Renewable Energy 156 (2020) 570e578
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Renewable Energy
journal homepage: www.elsevier.com/locate/renene
A study on the hydrogen consumption calculation of proton exchange
membrane fuel cells for linearly increasing loads: Artificial Neural
Networks vs Multiple Linear Regression
a, *
€
Yasin Ozçelep
, Selcuk Sevgen b, Ruya Samli b
a
b
Istanbul University-Cerrahpasa, Electrical & Electronics Engineering Dept., Turkey
Istanbul University-Cerrahpasa, Computer Engineering Dept., Turkey
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 21 October 2019
Received in revised form
7 April 2020
Accepted 16 April 2020
Available online 27 April 2020
This paper presents an experimental study about the proton exchange membrane fuel cell (PEMFC)
behavior on linearly increasing loads. The study mainly based on the effect of the linear load slope on
hydrogen consumption for 0e600 W range and 0e100 Watt/s slope. Experimental results are processed
by Artificial Neural Networks (ANN) and Multiple Linear Regression (MLR). The relationship between
total consumed energy, peak power, slope and hydrogen consumption are discussed and novel equations
are presented. The average error rates of ANN and MLR are 0.3189%, and 0.1124% while the average R2
values are 0.9965 for ANN simulation and 0.9545 MLR simulation. We presented that the energy and
exergy efficiency are decreased 6%, cost of the energy is increased 13% with the increasing slope of the
power. We also performed the sensitivity and uncertainty analysis. The results give information to
hydrogen system designers about an effective way to reach hydrogen consumption by performing both
of the modelling processes successfully.
© 2020 Elsevier Ltd. All rights reserved.
Keywords:
Hydrogen consumption
PEMFC
Efficiency
ANN
MLR
1. Introduction
While the hydrogen fuel cells gain importance due to efficiency,
their poor dynamic response increases hydrogen consumption and
occurs as one of the major problem for more efficient systems [1,2].
Because, saving hydrogen consumption improves the fuel economy
and thus increase the efficiency. To overcome this problem, hybrid
propulsion systems are proposed using fuel cells main power
source and battery/supercapacitors as auxiliary power sources
[3e7].
The hybrid propulsion systems are formed considering the
minimum hydrogen consumption strategy for efficiency and
hydrogen consumption should be calculated in design stage of the
system for optimum power train [2,3,8,9]. While a hybrid propulsion system is fulfilling the power demand, the fuel cell and
auxiliary power source are in a cooperation to supply needed current to load. Especially in a sudden demand, when the current is
constant on load side, the fuel cell current is in linearly increasing
mode. Thus, the mathematical equations proposed by the studies
* Corresponding author.
€
E-mail address: ycelep@istanbul.edu.tr (Y. Ozçelep).
https://doi.org/10.1016/j.renene.2020.04.085
0960-1481/© 2020 Elsevier Ltd. All rights reserved.
[10e13] to calculate the hydrogen consumption of the fuel cell
stack in constant current mode becomes invalid. Using equations
for constant current mode leads incorrect results. These results
effect the size, cost and efficiency of the system.
1.1. Literature review
In the literature studies about fuel cells, it can be seen that,
systems were modelled by different type of modelling techniques
such as ANN and MLR and compared with experimental results.
These two methods are also widely used in fuel cell modelling
[14e37]. Table 1 is for ANN studies about PEMFCs and Table 2 is for
ANN studies for other fuel cells. Similarly, Table 3 presents
regression studies for PEMFCs and the Table 4 presents regression
studies for other fuel cells. In this study the reasons for choosing
these modelling methods can be summarized as follows: We
focused on behavioral modelling of fuel cell and suppose fuel cell as
a “black box”. Therefore, we used ANN as one of the heuristic algorithm [14e28]. For modelling the PEMFCs, the regression
methods are also popular [29e37]. We used MLR for generating a
novel formula for linearly increasing loads.
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Table 1
Literature studies of PEMFCs with ANN.
Study Major research focus
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
Findings
Modeling a PEMFC stack for dynamic and steady-state operation An ANN model is developed to model some nonlinear structures within the hybrid model of a
using ANN-based submodels
PEMFC stack.
Static modelling by ANNs of a PEMFC
The PEMFC model based on an ANN showed a good congruence with the physical model,
represented by its semi-empirical equation.
