EJEEE
https://doi.org/10.62909/ejeee.2024.001 Edison Journal for Electrical and Electronics Engineering
Article
Fuel Cells with Proton Exchange Membrane Modeling and Con-
trol Techniques
Lalitesh Kumar Singh 1, *, , Qahtan Adnan Jameel 2,
1 chief executive officer, Vision Robotic India Pvt. Ltd, Delhi, India.; ceo@visionroboticindia.com
2 Dep. of computer and communication engineering, Islamic University of Lebanon, Lebanon;
qj76665@net.iul.edu.lb
* Correspondence: Tel.: +91-9899744637
Abstract: Comprehensive mathematical models with three distinct controllers (PID, FOPID, and
fuzzy + PID) for polymer electrolyte fuel cells (PEFCs) are constructed in this work. The models are
made to indirectly control the input hydrogen mass flow rate in order to set the output voltage of
the PEMFCs at a predetermined value. The simulation results demonstrate how effectively the es-
tablished model fits the task of characterizing a PEFC's performance. While the developed control-
lers are capable of stabilizing voltage, the fuzzy + PID controller performs better, exhibiting a re-
duced overshoot and a faster response time.
Keywords: fuzzy + PID controller; fuzzy + PID controller; FOPID controller; modeling
1. Introduction
Polymer electrolyte fuel cells, or PEFCs, have shown to be the best option for auto-
motive, stationary, and portable applications because of its great durability, low operating
temperature, and high-power density [1, 2].
In order to assess and forecast the behavior of the system and to maximize its output
performance, modeling studies and control strategies for PEFCs are crucial [3]. In ref. [4],
temperature regulation in a system model is achieved by employing traditional PID con-
trollers to enhance the PEFC dynamic stack behavior. A FOPID controller is employed in
ref. [5] to improve the PEFC's dynamic performance and efficiency. Fuzzy logical control
theory is applied in ref. [6] to optimize the PEFC system under high temperature condi-
tions.
An adaptive fuzzy logic controller (AFLC) is used in ref. [7] to obtain good control
effects for PEFC voltage control in the presence of fluctuations. Though very little research
has been done to compare the various controllers described above, each has been re-
searched in the past. A thorough mathematical model for perovskite energy converters
(PEFCs) is developed in this paper. More importantly, three distinct controllers—PID,
fuzzy + PID, and FOPID—are designed concurrently to control the PEFC system and
maintain a constant output voltage. Their various features and benefits are thoroughly
compared.
2. Materials and Methods
2.1. Static Model Electrochemical Equations
In this work, several necessary presumptions are taken into consideration for a more
practical examination of the PEFC models. These include perfect reactant gases, pure hy-
drogen as fuels, consistent temperature throughout the fuel cell, and the disregard of
Citation: L. Kumar Singh and. Q.
Adnan Jameel, “Fuel Cells with Pro-
ton Exchange Membrane Modeling
and Control Techniques”, ejeee, vol.
2, no. 1, pp. 1–5, Jan. 2024
Academic Editor: Prof. Dr. Omar Mo-
hammed Al-Shuja'a
Received: 2/11/2023
Revised: 10/12/2023
Accepted: 3/1/2024
Published: 15/1/2024
Copyright: © 2024 by the authors.
Submitted for possible open access
publication under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/license
s/by/4.0/).
EJEEE 2024, Vol.2 2 of 5
steam [8]. The electrochemical formulas utilized to describe the static characteristics of
PEFCs, such as voltage, power, efficiency, and temperature change, are all taken from [9].
2.2 The Dynamic Model
Fuel cells exhibit a phenomenon known as the "charge double layer," which is crucial
to comprehending the dynamic behaviors. Specifically, this phenomenon refers to the
build-up of charge or transfer of load on the surfaces of two separate charged materials
that come into contact with one another. The custody cover on the border electrode / elec-
trolyte functions as an electrical capacitor by storing electrical charges and energy [10].
Figure 1 shows the corresponding circuit diagram. The operating state settings, the exper-
imental data utilized for validation, and the thorough information about the PEFC's across
the static and dynamic method characteristics are all taken from [11].
Figure 1: Analogous circuit schematic
2.3 Voltage Control System
Because of its precise and quick correction to a control function, PID control is the
most exploited type of feedback regulator in modern functions. Three units make up this
composition: differential, integration, and proportion. An automobile tuning technique is
used to get the parameters [12]. Five parameters define the FOPID controller, a useful
fractional order structure used for control: (i) the proportional gain; (ii) the integrating
gain; (iii) the derivative gain; (iv) the integrating order; and (v) the derivative order. The
FOPID approach is based on ref. [13], with the two additional units (iv) and (v) indicating
that it is more accurate than the conventional PID controller. The fuzzy logical control
method and the PID control algorithm are combined to create the fuzzy + PID controller.
