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AIP Advances ARTICLE scitation.org/journal/adv
New hybrid maximum power point tracking
methods for fuel cell using artificial intelligent
Cite as: AIP Advances 13, 045207 (2023); doi: 10.1063/5.0144806
Submitted: 6 February 2023 •Accepted: 15 March 2023 •
Published Online: 4 April 2023
Masoud Safarishaal1,a) and Mohammad Sarvi2, b)
AFFILIATIONS
1Department of Electrical and Computer Engineering, University of Oklahoma, Norman, Oklahoma 73019, USA
2Iran Electrical Engineering Department, Imam Khomeini International University, Qazvin, Iran
a)Author to whom correspondence should be addressed: masoud.safari@ou.edu
b)Electronic mail: sarvi@eng.ikiu.ac.ir
ABSTRACT
An efficient way to raise the proton exchange membrane fuel cell’s (PEMFC’s) power generation efficiency and power supply quality is to
use maximum power point tracking (MPPT). Conventional MPPT approaches often have difficulty producing an effective control effect due
to the PEMFC’s inherent nonlinear characteristics. Another challenge for systems that track maximum power points is dealing with fast
changes in operational conditions that affect FC’s maximum power point (MPP). The main contribution of this study is the introduction of
two artificial intelligence-based MPP control approaches for fuel cells operating under rapidly changing operating conditions. These methods
are based on imperialist competitive algorithm-trained neural networks and adaptive neuro-fuzzy inference systems (ANFIS) (ICA NN). The
proposed approaches determine the fuel cell voltage that corresponds to the maximum power point. Following that, a fuzzy logic controller
is used to modify the duty cycle of a DC/DC boost converter for FC MPP tracking. The MATLAB environment is used to run simulations.
The results of the proposed method are compared with those of the conventional fuzzy method. The results demonstrate that the suggested
solutions function excellently in both normal operating conditions and quickly varying operating conditions. On the other hand, the suggested
approaches can quickly locate and monitor the MPP of FC. Additionally, the suggested techniques increase the FC system’s efficiency by
absorbing more power.
©2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0144806
I. INTRODUCTION
One of the most interesting green energies is fuel cell technol-
ogy, which is a type of power generation equipment that directly
transforms chemical energy into electric energy. Fuel cells are avail-
able in a variety of types. Proton Exchange Membrane (PEM) fuel
cells are one of the fuel cell types that are most frequently employed.
Because it can start up quickly, has a high-power density, and oper-
ates at a low temperature, the proton exchange membrane fuel cell
(PEMFC) is the best alternative to traditional power supply. These
features make PEM falling cells an excellent choice for home and
automotive applications. PEM fuel cells start up quickly, have a high-
power density, and have a low operating temperature. PEM falling
cell is a good choice for residential and automotive applications
due to these characteristics.1,2 There is a nonlinear P–I character-
istic in fuel cells. The literature has in-depth discussions of the fuel
cell P–I characteristic.3The low energy conversion efficiency of fuel
cells is one of their weaknesses. The Maximum Power Point (MPP),
which is impacted by temperature and membrane water content,
must therefore be operated around for a fuel cell system to perform
at its most efficient. The fuel cell has an ideal operating point where
it can produce the most power at a specific temperature and with a
specific amount of water in the membrane. Fuel cells have a nonlin-
ear output characteristic, and their generating power fluctuates with
the amount of water in the membrane and the ambient temperature.
Therefore, the ability to get the most power possible out of a fuel
cell is a key factor that must be considered for the best design of a
fuel cell system. To reduce the amount of fuel required, the MPP
controller will extract the most power possible from the PEMFC
system. For solar systems, a few MPPT techniques were proposed
and researched.4–6 These techniques have been classified into three
main categories:6offline techniques, online techniques, and hybrid
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FIG. 1. PEMFC model.
techniques. Open circuit voltage technique (OCV), short circuit
current method (SCC), and the MPPT method based on artificial
intelligence (AI) are a few examples of offline methods.7–10 Some of
the online maximum power point tracking approaches are Pertur-
bation and Observation (P&O), Extremum Seeking Control (ESC),
and Incremental Conductance (Inc Cond).11–13 The hybrid meth-
ods fall under the third group. The control signal for the algorithm
in these methods has two parts. According to one of the simplified
offline methods, the first part is calculated as a constant value that
is dependent on the fuel cell’s operational conditions and reflects
the fixed steady-state value. A steady-state search-based online tech-
nique may be used to produce the part of the control signal, which
would indicate attempts to precisely track MPP. These techniques
are expected to more effectively track MPP.6A hybrid approach
using the open circuit voltage and P&O was put forth for photo-
voltaic (PV) systems in Ref. 14. A modified P&O technique based
on fuzzy logic that is optimized for small fluctuations near the MPP
is utilized in Refs. 15 and 16 when the MPP region is reached. A
FIG. 2. P–I characteristics of the fuel cell: (a) at different temperatures and (b) at different membrane water content.
