A modified fractional‑order-based future search algorithm for performance enhancement of a PEMFC-based CCHP

ABSTRACT

Load control and cost optimization are considered to be crucial in tri-generation or combined cooling, heating, and power (CCHP) systems. In this study, an inventive CCHP system employs an FC system as its first mover and includes a heat exchanger, a heat recovery, as well as an auxiliary boiler, an electric chiller, and an absorption chiller. The electrical grid is linked to this system. The idea here is to maximize the system’s performance from a financial perspective and to make the annual expenditure of the system minimum over a 20–year period that is considered as the cycle life-span. It is a multi-objective optimization problem which is optimized using a newly introduced metaheuristic optimization method and a Fractional-order future search optimizer. The findings of this study are used to divine an ideal configuration of the CCHP. Finally, to demonstrate the higher efficiency of the suggested method, a comparison should be conducted among the optimization results of the fractional-order-based future search algorithm, the results of Non-dominated Sorting Genetic Algorithm II (NSGA-II), and standard future search algorithms in previous studies. Based on the results presented, the proposed Fractional-order Future Search Algorithm (FOFSA) was able to optimize the performance of a PEMFC-based CCHP system more effectively than conventional methods. The system’s exergy efficiency was found to decrease from 52% at 793 mA/cm2 current density to 36% at 1000 mA/cm2 current density. However, with the application of FOFSA, the suggested optimal system had a higher exergy efficiency of 41.6% and a yearly cost of $2765, resulting in the maximum annual greenhouse gas (GHG) reduction of 4.48E6 g. Therefore, in summary, the proposed FOFSA yielded an optimized CCHP system configuration that had higher energy efficiency, lower annual cost, and reduced GHG emissions. These findings highlight the effectiveness of the FOFSA method in optimizing the performance of PEMFC-based CCHP systems.

KEYWORDS:

• Combined heating
• cooling
• and power cycle; proton exchange membrane
• fuel cell; economic performance
• annual cost; fractional-order future search algorithm