Semi-empirical modelling of PEMFC by ANN
Using an ANN, empirical correlations of the PEMFC are presented in terms of process operating
variations.
Empirical modelling of PEMFC performance using ANN
Using ANN is proposed for providing a tool for the design and analysis of fuel cell total systems.
ANN modelling of 100 W portable PEMFC and experimental
An ANN is used to model a portable direct hydrogen fed PEMFC.
verification
High power fuel cell simulator based on ANN
The ANN shows excellent accuracy in modeling and prediction.
ANN modeling for fault diagnosis of PEMFC
A dynamic model of the PEMFC systems is analyzed and simulated by MATLAB and ANN.
ANN modeling for PEMFC
ANN model has been simulated the performance of PEMFC without complex computation.
Design optimization and thermal management of the PEMFC
ANN is utilized to model the friction factor and Nu number regarding three geometrical
using ANN
parameters.
Analysis of PEMFC failure modes by ANN
ANN is used for creating the optimal model of PEMFC toward diagnosing.
Implementation of sensor based on ANN to predict the PEMFC The optimal network architecture is shown and commented. The error backpropagation
hydration state
algorithm was used for an ANN training procedure.
Table 2
Literature Studies of other Fuel Cells with ANN.
Study Major research focus
Fuel
Cell
[25]
[26]
SOFC It shows that many behaviours can be successfully modelled by an ANN.
SOFC ANN and ANFIS techniques were used to predict performance parameters stack current and voltage of a
residential SOFC system.
SOFC The ANN modeling approach was successfully demonstrated for a short SOFC stack.
[27]
[28]
Modelling the SOFC behaviours by ANN
Predicting SOFC performance in residential
microgeneration installation
ANN modelling a short stack solid oxide fuel cell
based on experimental data
Modelling of biohydrogen generation in MECs using
an ANN
Findings
MEC ANN model efficiently encapsulated the non-linear relationship between the input parameters and the
hydrogen yield in MEC scale-up and industrial development in addition to other bioprocesses.
where SOFC is solid oxide fuel cell and MEC is microbial electrolysis cells.
Table 3
Literature studies of PEMFCs with regression.
Study Major research focus
Findings
[29]
The methods contribute on a very efficient way to the analysis and modelling of experimental data of a
PEMFC.
The MRA with respect to ANOVA of the derived correlations assured their significance.
[30]
[31]
[32]
[33]
[34]
[35]
Analysis of PEMFC experimental data using PCA and
MLR
Using the MLR with respect to ANOVA to model the
actual performance of PEMFC
All parameters on hydrogen crossover rate were
compared through MLR.
Analytical modeling of PEMFC
Electrical power prediction of PEMFC by using SVR
MLR analysis of independent parameters showed that the hydrogen crossover rate increases.
Tafel constants, ohmic resistance, and the concentration loss constant are estimated through regression.
A model using SVR combining with PSO algorithm for its parameter optimization was developed to
modeling and predicting the electrical power of PEMFC.
PEMFC based on SVR
SVR and PSO algorithm for receding optimization shows good result for the PEMFC output power predict
control.
PEMFC impedance estimation using regression analysis The linear regression method consisted of linear curves estimated for the real and imaginary impedance
components using least-squares equations.
where SVR is Support Vector Regression and PSO is Particle Swarm Optimization.
Table 4
Literature Studies of other Fuel Cells with Regression.
Study Major research focus
[36]
[37]
Fuel
Cell
Performance evaluation of MFC by artificial intelligence MFC
methods
Design of experiments for fitting regression models on SOFC
the tubular SOFC
Findings
The results conclude that the modelling methods can successfully model the performance of MFC.
The main generator physical variables have been correlated with the main operator input variables
through analytical relations.
where MFC is microbial fuel cell.
1.2. Comparison of fuel cells
In Tables 1e4 we presented ANN and regression studies in
literature for PEMFCs and other fuel cells. We saw that for all fuel
cell types, ANN and regression methods are widely used for
modelling and performance parameter prediction.
In the study, we proposed novel formulas for hydrogen consumption calculation of PEMFCs for linearly increasing loads. We
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Fig. 1. Linearly increasing load profile for 0.5 Wh
used both ANN and MLR methods in the study to calculate the
hydrogen consumption. We formed certain energy values and for
each energy values the slope of the linearly increasing load
changes. Thus, the peak power value of the load is also changes
depending on the slope for a certain energy value. We investigated
the total energy-slope and peak power-slope relations using ANN
and MLR. We performed the uncertainty analysis to validate the
experimental results. We also performed the energy, exergy, cost,
sensitivity analysis for the different energy and power slope values.