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FIG. 3. The block diagram of three MPP trackers for FC: (a) the proposed ANFIS-based MPP tracking, (b) the proposed ICA-based MPP tracking, and (c) the conventional
fuzzy MPP tracking.
hybrid method is presented in Refs. 17 and 18 that uses an offline
technique to get the PV array’s operating point near the MPP before
employing an online Inc conductance method to track the MPP
with high accuracy. The issue that the MPPT technique attempts to
FIG. 4. Power–voltage (P–V) characteristic of the fuel cell.
solve is how to automatically determine the maximum power point
voltage or current at which a system should operate to achieve the
maximum power output under predetermined (and unpredictable)
operating parameters. Ahmadi et al.19 proposed an MPPT for
PEMFC based on the particle swarm optimization (PSO) and PID
controller (PSO-PID), but there are problems of local optimization
and too slow optimization speed. Harrag and Messalti20 addressed a
variable step fuzzy-based MPPT controller, but the setting of fuzzy
rules and proportional quantization factors needed the support of
practical experience. Mallick and V. Mukherjee21 proposed an adap-
tive hybrid controller based on artificial neural network (ANN),
which successfully tracked MPP with less oscillation under variable
temperature.
In our study, two new hybrid control methods for tracking the
fuel cell system’s maximum power point are proposed in order to
increase the response to quickly changing conditions. First, Adap-
tive Neural Fuzzy Inference Systems (ANFIS) and a Fuzzy Logic
(FL) controller are combined to perform MPP tracking. To estimate
the fuel cell voltage that will produce the highest power, ANFIS is
applied. The ANFIS system inputs are temperature and membrane
water content, and its output is the reference voltage. Following
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FIG. 5. Membership functions of (a) input E, (b) input CE, and (c) output dD.
that, tracking MPP is carried out by modifying the duty cycle of
a DC/DC boost converter to ensure that the fuel cell voltage stays
at the MPP working point. The power electronics converter’s duty
cycle is changed to shift the operating point as rapidly as possible
toward the MPP region, which enhances transient response. Over
the past ten years, the fuzzy logic control has drawn much interest
due to its ability to handle nonlinearity, deal with imprecise inputs,
and not require a perfect mathematical model.19,20 ANFIS combines
the learning capability and other benefits of neural networks with the
knowledge representation offered by fuzzy inference systems, mak-
ing it applicable to a wide range of challenging issues. The simple
addition of new input parameters to the model without changing
the structure of the model and the automatic search for the non-
linear relationship between the inputs and outputs are additional
benefits of the ANFIS system over classic estimate techniques.21,22
The second method is to use a trained neural network and
the Imperialist Competitive Algorithm (ICA) to estimate the
maximum power point. Neural Networks (NNs) are currently uti-
lized frequently in prediction, modeling, and identification as an
acceptable method.23 For the implementation of MPP searching,
TABLE I. The fuzzy rule bases of the presented fuzzy controller.
E/CE NB NM NS ZE PS PM PB
NB NB NB NB NB NM NS ZE
NM NB NB NB NM NS ZE PS
NS NB NB NM NS ZE PS PM
ZE NB NM NS ZE PS PM PB
PS NM NS ZE PS PM PB PB
PM NS ZE PS PM PB PB PB
PB ZE PS PM PB PB PB PB
techniques based on NNs24,25 and FL26–28 have been used suc-
cessfully recently. However, determining the optimum weight fac-
tors for the network structure through trial and error takes a
lot of time and occasionally is not particularly precise. Therefore,
TABLE II. Model parameter.42
Parameter Value
Stack temperature, (K) 343
Faraday’s constant, F(C kmol−1) 96 484 600
Universal gas constant, R(J kmol−1 K) 8 314.47
No load voltage, Eo, (V) 0.6
Number of cells, No 88
Kr constant =No/4F(kmol s−1 A) 0.996 ×10−6
Utilization factor, U0.8
Hydrogen valve constant, KH2 (kmol s−1 atm) 4.22 ×10−5
Water valve constant, kH2O (kmol s−1 atm) 7.716 ×10−6
Oxygen valve constant, kO2 (kmol s−1 atm) 2.11 ×10−5
Hydrogen time constant, τH2 (s) 3.37
Water time constant, τH2O (s) 18.418
Oxygen time constant, τO2 (s) 6.74
Reformer time constant, τ1 (s) 2
Reformer time constant, τ2 (s) 2
Conversion factor, CV 2
Activation voltage constant, B(A−1) 0.047 77
Activation voltage constant, C(V) 0.013 6
Stack internal resistance, Rint (Ω) 0.003 03
Line reactance, X(Ω) 0.05
PI gain constants k5, k6 10
Voltage reference signal, Vr (p.u) 1.0
Methane reference signal, Qmethref (kmol s−1) 0.000 015
Hydrogen–oxygen flow ratio, rh–o 1.168
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FIG. 6. ICA-trained neural network and ANFIS output vs real output for (a) ICA NN train data, (b) ICA NN test data, (c) ANFIS train data, and (d) ANFIS test data.
evolutionary algorithms have been suggested today29–31 to deter-
mine the weighting factor. In this study, ICA is a cutting-edge
evolutionary algorithm that is used to train neural networks and
provide the best possible network structure.32 Atashpaz-Gargari
and Lucas33 introduced ICA in 2007, drawing inspiration from a
socio-human phenomenon.34–36 In this paper, ICA was used to opti-
mize the neural network’s weighting factor. The effectiveness and
TABLE III. Comparison of ANFIS and ICA-trained neural network.
