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Using MATLAB to model and simulate a photovoltaic system to produce hydrogen
Energy Conversion and Management 185 (2019) 101–129
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Using MATLAB to model and simulate a photovoltaic system to produce hydrogen
T
Tamer M. Ismaila, , Khaled Ramzya, , Basem E. Elnaghib, M.N. Abelwhabb, M. Abd El-Salamc ⁎
⁎
a
Department of Mechanical Engineering, Suez Canal University, Ismailia, Egypt Department of Electrical Power and Machines, Suez Canal University, Ismailia, Egypt c Department of Basic Science, Cairo University, Giza, Egypt b
ARTICLE INFO
ABSTRACT
Keywords: Hydrogen PEM electrolyzer Photovoltaic MATLAB Solar radiation
Energy is currently the basis for development in different areas worldwide. Traditional sources of energy such as coal, oil, and nuclear energy have serious repercussions on the environment and are non-renewable energies. Therefore, renewable energy, like solar, wind, and marine energy, are alternatives. Egypt is considered an important country that has climatic averages allowing the exploitation of renewable energy. Solar energy is available in Egypt, especially in Upper Egypt, throughout the year. Different models have been created to estimate and predict the global solar radiation intensity due to the shortage of measuring stations. This study presents a mathematical model to estimate and predict the global solar radiation intensity in Egypt. This model is compared and validated against published measurements of global solar radiation intensity. Furthermore, this study introduces a hybrid system used to produce hydrogen (photovoltaic generator–PEM electrolyzer). Modelling and simulating methods is done by running a flowchart in MATLAB to minimize the losses in the system and increase the quantity of hydrogen produced. The simulation includes the global solar radiation estimation and the photovoltaic generator–PEM electrolyzer. The experiment was conducted in March in Suez city, Egypt. The results obtained showed that the model of global solar radiation gives a good prediction for estimating the intensity of global solar radiation in Egypt. Furthermore, they concluded that there is a significant improvement in system performance that signifies an increase in the volume of hydrogen produced by the system. The whole model is simulated, and the simulation results fit the experimental data very well. The electrolyzer is powered by a PV panel and is modelled, sized, and experimentally validated.
1. Introduction Renewable energy uses natural elements that are renewed faster than they are consumed. Thus, solar, hydro, geothermal, and wind energy are renewable and environmentally friendly. The use of renewable and environmentally friendly energies is one of the best alternatives to fossil fuels, especially after Fukushima nuclear disaster in Japan. Although much research has already done in this field, the research effort has intensified so that future energy sources will be as green as possible. Energy production will be a challenge of great importance in the coming years as the energy needs of industrialized societies are increasing. However, developing countries will increasingly need energy to achieve development, and much of the world’s energy comes from fossil fuels. Today, renewable energies are gradually becoming energies full share, competing with fossil fuels in terms of cost and production
⁎
performance. However, their energy-to-electricity conversion systems often suffer from a lack of optimization that still makes them expensive, with significant inefficiencies in performance and reliability [1]. Solar energy has a great potential for the future. It is free and widely available. The sun generates energy through a thermonuclear process that converts about 650 × 106 tons of hydrogen into helium per second [2]. This process creates electromagnetic radiation that spreads into space, travelling at a speed of 300 × 103 km/s in all directions [2]. The sun is considered the main source of energy worldwide. Solar energy is used in many applications such as water heating, power generation, and heating or cooling. Furthermore, the electricity consumed globally in recent decades is strongly linked to the development of industry, transport, and communications. Today, much of the electricity produced is produced from non-renewable resources such as coal, natural gas, oil, and uranium. Their regeneration rate is extremely slow on a human scale. Solar radiation data are not available for large areas due
Corresponding authors. E-mail addresses: [email protected], [email protected] (T.M. Ismail), [email protected], [email protected] (K. Ramzy).
https://doi.org/10.1016/j.enconman.2019.01.108 Received 25 September 2018; Accepted 30 January 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
I0 ID Iel Nc Pr Q H2 Uc Utn Utno xn x n+ 1 A E Eh G ICC If Igen Ilight IPV k KT m n Ncell NOCT Np Ns P
p PEM PN PVG q R RS
diode saturation current (temperature dependent) reverse current of diode the current of electrolyzer (A) number of cells in an electrolyzer stack power required by the electrolyzer (W) hydrogen gas flow rate (Nm3·h−1) actual voltage of the cell (V) thermoneutral potential (V) standard thermoneutral potential (V) the present iteration the next iteration ideality factor global solar radiation (W/m2) the operating point current daily mean global irradiance on a horizontal surface, kWh/m2 an operational short circuit the voltage of the operating point the current delivered by the generator current photo, depending on the intensity of the irradiation cell current Boltzmann constant the clarity index, or the relationship between ground and extra-terrestrial radiation material index (1 or 2 depending on the technology used) number of electrons transferred per hydrogen molecule (n = 2) number of electrolyzer cells nominal solar cell operating temperature number of parallel modules in the photovoltaic field number series module in the photovoltaic field atmospheric pressure
RSH s S Sc T Tamb. Tcell Tel V Vf VOC VPV Z
F T e m s u , s
s
Ho H
to the low number of solar stations especially in remote locations. Thus, using the simulation models to predict the global and diffused solar radiation data is essential for many solar energy systems. These models depend on different parameters such as temperature, sunshine hour data, latitude angles, hour angles, site location and attitude angle such as Chandel et al. [3]; Gueymard [4] ASHRAE [5]; Iqbal [6]; Gueymard [7]. This will lead to a more or less short-term, non-zero risk of depletion of these resources. Although photovoltaic energy has been known for many years as being capable of producing electricity ranging from a few mill watts to a megawatt, it is also an attractive alternative to replace electricity supplied by conventional sources because it has many advantages, as follows:
number of parallel electrolyzer cells proton exchange membrane positive negative photovoltaic generator charge of the electron perfect gas constant resistance in series, modelling ohm losses of material and contacts parallel resistance, representing the parallel admittance of the current generator number of series electrolyzer cells generator surface Solar constant (1353 W/m2 = 4.8708 MJ/h·m2) temperature (K) ambient temperature cell temperature electrolyzer temperature volume of hydrogen produced (mL) the derivative of the function open circuit voltage voltage at the cell terminals number of electrons required to release a molecule angle of inclination, voltage temperature factor current temperature factor ground albedo faradic efficiency energy or thermal efficiency the efficiency of the electrolyzer photovoltaic module performance the overall performance the adaptation performance the time angle of the sunset on the inclined plane the time angle of the sunset on the horizontal plane standard enthalpy of formation (J·mol−1) change in enthalpy of formation (J·mol−1)
hydrogen to ensure the continuity of electricity production. Several hydrogen production techniques exist; some of these have reached commercial maturity while others are still experimental. The catalytic decomposition of natural gas, partial oxidation of heavy oils, gasification of coal, and water electrolysis are among the hydrogen production processes that have been industrialized [8]. However, pure and hybrid thermochemical cycles are at the research and development stage, while photochemical and photo-biological processes are still in the early stages of research. The electrolysis of water for hydrogen production is the most popular process. The use of solar energy in electrolysis processes is the most cost-effective and environmentally friendly method [9]. Hydrogen is considered a potential future energy carrier. Solar hydrogen is produced using renewable energies, especially solar energy, and hydrogen has a definite future in the field of energy. Therefore, the possibilities for its production on a large scale will be study. In large-scale production, consideration must be given to yields and economic opportunities. As part of the study, it is found that hydrogen has major advantages that ensure it has a bright future as an intermediate energy vector. Indeed, its applications cover a wide range of human energy needs; it can be used in the fields of transport and in stationary and portable applications and it also has a high energy efficiency. In addition, it is a clean if its production is based on a non-polluting energy such as solar radiation. This advantage is crucial because of recent controversies over the greenhouse effect. The photovoltaic conversion of global solar radiation into electricity is one way to exploit solar deposits using solar cells. A system coupling a photovoltaic field and an electrolyzer makes it possible to store the electricity in the form
