Cell voltage static-dynamic modeling of a PEM electrolyzer based on adaptive parameters: Development and experimental validation

doi:10.1016/j.renene.2020.09.106

Renewable Energy

Volume 163, January 2021, Pages 1508-1522

https://doi.org/10.1016/j.renene.2020.09.106 Get rights and content

Highlights

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An adaptive cell voltage model has been developed for PEM electrolyzer.
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The developed model is based on static and dynamic characterization.
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Dynamics and current ripple issues have been discussed.
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An equivalent electrical model has been used to model each cell voltage.
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Experimental tests have been performed to validate the e_ectiveness of the model.

Abstract

This article aims to propose and experimentally validate a static-dynamic electrical model of a proton exchange membrane (PEM) electrolyzer. The originality of this work concerns the cell voltage modeling according to static and dynamic operations. Indeed, the cells of the PEM electrolyzer may be subjected to degradations due to the operating conditions and current ripple generated by power electronics. Hence, cell voltage response and efficiency may be affected. For this reason, it is crucial to model each cell voltage to investigate the degradation and wear effects mainly caused by the dynamic operating conditions met when coupling with renewable energy sources and current ripple from power electronics. To develop an accurate model, static and dynamic operations are investigated on a commercial-400 W PEM electrolyzer stack. To enhance the accuracy of the model in replicating the real behavior of the electrolyzer, the parameters of the model are adapted according to the input current. The comparison between the experimental data and the developed model has enabled confirming the effectiveness of the model to reproduce the cell voltage static and dynamic behavior according to the input current.

Introduction

To face the rise of global temperature due to a large amount of greenhouses gases released by human activities (i.e. transportation, electricity, industrial), the development of renewable energy sources (RES) (i.e. wind energy, solar energy, hydro energy) has been growing up over the last decade [1,2]. Wind, sun, and water are abundant and inexhaustible sources and can be employed to generate green energy and fuel (i.e. hydrogen) to compensate for the depletion of fossil fuels [3]. Hydrogen can be produced either in large plants located in areas where energy from RES is exploitable with greater convenience or through small generation units that exploiting local renewable energy potential [[4], [5], [6]]. Water electrolysis is a well-established technology that represents one of the simplest processes to generate decarbonized hydrogen and oxygen by using electricity coming from RES [6,7]. In water electrolysis process based on RES, produced and stored hydrogen can be useful for transportation (e.g. development of hydrogen fueling stations for fuel cell electric vehicles), energy storage (e.g. to cope with intermittent energy disturbances), power-to-gas (e.g. production of green natural gas such as green methane), and industry (e.g. chemical, metallurgic, and electronic applications) [8,9]. Besides, compared to processes based on fossil fuels, the water electrolysis process allows generating high-purity hydrogen (up to 99.999 vol%), suitable for direct use in low-temperature fuel cells, which are sensitive to impurities of the hydrogen stream [10]. The water electrolysis is based on the principle of dissociation of water, where two molecules of water are separated into two molecules of hydrogen and one molecule of oxygen using electricity [11,12]. Currently, there are three main types of electrolyzers according to their electrolyte: Alkaline electrolyzer, Proton Exchange Membrane (PEM) electrolyzer, and Solid Oxide (SO) electrolyzer.

In recent years, the PEM electrolyzer technology has attracted a lot of attention from the field of scientific research and from industry due to its simplicity, high current density, high energy efficiency, compact system design, high-pressure operation, and specific production capacity [[13], [14], [15]]. Furthermore, compared to alkaline technology based on a liquid electrolyte (making slower the ion transportation), PEM technology is particularly fit to be coupled with RES since it offers high flexibility (i.e. large partial load range) by responding quickly to dynamics as it has been reported in the literature [16,17]. This feature is important to capture energy during dynamic operations, which are consistent when using RES. In Ref. [18], a survey of the most significant scientific and technological materials to manufacture the PEM electrolyzer has been reported. During the operation, the PEM electrolyzer is commonly integrated into the electrical grid including RES. Therefore, its operation is inherently intermittent, and the development of mathematical models replicating its dynamics is required even at the design stage since they ensure efficient and reliable operation of the electrolysis [19,20]. Besides, the PEM electrolyzer dynamic modeling is a powerful tool for simulation, investigation of control strategies through power electronics, prediction, and understanding of the behavior of hydrogen-generation systems [21,22].