Training data Testing data
MSE Correlation MSE Correlation
ANFIS 0.0073 0.9906 0.0051 0.9882
ICA-trained NN 0.0056 0.9894 0.0099 0.9862
accuracy of the suggested algorithm are evaluated under various
circumstances, and the findings are compared with those of the tra-
ditional fuzzy logic maximum power point tracking method. The
two MPPT methods for tracking the MPP of FC under rapidly vary-
ing operating conditions are the main contribution of this paper.
Under steady-state conditions, the proposed methods reduce oscil-
lations and increase power generation. By using sensors to assess
the temperature and water content of the membrane, it is possi-
ble to evaluate the suitability of the suggested solutions for practical
applications.
The remainder of this study is structured as follows: The simu-
lation of the PEM fuel cell system is described in Sec. II. Section III
presents the suggested MPP determination methods, which com-
bine the conventional fuzzy method with neural networks that have
been trained using ANFIS and ICA. Section IV presents the fuzzy
logic control algorithm that was employed for all three methods.
The results of the simulation are shown, analyzed, and discussed in
Sec. V. Finally, Sec. VI presents the conclusions.
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TABLE IV. Comparisons of the results of two proposed (ANFIS and ICA-trained neural network) MPP tracking methods and conventional fuzzy MPP tracking, as well as actual
value.
T=260 K, λ=12 T =280 K, λ=13 T =320 K, λ=9
FC maximum FC maximum FC maximum
Conditions methods power (W) Accuracy% power (W) Accuracy% power (W) Accuracy%
ANFIS 3627 99.32 5305 98.91 6121 99.70
ICA neural network 3619 99.10 5321 99.20 6091 99.21
Conventional fuzzy 3593 98.40 5203 97.01 6054 98.60
Actual value 3652 100 5364 100 6140 100
II. MODELING OF PEM FUEL CELL
A fuel cell is a device that uses a chemical reaction to produce
electricity. There are various fuel cell types. Fuel cells with a proton
exchange membrane are the most prevalent kind (PEMFCs). Nowa-
days, they are employed in a wide range of applications, including
powered vehicles, hybrid buses, portable computers, and stationary
powered vehicles.37 PEMFCs have numerous advantages, including
low operating temperatures, the potential for low costs and volumes,
sustained operation at high current densities, and long stack lives.38
In this study, the performance of the suggested maximum power
point tracking methods is examined using a PEMFC. The fuel cell
stack’s overall output voltage can be calculated as follows:39
Vcell =Enernst −Vact −Vohmic −Vcon. (1)
The Nernst equation is given by40
Enernst =1.229 −8.5 ×10−4(T−298.15)
+4.308 ×10−5T(lnPH2+0.5 ln PO2). (2)
The activation voltage drop can be calculated as follows:40
Vact =−[ξ1+ξ2⋅T+ξ3⋅T.ln (CO2)+ξ4.T. ln(i)], (3)
where ξ(i=1–4) are parametric coefficients for each cell model. CO2
is the concentration of dissolved oxygen at the gas/liquid interface
(mol cm−3), which can be calculated using
CO2=Po2
(5.08 ×106)×exp(−498T). (4)
The ohmic resistance (Rm) for the calculation of the ohmic voltage
drop is given by
Rm=rmtm
A, (5)
where40
rm=181.6[1+0.03(IA)+0.0062(T303)2(IA)2.5]
[λm−0.634 −3(IA)]exp [4.18(T−303T)] . (6)
The concentration overvoltage in the fuel cell is defined as follows:41
Vcon =RT
nF ln1−I
iLA(7)
when iLis the limiting current. The proportional relationship of the
flow of gas through a valve with its partial pressure can be stated as42
qH2
pH2=kan
√MH2=kH2(8)
and
qH2O
pH2O=kan
√MH2O=kH2O. (9)
For hydrogen, the derivative of the partial pressure can be calculated
using the perfect gas equation as follows:42
d
dtpH2=RT
Van (qin
H2−qout
H2−qr
H2). (10)
The relationship between the hydrogen flow and the stack current
can be written as
qr
H2=N0I
2F=2krI. (11)
Using Eq. (4), Eq. (3) can be rewritten in the sdomain as
PH2=1kH2
1+τH2s(qin
H2−2krI), (12)
where τH2=Van
kH2RT s.
Using MATLAB/SIMULINK software, a simple fuel cell model
was developed following the above equations. In Fig. 1, the fuel cell
model is depicted.
A current ramp time is always used to determine the power vs
voltage (or current) characteristic. Then, a PEMFC current ramp is
imposed, as indicated in Fig. 2. The P–I parameters of the fuel cell
at various temperatures are also shown in Fig. 2(a). Most PEM cells
have temperatures between 60 and 80 ○C. This figure illustrates how
the MPP of FC moves when the temperature changes.
The P–I parameters of the fuel cell are shown in Fig. 2(b) for
various fuel cell membrane water contents. The MPP is altered by
variations in membrane water content, as this figure illustrates. As
a result, an MPP tracker is required to locate and monitor fuel cell
MPP.