1. Producing this renewable electricity does not emit greenhouse gases; however, the environmental impact of manufacturing the system must be reduced. 2. Photovoltaic energy is exploitable both in mountainous regions, remote villages, and in the center of a big city, in southern and northern regions, because sunlight is available everywhere and almost inexhaustible. Photovoltaic electricity can be produced as close as possible to where it will be consumed, in a decentralized manner, and directly by the user, making it accessible to a large part of the global population. However, in the field of renewable energy, especially photovoltaics, there is a problem of continued electricity production in the night or on cloudy days. To manage that, a techniques is used such as batteries and 102
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of a gas (hydrogen). As a substitute for fossil fuels, hydrogen has excellent physicochemical and thermal properties that give it the quality of a universal fuel. This energy vector is the only one that can be produced from water and several renewable energy sources and can then be used without being detrimental to the environment [10]. Several numerical and experimental studies have been done on hydrogen production facilities that use renewable energies. Chen [11] studied the configuration of hybrid power systems (solar-hydrogen fuel cells) to supply electric vehicles; the electricity from photovoltaic cells placed on the roof was converted to hydrogen through electrolysis. Fuel cells are used to power electric vehicles. Yunez-Cano et al. [12] studied the feasibility of integrating hybrid photovoltaic/hydrogen (PV/H2) systems into houses in Mexico. The PV/H2 system supplies the load, with electricity generated by the main source (PV), excess energy is electrolyzed to produce hydrogen, and the fuel cell provides a backup in case of insufficient energy. Kely et al. [13] studied the application of high-pressure hydrogen produced by water electrolysis in fuel cell motor. However, further studies have shown that hydrogen can be used in other regions without the use of fuel cells. Topriska et al. [14] describe the development of semi-empirical numerical models for solar hydrogen systems; these consist of proton exchange membrane (PEM) electrolysis by photovoltaic panels to produce hydrogen as fuel for cooking applications. Pedrazzi et al. [15] developed a mathematical model and software for solar hydrogen hybrid system. The results showed that the virtual hybrid system can bring about complete grid independence and the hydrogen production balance is positive after a year’s operation with a system efficiency of 7%. Ohta [16] revealed the feasibility of using hydrogen in treatment strategies. Ahmadi et al. [17] analyzed the model system using MATLAB simulations to calculate the hydrogen production, exergy damage, and exergy efficiency of hydrogen production based on an ocean thermal energy conversion system. The system was coupled with a solar enhanced PEM electrolyzer. Bousquet et al. [18] developed an empirical method to simulate the generation of electrolytic or fuel cells. A dynamic model for PEM electrolysis was proposed and evaluated by Gorgun [19]. Onda [20] developed a two-dimensional mathematical model for analyzing PEM electrolytes. Ulleberg [21] demonstrated an alkaline electrolytic cell model based on thermodynamics and heat transfer theory. Recently in renewable energy systems research, Kélouwani et al. [22] developed and demonstrated an independent renewable energy system with hydrogen storage. Khan et al. [23] modelled a small wind-fuel cell hybrid energy system. Assaf and Shabani [24] used the MATLAB to simulate a solar-hydrogen combined heat and power system integrated with solar-thermal collectors to supply power and heat to the applications. From the results they concluded that the maximum thermal reliability that could be obtained is around 96%. It is in this context of announced crisis that renewable resources, varied and inexhaustible, can become an alternative to fossil resources. Their conversion into thermal, chemical, or electrical energy does not present any danger to humans, any more than ecological danger. The production of energy can be centralized or decentralized, allowing the development of a local economic fabric. As energies from renewable primary sources such as solar, wind, and hydro cannot be stored directly, it is necessary to develop a new energy vectors, such as hydrogen, to promote the development of renewable primary sources. PV hydrogen is a renewable source for producing clean fuel and electricity [25]. Wang et al. [26] studied the characteristics of single-stage photovoltaic grid-connected/hydrogen production multi-inverter system using modal analysis. The results showed that the simulation results verified the correctness and effectiveness of the modal analysis. MATLAB/Simulink of a PEM electrolyzer powered by a solar panel was developed by Albarghot and Rolland [27]. They concluded that the experimental and simulated results were matched. Several PV-hydrogen plants are operated in countries such as Finland [28], Germany [29], Italy [30], Japan [31], Spain [32], Saudi Arabia [33], Switzerland [34], and the United States [35,36]. Most of these facilities are demonstration
units managed by public bodies. What motivates us to do this work which studied the production of hydrogen by a hybrid system (photovoltaic generator - PEM electrolyzer), with the aim of minimizing the losses in the system, by the modeling of the system elements and the simulation of operation by executing a flowchart under MATLAB. To increase the amount of hydrogen produced and make this solution cost-effective compared to other solutions, in order to facilitate the use of hydrogen as a storage element of electricity by use of fuel cells, based on their physical and chemical characteristics. Therefore, the main aim of the present research is to contribute to understanding a new technology for the production and storage of clean energy. This study is designed to stimulate future work in this area. In this study, a simulation of a PV system to produce hydrogen by water electrolysis is presented; the photovoltaic panels ensure the production of electrical energy, and climate data for the month of March in Suez, Egypt is used. In most studies and researches the global solar radiation is measured and used in the simulation method as a measured values, but in this study the global solar radiation was modelled using MATLAB and matched with the PV system model to produce hydrogen. So a simulated model was built, validated, and compared with published data due to the importance of estimating the global solar radiation intensity. This model is used to estimate the global solar radiation intensity during the year at any location. Furthermore, system elements were modelled and a flowchart for simulating system performance was run in MATLAB to determine the most favorable conditions for improved hydrogen production. Mathematical models that describe the electrical behavior of the photovoltaic panel and the electrolyzer are presented. The simulation concerns the direct coupling of the hydrogen production system by directly coupling the photovoltaic generator and the PEM electrolyzer. The results obtained show that it is possible to choose an appropriate hydrogen production system. 2. Global solar radiation modelling Global solar radiation data are required for many applications and many areas of research. Most of the energy produced from the sun is transmitted radially as electromagnetic waves called global solar radiation (energy). Solar energy can also be converted to useful forms such as thermal and electrical energy. As global solar radiation passes through the atmosphere, some of it is absorbed, scattered, and reflected by air molecules, water vapor, clouds, dust, and pollutants. The scattered and reflected part returns to the Earth as diffuse solar radiation. The global solar radiation that reaches the surface of the earth without being depleted or diffused is called direct (beam) solar radiation. Global or total global solar radiation is the sum of the diffuse and direct solar radiation. Several models have been developed to predict global solar radiation in many different countries. In Egypt, the solar energy incident on land has a magnitude of 12–30 MJ/m2/day, and the duration of sunshine ranges from 3500 to 4500 h per year [37]. Furthermore, in Egypt, there are few meteorological stations that measure components of global solar radiation. Therefore, some empirical models have been developed to calculate global solar radiation over different sites in Egypt. Morcos [38] developed a mathematical model to calculate the total radiation on a tilted surface in Assiut, Egypt. This model depends on a study by Liu and Jordan [39], in which radiation on a tilted surface consists of three components: beam solar radiation, diffuse radiation, and global solar radiation reflected from the ground, buildings, and trees. The total global solar radiation on the tilted surface E, is the sum of the three terms and given as:
E = Eb Rb +
Ed (1 + cos ) + 2
g (Eb
+ Ed )(1 2
cos ) (1)
where Eb and Ed are beam and diffuse global solar radiation intensities on horizontal surfaces and g is the diffuse ground reflectance. The 103
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geometric factor Rb is the ratio of the beam radiation on the tilted surface to that on a horizontal surface and it is given as
horizontal surface is given by
cos Rb = cos z
The standard clear day radiation is determined from the following relationship:
Ed = Ion d cos
(2)
where
cos = sin sin cos
E = Ion
sin cos sin cos + cos cos cos cos
b cos
(12)
z
+