The dynamic modeling research for PEM electrolyzers has been intensified in the last few years, inspired by PEM fuel cell models [19,23]. The first work about the dynamic model has been reported in Ref. [24], where the authors have developed a model including four subsystems related to the anode, cathode, membrane, and an auxiliary component that models the relation between voltage and electric current. Some years later, the work [21] presented the development of a complete model based on modules describing the behaviors of the anode, cathode, membrane, and cell voltage. In Ref. [25], an electrochemical model of the electrolyzer stack to calculate the theoretical open-circuit using thermodynamic analysis has been developed. The work [26] has reported a model based on thermodynamics and electrochemical equations. This model has fitted a steady-state electric model with a dynamic thermal model. Following this approach, recent reviews for alternative PEM and alkaline dynamic models have been presented in Ref. [27,28]. However, dynamic models for the electrolyzer voltage are very scarce; in Ref. [29] a static-dynamic model for voltage based on the thermodynamic, activation, double-layer, and ohmic effects has been developed, unfortunately, this model only applies for alkaline electrolyzer. The work [30] has investigated the voltage responses of a PEM electrolyzer supplied by dynamic current profiles. Hence, the authors have developed a static-dynamic model for the stack voltage considering dynamic operating conditions. They have demonstrated that dynamic behavior is strongly dependent on the input current. However, the parameters used in the paper [30] have been determined for a specific current range, making the model less reliable for other operating conditions. Based on this previous work, a complementary work has been carried out in Ref. [31] to develop a static-dynamic model for PEM electrolyzer voltage associated with an algorithm to compute its parameters based on different electrical current inputs. Hence, the accuracy of the model in replicating the dynamic behavior of the electrolyzer can be improved.

In the continuity of this previous work, it has been decided to analyze the cell voltages and their responses according to static and dynamic operations. This analysis is carried out by performing experiments on a commercial-400 W PEM electrolyzer (composed of three cells) to develop an accurate cell voltage static-dynamic model based on adaptive parameters according to the input current. The experiments consist of increasing and decreasing the current with a step of 1 A on each cell to investigate its behavior. This work on modeling each cell voltage instead of the stack voltage (as presented in Ref. [31]) is motivated by the fact that cell voltage response and efficiency may undergo degradations during their operations due to dynamic solicitations (particularly important in RES) and low and high-frequency current ripple from power electronics (AC-DC and/or DC-DC converters) [32,33]. Several works on performance degradation in PEM water electrolysis have been reported in the literature [[34], [35], [36], [37], [38]]. These relevant works have demonstrated that PEM water electrolysis cells may be subjected to degradations due to dynamic operations and operating conditions (e.g. current density, temperature). However, the effects of current ripple from power electronics on PEM electrolysis cell performance are still a remaining key issue [32]; while many works have been reported for PEM fuel cells [[39], [40], [41]]. For this reason, cell voltage modeling is a powerful tool to study the degradation and wear effects from dynamic operations and current ripple.

This work is divided into five sections. After introducing the current state-of-the-art and motivations to carry out this work, Section 2 aims at presenting the experimental test rig and the responses of PEM electrolyzer cells during dynamic operations. Besides, a discussion is provided regarding the current ripple issues and their impacts on voltage cell efficiency. Then, in Section 3, the PEM equivalent electrical circuit is presented, and its mathematical modeling is provided. Afterward, in Section 4, the algorithm to determine the parameters of the model based on different electrical current inputs is introduced and explained in detail. Finally, in Section 5, the equivalent electrical model based on adaptive parameters is validated by comparing the obtained results with experiments performed on a commercial-400 W PEM electrolyzer. Besides, a discussion is provided to summarize and conclude on the obtained results.