III. THE PROPOSED MPP TRACKING METHODS
The traditional fuzzy MPP tracking method as well as the two
proposed MPP tracking methods are presented in this section. A
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fuzzy controller and an ANFIS MPP determination are included in
the first suggested technique. The MPP of the fuel cell is determined
using a trained neural network trained using the imperialist compet-
itive algorithm in the second proposed MPP tracking methodology,
and then a fuzzy controller is utilized, much like in the first, to track
this point. The third method (the standard fuzzy method) is offered
for comparison with the proposed methods. In Ref. 43, the authors
suggested a conventional fuzzy MPP tracking approach. The block
diagram for the three maximum power point tracking strategies is
shown in Figs. 3(a)–3(c).
A. The proposed ANFIS-based MPP tracking
In this study, ANFIS is utilized to determine the voltage that,
under any operating conditions, corresponds to the FC’s maxi-
mum power point (Vmax). An ANFIS is a neural network that is
FIG. 7. (a) Temperature variations (b) fuel cell power for proposed, conventional, and theoretical methods.
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TABLE V. Comparisons of the proposed and conventional fuzzy methods at different temperatures and constant cell membrane water content.
T=270 K, λ=12 T =310 K, λ=12 T =290 K, λ=12
FC maximum FC maximum FC maximum
Conditions methods Ts(s) Accuracy% power (W) Ts(s) Accuracy% power (W) Ts(s) Accuracy% power (W)
ANFIS 0.12 98.63 3601 0.13 99.15 7144 0.06 99.68 5686
ICA neural network 0.15 98.00 3578 0.17 97.02 6991 0.11 98.36 5611
Conventional fuzzy 0.26 93.83 3426 0.28 96.05 6921 0.27 95.38 5441
Real value ⋅⋅⋅ 100 3651 ⋅⋅⋅ 100 7205 ⋅⋅⋅ 100 5704
functionally comparable to a fuzzy inference model and that simul-
taneously benefits from neural networks’ superior modeling abilities
and fuzzy systems’ superior modeling abilities. In the suggested solu-
tion, a fuzzy controller adjusts fuel cell voltage to the voltage that
the ANFIS determines corresponds to maximum power. Section IV
details about the fuzzy controller. A system made up of a PEM fuel
cell, a DC/DC boost converter, a resistive load, and an MPP tracker
(which includes an ANFIS and fuzzy controller) is taken into con-
sideration to study the performance of the suggested model. The
switching element of the DC/DC boost converter is turned on and
off using the PWM signal.
To determine the parameters of a first-order Sugeno-style fuzzy
inference system, an ANFIS employs a hybrid learning technique
that combines the least-squares estimator with the gradient descent
method.21 200 data pairs are employed to train the ANFIS. The
ANFIS system inputs are temperature and the water content of the
cell membrane, and its output is Vmax according to the specifi-
cation given earlier. For each input, three Gaussian membership
functions are taken into consideration. The ANFIS model’s gener-
alization abilities are tested using a different dataset that was not
used in the training set. The amount of data used in the testing
process is less than that used in the training step. Data from both
training and testing are normalized. Using the max–min technique,
each term is mapped to a number between −1 and 1. The ANFIS is
trained using these normalized data as inputs (operating conditions)
and outputs (reference voltage). After 50 iterations, the training
error is 0.001857 and the correlation for the test data is 0.99%.
The results indicate that ANFIS is a quick and precise prediction
technique.
B. The proposed ICA trained neural network
based MPP tracking
A data-driven black box model, called an artificial neural net-
work (ANN), can resolve extremely complicated nonlinear issues.
The major benefit of ANNs is that, by completing effective train-
ing, a network with enough hidden units may estimate any con-
tinuous function to any degree of accuracy. However, they are
constrained and have issues such as convergence to regional opti-
mal points. In order to improve the convergence rate and learn-
ing process, the Imperialist Competitive Algorithm (ICA), a new
and effective algorithm, is used in this research to train the MLP
neural network. Atashpaz-Gargari and Lucas33 introduced ICA in
2007, drawing inspiration from a socio-human phenomenon. An
MLP neural network’s weights are optimized using ICA using an
evolutionary method. The ICA is based on an optimization approach
with sociopolitical influences that, like many other evolutionary
algorithms, begins with a random beginning population or set of
empires. Any empire is made up of nations that can be divided
into colonial and imperialist states. The most powerful empire con-
quers more nations (by sending out more colonists and imperialists),
and the strength of empires is determined by a cost function that
the user selects. Imperialist nations seek to subjugate other nations
and convert them into colonies. As a result, it is highly probable
that stronger empires will progressively gain strength throughout
the colonial rivalry, while weaker ones lose it. Accordingly, any
empire that fails to dominate the imperialist competition and gains
power will be eliminated from the scene of the competition. One
may see competition, the eventual eradication of colonies near
the empires, and some degree of convergence. After a while, all
empires will be eliminated except for the strongest, and this one
will rule over all colonies. The goal of this imperialist competi-
tion is to unite all the polar regions under the control of a single,
powerful imperialist. In this work, the number of starting nations
is supposed to be Nc =80, the number of decades is Nd =60,
and the number of initial imperialists is assumed to be Np =8.