Fig. 3. A general MLP-ANN structure.
2.2. Methods
2. Material and methods
2.1. Material
In the study, we used PEMFC, formed 46 cells and maximum
ratings are 46V/70 A. The energy values are determined as 0.5 Wh,
1 Wh, 2 Wh, 3 Wh, 4 Wh and 5 Wh. We limited the power 600 W
for test conditions due to measurement equipment limitations. The
slope values (S(Watt/s)) are determined as 0.2, 0.5, 1, 2, 5, 10, 20 and
50. We measured the hydrogen consumption using Red-y flow
meter. The load profile is adjusted using Gwinstek PEL-3111 electronic load. The load profile for 0.5 Wh is presented in Fig. 1.
For each energy value and slope value hydrogen consumption is
measured.
2.2.1. Artificial Neural Networks (ANN)
ANN is a representation of human brain which consists of
interconnected neurons (Fig. 2). ANN is a powerful tool for solving
many problems because of its properties such as nonlinearity, information processing, learning and adaptation. Also, “large number
of simple units”, “highly parallel and strongly connected units” and
“robustness against the failure of single units” are some important
characteristics of ANN structure. There are many types of ANN in
the literature: Hopfield networks, Elman networks, CohenGrossberg networks, neutral-type networks, bidirectional networks and so on. Multi-Layer Perceptron Artificial Neural Network
(MLP-ANN) model is a type of neural network that consists of an
input layer, an output layer and one or more hidden layers (Fig. 3). A
MLP-ANN is known to be one of the successfully developed
methods which was widely used in solving many prediction
problems.
Fig. 2. A general ANN neuron structure.
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Table 5
Hydrogen consumption of the fuel cell for different operating conditions.
Total Energy (W-hour)
Slope (Watt/s)
Peak Power Value (Watt)
Hydrogen Consumption (lt)
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
0.2
0.5
1
2
5
10
20
50
100
0.2
0.5
1
2
5
10
20
50
0.2
0.5
1
2
5
10
20
0.2
0.5
1
2
5
10
0.2
0.5
1
2
5
10
0.2
0.5
1
2
5
10
26.83
42.42
60
84.85
134.16
189.73
268.32
424.26
600
37.94
60
84.85
120
189.73
268.32
379.47
600
53.66
84.85
120
169.7
268.32
379.43
536.65
65.72
103.92
146.96
207.84
328.63
464.75
75.89
120
169.7
240
379.47
536.65
84.85
134.16
189.73
268.32
424.26
600
0.71
0.57
0.65
0.58
0.52
0.59
0.59
0.67
0.73
1.13
1.11
1.09
1.12
1.15
1.18
1.12
1.68
2.21
2.17
2.22
2.36
2.4
2.48
2.62
3.35
3.32
3.39
3.73
3.57
3.86
3.52
4.48
4.51
4.6
5.16
5.3
5.44
5.55
5.67
5.9
6.28
7.04
Fig. 4. Hydrogen consumption-slope curve for 0.5 Wh and 1 Wh
2.2.2. Multiple linear regression (MLR)
Regression analysis is one of the most widely used techniques
for analyzing multifactor data. It is a useful technique to express the
relationship between an output variable and a set of input variables. These variables can be obtained from experimental studies or
real-world data. MLR is a model in which there are more than one
Fig. 5. Hydrogen consumption-slope curve for energy values in fluctuation region.
input parameters. The formulation of the model is in Equation (1).
y ¼ b0 þ b1 x1 þ b2 x2 þ … þ bk xk þ ε
(1)
where y is the output, xi ði ¼ 1; 2; …; kÞ are inputs, bi ði ¼ 1; 2; …; kÞ
are the coefficients for the corresponding variables, b0 is the constant term and ε is the associated error term [38].
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sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pk
2
b
i¼1 ð yi yi Þ
RMSE ¼
k
(2)
where ybi ði ¼ 1; 2; …; kÞ are the real outputs, yi ði ¼ 1; 2; …; kÞ are
the estimated outputs and k is the number of outputs.
3.1. Experimental study
Fig. 6. Hydrogen consumption-consumed energy curves for different slopes.
