Model-based aging tolerant control with power loss prediction of Proton Exchange Membrane Fuel Cell
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:
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We develop a control law which takes into account the SoH
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Based on the SoH estimation, the strategy is able to adjust the objective in order to compute the correct input references during the aging
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An algorithm estimating the maximum power the converter can provide through aging is detailed
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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:
Between the electrodes is created a difference of potential 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 . 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:
Obtaining 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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2022, Journal of Power SourcesCitation 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].