In Refs. 33–35, more information regarding the ICA algorithm is
provided. Section Vprovides details on correlation and error rates
to contrast ICA-trained neural network based and ANFIS-based
approaches.
C. Conventional fuzzy method
To evaluate how well the proposed approaches perform, their
effectiveness is compared to both actual data and the conventional
fuzzy tracking method. Power–current (P–V) curves have a slope
that is zero at the MPP, positive to the left of it, and negative to the
right. The inputs to the MPP tracking controller are error (E) and
error variation (CE), and the output of the MPP controller is the
duty cycle variation of the DC/DC boost converter (dD),
E(K)=ΔP
ΔV=P(k)−P(k−1)
V(k)−V(K−1), (13)
CE =E(K)−E(K−1). (14)
Figure 4 shows the P–V characteristic of fuel cells per unit. In this
figure, the positive and negative slopes are shown on the left and
right sides of MPP, respectively.
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IV. FUZZY LOGIC CONTROLLER
Fuzzy logic controllers have been employed in this paper for
the three strategies that have been given. The duty cycle varia-
tion of the DC/DC boost converter (dD) is the fuzzy controller’s
output. Its inputs are error (E) and error variation (CE), respec-
tively. E is the difference between the maximum power as estimated
by ANFIS or ICA-trained neural networks and the FC voltage.
Error and error variation for the proposed methods are defined as
follows:
E=Vf c −Vmax, (15)
CE =E(K)−E(K−1). (16)
FIG. 8. (a) λvariation and (b) fuel cell power for proposed and conventional fuzzy MPP tracking methods as well as real value.
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There are seven triangular fuzzy subsets for each membership
function of the input and output variables. The membership func-
tion of input E is displayed in Fig. 5(a), and the membership function
of input CE (k) is shown in Figs. 5(b), and Fig. 5(c) displays the out-
put dD’s membership function. 49 fuzzy rules make up the fuzzy rule
algorithm, as illustrated in Table I.
For instance, if the operating point (determined by the ANFIS
or ICA-trained neural network system) is far to the right of the MPP,
E is NB, and CE is zero, then the fuel cell voltage should decrease
to reach the MPP, and dD should be NB (negative) to advance the
operating point in that direction. The max–min fuzzy combination
operation and Mamdani’s fuzzy inference method are employed in
this study, and the output of the fuzzy logic controller is computed
through defuzzification using the center of gravity. The duty cycle is
defined as follows:
dD =∑n
j=1u(dDj)−dD j
∑n
j=1u(dDj). (17)
Table I shows the fuzzy rule bases of the presented fuzzy controller,
where E and CE are inputs and dD is the output.
V. SIMULATIONS AND RESULTS
A comparison of the results of ANFIS and ICA-trained neural
networks is presented in the first part of the investigation into the
effectiveness and accuracy of the suggested MPP tracking methods.
After running simulations for three different scenarios, including
typical operating conditions and rapid changes in the fuel cell’s tem-
perature and water content of the membrane, two MPP tracking
methodologies are compared to the traditional fuzzy MPP tracking
strategy. MATLAB/SIMULINK are used to run simulations. Table II
shows the simulated model parameter in this paper. We consider
and model a PEM fuel cell system with a DC/DC boost converter, a
resistive load, and an MPP tracker (as shown in Fig. 3).
A. Comparison between ANFIS and ICA-trained
neural network outputs
Two different proposed estimator systems are compared in
this section. The output of an ICA trained neural network is com-
pared with the real output for train data and test data in Figs. 6(a)
and 6(b), respectively. The ANFIS output for train and test data
is compared with the real output in Figs. 6(c) and 6(d). These
graphs show the correlation between the results of the suggested
methods and the actual output. The estimate is more accurate the
closer the correlation rate is to 1. Additionally, the Mean Squared
Error (MSE) is produced to compare the accuracy of the suggested
methods. One method of measuring the mismatch between val-
ues implied by an estimator and the actual values of the quantity
being evaluated is to use the MSE of the estimator. The MSE of an
estimator with respect to the estimated parameter (V) is given as
follows:
MSE =1
nn
i=1(VPi −VTi)2, (18)
where VPi and VTi are ith element of Vpand VT.Vpis a vector
of n predictions values, and VTis a vector of the true values. Both
ANFIS and ICA-trained neural networks’ MSE, and correlation val-
ues are computed for the training and testing sets of data. Table III
displays these outcomes. The results demonstrate that the results of
both the approaches are satisfactory in terms of model correctness,
while the results of ANFIS are marginally more precise. However,
an ICA-trained neural network will perform better with more input
data.
B. Normal operating conditions
The settings for the temperature and membrane water content
are fixed in this section. In the first scenario, the temperature is set
at 40 ○C and the value of the membrane water content is set at 12.
In the second scenario, 13 and 55 ○C are taken as the values for the
temperature and membrane water content, respectively. The mem-
brane water content and temperature are finally considered to be
9 and 70 ○C, respectively, in the third scenario of the study. The
results of all three approaches are shown in Table IV, together with
a real value under three different normal operating situations. These
findings demonstrate that, in comparison to the usual approach
under study, the placement of the fuel cell’s greatest power point
when utilizing the suggested ways is the closest to the theoretical
power. The results also indicate that, when compared to an ICA-
trained neural network, ANFIS’s output is closest to theoretical
values and its results are significantly more accurate.
