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New Hybrid Maximum Power Point Tracking Methods for Fuel
Cell using Artificial Intelligent
Mohammad Sarvi*, Masoud Safarishal**
Electrical Engineering Department, Imam Khomeini International University, Qazvin, Iran
*sarvi@eng.ikiu.ac.ir, **masoud.safarishaal66@gmail.com
Abstract: In this paper, two maximum power point tracking (MPPT) methods for Fuel Cell (FC)
systems based on Adaptive Neuro-Fuzzy Inference Systems (ANFIS) and Imperialist Competitive
Algorithm trained Neural Network (ICANN) are presented. The first operation voltage of the fuel
cell corresponding to maximum power point is determined based on the data, and then the duty
cycle of a DC/DC converter is adjusted using fuzzy logic controller to force the system that
operates in conditions which match up with its maximum power point, in order to minimize the
fuel consumption. The proposed systems and conventional fuzzy controller system are simulated
in the MATLAB environment and results show acceptable operation under fast variation of
conditions as well as normal conditions in minimum time.
Keywords: Fuel Cell; Maximum Power Point Tracking; Fuzzy; Adaptive Neuro Fuzzy Inference System;
Imperialist Competitive Algorithm; Neural Network.
1. Introduction
Modern power systems are becoming more complex and vulnerable to extreme events. These
extreme events can seriously affect the operation of power systems, resulting in outages and even
cascading failures [1]. As fossil fuel reserves are rapidly depleting, prices for fossil commodities
are volatile, and fossil fuel has a negative environmental impact, most of the recent research
focuses on the use of renewable forms of energy [2]. In the generation of energy, a future based
on clean, environmentally friendly energy is important. Fuel cells are one of the cleanest and most
efficient energy generation methods in the realm of renewable resources, according to several
studies. Recent years have seen the development of many electrochemical devices (fuel cells) that
use hydrogen and oxygen to generate electricity .
Today's Proton Exchange Membrane (PEM) fuel cell is one of the most commonly used
types of fuel cells [4]. Because of low operating temperature, high power density, and fast startup,
PEM fell cell is a promising candidate for residential and vehicular applications [5]. Fuel cells
have nonlinear power-current (P-I) characteristics. Extensive discussions on the fuel cell P-I
characteristic can be found in the literature [6]. On the other hand, their weakness is their low
energy conversion efficiency. Therefore, to improve the performance of the FC, it must operate
around the Maximum Power Point (MPP) which is influenced by temperature and membrane water
content. The FC has an optimum operating point to generate the maximum power with certain
membrane water content at a certain temperature. The P-I characteristic of the fuel cell is nonlinear,
and the generating power changes with membrane water content and air temperature. Hence, the
ability to extract the maximal power from a fuel cell is an important issue that must be considered
for the optimal design of a fuel cell system. Some MPPT methods were proposed and investigated
in [7-17]. In [6], these methods have been classified into three broad categories: offline methods,
online methods, and hybrid methods. The problem addressed by the MPPT technique is to
automatically find the maximum power point voltage or current at which a system should operate
to obtain the maximum power output under given (and random) operating conditions. In this paper,
in order to improve the speed of response to rapidly changing conditions, two new hybrid control
methods are proposed for maximum power point tracking of the fuel cell system. In the first one,
MPP tracking is done by the combination of Adaptive Neural Fuzzy Inference Systems (ANFIS)
with the Fuzzy Logic (FL) controller. ANFIS is used to determine the optimal voltage of a fuel
cell corresponding to maximum power. Temperature and membrane water content are the input of
the ANFIS system and the reference voltage is its output. Afterward, the fuzzy logic controller is
used to track MPP when tracking is done by adjusting the duty cycle of a DC/DC boost converter
so that the fuel cell voltage remains at MPP operating point. The duty cycle of the power
electronics converter is adjusted in order to push the operating point towards the MPP region as
quickly as possible, thereby improving the transient response. Using fuzzy logic control has