It has the ability to change PID parameters online, which could significantly enhance con
troller performance [14].
A PEFC system has numerous characteristics that can readily alter its output voltage.
It is a nonlinear, intricate, and strongly coupled system. In this study, the controllers reg-
ulate the mass flow rate of hydrogen to balance its voltage. Figure 2 displays the architec-
ture of the entire control system as well as the structures of three distinct controllers.
Figure 2: The controllers' and the control system's overall structures
EJEEE 2024, Vol.2 3 of 5
3. Results
3.1 The Static Model
Figure 3 displays the static behavior of the PEFC. From 0.1 A to 34.9 A, the supplied
load current is progressively increased. The calculated polarization curve shows an excel
lent agreement with the experimental results, as shown in Figure 3(a). The activation po-
larization causes the stack voltage to fall quickly at first. Ohmic polarization causes it to
decrease linearly with increasing current, and when the current increases more, the volt-
age lowers dramatically. As the power behavior is displayed in Figure 3(b), a peak with a
value of 833.9 W at the current of 30.9 A is visible. The behavior of the stack efficiency,
which is displayed in Figure 3(c), is comparable to that of voltage. For low current and
low power, the efficiency is excellent, which is crucial for assessing the PEFC system.
Figure 3: PEFC static model simulation results
3.2 The Dynamic Model
The dynamic behavior of PEFC is seen in Figure 4. In Figure 4(a), the load receives
4.9 A from the stack after 2.99 s, and concurrently, the current is increased to 14.99 A,
staying at that level for 5.99 s. At last, the load current is reduced to 5 A, lasting until the
simulation's 10-second end. Figure 4(b) shows the voltage curve, and it is evident that
there is a reaction delay when the load current suddenly changes. Before the current is
increased, the voltage is 39.459 V; it is 34.95 V when the current is maintained at 14.99 A;
and it is 39.45 V once more after the load is reduced. The stack power response is depicted
in Figure 4(c), peaking at the first instant of rise in load current and reaching a maximum
value of 579.98 W. When the current starts to drop, the power shows a minimum of 179.97
97 W. In a steady-state scenario, the power would be 195.48 W at 4.99 A of current and
529.8 98 W at 14.99 A of current. The stack efficiency is displayed in Figure 4(d). Given
their direct relationship, the curve and the voltage curve are only slightly different. It is
clear that when load current is raised, efficiency significantly decreases. The steady-state
values for stack efficiency are 52.99% (HHV) for a current of 4.99 A and 45.98% (HHV) for
a current of 14.99 A. It is evident that when load current increases, efficiency significantly
decreases. This is something that needs to be considered while assessing a certain system.
Figure 4: a and b show the PEFC dynamic model simulation results.
EJEEE 2024, Vol.2 4 of 5
Figure 4: c and d show the PEFC dynamic model simulation results.
3.3 Voltage Control System
The three distinct controllers are built and implemented in accordance with Figure
4(d) using the parameters, with the outcomes displayed in Figure 5. The input current in
Figure 5(a) starts at 3 A and increases to 5 A after 30 seconds, staying at that value until
the simulation is finished. It is evident from Figure 5(b) that each of these three controllers
is able to describe the systematic disturbance and keep the voltage at the specified level.
With a lesser overshoot, it is evident that the FOPID controller outperforms the PID con
troller by a little margin. The Fuzzy + PID controller performs the best, responding the
fastest and with the least amount of overshoot.
Figure 5: Voltage control results
5. Conclusions
This work develops extensive scientific patterns of PEFCs, including PID, FOPID,
and Fuzzy + PID controllers. These controllers are intended to manage the output voltage
of PEFCs by adjusting the mass flow rate of hydrogen. Fuzzy + PID controllers are chosen
because they can adjust PID parameters online, which will improve control performance
when compared to traditional PID controllers. The use of FOPID controllers is prompted
via the statement that the existence of additional tuning parameters (fractional parame-
ters) allows excellent plasticity in realizing the model designs. The results of the simula-
tion demonstrate that the created model is a good fit for explaining both the dynamic
behavior and steady-state performance of the PEFC. Furthermore, a very good agreement
between the model predictions and experimental studies is demonstrated. The Fuzzy +
PID controller displays the highest deed with a reduced overshoot and a faster response
time, but all three controllers are equally good in tracking the reference voltage and limit-
ing system disruption. The findings in this research can be applied to better optimize the
fuel cells' total cost and efficiency.
Conflicts of Interest: Declare conflicts of interest or state “The authors declare no conflict of inter-
est.”
EJEEE 2024, Vol.2 5 of 5
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