d cos z
(1 + cos ) + 2
g( b
+
d ) cos z (1
cos )
2
(3)
(13)
On the other hand, Z is the zenith angle that depends on the latitude of the location and the solar hour angle . The last is given as:
The fact that both the theoretical curves and experimental points in Morcos [38] show that the values of d correspond to a fixed value of d depend only very moderately upon the air mass. This indicates that, for the degree of accuracy sough here, a relationship independent of the air mass is adequate. For Eq. (11), a straight line obtained using the least squares method, is the best fit for the experimental points. In this work, the model was simulated and a sub-routine built in MATLAB to investigate the global solar radiation. This model was checked, compared with published measured global solar radiation over different cities in Egypt, and validated. The model described previously was evaluated based on the coefficient of determination R2. This value can be used to test the linear relationship between calculated and measured values; its value should be as close to unity as possible and is given by the following equation [40]:
+ cos sin sin cos cos
cos
Z
= cos cos cos
+ cos sin sin sin
(4)
+ sin sin
where is solar declination angle, , is the tilt angle, and is the surface azimuth angle. The hour angle is equivalent to 15° per hour, with a positive value in the morning and a negative value in the afternoon, is determined using the following:
=
360 × (t 24
12)
(5) (6)
= 23.45sin [(360/365) × (284 + N )]
where t is the hour of the day and N is the day number, beginning with January first. The value of the diffuse ground reflectance is 0.2 [38] when there is no snow cover. The beam and diffuse radiation on a horizontal surface, Eb and Ed, are determined using standard clear sky conditions. The beam global solar radiation on a horizontal surface for clear sky hours is given by
Eb = Ion b cos
R2 = 1
(14)
b
= a o + a1 e
360N 360
E¯ m =
(8)
where Sc is the solar constant. The constants ao, a1, and k are determined according to the correction factors of Eq. (10) as below:
ao = 0.4237
0.00821(6
a1 = 0.5055 + 0.00595(6.5 k = 0.2711 + 0.01858(2.5
AL ) 2 AL )2 AL ) 2
(10)
where AL is the altitude of the observer in kilometers. For changes in climate, correction factors are applied to ao*, a1*, and k*. These correction factors are ro = ao /ao*, r1 = a1/a1*, and rk = k/k*; these are given in Table 1. To estimate the clear sky diffuse radiation on a horizontal surface, Morcos [38] used the following empirical correlations for beam and diffuse radiation for clear sky: d
= 0.2710
0.2939
(11)
b
where d is the ratio of clear sky diffuse radiation to the extraterrestrial radiation on a horizontal plane and. The clear sky diffuse radiation on a
np i=1
ro
r1
rk
Tropical Mid-latitude summer Sub-arctic summer Mid-latitude winter
0.95 0.97 0.99 1.03
0.98 0.99 0.99 1.01
1.02 1.02 1.01 1.00
(15)
Em (16)
np
Tcell = Tamb +
Table 1 Correction factors for climate types [38]. Climate Type
Ec E¯ m )
where np is the number of experimental points. Temperature T and irradiation G have a direct impact on the performance of a photovoltaic cell. When the cell temperature increases the open circuit voltage decreases substantially while the short circuit current increases slightly. Then it can be noticed that the PV cells have better performance in a cold environment with clear sky, unlike a warm environment. For crystalline silicon cells, Voc drops by about 0.37% for each additional degree Celsius, Icc increases by 0.05% for the same conditions. The temperature of the PVG depends not only on the ambient temperature but also on the effects of the irradiation of the cell. Since only a small fraction of the insolation that affects the module is converted into electricity, most of the incident energy is absorbed and converted into heat [31]. To help system designers take into account variations in cell performance with temperature, manufacturers often provide an indicator called NOCT. The temperature of the NOCT cell is in a module when the ambient temperature is 20 °C, solar radiation equal to 0.8 kW/m2, and wind speed at 1 m/s. To account for other environmental conditions, the following expression may be used:
(9)
k / cos z
)2
where Em and Ec are the measured and calculated global solar radiation, respectively. The term E¯ m in Eq. (15) is the average measured global solar radiation and can be defined as follows [40]:
where Ion is the hourly extra-terrestrial radiation, measured on the plane normal to the radiation (MJ/m2) and b is the atmospheric transmittance for beam radiation. Ion and b are calculated from the following equations:
Ion = Sc 1 + 0.033cos
( Em ( Em
R2 = 1
(7)
z
Error between experimental and predicted results Experimental result deviation
NOCT
20 °C ×G 0.8
(17)
where Tcell, Tamb is the Cell temperature and ambient temperature, respectively, G is the solar irradiation (kW/m2). 3. Modelling and simulation of direct coupling PVG-Electrolyzer In this section, a study of a solar hydrogen production system is 104
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presented based on the direct coupling between a photovoltaic generator (PVG) and a PEM electrolyzer. For this study, the PVG, the electrolyzer, and the simulation of the direct coupling were modelled.
If V = 0 (short circuit case):
ICC = IL
3.1. Modelling the photovoltaic generator
0 = IL
ID = Io e
Vth =
IRSh =
I = IL
V + (I . R s ) Vth
1
Io exp
V + (I . RS ) Vth
V + (R S × I ) RSh
1
Io exp
V + (I × RS ) Vth
1
Io exp q
(V + (I × RS )) A × TC × K
0 = IL
Io exp q
Im = IL
Io exp
(21)
Im = ICC 1
(22)
RS =
1
(27)
A TC q
VOC A × TC × K
(Vm + (Im. RS )) A × TC × K
q
1
(30)
VOC C A × TC × K
exp q
(V
exp q K
(29)
VOC + (IRS )) A × TC × K
Vm
(
Im Icc
ln 1
(31) (32)
VOC + (I . RS ) A × TC × K
)+V
(33)
Vm
OC
(34)
Im
To determine the Ideality factor (A):
dP dI dV =0= +I dV dV dI
(35)
q (2Vm
A=
(23)
1
(26)
(28)
I = ICC 1
ns KT
By replacing Vth in the current equation,
I = IL
(Vm + (Im. RS )) A × TC × K
Io exp
Io = ICC exp
A : Ideality factor (between 1 and 2 according to the technology used). For modules supposedly devoid of leaks (infinite Rsh and IRSH 0 ), this relationship is given as follows:
I = IL
1
ICC = IL
(20)
V + (Rs × I ) RSh
(25)
In order to determine the unknown parameters, a simplified explicit method [42] was used and it is suppose that:
(19)
A × Tc × K q
VOC A × TC × K
Io exp q
Im = IL
(18)
IRsh
1
At the maximum power point:
3.1.1. The Current-Voltage (I-V) characteristic simulation models The photovoltaic cell model used in the present work is shown in Fig. 1 as below. Based on the PV cell model circuit, the node law is applied to find the relationship between the current and the voltage [41]:
ID
ICC · RS A × TC × K
If I = 0 (open circuit case):
A PV module converts global solar radiation into electricity directly, and the intensity of global solar radiation and the temperature are essential to its current and output voltage. Thus the predicting the performance of a cell/module/PV generator requires the development of a mathematical model that allows study of its operation (e.g., global solar radiation intensity, temperature) for different meteorological conditions. Many studies focus on the development of mathematical models to simulate current-voltage (I-V) characteristics of a cell/module/PV generator, while others are oriented towards modelling the performance of PV modules in terms of electrical power produced.
I = IL
Io exp q
ISC ICC
Im
VOC )
(
+ ln 1
Lm ICC
)
(36)
ns : The serial cell number (24)
3.1.2. Photovoltaic field
There are four unknown parameters in this equation: IL (photocurrent), Io (saturation current), A (Ideality factor), and Rs (series resistance) There are three remarkable cases in the I-V feature:
Io (gen) = NP × Io (mod)
(37)
Vr (gen) = NS × Vr (mod)
(38)
RS (gen) =
NS NP
RS (mod)
(39)
Therefore, the generator equation takes the following form:
Igen = ICC
Io exp q
Vgen + (Igen· RS (gen) ) A × TC × K
1
NP : number of parallel cells in the photovoltaic field NS : number of serial cells in the photovoltaic field Igen : the current delivered by the generator ICC : Short-circuit current Fig. 1. Equivalent electrical diagram of a photovoltaic cell.
And the V-I relationship can be written as follows: 105
(40)
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Vgen =
Igen + Icc + Io
Igen· RS (gen) + Vth × log
Vthmod =
(41)
Io
TC TC (ref )
Io = Io (ref ) ×
G Gref
G Gref
q 1 × A×K Tcref +
× T
× ICC (ref ) + a × T
Vm = Vm (ref ) +
Im =
× exp E ×
A×K×T G × log q Gref
VOC = VOC (ref ) +
ICC =
3
A
K q
T
× Im (ref ) + a × T
log
1 TC
3.2. Modelling electrolysis An electrolyzer is a device that uses electrical energy to produce chemical reactions. In this study, the electrolyzer was used to perform water electrolysis to produce hydrogen. PEMs are made from pure polymer membranes or composite membranes where the materials form a polymer matrix, and one of the most common materials used is Nafion. Fig. 3 shows the structure of a PEM electrolyzer.
(43)
(44)
3.2.1. Electrolyzer model The water electrolyzer consists of several electrolyzer cells connected in series and in parallel. The electrolyzer model considered here is based on the characteristics of the individual cells. The calculation of the operating voltage required, and the flow rates of hydrogen and oxygen, are all done on a per cell basis, while the corresponding values for the entire electrolysis unit are found simply by multiplying by the number of series and parallel cells. The main inputs and outputs of an
(45)
G Gref
+
T
(48)
Fig. 2 shows the flowchart used in MATLAB simulation with a subroutine to estimate global solar radiation.
(42)
TC (ref )
TC (ref )
α: coefficient of variation of current as a function of temperature β: coefficient of variation of the voltage as a function of the temperature.