C. Rapidly changing of the fuel cell temperature
The temperature changes here in a step-like manner. Based
on an estimated constant, the membrane’s water content is 12. As
illustrated in Fig. 7, the temperature rises from 50 to 70 ○C at time
TABLE VI. Comparison of the proposed and conventional fuzzy MPP methods at different cell membrane water content (λ) and constant temperature.
T=300 K, λ=9 T =300 K, λ=13 T =300 K, λ=11
FC maximum FC maximum FC maximum
Conditions methods Ts(s) Accuracy% power (W) Ts(s) Accuracy% power (W) Ts(s) Accuracy% power (W)
ANFIS 0.11 98.32 4858 0.12 98.71 6836 0.09 99.00 5896
ICA neural network 0.12 97.49 4817 0.12 97.55 6756 0.13 98.79 5883
Conventional fuzzy 0.2 96.21 4754 0.25 96.12 6657 0.28 95.83 5707
Real value ⋅⋅⋅ 100 4941 ⋅⋅⋅ 100 6925 ⋅⋅⋅ 100 5955
AIP Advances 13, 045207 (2023); doi: 10.1063/5.0144806 13, 045207-10
© Author(s) 2023
AIP Advances ARTICLE scitation.org/journal/adv
t=4 s and subsequently drops from 70 to 60 ○C at time t =6 s (a).
Two novel and traditional fuzzy MPP tracking algorithms are used
to track the power related to the maximum power point at various
temperatures and a constant membrane water content, as illustrated
in Fig. 7(b). These results demonstrate that the proposed ANFIS and
ICA neural network based MPP approaches outperform more tradi-
tional fuzzy MPP tracking methods in terms of performance (lower
transient and more accurate response). In contrast, compared to the
traditional fuzzy MPP method, the proposed methods calculate the
maximum power point more quickly and accurately. Other positive
aspects of the suggested approaches are their small settling time (Ts)
and lack of overshot. The results for traditional fuzzy MPP tracking,
ANFIS and ICA neural network MPP tracking, and actual value are
presented in Table V.
D. Rapidly changing of the fuel cell
membrane water content
This study explores how well the suggested MPP tracking meth-
ods operate when the water content of cell membranes varies at
a fixed temperature (55 ○C). According to Fig. 8, the membrane
water content changes from 9 to 13 at t =4 s and from 13 to
11 at t =6 s (a). According to Fig. 8, the respective MPPs are
modified (b). This graph displays the output power of fuzzy MPP
trackers, ANFIS, and ICA neural network based MPP algorithms.
The proposed MPP methods perform better than the conven-
tional fuzzy MPP trackers, according to the results, when the MPP
is changing quickly. The properties of the suggested MPP track-
ing system, which increases the system’s efficiency by absorbing
more power, are highlighted in Fig. 8(b). According to the find-
ings in Table VI, the suggested ANFIS an ICA neural network MPP
tracker absorbs more energy than a traditional fuzzy tracker by
roughly 1%.
VI. CONCLUSION
In this paper, a new ANFIS and ICA-trained neural network
based MPP tracker was introduced in order to improve the fuel cell
system efficiency. On the other hand, this paper’s primary contribu-
tion is the description of two reliable MPP approaches for tracking
FC’s MPP in the time of rapid operational condition changes. The
suggested approaches accelerate the process of determining the pre-
cise maximum power point of a fuel cell system under conditions
by combining fuzzy MPP tracking with artificial intelligence pro-
vided by ANFIS and neural networks. The neural network trained
by ANFIS and ICA is used to calculate the FC voltage corresponding
to the maximum power (Vmax). MATLAB/SIMULINK is used to
model a typical system made up of a PEM fuel cell, a DC/DC boost
converter, a resistive load, and an MPP tracker (including ANFIS,
ICA-trained neural network, or conventional fuzzy). Simulations are
run under three different scenarios, including normal operating con-
ditions, rapid temperature changes in the fuel cell (when the water
content is fixed), and water content in the membrane (when the
temperature is fixed). The results reveal that when compared to the
conventional fuzzy approach, the proposed methods provide bet-
ter transient response because they can quickly locate the maximum
power point. Therefore, the suggested approaches can track MPP in
operating conditions that are constantly changing. Additionally, it
is discovered that the outcomes of the suggested MPP tracker are
quite accurate across a broad range of temperature and membrane
water content levels. The proposed MPP tracking algorithms also
have a small settling time and negligible overshot, which are posi-
tive characteristics. The ANFIS system has been proven to be more
accurate than the other models by comparisons made with actual
results. However, with more input data, the ICA-trained neural net-
work will perform better since it determines the synaptic weights
more precisely.
The application of the proposed algorithm in the actual PEMFC
system and a few other innovative energy systems will be the main
emphasis of our upcoming study, and we will also perform more
extensive research on the MPPT algorithm to greatly enhance MPPT
application effectiveness, tracking speed, and accuracy.