Nomenclature

Symbol	=	Explanation
CCHP	=	Combined cooling, heating, and power
NSGA-II	=	Non-dominated Sorting Genetic Algorithm II
FOFSA	=	Fractional-order Future Search Algorithm
GHG	=	Greenhouse gas
IMPO	=	Improved marine predators optimizer
PROX	=	Preferential oxidation
PCM	=	Phase change material
DAC	=	Desiccant air conditioning
HX	=	Heat-exchanger
MEA	=	Membrane-electrode assembly
$N_s$	=	The connected cells’ quantity
$E_N$	=	The open-circuit Nernst relation ($V$)
$V_{loss}$	=	The overall voltage loss ($V$)
$V_{con}$	=	Concentration loss ($V$)
$V_{act}$	=	Activation loss ($V$)
$V_{\mathrm{\Omega }}$	=	Ohmic loss ($V$)
$E_N$	=	The stack output voltage ($V$)
$E_0$	=	The open-circuit voltage of the cell ($V$)
$F$	=	The Faraday’s constant ($C/mol$)
$R$	=	The universal gas constant ($J/\left(mol.K\right)$)
$T$	=	The operating temperature
$P_{O_2}$	=	The partial pressure of $O_2$ ($Pa)$
$P_{H_2}$	=	The partial pressure of $H_2$ ($Pa)$
$P_{H_{2}O}^c$	=	The partial pressure of steam ($Pa)$
$R_{hc}$	=	The vapor relative humidity in cathode
$R_{ha}$	=	The vapor relative humidity in anode
$I$	=	The FC’s current operating ($A$)
$A$	=	The FC’s membrane active area ($m^2$)
$P_C$	=	The inlet partial pressure in electrodes for cathode ($Pc$)
$P_A$	=	The inlet partial pressure in electrodes for anode ($Pa$)
$R_c$	=	The resistance of connections ($k\mathrm{\Omega }$)
$R_m$	=	The resistance of membrane ($k\mathrm{\Omega }$)
${\rho }_m$	=	The resistivity of the membrane ($\mathrm{\Omega }.m$)
$l$	=	The thickness of the membrane ($m$)
$\lambda$	=	A changeable variable
$I$	=	The current of fuel cell stack ($A$)
$I_0$	=	The limiting current ($A$)
$n$	=	The charge transfer coefficient
$b_m$	=	The mass transfer voltage ($V$)
${\eta }_{ex}$	=	The system’s exergy efficiency
$P_{CCHP}$	=	The produced electric energy in the system
$E{x}_e$	=	The provided cooling exergy
$E{x}_{hw}$	=	The provided hot water exergy
$E{x}_{CCHP}$	=	The consumed fuel exergy in the system
$S_{H2}$	=	The $H_2\hspace{0.17em}$stoichiometry
$R_{H2}$	=	The molar rate of fuel consumption ($mol.s^{-1}$)
$E{x}_{H2}$	=	The exergy of the standard chemical for 1 mol hydrogen
$\hspace{0.17em}{T}_c$	=	The temperature of chiller’s cooling water
$T_0$	=	The surrounding temperature
$\hspace{0.17em}{T}_{hw}$	=	The temperature of hot water
$Cos{t}_{inv}$	=	The CCHP system’s original investment cost
$Cos{t}_f$	=	Overall fuel cost
$Cos{t}_{mt}$	=	Maintenance cost
$Cos{t}_f$	=	Total fuel cost of the proposed system
$M{c}_{H2}$	=	hydrogen’s molar capacity ($kg/mol$)
$Cos{t}_{H2}$	=	The hydrogen generation unit cost ($\mathrm{\$}/kg$)
$T_{rt}$	=	The overall functioning duration of the system ($year$)
$C{o}_{av}$	=	The CCHP system’s average yearly cost
PER	=	Pollution-related emission reduction
$E{m}_{st}$	=	The station’s air pollutant emissions
$E{m}_{GHG}$	=	The formed greenhouse gas emissions during the production of energy
$E_{eq}$	=	In the two systems, all of the energy kinds were translated into equal electric power
$E_{hw}$	=	The heated water’s transformed electricity
$E_{FC}$	=	The electricity of the fuel cell
$E_c$	=	The altered cooling volume
$CO{P}_{tc}$	=	The electric air-conditioning
$CO{P}_{WH}$	=	Co-efficient performance of Water heater
$E{m}_{red}$	=	The yearly reduction in green-house gas emission
$E{m}_{H2}$	=	The annual green-house gas emissions from $H_2\hspace{0.17em}$generation
$E_{GHG}$	=	The greenhouse gas emissions created by the wind-based $H_2$ generation system
$H{V}_{H2}$	=	The heat value of the system’s annual hydrogen consumption

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Biao Lu

Biao Lu obtained a master's degree in computer science and a master's degree in computer application from Nanjing University of Posts and telecommunications in Nanjing, China. She is a professor and her main research interests are artificial intelligence and software engineering Dr. Navid Razmjooy is a Postdoc researcher at the industrial college of the Ankara Yıldırım Beyazıt Üniversitesi. He is also a part-time assistant professor at the Islamic Azad University, Ardabil, Iran. His main areas of research are the Renewable Energies, Machine Vision, Soft Computing, Data Mining, Evolutionary Algorithms, Interval Analysis, and System Control.

Navid Razmjooy

Navid Razmjooy studied his Ph.D. in the field of Electrical Engineering (Control and Automation) from Tafresh University, Iran (2018). He is a senior member of IEEE/USA and YRC in IAU/Iran. He has been ranked among the world's top 2% scientists in the world based on the Stanford University/Scopus database. He published more than 200 papers and 6 books in English and Persian in peer-reviewed journals and conferences and is now Editor and reviewer in several national and international journals and conferences.