3.1.3. Plotting and evolution of the current-voltage (I-V) characteristic The I-V curve of Eq. (40) is an arbitrary reference curve applicable to the global solar radiation intensity and temperature of the cell in particular. For other values of global solar radiation intensity and temperature, the evolution of Eq. (40) is done by the following equations [43]:
T = TC
(Vthmod (ref ) × TC )
(46)
(47)
Fig. 2. Flowchart for the MATLAB program with a subroutine to estimate global solar radiation. 106
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where VNcell is the total voltage of the electrolyzer, Ncell is the number of electrolyzer cells, and Ie is the total current of the electrolyzer. s and p represents the number of cells in the series and parallel, respectively. i. Hydrogen production rate According to the ideal gas law, the volume of gas produced is calculated using the following equation:
Fig. 3. Electrolysis using a proton exchange membrane.
V=
nRT ItRT = = Q H2 × t P ZFP
(52)
n=
I×t Z×F
(53)
Then, by using the trapezium integration method, the volume of hydrogen produced was calculated over a period of time.
Q H2 =
Ncell × R × I f × T Z×F×P
=
Ncell × 8.32 × I f × T
(54)
2 × 96500 × 0.1013
where V: volume of hydrogen produced (ml) Q H2 : hydrogen production rate (ml /s) T : electrolyte temperature R : ideal gas constant Z : number of electrons required to release a molecule Ncells: number of electrolyzer cells (s × p) F: Faraday constant P: atmospheric pressure t: time corresponding to volume produced (V) I f : Electrolyzer operating current ii. Electrolyzer efficiency
Fig. 4. The main inputs and outputs of an electrolyzer.
electrolyzer are shown in Fig. 4. This study used a laboratory-type PEM electrolyzer consisting of a cell with the compound Pt/Nafion/Pt, an EME electrode, and a membrane electrode with a platinum-plated membrane surface [42]. The electrolyzer is a load for the system, with its operating point defined according to its connection with the energy source. The equivalent diagram for the electrolyzer is shown in Fig. 5. The cell voltage of an electrolyzer is expressed in four terms:
Uel = Uth + Uanod + Ucathode + Uohm
The efficiency of electrolyzer is given by the following equation [45]:
(49)
where
el
Uth: Uanode: Ucathode: Uohm:
Theoretical tension Anodic overvoltage (V) Cathode overvoltage (V) Drop in voltage in the internal electrolyzer resistance Rel
Ie p
(55)
3.2.2. The current-voltage of the electrolyzer For the present study, a PEM type electrolyzer is chosen. From the experimental graphs with temperature deflections, the graph of the temperature T equals to 80 °C was chosen and the points (I-V) indicated in Table 2 were determined. Fig. 6 shows the I-V curves of the experimental electrolyzer and those simulated for a Tel of 80 °C.
(50)
The parameters a , b, and c are defined for the particular features (e.g., geometry, membrane, flow, materials, temperature, and pressure) for an electrolyzer cell. According to Eq. (50), the voltage-current relationship based on Tafel’s law for this electrolyzer configuration is given by the following equation [44]:
VNcell = s × a + b × log
1.23 × s VF
VF : The voltage of the operating point s : number of cells in the series
According to Tafel’s law, the cell voltage is expressed as a function of the current density [44]:
Ve = a + b × log(I ) + c × I
=
Table 2 Experimental electrolyzer data extracted from the I-V characteristics [45]. Temperature = 80 °C
(51)
Fig. 5. Equivalent electrical diagram of the electrolyzer according to the electrochemical model. 107
Current (A)
Volt (V)
0.14286 0.28571 0.42857 0.5714 0.85714 1.000 1.285714 1.714285 2.000 2.571428 3.000 4.000 5.000
1.685714 1.733333 1.762069 1.7896552 1.8275862 1.8500 1.873333 1.9066667 1.933333 1.973333 2.0071429 2.0821429 2.1500
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2.5
Volt (V)
2
1.5 Experimental 1
Mathema cal Model
0.5
0 0
1
2
3
4
5
6
Current (A) Fig. 6. The I-V curves of experimental and simulated electrolyzer data for Tel = 80 °C [45].
To determine the factors a , b, and c, three points from the relevant graph of electrolyzer data were chosen and replaced the values of the current and voltage with the points in the equation (50). Thus the following system of equations are obtained:
1.6857143 = a + b × log
( )+c×( ) 1 7
1 7
1.85 = a + b × log(1) + c × (1) 2.15 = a + b × log(5) + c × (5)
(56)
The solution of this system of equations gives the three factors:
a = 1.8018 b = 0.0632 c = 0.0482
(57)
Thus, the model of an electrolyzer cell is written as follows: (58)
V = 1.801 + 0.0632 × log(I ) + 0.0482 × I 3.3. Modelling the coupled PVG-electrolyzer
The directly coupled energy source is the PV generator and the electrolyzer that act as the load in this system. To study this PVGelectrolyzer system, the graphs of the I-V characteristic are coupled to find the point of operation of the electrolyzer because it represents the intersection between the two graphs; this is shown in Fig. 7. The flowchart of the direct coupling organization chart is shown in Fig. 8.
Fig. 7. The operating point of the photovoltaic generator–electrolyzer system.
Eq. (59) is nonlinear. This equation will be solved using the NewtonRaphson method used in [43]:
3.3.1. Calculation of the operating point:
•
+ Vth × log
= xn + 1
(59)
The overall yield is calculated using the following: s
lyzer: Ig = Ie
1.801
0.0632 × log(I )
+ Vth × log
Igen + Icc + Io Io
0.0482 × I =0
is the stopping criterion
ii. The overall efficiency of the system
Igen + Icc + Io
• The current of the generator must be equal to that of the electrof(I ) =
(62)
xn
Such that
I(gen) × Rs (gen) Io
(61)
where f (xn ) is the derivative of the function f (xn) , x n is the present iteration, and xn+1 is the next iteration.
i. Coupling conditions The voltage of the electrolyzer must be equal to that of the PV generator:
1.801 + 0.0632 × log(I ) + 0.0482 × I =
f (x n ) f (x n )
x n+ 1 = xn
=
I f × 1.23 × S E×S
(63)
E: Global solar radiation (W/m2): S generator area (m2) iii. Adaptation performance
I(gen) × Rs (gen) (60)
u
108
=
I f . Vf Im. Vm
(64)
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4.2. Results of simulation with the photovoltaic generator Before executing the steps in the flowchart, the BP 585F type PV cell was chosen [50] with the characteristics for standard conditions (E = 1000 W/m2; ambient temperature for surrounding environment = 25 °C; see Table 3). (a) Results of simulation with an ambient temperature of 25 °C and varying global solar radiation values The simulation results of the I-V characteristic of the photovoltaic generator (PVG) are shown in Fig. 10 for different values of global solar radiation (200, 400, 600, 800, 1000 W/m2) and a constant temperature of 25 °C. According to Fig. 10, the electrical power delivered by the module varies enormously with global solar radiation. As the energy supply for the electron-hole separation is ensured by the light energy, the increase in sunshine automatically leads to an increase in separate electron-hole pairs. The current output IPh (current created by converting light photo-current) is therefore proportional to the amount of sunlight (global solar radiation). Fig. 11 shows the simulation of the power-voltage (P-V) characteristic with different values of global solar radiation at T = 25 °C. The maximum power from the P-V generator can produce a more or less constant voltage that represents the point of maximum power. These results, obtained for the model presented above, show that the I-V characteristic depends on the intensity of the solar radiation. The current delivered by the PV generator and the voltage increase with the global solar radiation; consequently, the power produced by the PV generator increases also. The open circuit voltage is little influenced by the variations in solar radiation, in contrast to the current of the short circuit, which increases in a consistent manner. (b) Results of simulation with fixed global solar radiation E = 1000 W/ m2 and different temperatures The second parameter that has a direct influence on the I-V characteristic of the PV generator is temperature. Simulation results showed that variations in temperature influenced the voltage and the current such that the short-circuit current (Icc) increases slightly with the increase in the temperature, whereas the voltage of the open circuit (Voc) decreases, as shown in Fig. 12. Previous reviews show that the cells are sensitive to temperature variations; the internal resistance of the module increases with the increase in the latter. When the temperature of a cell increases, the current increases slightly but the voltage decreases, reducing the power. Fig. 13 shows that the power variation is opposite to that of the temperature.
