippets

PEMFC description

A PEMFC is an electrochemical converter based on the reverse principle of electrolysis, where at the anode, the hydrogen is divided into proton H⁺ and electrons. While the electrons flow through an external circuit, the H⁺ ions are crossing the Proton Exchange Membrane. At the cathode, the oxygen reacts with the species described previously in an exothermic manner following: $2 H^{+} + \frac{1}{2} O_{2} + 2 e^{-} \Rightarrow H_{2} O + heat$

Between the electrodes is created a difference of potential $E_{r e v}$ which value depends on the chemical

EMR for modeling

Among the several graphical formalisms to model a multi-physical system, the Energetic Macroscopic Representation (EMR) aims at representing the transfer of energy in a macroscopic manner. It is shown by two arrows connecting subsystems representing the effort e (potential variable) and the flow f (kinetic variable). The product of these dual variables gives the power $P = e f$ . Moreover, two of the strong concept of the formalism are the principle of action-reaction and the representation of the

Degradation Tolerant Control framework

This section describes a strategy aiming at controlling a PEMFC in spite of the aging. First, a strategy of constant power regulation is presented. It allows generating the current and voltage references in the PCS in order to obtain the desired power.

Secondly, once the performances of the PEMFC diminish with the aging, the converter will not be able, at a moment, to supply the desired power. Therefore, an estimator of the maximal power the fuel cell can provide is also presented (see MPPT in

Background

Prognostics aim at estimating the time remaining before one or several failures appear on a system. This Remaining Useful Life is defined as the difference between the predicted End of Life time and the current time as: $R U L (t_{k}) = t_{E o L} - t_{k}$

Obtaining $t_{E o L}$ is usually done in two steps: first the present SoH is obtained (see Time Varying EMR Model for PEMFC Control·B), then a prediction is made until the forecasted SoH reaches a threshold. The prediction algorithms for prognostics can be divided into

Conclusion

The Degradation Tolerant Control of PEMFC system is a very young research subject which allows to take into account the aging in the control loop. This methodology requires several steps. First of all, a time varying parameters multi-physical model of PEMFC in the EMR formalism is presented. The degradation which affects the electrochemical parameters is integrated in this model to take into account the aging. A PCS is then developed by inversion of the EMR model where the not reasonable

Elements of the EMR and PCS formalism

	Source of energy
	Multi physical domain converter
	Control block without controller
	Mono physical domain converter
	Element with energy accumulation
	Control block with controller
	Multi physical domain coupling device (energy distribution)
	Mono physical domain coupling device (energy distribution)
	Observer

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State-of-Health observer for PEM fuel cells—A novel approach for real-time online analysis
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Determining the State-of-Health (SoH) of fuel cell systems during operation is vital for implementing model-based control strategies that aim to minimize degradation and extend the fuel cell lifetime. This paper introduces a novel observer architecture designed to estimate the internal states as well as the SoH of fuel cell systems in real time. The proposed observer offers three key advantages: (1) it decouples the dynamics of internal states from SoH, thus enhancing numerical stability, (2) by incorporating multiple measurement points, assessing the SoH for various components within the fuel cell (e.g. membrane, catalyst layer) becomes possible, and (3) in combination with the used physical real-time capable model, the observer architecture facilitates real-time evaluation of the SoH during dynamic operation. The observer’s benefits are demonstrated through simulations and measurement data.
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A reduced-order model (ROM) is developed for proton exchange membrane fuel cells (PEMFCs) considering the non-isothermal two-phase effects, with the goal of enhancing computational efficiency and thus accelerating fuel cell design development. Using analytical order reduction and approximation methods, the fluxes and source terms in conventional 1D conservation equations are reduced to six computing nodes at the interfaces between each cell component. The errors associated with order reduction are minimized by introducing new approximation methods for the potential distribution, the transport properties, and the membrane hydration status. The trade-off between model accuracy and computational efficiency is studied by comparing the simulation results and computational times of the new model with a full 1D model. The new model is nearly two orders of magnitude faster without sacrificing too much accuracy (<4% difference) compared to the 1D model. The new model is then used to analyze the influence of the membrane electrode assembly (MEA) design on cell performance and internal state distributions, offering insights into MEA structural optimization. The model can be readily extended to account for more detailed physico-chemical processes, such as Knudsen diffusion or the influence of micro-porous layers, and it can be an effective tool for understanding and designing PEMFCs.
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Citation Excerpt :
This method aims at generating the reference current and considering the degradation state at the same time. Besides, the reference value of the gas can be calculated by the energetic macroscopic representation (EMR) model, and the maximum power which can be provided by the fuel cell stack is identified by the maximum power point tracking (MPPT) algorithm [95,96]. Recently, the FDKF and the four voltage degradation models (linear, quadratic, logarithmic, and exponential) are combined by Ao et al. [99].
The proton exchange membrane fuel cells (PEMFC) system is a promising eco-friendly power converter device in a wide range of applications, especially in the transportation area. Insufficient service life is one of the key issues that hinder its large-scale commercial application. Degradations of the materials, suboptimal operating procedures, and disturbances from the external environment and load all would have a terrible impact on the durability performance of PEMFC. Prognostic and health management (PHM) can estimate the remaining useful life (RUL) in advance and make the proper decisions at the right time to extend the service life of the system by condition-based maintenance. At the very least, the PHM can provide degradation information and reserve enough maintenance time for the operators to avoid some fatal damages. Analyzing the working principles and the degradation phenomena of the PEMFC system are the foundations of degradation prediction. Developing accurate and dynamic models to describe the degradation mechanisms, exploring accurate, efficient, and robust methods to realize the RUL prediction are some critical challenges of PHM nowadays, especially under dynamic operating conditions. This paper focuses on comparing different models for degradation mechanisms, discussing some key issues of PHM, and reviewing the degradation prediction methods.

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Model-based aging tolerant control with power loss prediction of Proton Exchange Membrane Fuel Cell

Highlights

Abstract

Introduction

Section snippets

PEMFC description

EMR for modeling

Degradation Tolerant Control framework

Background

Conclusion

Elements of the EMR and PCS formalism

Energy

Int J Hydrogen Energy

Int J Hydrogen Energy

Int J Hydrogen Energy

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Appl Energy

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Reliab Eng Syst Saf

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Renew Energy

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Struct Saf

Energy storage systems for transport and grid applications

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The department of energy hydrogen and fuel cells program plan

US Dep Energy

A review of the main parameters influencing long-term performance and durability of pem fuel cells

JPS