Section snippets

Description of the experimental test rig

To analyze the dynamics of the three cells that are part of a commercial PEM electrolyzer, an experimental test rig has been realized at the GREEN laboratory, IUT de Longwy, as shown in Fig. 1. The experimental test rig is composed of the following devices and components: (1) a laptop with a virtual control panel to control the DC power supply, (2) a DC power supply, (3) a 4-channel oscilloscope, (4) a pure water tank, (5) a commercial-400 W PEM electrolyzer (composed of three cells), (6) a

Equivalent electrical circuit and mathematical modeling

As it is widely known, the real cell voltage $V_{cell}$ in a PEM electrolyzer can be expressed as the sum of the reversible voltage and its overvoltages [15]. $V_{cell} = V_{rev} + η_{act} + η_{ohm} + η_{con}$ where $V_{rev}$ is the reversible voltage, $η_{act}$ , $η_{ohm}$ , and $η_{con}$ are the activation, ohmic and concentration overvoltages.

On one hand, the equation (1) represents the static model of the electrical domain. This static model has been employed by many authors as reported in the literature [45,46]. On the other hand, in Ref. [30

Assessment of the parameters of the developed models

In this section, the parameters of the equation (13) are estimated for each cell of the PEM electrolyzer stack (cell 1, cell 2, and cell 3). These parameters are: $V_{rev}$ , $R_{mem}$ , $η_{act, c} (0)$ , $η_{act, a} (0)$ , $C_{c}$ , $C_{a}$ , $R_{c}$ , $R_{a}$ , $τ_{c}$ , and $τ_{a}$ . Using the Ohm’s law, $η_{act, c} (0)$ and $η_{act, a} (0)$ are obtained as: $\begin{matrix} η_{act, c} (0) = R_{c} \cdot i_{cell}, & η_{act, a} (0) = R_{a} \cdot i_{cell} . \end{matrix}$

The parameters $R_{c}$ and $R_{a}$ have been determined by employing the equations (6), (7). To make easier the construction of an electrical circuit, the capacitors are considered

Validation and discussion

First of all, the developed model and its parameters have been tested by using the experimental data. From these data, the PEM electrolyzer cell voltages can be obtained by simulations. Besides, to assess the effectiveness of the model in reproducing the real behavior of the electrolyzer, the relative error $E_{r}$ and the mean error $E_{m}$ have been calculated for all different experimental tests as follows: $\begin{matrix} E_{r} = (\frac{100}{N_{d}}) \cdot \overset{N_{d}}{\sum_{k = 1}} | \frac{V_{exp, k} - V_{sim, k}}{V_{exp, k}} |, & E_{m} = \frac{\overset{N_{d}}{\sum_{k = 1}} | V_{exp, k} - V_{sim, k} |}{N_{d}} \end{matrix}$ where $N_{d}$ is the number of

Conclusion

The main objective of this work was to develop an equivalent electrical model with adaptive parameters for static and dynamic operating conditions. The originality of the modeling approach consists in modeling the electrical domain of each cell to increase the reliability of the model in predicting the cell and stack voltage. This approach is motivated by the fact that the cells composing the PEM electrolyzer may be subjected to degradations during its operation due to current ripple from power

CRediT authorship contribution statement

Ángel Hernández-Gómez: Software, Validation, Formal analysis, Writing - original draft, Visualization. Victor Ramirez: Conceptualization, Formal analysis, Investigation, Writing - review & editing, Visualization, Supervision, Funding acquisition. Damien Guilbert: Conceptualization, Methodology, Investigation, Resources, Data curation, Writing - original draft, Visualization, Project administration. Belem Saldivar: Writing - review & editing, Visualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work has been supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) Mexico.

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