3. Results and discussion
In this study, first of all, experimental results of hydrogen
consuming were presented. After that, the MLR formulation of the
system was given, the ANN characteristics were explained and all
three results (experimental, MLR and ANN) were compared with
average error rates and Root Mean Square Error (RMSE) values. The
formulation of RMSE is given in Equation (2).
In Table 5, we presented the total energy, slope and corresponding calculated peak power, average power, time values of the
experiments. The last column of the table presents the measured
hydrogen consumption.
We presented the hydrogen consumption vs slope curves using
experimental results. In Fig. 4, the hydrogen consumption is shown
according to slope for the load for 0.5 Wh and 1 Wh.
As seen in Fig. 4 hydrogen consumption fluctuates for the slope
20 W/s and below. We extracted the hydrogen consumptions from
experimental results for the other energy values and presented in
Fig. 5 in the fluctuation region.
We presented hydrogen consumption for certain energy values
for different slopes in Fig. 6.
In Fig. 6, it’s seen that hydrogen consumption increases almost
linearly with the increasing energy. The different slopes cause
fluctuations on hydrogen consumption on recent energy values.
In Fig. 7, slope and hydrogen consumption relation is presented
for different power levels. As it is seen from the figure; for all of the
low, medium and high power levels, the relation is nonlinear and it
can be formulized with power function.
Fig. 7. Hydrogen consumption-slope curve for different power values a) 84.85 W b)268 W c) 600 W.
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Fig. 8. Comparison of experimental, ANN and MLR results for total energy-slope.
Fig. 9. Comparison of experimental, ANN and MLR results for peak power-slope.
Table 6
The average error rates for investigated relations.
Total energy-slope
Peak power-slope
ANN
MLR
0.1124
0.2488
0.3189
1.4732
3.2. Modelling studies
3.2.1. ANN modelling
In this study, the inputs of ANN structure were x1 and x2 while
the output is y. Respectively, 70%, 15% and 15% of input data were
used for training, validation, testing and the systems were simulated for total energy-slope and peak power-slope in MATLAB
platform. The simulations are depicted in the Fig. 8 and Fig. 9 below.
The average R2 values are 0.9965 for ANN simulation and 0.9545 for
MLR simulation for total energy-slope and 0.9837 for ANN simulation and 0.4015 for MLR simulation for peak power-slope.
Fig. 10. Energy efficiency of PEMFC for different slope and consumed energy values.
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The second formula is generated for peak power-slope and
presented in Equation (4).
y ¼ 1:5382 þ 0:0084x1 0:0805x2
(4)
where y is hydrogen consumption, x1 is peak power (Watt), x2 is
slope (Watt/s).
The experimental, ANN, MLR results of experiments and the
differences are given in the Fig. 8 for total energy-slope and in Fig. 9
for peak power-slope, respectively.
The average error rates are presented in Table 6 for the investigated relations.
As seen in Figs. 8e9 and Table 6 ANN modelling gives better
results than MLR. And, it can be said that using the total energyslope data is more suitable for modelling.
Fig. 11. Exergy efficiency of PEMFC for different slope and consumed energy values.
4. Data analysis
We performed energy, exergy, sensitivity, uncertainty and cost
analysis of the PEMFC under test conditions. In this data analysis
section, we defined the range of slope is 0.2e10 W/s because the
slope values are common for all energy levels given in Table 5.
Energy Analysis is based on the energy efficiency of the PEMFC.
Energy efficiency(ƞen[%]) is calculated by net power (E_ net[W])
divided by higher heating value of the hydrogen (HHV[J/kg]) times
_ H2[kg/s]). We used experimental results and
hydrogen flow mass(m
the standard values in the literature in Equation (5) [39e42].
hen ½% ¼
Pnet
_ H2
HHVH2 x m
We presented the result in Fig. 10 for different consumed energy
and slope values.
As seen in Fig. 10, increasing slope and consumed energy decreases the energy efficiency of the PEMFC.
Exergy analysis is based on exergy efficiency of PEMFC as energy
analysis. The exergy efficiency(ƞex[%]) of a fuel cell system is [%]) is
calculated by net power (E_ net[W]) divided by the exergy rate of the
reactants (air(E_ air[W]) þ hydrogen E_ H2[W]). We used experimental
results and the standard values in the literature in Equation (6)
[40e49].