NOMENCLATURE:
Enernst Nernst voltage (v)
Vact Activation voltage (v)
VOhmic Ohmic voltage (v)
ξi(i=1,2,3,4) Parametric coefficients
VCon Concentration over voltage (v)
PH2 Hydrogen pressure (Pa)
PO2 Oxygen pressure (Pa)
TTemperature (K)
CO2 Concentration of dissolved oxygen
(mol cm−3)
RmOhmic resistance (Ω)
rmMembrane resistivity (Ωcm)
ACell active area (cm2)
tmMembrane thickness (cm)
iLLimiting current (A)
FFaraday constant, 96487 Charge =mol
λmMembrane water content
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Masoud Safarishaal: Conceptualization (equal); Data curation
(equal); Formal analysis (equal); Investigation (equal); Methodology
(equal); Resources (equal); Software (equal); Visualization (equal);
Writing – original draft (equal). Mohammad Sarvi: Conceptualiza-
tion (equal); Formal analysis (equal); Methodology (equal); Project
administration (equal); Resources (equal); Supervision (equal); Val-
idation (equal); Visualization (equal); Writing – review & editing
(equal).
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
AIP Advances 13, 045207 (2023); doi: 10.1063/5.0144806 13, 045207-11
© Author(s) 2023
AIP Advances ARTICLE scitation.org/journal/adv
REFERENCES
1T. Zhang, P. Wang, H. Chen, and P. Pei, “A review of automotive proton
exchange membrane fuel cell degradation under start-stop operating condition,”
Appl. Energy 223, 249–262 (2018).
2H. Wu, “A review of recent development: Transport and performance modeling
of PEM fuel cells,” Appl. Energy 165, 81–106 (2016).
3L. P. Fan and X. Ma, “Maximum power point tracking of PEMFC based on hybrid
artificial bee colony algorithm with fuzzy control,” Sci Rep 12, 4316 (2023).
4V. Salas, E. Olías, A. Barrado, and A. Lázaro, “Review of the maximum power
point tracking algorithms for stand-alone photovoltaic systems,” Sol. Energy
Mater. Sol. Cells 90, 1555–1578 (2006).
5T. Esram and P. L. Chapman, “Comparison of photovoltaic array maxi-
mum power point tracking techniques,” IEEE Trans. Energy Convers. 22, 2
(2007).
6A. Reza Reisi, M. Hassan Moradi, and S. Jamasb, “Classification and comparison
of maximum power point tracking techniques for photovoltaic system: A review,”
Renew. Sustain. Energy Rev. 19, 433–443 (2013).
7M. Sarvi and M. Barati, “Voltage and current based MPPT of fuel cells under vari-
able temperature conditions,” in 45th International Universities Power Engineering
Conference (IEEE, 2010), pp. 1–4.
8M. M. Algazar, H. AL-monier, H. A. EL-halim, and M. E. E. K. Salem, “Maximum
power point tracking using fuzzy logic control,” Int. J. Electr. Power Energy Syst.
39, 21–28 (2012).
9N. Bizon, “Nonlinear control of fuel cell hybrid power sources: Part I -voltage
control,” Appl. Energy 88, 2559–2573 (2011).
10I. Yahyaoui, M. Chaabene, and F. Tadeo, “Evaluation of Maximum Power Point
Tracking algorithm for off-grid photovoltaic pumping,” Sustainable Cities and
Society 25, 65–73 (2016).
11A. K. Abdelsalam, A. M. Massoud, S. Ahmed, and P. N. Enjeti, “High-
performance adaptive perturb and observe MPPT technique for photovoltaic-
based micro-grids,” IEEE Trans. Power Electron. 4, 26 (2011).
12N. Bizon, “Energy harvesting from the FC stack that operates using the
MPP tracking based on modified extremum seeking control,” Appl. Energy 104,
326–336 (2013).
13Y.-C. Kuo, T.-J. Liang, and J.-F. Chen, “Novel maximum-power-point-tracking
controller for photovoltaic energy conversion system,” IEEE Trans. Ind. Electron.
48, 594–601 (2001).
14M. H. Moradi and A. R. Reisi, “A hybrid maximum power point tracking
method for photovoltaic systems,” Sol. Energy 85, 2965–2976 (2011).
15N. S. Souza, L. A. C. Lopes, and X. J. Liu, “An intelligent maximum power point
tracker using peak current control,” in Proceedings of IEEE 36th Power Electronics
Specialists Conference (Recife, Brazil, 2005), pp. 172–177.
16N. S. Souza, L. A. C. Lopes, and X. J. Liu, “Comparative study of variable size
perturbation and observation maximum power point trackers for PV systems,”
Electr. Power Syst. Res. 80, 296–305 (2010).
17K. Irisawa, T. Saito, I. Takano, and Y. Sawada, “Maximum power point tracking
control of photovoltaic generation system under non-uniform insolation by means
of monitoring cells,” in Conference Record of the Twenty-Eighth IEEE Photovoltaic
Specialists Conference (IEEE, 2000), pp. 1707–1710.