Fig. 8. Flowchart of direct coupling organization.
iv. Photovoltaic generator output s
=
I f × Vf E
(65)
(c) Results of simulation using real data from Suez city
4. Results and discussion
To test the module with real data, the variation in global solar radiation and temperatures for the month of March in Suez city in 2016 (Table 4) was used. The global solar radiation and temperatures increased over the course of the day and reached the maximum values from the period 12:00–14:00 before decreasing towards the end of the day. The global solar radiation are at their minimum from 08:00 and 15:00 to 17:00 and reaches its maximum of 790 W/m2 from 12:00 to 13:00, while the temperature reaches its maximum, 41 °C, at 13:00. The measured data was validated using the solar radiation model and the results were obtained using MATLAB. Fig. 14 shows the results of simulating the I-V characteristic with real data from Suez city. The current increases very rapidly when the temperature rises, causing a less pronounced decrease in the open circuit voltage and thus resulting in a relative decrease in the available power.
4.1. Validation results of the global solar radiation model The measured and estimated values from a previous model of hourly global solar radiation for Suez, Mansoura, Al Arish, and Al Menia are given in Fig. 9. The predicted values with the measured global solar radiation of Nafey et al. [46] for Suez, Egypt is shown in Fig. 9-a. This figure shows that the present models can be used to estimate the global solar radiation for Suez with an R2 of 0.975. Fig. 9b represents the variations in hourly global measured data for Mansoura, Egypt as reported by Taha [47] with predicted values from the present model. This figure shows that the present models can be used to estimate the global solar radiation for Mansoura with an R2 of 0.978. The results for Al Arish and Al Menia are shown in Fig. 9c and d; again, they showed that the present model results in a good prediction for global solar radiation, with R2 values of 0.945 and 0.973 for data published in Trabea [48] and Shaltout [49], respectively.
(d) Effect of PV surface temperature on the I-V characteristics of a PV panel 109
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Fig. 9. The variation in measured and predicted global solar radiation in different cities in Egypt.
Fig. 15 shows the output power of the PV plate, where the temperature distribution is constant under global solar radiation. In these figures, the curves for I-V and P-V characteristics are based on different PV panel temperatures. Analysis of these two figures, if PV plate temperature, will lead to a gradual decrease in output voltage. However, the output current of PV panels will change only slightly as the temperature increases; when they increase by 10 °C, the output power decreases by about 5%. The minimum output power of the digital PV plates used is 79.5 W and the PV panel temperature is 65 °C; however, when the temperature of PV plate drops to 25 °C, the maximum value of PV plate is 100 W. The potential for ambient temperature to pass through a day usually
Table 3 Photovoltaic cell characteristic type BP 585F [43]. Pm(w)
85
Vco (v) Icc (A) Vm (v) Im (A) α (mA/°C) β (mA/°C) Ns NOCT (°C)
22.03 5 18 4.72 3.2 −80 36 47
6 E=200 (W/m2)
Current (A)
5
E=400 (W/m2) E=600 (W/m2)
4
E=800 (W/m2) 3
E=1000 (W/m2)
2 1 0 0
5
10
15
20
25
Volt (V) Fig. 10. Simulation of the I-V characteristic with different values of global solar radiation (E) for T = 25 °C. 110
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Power (W)
90
E=200 (W/m2)
80
E=400 (W/m2)
70
E=600 (W/m2)
60
E=800 (W/m2)
50
E=1000 (W/m2)
40 30 20 10 0 0
5
10
15
20
25
Volt (V) Fig. 11. Simulation of the P-V characteristic with different values of global solar radiation (E), for T = 25 °C.
depends on changes in global solar radiation intensity. Locations rich in global solar radiation have a high potential for developing PV systems with maximum output. Fig. 16 shows the characteristics of the P-V curve under varying values of global solar radiation at a constant ambient temperature and heat transfer rate. In Eq. (66), the average ambient temperature is assumed to be 25 °C, the equation of the heat transfer coefficient (hc ) is 15 W/m2, and the average wind speed (v) is 2.5 m/s for the PV plate.
temperature on their output performance under different solar radiation intensities. The maximum output power generated by PV panels will be a combination of the high global solar radiation and low temperature. As Fig. 17 shows, the most effective power generation rate for a PV plate is 15.5%, when its temperature is 25 °C and solar radiation intensity is 1000 W/m2. These values are similar to the standard test conditions (STCs) for PV panels. Unfortunately, the efficiency of PV plates decrease when they are exposed to high temperatures; when the latter is 65 °C, the power generation efficiency is 12.27% under the worst conditions. However, when the temperatures of the PV plates are 55 °C, 45 °C, and 35 °C, the efficiencies become 13.1%, 13.8% and 14.7%, respectively.
(66)
hc = 5.7 + 3.8v
An increase in global solar radiation increased the temperature of the PV plates. The maximum temperature was recorded at a maximum global solar radiation of 1000 W/m2, and the lowest temperature of 200 W/m2 was recorded at a low horizontal radiation. The temperature difference between these two values was about 49.5%. Global solar radiation is also a key factor in power generation from PV panels. Fig. 16 shows that the maximum output power increases global solar radiation increases. Unfortunately, the rated power cannot reach 100% due to the rise in the temperature of the PV plate. A worse output power was observed when global solar radiation was low. The payback period of the integrated PV system mainly depended on the effective output power of the PV panel, because the latter are considered the main components of the former. Fig. 17 shows the effect of PV plate
4.3. Results of simulations modelling a coupled PVG-electrolyzer In order to create the coupling flowchart, the global solar radiation E (W/m2) and temperature (T) data were measured and recorded for Suez in 2016. The current results of simulations in which a BP 585F solar panel and a single PEM electrolyzer cell were coupled. After executing the direct coupling flow chart in MATLAB, the following results were obtained:
6
T= 20°C T= 30°C
5
Current (A)
T= 40°C 4
T= 50°C T= 60°C
3 2 1 0 0
5
10
15
20
25
Volt (V) Fig. 12. Simulation of the I-V characteristic at different temperatures, for a global solar radiation value of E = 1000 W/m2. 111
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100 T= 20°C
90
T= 30°C
80
T= 40°C
Power (W)
70
T= 50°C
60
T= 60°C
50 40 30 20 10 0 0
5
10
15
20
25
Volt (V) Fig. 13. Simulation of the P-V characteristic at different temperatures, for a global solar radiation value of E = 1000 W/m2.
(a) The I-V characteristics of the coupling
The efficiency of the electrolyzer varied inversely with the increase in global solar radiation; at 08:00, and from 15:00 to 17:00, the yield values became important. From the interval 12:00 to 13:00 the yield reaches its minimum value. The overall system performance produced low values of between 1% and 1.02%. As shown in Fig. 20, this is because the efficiency of generator use was low, between 12.5% and 15% (non-adaptation) and because the generator yield was also low. Based on the results of this simulation, the efficiency of the utilization (adaptation) and overall system performance appear to be very low. To improve these yields, a new design of the electrolyzer will be proceed. In this system, electrolytes that decompose into hydrogen and oxygen are a key component, and the technical challenge is to make them work despite the irregular electricity from solar energy. Some researchers have numerically analyzed the operation of alkaline water electrolytic cells under static and intermittent conditions [51–54] and photovoltaic conditions [55]. These studies focused mainly on electrolysis in cells with a fluctuating power supply. The reaction of the cell is analyzed by monitoring the voltage, temperature and pressure, current efficiency, time variations in oxygen, and the hydrogen concentration. The power consumption and working voltage of the electrolytic cell are mathematically modelled. The working voltage is considered a function of current density and parameters affecting the cell behavior, such as temperature, pressure, bubbles, and concentration [56]. Instead, other researchers have studied the effect of the structure of AC/DC converters on the thermal properties of alkaline
Fig. 18 shows the I-V characteristics of the PV generator and the electrolyzer when a single cell is used under conditions of different global solar radiation and temperatures. The operation of the electrolyzer is defined by intersections between the I-V curve of the PVG and the electrolyzer. The electrolyzer curve does not pass through the maximum power points of the PV generator throughout the day. The simulation results for the day of March 21, 2016 are given in Table 4. (b) Utilization performance (adaptation) According to Fig. 19, the variation in the yield went through three stages depending on the time of day: i. From 08:00 to 11:00, the utilization efficiency increases to 14.7%. In this period, there was an increase in the coupling voltage Vf and a decrease in maximum power point voltage with a very slight variation in the current, signifying the progression of the coupling power to the maximum PV module power. ii. From 11:00 to 15:00, the operating efficiency reached maximum working value of 14.9%, with a global solar radiation of 790 W/m2 and a temperature of 41 °C. From 15:00 to 17:00, the utilization efficiency decreased to 13%, starting at 13:00. (c) Efficiency of the overall system and electrolysis
Table 4 Characteristics of a coupled electrolytic cell with a module for the data of measured in March in Suez city, Egypt, in 2016. Time
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
E (W/m2) T (°C) Im (A) Vm (V) Icc (A) If (A) Vf (V) Vco (V) Pm (W) Q (ml/s) V (l) ηe (%) ηu (%) ηs (%) ηm (%)
323 29 1.572 15.75 1.663 1.662 1.913 19.78 25.04 0.25 0 64.29 12.70 1.005 1.56
426 31 2.076 15.57 2.20 2.195 1.956 19.6 32.80 0.33 1.043 62.87 13.09 1.006 1.6
569 33 2.773 15.30 2.93 2.932 2.01 19.32 43.24 0.44 2.430 61.18 13.63 1.006 1.64
700 35 3.412 14.97 3.608 3.607 2.056 19 52.34 0.542 4.198 59.82 14.17 1.006 1.68
787 39 3.844 14.53 4.064 0.065 2.086 18.56 57.56 0.610 6.272 58.97 14.72 1.008 1.7
790 40 3.865 14.37 4.086 4.086 2.086 18.39 57.33 0.614 8.476 58.93 14.87 1.009 1.71
724 41 3.543 14.54 3.746 3.746 2.065 18.57 53.06 0.563 10.59 59.56 14.58 1.010 1.69
636 37 3.109 14.9 3.287 3.287 2.035 18.93 47.46 0.494 12.49 60.43 14.09 1.009 1.67
488 37 2.394 15.05 2.53 2.531 1.982 19.08 36.80 0.380 14.07 60.07 13.62 1.012 1.63
364 36 1.706 15.20 1.803 1.803 1.925 19.22 26.37 0.271 15.24 63.89 13.16 1.017 1.59
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4.5
E=323w/m2, T=29°C E=426w/m2, T=31°C E=569w/m2, T=33°C E=700w/m2, T=35°C E=787w/m2, T=39°C E=790w/m2, T=41°C E=724w/m2, T=40°C E=636w/m2, T=37°C E=488w/m2, T=37 °C E=488w/m2, T=37 °C E=364w/m2, T=36 °C
4
Current (A)
3.5 3 2.5 2 1.5 1 0.5 0 0
5
10
15
20
25
Volt (V) Fig. 14. Simulation of the I-V characteristic with real data from Suez city, Egypt.