received significant attention over the last decade because it can deal with imprecise inputs, does
not need an accurate mathematical model and can handle nonlinearity [19, 20]. ANFIS combines
advantages of neural networks such as the learning power, with knowledge representation of a
fuzzy inference system, so ANFIS can be applied to many complicated problems. Also, the
advantages of ANFIS system over the traditional estimation methods are simple complementing
of the model by new input parameters without modifying the existing model structure and
automatic searching for the nonlinear connection between the inputs and outputs [21, 22]. In the
second proposed method, Imperialist Competitive Algorithm (ICA) trained a neural network to
determine the maximum power point. Machine learning become useful tools in a variety of
applications such as model validation, modeling, and prediction [23, 24]. In recent years, methods
based on NNs [25] and FL [26–28] have been successfully employed for the implementation of
MPP searching. But finding the best weight factors in the network structure by trial and error takes
a lot of time and sometimes may not be very accurate. Hence, to find the weighting factor,
evolutionary algorithms have been proposed today [29-31]. In this article, ICA as a novel
evolutionary algorithm used to train the neural network and achieve the best structure of the
network [32]. ICA has been proposed by Atashpaz-Gargari and Lucas [33], in 2007, which has
inspired from a socio-human phenomenon [34-36]. The ICA has been applied for optimizing the
weighting factor of the neural network. The performance and accuracy of the proposed algorithm
are investigated in different conditions and its results are compared with conventional fuzzy logic
maximum power point tracking method. The main contribution of this paper is the presentation of
two robust and reliable MPPT methods for tracking of MPP of FC under fast variation of operating
conditions. The results of the proposed methods reduce oscillations and increased power yield
under steady state conditions
The rest of this article is organized as follows: In section 2, the modeling of the PEM fuel
cell system is presented. In section 3, the proposed MPP determination methods using ANFIS and
ICA trained the neural network, as well as conventional fuzzy methods, are presented. Fuzzy logic
control algorithm which has been used for all three approaches is presented in section 4. In section
4, simulation results are presented, analyzed and discussed. Finally, the conclusions are presented
in section 5.
2. Modeling of PEM fuel cell
In this article, a PEMFC is used to investigate the performance of the proposed maximum power
point tracking methods. The mathematical model of the output voltage for PEMFC stack is
formulated as follows [37-39]:
V E V V V
cell nernst act ohmic con
(1)
Where [40, 41]:
45
1.229 8.5 10 ( 298.15) 4.308 10 (ln 0.5 ln )
22
E T T P P
nernst H O
(2)
[ . . . ln( ) . .ln( )]
1 2 3 4
2
V T T C T i
act O
(3)
2
6
(5.08 10 ) exp( 498/ )
2
Po
COT
(4)
.V R I
ohmic m
(5)
ln(1 )
RT I
Vcon nF i A
L
(6)
A PEMFC model has been developed using MATLAB/SIMULINK software. The fuel cell model
can be shown as in Fig. 1. Also, Fig.2 shows the power current (P-I) characteristics of the fuel cell
at different temperatures. As this Fig 2 shows, the MPP of FC is moved with changing of
temperature and membrane water content.
Kr SUM
-
2Kr
SUM
-
qO2
(1/4.22e-5)/
(3.37S+1)
(1/2.11e-5)/
(6.47S+1)
qH2
Ifc +
+
Polarization
Curve
Model
Temperature
Lambda
PH2
PO2 Vfc
Pfc
Fig. 1. PEMFC Model.
Fig.2. P-I characteristics of the fuel cell; a) at different temperature b) at different membrane water content.
3. The Proposed MPP Tracking Methods
In this section, two proposed MPP tracking methods as well as the conventional fuzzy MPP
tracking method are presented. The first proposed method includes an ANFIS MPP determination
and a fuzzy controller. In the second proposed MPP tracking approach, the Imperialist Competitive
Algorithm trained Neural Network is used to determine the MPP of a fuel cell and the then fuzzy
controller is used to track this point like the previous method. In order to compare the proposed
methods with the conventional method, the third method (conventional fuzzy method) is presented.
Authors proposed a conventional fuzzy MPP tracking method in [43]. Fig. 3 (a, b and c) shows the
block diagram of three mentioned maximum power point tracking strategies.
