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Self-adaptive henry gas solubility optimizer for identification of solid oxide fuel cell

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Abstract

Fuel cell is the best suggestion to replace internal combustion engines. Fuel cell systems have no pollution and no moving parts. The efficiency of fuel cells is more than three times that of internal combustion engines. Modeling the behavior of solid oxide fuel cells has special complications, and determining its performance according to its structural characteristics is one of the required parameters to further understand the behavior of solid oxide fuel cells. In this study, a new methodology is presented for optimal parameters estimation of the solid oxide fuel cell (SOFC) model. This paper's major goal was to provide a novel, efficient method for estimating the SOFC model's unknown parameters. To achieve this, the sum of squared errors between the output voltage of the proposed model and the experimental voltage measurements should be as little as possible. To reduce the error value, this study developed a better metaheuristic algorithm dubbed the Self-adaptive Henry Gas Solubility Optimizer. The developed method was then used with a 96-cell SOFC stack, and the sensitivity analysis was carried out while using various optimization algorithms at various temperatures and pressures. When 150 data points from a temperature sensitivity analysis at five temperatures, including 625 °C, 675 °C, 725 °C, and 775 °C under constant pressure, values of 3 atm, were taken into consideration, the smallest error was 9.41 e–5 for 575 °C. For pressure variations between 1 and 5 atm at constant temperatures of 775 °C, the lowest inaccuracy was 8.21 e–3 for 1 atm. Simulation results show that the proposed approach is more effective than the other techniques as an identifying tool.

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Abbreviations

SOFCs:

Solid oxide fuel cells

FCs:

Fuel cells

IRFO:

Improved Red Fox Optimizer

SSE:

Sum of Squared Error

MPO:

Marine Predator Optimizer

ECM:

The electrochemical model

SSM:

The steady-state model

\({V}_{T}\) :

The outputted voltage of the SOFC

\({V}_{\Omega }\) :

The ohmic voltage drop

\({V}_{act}\) :

The activation voltage

\({\mathrm{V}}_{\mathrm{C}}\) :

The concentration voltage drop

\(\mathrm{N}\) :

The quantity of the cells

\({E}_{N}\) :

The open circuit voltage

\({E}_{0}\) :

The reversible potentiality

\(T\) :

The operational temperature

\({P}_{{O}_{2}}\) :

The partial pressure for \({O}_{2}\)

\({P}_{{H}_{2}}\) :

The partial pressure for \({H}_{2}\)

\({P}_{{H}_{2}O}\) :

The partial pressure for \({H}_{2}O\)

\({P}_{a}\) :

The inlet pressure in anode

\({P}_{c}\) :

The inlet pressure in cathode

\({R}_{ha}\) :

The relative humidity of vapor at the positive electrodes sides

\({R}_{hc}\) :

The relative humidity of vapor at the negative electrodes sides

\({P}_{{H}_{2}}^{*}\) :

The partial pressure of the hydrogen

\({P}_{{O}_{2}}^{*}\) :

The partial pressure of oxygen

\({P}_{{H}_{2}O}^{*}\) :

The partial pressure of water

\({V}_{A}\) :

The activation voltage drop

\({C}_{T}\) :

The Tafel coefficient

\(S\) :

The slope

\({R}_{\Omega }\) :

The resistance of the device area (kΩ cm2)

\({I}_{L}\) :

The constraint of current density (mA cm2)

\({I}_{0}^{c}\) :

The exchanging flow’s current density of the cathode

\({I}_{0}^{a}\) :

The exchanging flow’s current density of the anode

MSE:

The means square error

\(N\) :

The sample number of the voltage data

\({V}_{T}\) :

The terminal output voltage data

\({V}_{exp}\) :

The experimental output voltage data

SS:

Sum of squares

GoF:

Goodness-of-fit

RMSE:

Root mean squared error

PUBG:

Player Unknown's Battlegrounds

\({z}_{dam.d}\) :

The location of the injured soldier

\(r\) :

Random amount in the range [0, 1]

\({z}_{j}\) :

The amount of damage of \(jth\) soldier

\({ub}_{d}\) :

The upper bounds in solution space

\({lb}_{d}\) :

The lower bounds in solution space

\(\omega\) :

The initial value of solution space

\({z}_{best.d}\) :

The best solution ever found in dimension \(d\)

\(SD\left(\overline{{z }_{d}}\right)\) :

The standard deviation of entire population

\(m\) :

The number of iterations

\(n\) :

The number of populations

\({\overrightarrow{z}}_{\mathrm{j}}^{\mathrm{new}}\) :

The opposite position of \({\overrightarrow{z}}_{j}\)

\({\overrightarrow{z}}_{\mathrm{j}}^{min}\) :

The minimum limitations of the solution

\({\overrightarrow{z}}_{\mathrm{j}}^{max}\) :

The maximum limitations of the solution

\({r}_{1}\left(j+1\right)\) :

The chaotic random value generated during the current iteration

\({r}_{1}\left(j\right)\) :

The chaotic random value generated in the preceding iteration

PSO:

Particle Swarm Optimizer

WO:

Whale Optimizer

AO:

Archimedes Optimizer

SCSO:

Simplified competitive swarm optimizer

SBO:

Satin Bowerbird Optimizer

CGWO:

Chaotic grey wolf optimization algorithm

TLBO:

Teaching-learning based algorithm

DBRA:

Developed Battle Royal optimizer algorithm

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Acknowledgements

2021 University-level Research Projects (Natural Sciences) (GKY-2021KYYBK-2), Study on performance stability of cathode materials for solid oxide fuel cells. 2020 University-level Research Projects (Natural Sciences) (GKY-2020KYYBK-2), Preparation and performance study of solid oxide fuel cell cathode material La0.5Ba0.5CoO3-δ.

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Guangdong University of Science and Technology, Dongguan, 523083, Guangdong, China

    Hongxia Xu

  2. Department of Engineering, Ardabil Branch, Islamic Azad University, Ardabil, Iran

    Navid Razmjooy

  3. Department of Computer Science and Engineering, Division of Research and Innovation, Saveetha School of Engineering, SIMATS, Chennai, 602105, Tamil Nadu, India

    Navid Razmjooy

  4. College of Technical Engineering, The Islamic University, Najaf, Iraq

    Navid Razmjooy

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  1. Hongxia Xu
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Correspondence to Hongxia Xu.

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Xu, H., Razmjooy, N. Self-adaptive henry gas solubility optimizer for identification of solid oxide fuel cell. Evolving Systems 15, 133–151 (2024). https://doi.org/10.1007/s12530-023-09517-w

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