T=25°C and Pmpp=100W
90
T=35°C and Pmpp=95.0W
80
T=45°C and Pmpp=90.0W
70
T=55°C and Pmpp=84.6W
60
T=65°C and Pmpp=79.5W
Power (W)
100
50 40 30 20 10 0 0
5
10
15
20
25
Volt (V) Fig. 15. The characteristics of a PV panel when E = 1000 W/m2 is constant and PV panel temperatures are different.
E=200 W/m² and T= 45°C
80
E=400 W/m² and T= 56°C
70
E=600 W/m² and T= 67°C
Power (W)
60
E=800 W/m² and T= 78°C
50
E=1000 W/m² and T= 89°C
40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
Volt (V) Fig. 16. P-V characteristics at various temperatures and global solar radiation intensities.
water electrolytic cells [57]. To ensure that the electrolyzer adjusted to the PV generator with a global solar radiation of E = 569 W/m2, the numbers of the series and parallel cells of the electrolyzer were calculated using the following steps. The s and p values were rounded to integers because they were
often decimals. To calculate p and s, the following equation were solved:
Vf = Vmax = s × 1.801 + 0.0632 × log
113
Imax I + 0.0482 × max p p
(67)
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16
Efficiency at output Power [%]
15 14 13
T = 25°C
12
T = 30°C
11
T = 40°C T = 50°C
10
T = 60°C
9 8
0
200
400
600
800
1000
1200
Global solar radiation (W/m²) Fig. 17. The efficiency of output power at various PV panel temperatures and global solar radiation intensities.
4.5 4
MPP
3.5
Current (A)
3 2.5 2 1.5 1
Electrolyzer
0.5 0 0
5
10
15
20
25
Volt (V) Fig. 18. Current-voltage characteristics of a coupled electrolyzer cell and photovoltaic module.
16 14
Usage efficiency (%)
12 10 8 6 4 2 0
0
2
4
6
8
10
12
14
16
Time (hour) Fig. 19. The variation in the usage efficiency of a coupled PV module and electrolyzer cell. 114
18
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Usage of electrolyzer (%)
80
Usage of System (%)
0.8
70
Usage of Electrolyzer (%)
0.7
60
0.6
50
0.5
40
0.4
30
0.3
20
0.2
10
0.1
Usage of system (%)
0.9
90
0
0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 20. The variation in the electricity yields calculated.
Icell =
Imax p
production also increases, reaching the maximum value between 12:00 and 13:00. According to the electrolyzer yield curve, the pace reaches its maximum value from 08:00 to 11:00 and 15:00 to 17:00 and its minimum value from 11:00 to 14:00, because the electrolyzer output varied inversely with voltage (Fig. 23). According to Figs. 25 and 26, the overall system performance varied between 6% and 8% compared to the first case because the utilization yield (adaptation) varied between 92% and 99.7%. The judicious choice of the number of cells s and parallel series p of the electrolyzer improved the system adaptation result such that system operating points would be as close as possible to the maximum power points (MPP) of PVG. From these results from the mathematical models, which describe the behavior of the PV module and the electrolyzer, we became interested in a system consisting of these two elements. The operating points, maximum powers of the module, different yields, and the hydrogen production will be determined. The result of the simulation in the first case (a single celled electrolyzer) showed that the maximum value of the utilization yield was 15% and that of the maximum overall system yield was 1%; these low values are due to the non-adaptation of the system. To improve the system adaptation, the electrolyzer dimensions were changed; the results obtained showed a clear
(68)
The resolution of this system is s = 8; p = 1. 4.4. Results of simulating the electrolysis sizing Fig. 21 represents the I-V characteristic of a PV generator and an electrolyzer when s = 8 and p = 1, the different values of global solar radiation and temperature. A remarkable approximation between the maximum power points and the system operating points were seen, especially for the averages of the global solar radiation. To reduce losses caused by non-adaptation of the system, the I-V coupling characteristics of the new electrolyzer configuration were simulated using the program developed. The results obtained are shown in Figs. 22–25, which indicate that the current variations, hydrogen flows, and power vary proportionately with the global solar radiation. This occurs because the curves of these parameters reach their maximum values between 12:00 and 13:00 and their minimum values at 8:00 and 17:00 and are thus correlated with the evolution of the global solar radiation curve. Further analysis of Figs. 9 and 22–25, show that there is a strong relationship between hydrogen production and the intensity of global solar radiation. As the global solar radiation increases, hydrogen 4.5 4
MPP
3.5
Current (A)
3 2.5 2 1.5 1
electrolyzer
0.5 0 0
5
10
15
20
25
Volt (V) Fig. 21. I-V Characteristics of a coupled photovoltaic generator and an electrolyzer when s = 8, p = 1. 115
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18
6 Volt (V) Current (A)
16
4
Volt (V)
Current (A)
14
12
2
10
8
6
0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 22. Variations in current and voltage as a function of time.
4.5 4
Hydrogen flow rate (ml/s)
3.5 3 2.5 2 1.5 1 0.5 0
0
2
4
6
8
10
12
14
16
18
14
16
18
Time (hour) Fig. 23. Evolution of time-dependent hydrogen flow.
60
Electrolyzer power (W)
50
40
30
20
10
0
0
2
4
6
8
10
12
Time (hour) Fig. 24. Change in electrolyzer power over time. 116
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120
Hydrogen volume (L)
100 80 60 40 20 0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 25. Change in hydrogen volume as a function of time.