3.1. The Proposed ANFIS based MPP Tracking
In this paper, ANFIS is used to find voltage corresponding to the maximum power point of FC
(Vmax) in any operating conditions. An ANFIS is a neural network that is functionally equivalent
to a fuzzy inference model which has the advantage of the learning capabilities of neural networks
and modeling superiority of fuzzy systems simultaneously. In the proposed method, ANFIS
determines fuel cell voltage corresponding to maximum power and the fuzzy controller adjusts
fuel cell voltage to this determined voltage. The fuzzy controller is detailed in section 4. In order
to investigate the performance of the proposed model, a system consisting of a PEM fuel cell, a
DC/DC boost converter, a resistive load, and MPP tracker (including ANFIS and fuzzy controller)
is considered as shown in Fig.3 (a). The PWM signal is used to turn on and off of the DC/DC boost
converter switching element.
Lambda
Temperature
Fuel Cell
DC/DC
Converter
Load
Fuzzy
controller
Vfc
Ifc
ANFIS Vmax PWM
Lambda
Temperature
Fuel Cell
DC/DC
Converter
Load
Fuzzy
controller
Vfc
Ifc
ICA trained
Neural Network
Vmax PWM
(a) (b)
Lambda
Temperature
Fuel Cell
DC/DC
Converter
Load
Fuzzy
controller
Vfc
Ifc
PWM
Dp/Dv
Pfc
(c)
Fig.3. The block diagram of three MPP tracker for FC; a) the proposed ANFIS based MPP tracking, b) the
proposed ICA based MPP tracking, c) the conventional fuzzy MPP tracking.
To train the ANFIS, a number of 250 data pairs are used. Temperature and cell membrane
water content (λ) are the inputs of the ANFIS system, where Vmax with the above definition is
ANFIS output. Three Gaussian membership functions are considered for each input. A separate
data set, not included in the training set, is employed for verifying the ANFIS model generalization
capabilities. The training and testing data are normalized. These normalized data are utilized as
the inputs (operating conditions) and outputs (reference voltage) to train the ANFIS. After 70
epochs, training error reaches 0.001857 and correlation for testing data is equal to 0.99 percent.
Results show ANFIS is a rapid and accurate prediction method.
3.2. The Proposed ICA Trained Neural Network Based MPP Tracking
Imperialist Competitive Algorithm (ICA) is applied to train MLP neural networks for enhancing
the convergence rate and learning process. ICA has been proposed by Atashpaz - Gargari and
Lucas [33]. ICA uses an evolutionary algorithm in order to optimize the weights of an MLP neural
network. The ICA algorithm is a colonial competition inspired by the idea of human socio-political
evolution. In the original algorithm, the number of colonial countries together with their colonial
countries seeks to naturally find the general optimal point to efficiently solve the optimization
problem. In this work, the numbers of initial countries are assumed to be Nc= 75 and the number
of decades is Nd=65 and the number of initial imperialists is assumed to be Np= 8.
5.3.3. Conventional Fuzzy Method
The performance of the proposed methods is compared with the conventional fuzzy tracking
method as well as actual data. As shown in Fig.4 at the MPP slope of power–voltage (P-V) curve
is zero, at the left of the MPP slope is positive, and negative on the right. Fig.4 shows the power-
voltage characteristic of a fuel cell. The inputs of MPP tracking controller are error (E), and error
variation (CE), also output of MPPT controller is duty cycle variation of DC/DC converter (dD),
where the error (E) and error variation are as following:
( ) ( 1)
() ( ) ( 1)
P P k P k
EK V V k V K
(7)
( ) ( 1)CE E K E K
(8)
Fig.4. Power-voltage (P-V) characteristic of fuel cell.
For all three presented methods, the fuzzy logic controller has been used. The inputs of the fuzzy
controller are an error (E), and error variation, (CE), and output of the fuzzy controller is duty
cycle variation of DC/DC boost converter (dD) is. E is the difference between FC voltage and FC
voltage corresponding to maximum power determined by ANFIS or ICA trained neural networks.
Error and error variation for proposed methods are defined as the following:
maxfc
E V V
(9)
( ) ( 1)CE E K E K
(10)
Each of the membership functions of input and output variables has 7 triangular fuzzy subsets.