18K. Kobayashi, I. Takano, and Y. Sawada, “A study on a two-stage maximum
power point tracking control of a photovoltaic system under partially shaded
insolation conditions,” in IEEE Power Engineering Society General Meeting (IEEE,
2003), pp. 2612–2617.
19S. Ahmadi, S. Abdi, and M. Kakavand, “Maximum power point tracking of a
proton exchange membrane fuel cell system using PSO-PID controller,” Int. J.
Hydrogen Energy 42, 20430–20443 (2017).
20A. Harrag and S. Messalti, “How fuzzy logic can improve PEM fuel cell MPPT
performance?,” Int. J. Hydrogen Energy 43, 537–550 (2017).
21N. Mallick and V. Mukherjee, “Maximum power point tracking supported pro-
ton exchange membrane fuel cell based intelligent dynamic voltage restorer,” Int.
J. Hydrogen Energy 45, 29271–29287 (2020).
22R. Jang, C. Sun, and E. Mizutani, Neuro-fuzzy and Soft Computation (Prentice
Hall, New Jersey, 1997).
23S. A. Kalogirou, “Artificial neural networks in renewable energy systems
applications: A review,” Renew. Sustain. Energy Rev. 5, 373–401 (2001).
24T. Hiyama and K. Kitabayashi, “Neural network based estimation of maxi-
mum power generation from PV module using environmental information,” IEEE
Trans. Energy Convers. 12, 241–247 (1997).
25T. Hiyama, S. Kouzuma, and T. Imakubo, “Identification of optimal operating
point of PV modules using neural network for real time maximum power tracking
control,” IEEE Trans. Energy Convers. 10, 360–367 (1995).
26C. B. Salah and M. Ouali, “Comparison of fuzzy logic and neural network in
maximum power point tracker for PV systems,” Electr. Power Syst. Res. 81, 43–50
(2011).
27S. Caux, W. Hankache, M. Fadel, and D. Hissel, “On-line fuzzy energy man-
agement for hybrid fuel cell systems,” Int. J. Hydrogen Energy 35, 2134–2143
(2010).
28A. S. Mahdi et al., “Maximum power point tracking using perturb and observe,
fuzzy logic and ANFIS,” SN Appl. Sci. 2, 89 (2020).
29P. Tang and Z. Xi, “The research on BP neural network model based on guaran-
teed convergence particle swarm optimization,” in 2th International Symposium
on Intelligent Information Technology Application (2008), 2, pp. 13–16.
30X. Qu, J. Feng, and W. Sun, “Parallel genetic algorithm model based on AHP and
neural networks for enterprise comprehensive business,” in IEEE International
Conference on Intelligent Information Hiding and Multimedia Signal Processing
(IEEE, 2008), pp. 897–900.
31Y. Ma and Y. Xie, “Evolutionary neural networks for deep learning: A review,”
Int. J. Mach. Learn. & Cyber. 13, 3001–3018 (2022).
32M. Mahmoudi, N. Forouzideh, C. Lucas, and F. Taghiyareh, “Artificial neural
network weights optimization based on imperialist competitive algorithm,” in 7th
International Conference on Computer Science and Information Technologies,
Yerevan, 2009, pp. 244–247.
33E. Atashpaz and C. Lucas, “Imperialist competitive algorithm: An algorithm
for optimization inspired by imperialistic competition,” in IEEE Congress on
Evolutionary Computation (IEEE, 2007), pp. 4661–4747.
34H. Duan and L. Huang, “Imperialist competitive algorithm optimized artificial
neural networks for UCAV global path planning,” Neurocomputing 125, 166–171
(2014).
35C. Lucas, Z. Nasiri-Gheidari, and F. Tootoonchian, “Application of an impe-
rialist competitive algorithm to the design of a linear induction motor,” Energy
Convers. Manage. 51, 1407–1411 (2010).
36E. Atashpaz Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial
competitive algorithm: A novel approach for PID controller design in MIMO
distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355
(2008).
37J.-H. Wee, “Applications of proton exchange membrane fuel cell systems,”
Renew. Sustain. Energy Rev. 11, 1720–1738 (2007).
38F. Barbir and T. Gomez, “Efficiency and economics of proton exchange
membrane (PEM) fuel cells,” Int. J. Hydrogen Energy 21, 891–901 (1996).
39Z.-d. Zhong, H.-b. Huo, X.-j. Zhu, G.-y. Cao, and Y. Ren, “Adaptive maximum
power point tracking control of fuel cell power plants,” J. Power Sources 176,
259–269 (2008).
40J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, P. R. Roberge, and T.
J. Harris, Electrochem. Soc. 142, 1–8 (1995).
41Fuel Cell Handbook, 7th ed. (EG&G Technical Services, Inc. U.S. Department of
Energy, 2004).
42J. Padullés, G. W. Ault, and J. R. McDonald, “An integrated SOFC plant
dynamic model for power systems simulation,” J. Power Sources 86, 495–500
(2000).
43M. Sarvi, M. Kazeminasab, and M. Safari, “A new fuzzy control method for max-
imum power point tracking of PEMFCs system,”in Second Iranian Conference of
Hydrogen and Fuel Cell, Tehran, Iran, 2012.
AIP Advances 13, 045207 (2023); doi: 10.1063/5.0144806 13, 045207-12
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