80
8 Electrolyzer yield (%)
60
Electrolyzer yield (%)
7
Overall yield (%)
6
50
5
40
4
30
3
20
2
10
1
0
Overall yield (%)
70
0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 26. Change in system and electrolyzer yields as a function of time.
improvement in the power transfer between the PVG and the electrolyzer (see Fig. 27). During the trial experimental period, the electrolyzer produced hydrogen ready to be stored for a period of 180 h at a very unstable production rate, varying from 0.05 Nm3 h−1 to 0.5 Nm3 h−1. Fig. 28 shows the percentage of the electrolyzer working time as a function of the different H2 rates produced. The histogram in Fig. 28 shows that the electrolyzer operated under a fluctuating input current. This occurred because it produced the hydrogen at a very high flow rate (between 0.4 and 0.5 Nm3 h−1) for 33.1% of the time. The standard deviation for the data in Fig. 28 is 3.44%. During the cloudy or partially overcast days, the effectiveness of the electrolyzer was intermittent because it worked in a transient state. These conditions occurred during daylight hours and caused periods of low work. During clear sky days, the electrolyzer worked continuously and the production of hydrogen was affected by the intensity of the solar radiation. Fig. 29 shows that the measured power required increased with the increase in the hydrogen flow rate. The measured power required showed a linear relationship with the hydrogen gas flow rate with a coefficient of determination (R2) of 0.973, and fit these data as a second-degree polynomial as follows:
Pr =
0.0145Q H2 2 + 0.3886Q H2 + 0.2082
equivalent to the electrical current in the circuit. The overall hydrogen production rate Q H2 (Nm3 h−1) in the electrolyzer is based on Nc cells connected in a series. For an ideal gas molar volume of 22.414 × 10 3 m3 mol 1 and a standard temperature of 273 K at pressure of 105 Nm−2 [57,58], the Faradic efficiency F , can be calculated as follows:
Q H2 = 80.69
F
Nc Iel = 80.69 n×F
F
Nc Pr U×n×F
(70)
The power Pr required by the electrolyzer is given as [59]:
Pr = Uc Nc Iel = UIel
(71)
where Pr is the dissipated power required, Iel is the electric current, Uc is the potential difference between the cathode and the anode [59], and U is the voltage supplied to the electrolyzer. The Faradic efficiency is defined as the ratio between the effective and theoretical maximum amount of hydrogen produced in the electrolyzer system; it is a very good way to assess the electrolysis system. The increase in temperature causes a lower Faradic efficiency due to the lowered resistance and increased in parasitic current. The thermal efficiency or energy efficiency T is an expression commonly used to describe the electrolysis system and can be calculated as follows [57]:
(69)
According to Faraday’s law, the hydrogen production rate is directly proportional to the electron transfer rate at the electrodes and
T
117
=
Ho H
(72)
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100 99
Usage efficiency (%)
98 97 96 95 94 93 92 91 90 8
10
12
14
16
18
Time (hour) Fig. 27. Change in usage efficiency as a function of time.
18
Acttual time/ total time (%)
16 14 12 10 8 6 4 2 0
0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 28. The percentage of time that the electrolyzer worked as a function of the different flow rates of the hydrogen gas produced.
3
Required power (kW)
2.5 2 1.5 1 0.5 0 0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 29. The measured power required by the electrolyzer as a function of flow rates of the hydrogen gas produced.
This is defined as the ratio of the enthalpy change based on the thermoneutral potential Utno and the actual potential Uc. In another words, it is calculated as the ratio between the specific energy
consumption (with respect to HHV) and the actual specific energy consumption (MJ·N·m−3). Therefore, for a thermal efficiency of 100%, the electrolyzer would consume 10.58 MJ for each Nm−3 of hydrogen 118
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1.2
Faradic efficiency
1 0.8 0.6 0.4 0.2 0 0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 30. Faradic efficiency of the electrolyzer as a function of the rate of the H2 produced.
Electrolyzer energy efficiency
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 31. The energy efficiency of the electrolyzer versus hydrogen gas produced.
produced. At a standard pressure and temperature (105N·m−2 and 298 K, respectively), the enthalpy variation H can be evaluated based on pure hydrogen (H2), water (H2O), and oxygen (O2) as follows: H o = 286 kJ mol 1, assuming that oxygen and hydrogen represent ideal gases while water represents an incompressible fluid [21]. The Faradic efficiency F can be calculated from equation (70) and is shown in Fig. 30. The predicted result occurs due to the manner in which the electrolyzer works, as it needs to continuously adjust itself to changes in operating conditions without reaching a steady–state requirement. An analysis of Fig. 30 shows that the Faradic efficiency was higher than 90% when the hydrogen production rate was greater than 0.4 Nm3 h−1 and the power required by the electrolyzer was close to the power rating of 2.5 kW, under the operating conditions shown in Fig. 29. The T of the electrolyzer under experimental conditions was evaluated using Eq. (72) and is shown in Fig. 31. The model of this equation is rough because the H o is evaluated at a standard pressure and temperature and under the assumption that hydrogen is an ideal gas and water is an incompressible fluid. Eq. (72) allows the estimation of the performance of the electrolyzer; the T value of the electrolyzer increased 45% (from 0.46 to 0.67) at a hydrogen flow rate ranging from 0.05 to 0.5 Nm3 h−1. A literature review shows that similar results were obtained when testing hybrid systems that include electrolyzers and PV panel combinations [60]. The average energy efficiency of 5 kW alkaline electrolyzer set up in Zollbruck, Switzerland, inside a domestic system, was
62% after evaluation for three summer days. In clear sky conditions in the morning, cloud cover in the afternoon caused strong variations in the current and thus in the electrolyzer performance [61]. In California, USA, a 9.2 kW PV medium pressure bipolar alkaline PEM electrolyzer hybrid system was built and tested for eleven months. The electrolyzer efficiency was high, at 75%, for more than 70% of the daily averages. The results of a single day of operations showed an average Faraday efficiency of 96% [54]. The test results for the hybrid system providing thermal power and electric energy to the different units showed that when the electrolyzer cycled on and off, the cell electrode catalyst could be degraded. Therefore, an advanced battery should be used to minimize electrolyzer cycling and provide short-term energy storage [62]. Zini and Tartarini [61] discussed and analyzed different case studies and reported that since the electrolyzer was switched on and off frequently if the input current was highly variable, some back-up systems should be considered to stabilize the electrolyzer input power and increase the overall performance of the system. Furthermore, the results acquired showed that the efficiency of the electrolyzer was low because of the irregular solar energy supply, and that this problem did not allow the hydrogen produced to be stored suitably inside the tanks. It is necessary to avoid shutdowns of H2 production as these require the system to have significant idle time before restarting. Little et al. [63] showed that when the electrolyzer is switched off, the hydrogen in the cathode reverses the potential of the cell stack, generating corrosion in the cell 119
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Fig. 32. The modified integrated power system. The battery bank is connected to: (a) the electrolyzer; (b) the fuel cell.
answered storage technology in a stand-alone PV system is that of lead acid. The latter is treated in various articles published in the literature [69–71] the trade-off between the benefits of availability, reliability and cost. This model is based on an electrical diagram. It defines the voltage across the battery according to some parameters such as the imposed current, its state of charge and its temperature. It takes into account the faradic efficiency in charge to calculate the evolution of its state of charge, while integrating the phase of degassing (hydrogen evolution) which is a phenomenon peculiar to lead batteries, causing a significant increase of the voltage in end of charge [72]. The phenomena of self-discharge and aging have not been taken into account. In this model, for nb cells in series, the voltage across the battery is given below:
membranes and reducing the lifetime of the electrolyzer, even if a minimum current is also imposed to maintain the purity of the hydrogen gas. These constraints in the operation of the electrolyzer require some form of short-term energy storage to reduce the short-term fluctuations in electric input. A battery bank can supply 1200 Ah and could be charged using the PV modules or the fuel cell, as shown in Fig. 32. The energy from the PV cells are affected by the intensity of the solar radiation and should be accumulated using the battery bank; therefore, there will be a continuous feed of current to the electrolyzer. Using the connections shown in Fig. 32a, the current from the AC/DC rectifier, affected by change in the PV panel performance, feeds the battery bank which in turn can continuously power the electrolyzer. In this way, the system would operate correctly and a suitable quantity of hydrogen can be produced and stored in the tanks. By employing the arrangement shown in Fig. 32b, a constant current produced by the fuel cells is stored inside the battery bank. This new layout using the battery bank will be adopted in future tests and the performance of the integrated power system will be evaluated. This proposed solution stems from the results of simulations of the electrolyzer on/off cycle and fuel cells in an integrated power system that employed a battery as a short-term energy buffer [64].
Vbat = nb × Eb ± nb × Rbat × Ibat
(73)
where Vbat and Ibat are the voltage and current of the battery (according to the receptor convention), Eb is the emf (electromotive force) of a cell of the battery and Rbat its internal resistance. The description of the behavior of the battery according to the CIEMAT model, requires three equations corresponding to the three modes of operation: the discharge regime, the charging regime and the battery overload regime. All of these equations take into account the standardized expression of the battery capacity Cbat . The SOC state of charge of the battery is a function of the residual charge and the charging or discharging regime.
5. Simulation of hybrid system The investigation of hybrid system is designed and manufacturing for generating, storing and supplying electric power to local loads. The hybrid system is simulated to predict and evaluate its performance before implementation and is often installed in remote and rural areas. Therefore, in the design process it’s important to improve the system configuration, sizes of components and control settings. The design via simulation methods allows studying the different options, considering various influencing variables and effectively fulfils the system/user requirements. Mathematical models of the system components are associated to form a general representation of the system, through a central controller unit that defines the best way in which components interact to simulate the operation of the system. In this section, a hybrid system will be simulated and the components of the system have been modelled and validated with the previous work. The comparison between the different topologies of the system such as DC and AC coupled, with different PCU types at two different locations on the basis of the energy point of view is studied.