4. Simulations and Results
In order to investigate the performance and accuracy of the proposed MPP tracking methods,
at the first step, a comparison between ANFIS and ICA trained neural network performances are
presented. Thereafter simulations are performed for three different cases including of normal
operating conditions and fast variation of the fuel cell temperature and the membrane water
content, and then two proposed MPP tracking approaches are compared with conventional fuzzy
MPP tracking method. Simulations are performed in the MATLAB/SIMULINK environment. A
system consisting of a PEM fuel cell, a DC/DC boost converter, a resistive load, and MPP tracker
is considered and simulated (as shown in Fig.3).
5.1. Comparison between ANFIS and ICA trained neural network outputs
In this section, two proposed estimator systems are compared with each other. Figs.5 (a) and (b)
show ICA trained neural network output versus real output for train data and test data respectively.
Figs.5 (c) and (d) show ANFIS output versus real output for train and test data. In these figures,
the correlation of actual output with proposed methods outputs are displayed. Whatever the
correlation rate is closer to 1, the estimator is more accurate. In addition, in order to compare the
accuracy of the proposed methods, the Mean Squared Error (MSE) is computed. MSE of an
estimator is one of many ways to quantify the difference between values implied by an estimator
and the actual values of the quantity being estimated. The MSE of an estimator with respect to the
estimated parameter (V) is given as follows:
2
1
1()
n
Pi Ti
i
MSE V V
n
(11)
Where VPi and VTi are ith elements of Vp and VT. Vp is a vector of n predictions values, and VT
is a vector of the true values. The MSE and correlation value for both ANFIS and ICA trained
neural networks are calculated for training and testing data. These results are shown in Table 1.
As the results show, the accuracy of the model is acceptable in both methods, although ANFIS's
results are slightly more accurate. Although, with more input data, ICA trained neural networks
will perform better.
(a) (b)
(c) (d)
Fig.5. ICA trained neural network and ANFIS output versus real output for a) ICA NN train data b)
ICA NN test data c) ANFIS train data and d) ANFIS test data.
Table 1. 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
5.2. Normal Operating Conditions
In this section, the values of membrane water content and temperature are fixed. In the first case,
the value of membrane water content (λ) is assumed to be 12 and the value of temperature is
assumed to be 40°C. In the second case, the values of membrane water content and temperature
are assumed to be 13 and 55°C, respectively. Finally, in the third case of study, membrane water
content and temperature are assumed to be 9 and 70°C, respectively. Table 3 shows the results for
all three presented methods and real value at three different normal operation conditions. These
results show that by using the proposed methods, the location of the maximum power point of the
fuel cell is the nearest to the theoretical power as compared to the studied conventional method.
Results also show ANFIS's results were slightly more accurate and its output is nearest to
theoretical values as compared to ICA trained neural network. Table 2. 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.
Table 2. Comparisons of the results ANFIS and ICA trained neural network normal operation
Conditions
Methods
T=260°K, λ =12
T=280°K, λ =13
T=320°K, λ =9
FC Maximum
power(W)
Accuracy%
FC Maximum
power(W)
Accuracy%
FC Maximum
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
5.3. Changing of the Fuel Cell Temperature
In this case, a step change is applied to the temperature. The membrane water content is assumed
constant and is equal to 12. The temperature changes from 50°C to 70°C at t=4 seconds, and then
it changes from 70°C to 60°C at t=6 seconds, as shown in Fig.6 (a). The power corresponding to
a maximum power point is tracked by two proposed and conventional fuzzy MPP tracking methods
at different temperature and constant membrane water content, as shown in Fig.6 (b). These results
show the proposed ANFIS and ICA neural network based MPP methods provide better
performance (lower transient and more accurate response) than the conventional fuzzy MPP
tracking method. On the other hand, the proposed methods determine the maximum power point
faster and with more accuracy in comparison with conventional fuzzy MPP methods. Also, small
settling time (Ts) and no overshoot are other good features of the proposed methods. Table 3 shows
results for ANFIS and ICA neural network MPP tracking and conventional fuzzy MPP tracking,
as well as an actual value.
.
(a)
(b)
Fig.6. a) Temperature variations b) fuel cell power for proposed, conventional, and theoretical methods.
Table 3. Comparisons of proposed and conventional fuzzy methods at different temperature and constant
cell membrane water content.