Fig. 12. Cost analysis of all energy and slope combination.
E_
net
hex ½% ¼ _
ðEair þ E_ H2 Þ
Fig. 13. Relative uncertainty of all energy and slope combination.
3.2.2. MLR modelling
To generate novel formulas, we focused on total energy-slope
relation and peak power-slope relation in MLR. The first formula
of this experimental study is determined for total energy-slope in
Equation (3).
y ¼ 0:1441 þ 1:2332x1 þ 0:0084x2
(5)
(3)
where y is hydrogen consumption, x1 is watt-hour, x2 is slope
(Watt/s).
(6)
reac:
We presented the exergy efficiency results in Fig. 11 for different
consumed energy and slope values.
As seen in Fig. 11, increasing slope and consumed energy decreases the exergy efficiency of the PEMFC.
Cost analysis is investigated in the meaning of unit energy cost,
annual energy cost, payback period in the literature [50e52]. In our
study we investigated the unit energy cost change for the different
slopes. For all energy and slope combination we calculated the unit
energy cost[$/J] using experimental results and presented its percentage value in Fig. 12.
As seen in Fig. 12, cost increases with the increasing energy and
slope value.
Sensitivity analysis is performed using different methods in
literature [53e57]. Since our aim is the extracting the relation between input and output, we used the derivative-based approach
[53,54].
vy
SX ¼ vx
(7)
where, S is the sensitivity of the input parameter x and y is the
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output. We performed sensitivity analysis for Equation (3) and
Equation (4). After the derivation of Equation (3) we found that S
energy ¼ 1.2332 and Sslope ¼ 0.0084. And after the derivation of
Equation (4) we found that Speakpower ¼ 0.0084 and Sslope ¼ 0.0805.
When we consider the Equation (3), we saw that, the sensitivity of
energy is so high according to the slope. But, when we consider the
Equation (4), the sensitivity of peak power is low according to the
slope.
Uncertainty analysis is used for the validate the experimental
results [40,58e60]. We calculated relative uncertainty by dividing
the Equation (8) to output value for each energy and slope value.
We used Equation (3) and Equation (4) for output function. In
Equation (3), the independent variables are energy and slope. In
Equation (4) the independent variables are peak power and slope.
Our independent variables are set from GW INSTEK PEL-3111
electronic load. The accuracy of the electronic load is 0.4% in dynamic operation [61]. We used that value to calculate the independent variables uncertainties (wi).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
n
vy
vy
Wy ¼
W1
þ…þ
Wn
vX1
vXn
(8)
We presented the relative uncertainty results in Fig. 13 for
different consumed energy and slope values.
As seen in Fig. 13 uncertainty levels are valid for all slope values.
5. Conclusion
This paper analyzes hydrogen consumption for linearly
increasing loads. Experimental results are processed by ANN and
MLR modelling techniques. In these modelling process, ANN gives
better results than MLR. The results of the present study have
demonstrated that total energy-slope relation more convenient for
a novel equation. The average error rates of ANN and MLR are
0.3189%, and 0.1124% while the average R2 values are 0.9965 for
ANN simulation and 0.9545 MLR simulation. When total energy
and slope were compared, it was seen that total energy dominated
hydrogen consumption. But, when the peak power and slope were
compared the slope dominated the hydrogen consumption. The
energy and exergy efficiency are decreased with the increasing
slope value approximately %6. Cost of the energy is increased with
the increasing slope value approximately 12%. The hydrogen consumption is highly sensitive to the energy value according to slope
of the power. If we compare the peak power and slope of the power,
it is seen that the system is more sensitive to the slope of power
than the peak power. We also investigated the relative uncertainty
of the system to validate the experimental data.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
CRediT authorship contribution statement
€
Yasin Ozçelep:
Supervision, Conceptualization, Methodology,
Visualization, Investigation, Data curation, Writing - review &
editing, Funding acquisition, Resources. Selcuk Sevgen: Data
curation, Visualization, Investigation, Software, Writing - review &
editing. Ruya Samli: Writing - original draft, Validation, Writing review & editing, Funding acquisition, Formal analysis.
577
Acknowledgements
This work was supported by Scientific Research Project Unit of
Istanbul University-Cerrahpasa (Project Number: FBA-2018-29185)
_
and Scientific and Technical Research Council of Turkey (TÜBITAK)
(Project Number: 118E682).
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