5.4. Changing of the Fuel Cell Membrane Water Content
In this section, the performance of the proposed MPP tracking methods under variation of cell
membrane water content in constant temperature (55°C) is investigated. The membrane water
content is changed from 9 to13 at t=4 seconds, and then it is changed from 13 to 11 at t=6 seconds,
as shown in Fig.7 (a). The corresponding MPPs are changed as shown in Fig.7 (b). This figure
shows the output power of the ANFIS and ICA neural network based MPP methods as well as
fuzzy MPP trackers. Results show the proposed MPP methods have a better performance than
conventional fuzzy MPP trackers when a rapidly changing of the MPP occurs. Fig.7 (b) highlights
clearly the features of the proposed MPP tracking system, which improves the performance of the
system by absorbing a higher power. The results in Table 4 show an enhancement of about 1% in
energy absorbed by the proposed ANFIS an ICA neural network MPP tracker in comparison with
a conventional fuzzy tracker.
Conditions
Methods
T=270°K, λ =12
T=310°K, λ =12
T=290°K, λ =12
Ts(s)
Accuracy%
FC
Maximum
power(W)
Ts(s)
Accuracy%
FC
Maximum
power(W)
Ts(s)
Accuracy%
FC
Maximum
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
(a)
(b)
Fig.7. a) λ variation, b) fuel cell power for proposed and conventional fuzzy MPP tracking methods
as well as real value.
Table 4. Comparison of proposed and conventional fuzzy MPP methods at different cell membrane water
content (λ) and constant temperature.
Conditions
Methods
T=300°K, λ =9
T=300°K, λ =13
T=300°K, λ =11
Ts(s)
Accuracy%
FC Max
power(W)
Ts(
s)
Accuracy%
FC Max
power(W)
Ts(s)
Accuracy%
FC
Maximum
power(W)
ANFIS
0.11
98.32
4858
0.1
2
98.71
6836
0.09
99.00
5896
ICA neural network
0.12
97.49
4817
0.1
2
97.55
6756
0.13
98.79
5883
Conventional Fuzzy
0.2
96.21
4754
0.2
5
96.12
6657
0.28
95.83
5707
Real Value
-
100
4941
-
100
6925
-
100
5955
6. Conclusion
In this paper, a new ANFIS and ICA trained neural network based MPP tracker was
presented. The proposed methods combine a fuzzy MPP tracking with the artificial intelligence of
ANFIS and neural network to speed up the procedure of reaching the accurate maximum power
point of a fuel cell system under different conditions. ANFIS and ICA trained neural networks are
used to determine FC voltage corresponding to maximum power (Vmax). A typical system
consisting of a PEM fuel cell, a DC/DC boost converter, a resistive load, and MPP tracker
(including ANFIS, ICA trained Neural Network or conventional fuzzy) is considered and
simulated in MATLAB/SIMULINK. Simulations are performed for three different conditions
including normal operating conditions and fast variation of the fuel cell temperature (when the
water content is fixed) and the membrane water content (When the temperature is fixed). Results
show, in comparison with the conventional fuzzy algorithm, proposed methods provide a better
transient response because the proposed method determines the maximum power point faster and
also gives smoother output power at steady state
It is found that the results of the proposed MPP tracker are very close to the actual values
over a wide range of temperature and membrane water content levels. Also, small settling time
and no overshoot are the good features of the proposed MPP tracking methods. According to the
comparisons on the actual results, it has been shown that the ANFIS system is more accurate than
the other models.
Nomenclature:
Enernst
Nernst Voltage (v)
Vact
Activation Voltage (v)
VOhmic
Ohmic Voltage (v)
i
(i =1,2,3,4)
Parametric Coefficients
VCon
Concentration Over voltage(v)
PH2
Hydrogen pressure (Pa)
PO2
Oxygen pressure (Pa)
T
Temperature(K)
CO2
Concentration of Dissolved Oxygen(
3
.mol cm
)
Rm
Ohmic Resistance(
)
rm
Membrane Resistivity(
cm
)
A
Cell Active Area (
2
cm
)
tm
Membrane Thickness (
cm
)
iL
Limiting Current (A)
F
Faraday constant, 96487 Charge (mol)
m
Membrane water content
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