• Modelling capacity C
bat
The model of the capacity Cbat gives the quantity of energy that can restore the battery according to the average current of discharge Ibat . This capacity is given by:
Cbat =
1.67C10 1 + 0.67 ×
( )
Ibat 0.9 I10
(1 + 0.005 × T ) (74)
With:
I10 : Nominal battery current (in A) given by the manufacturer; C10 : Nominal capacity of the battery (in Ah) in a constant current discharge regime for 10 h. It is given by the manufacturer and it is such that: Cnom = C10 = 10 × I10
5.1. Modelling the battery storage system
(75)
T : The heating of the battery compared to the ambient temperature of 25 °C. It is assumed to be identical for all elements of the
The storage of energy for an autonomous photovoltaic system has been the subject of several publications [65–68]. Currently, the most 120
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battery. The state of charge of the battery SOC is a function of the capacity Cbat and the amount of charge missing from the battery Qd .
Rb
(76)
Qd Cbat
Vbat
(77)
Qt
1
+
charge
× Qech (t )
Qt
1
+
discharge
g
(79)
=1
exp
(80)
20.73 Ibat I10
+ 0.55
(EDC
= 1.965 + 0.12SOC
Rb
discharge
= Rbat =
(81)
0.007 T ) (83)
= nb × Eb
Vbat
discharge
= nb × (2.085 + 0.12(1
discharge
nb × Rb
discharge
× |Ibat |
tg g
(89)
1 + 852 ×
( )
Ibat 1.67 C10
(90)
Ibat × (1 C10
Ibat × (1 C10
0.002 × T )
0.002 × T )
(91) (92)
In the electrolyser and the fuel cell, the same electrochemical reactions take place. The electrical model of these components is identical. The electric model to describe the polarization curve (characteristic in current-voltage of the fuel cell) was chosen, is the model of Kim (J. Kim et al., 1995). This model is semi-empirical, that is, based on theoretical equations but using parameters to fit the model to the experimental data obtained from literature survey.
Hence the expression of the battery voltage, for this discharge regime: discharge
t
• Electric model
(82)
Vbat
exp
Several models are needed to correctly simulate the behavior of the fuel cell. The electrical model calculates the operating point as a function of the requested current, the temperature and the pressure of the gases while the thermal model makes it possible to calculate the evolution of the temperature in the component.
1)
1 4 0.27 + + 0.02 (1 C10 1 + |Ibat |0.3 EDC1.5
Vg ) 1
5.2. Modelling of the fuel cell
In discharge regime, the emf and the internal resistance are determined by the following: discharge
(88)
× Ibat
The different mathematical formulations presented above, allowed us to develop, under the Matlab-Simulink environment, the model of the CIEMAT battery.
• Modelling the discharge of the battery Eb
charge
1.73
Vec = 2.45 + 2.011 × ln 1 +
The Faradic efficiency under load depends on the charge rate, it has a value close to 100% for low load currents and a low state of charge. Then, it gets worse as we approach full load. charge is given by the following relation: charge
nb × Rb
= nb × Vg + nb × (Vec
Vg = 2.24 + 1.97 × ln 1 +
For the CIEMAT model, the Faradic efficiency is taken into account in the case of the load and is assumed equal to 1 in the discharge regime.
= 1(10)
charge
The gassing voltage Vg and the ending charge voltages Vec have the following expression:
• Faradic yield modeling
discharge
overcharge
=
t 0
= nb × Eb
With: tg the moment the “gassing” begins. Thus (t-tg) is the duration during which the gassing takes place. The time constant g is expressed as follows:
(78)
Ibat (t ) dt
charge
Vbat
where the amount of charge exchanged Qech is:
Qech (t ) =
(87)
For this overcharge regime, the expression of the battery voltage is then given by the equation:
if Ibat > 0
× Qech (t ) if Ibat < 0
0.48 + 0.036 (1 EDC )1.2
• Modelling of the battery overcharge
The quantity of charge Qbat at a time t, is obtained as a function of the value of the current Ibat, the Faradic efficiencies ( charge & discharge ) and the state of charge SOC calculated at the previous instant Qt 1 , according to:
Qbat =
1 6 + C10 1 + (Ibat )0.86 (1
Hence the expression of the voltage of the battery before the overload:
where t is the operating time of the battery with a current Ibat . The expression of the state of charge of the battery EDC is given by:
EDC = 1
= Rcharge =
0.025 T )
The time evolution of the latter, depends on the operating mode of the battery, it is defined by:
Qd = Ibat × t
charge
• Voltage
(84)
Ibat C10 (85)
The actual voltage is strictly less than the electromotive force E because of the different voltage drops that occur in any electrochemical generator. It decreases with the current flow. The curve of the voltage V across the terminals of an element is usually plotted as a function of the current density J (see Fig. 33).
In the charging regime and before the appearance of the phenomenon of “Gassing” (gaseous release of hydrogen and oxygen), the emf and the internal resistance are determined by:
where VRP : Tension of an elementary cell of the released power (RP) (V); JRP : current density of an elementary cell of the RP (A·cm−2). Origins of the voltage drop
× (1
0.007 T )
EDC ))
nb ×
• Modelling the battery charge
Eb
charge
= 2 + 0.16EDC
•
(86) 121
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1
VRP (volt)
0.95
0.9
0.85
0.8
0.75
0
0.2
0.4
0.6
0.8
1
1.2
1.4
JRP (A.cm-2) Fig. 33. Curve of the voltage across a fuel cell element as a function of the current density.
As for any electrochemical generator, the voltage drop results essentially from three phenomena is distinguish as follows:
diffusion zone. By cons, it is not usable for a low current density, lower than the exchange current density Jo of the electrode, because of the J term – Aln RP . b
( )
• the activation voltage drop ΔV act; • the resistive voltage drop ΔV ohm; • the concentration voltage drop ΔV conc
• Effect of operating conditions The pressure and the temperature act on both the electromotive force and the voltage drop.
The voltage across an element can be written as:
VRP = ERP
Vact
Vohm
Vconc
(93)
(a) Influence of pressure
With
ERP = ET° +
Vact = Aln
RT ln(PH2 PO1/2 2 ) 2F
(94)
J b
(95)
An increase in pressure causes an increase in the electromotive force. This effect is increased on the voltage because the voltage drop decreases at high pressure. However, the use of the compressor to increase the pressure, it leads to a significant consumption of power. To evaluate the interest of working at high pressure, it is therefore necessary to compare the increase in power due to the increase in voltage with the power loss due to compressor consumption.
(96)
A = Aa + Ac
Coefficients of the Tafel equation at the anode and at the cathode (V);
Vohm = rJ
(97)
(b) Influence of temperature
Vconc = mexp(n × J )
(98)
The increase in temperature leads to a decrease in the electromotive force. This negative effect is counterbalanced by a reduction in voltage drops. Increasing the ionic conductivity of the electrolyte results in a decrease in the resistive voltage drop. On the other hand, a high temperature increases the reaction rate, which reduces the activation voltage drop.
which gives;
VRP = ERP Aa
Aln Ac
bRP = JoaA × JocA
JRP bRP
rRP JRP
mexp(n × J )
(99)
Exchange currents at the anode and at the
cathode (A·cm
2
• Power
(100)
The electric power PRP supplied by a fuel cell formed of N series elements is:
rRP : Specific surface resistance of the membrane (ῼ·cm−2); m (V) and n (cm2/A): Empirical coefficients (parameters related to diffusion); R: constants r of perfect gases; F: number of faradays (96,485 C·mol−1); T: Temperature (K). NB: For a PEMFC fuel cell, RT A = 2F , where is the load transfer coefficient (0 1).
PRP = NCRP VRP IRP = NCRP VRP JRP S ARP
(101)
PRP : Total power supplied by the fuel cell (W) S ARP : Active surface of an elementary cell of the fuel cell (cm2) NCRP : Number of elementary cells in series of the fuel cell (–) IRP : Intensity of the current of a cell of the fuel cell (A). In order for the fuel cell to operate, part of the electrical power released by it must be sent to its auxiliaries (devices that provide cooling of the fuel cell and supply of reagents to the battery and
The parameters of Eq. (98) depend on the temperature, the pressure and the oxygen partial pressure. This model makes it possible to represent all the parts of a polarization curve of a stack, up to the 122
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different sensors and solenoid valves). This power is expressed by the following equation:
PauxRP = CCauxRP + CVauxRP PRP
and the intrinsic power consumption of the system. The present approach method is inspired by the control of the Ulleberg facility [73], an energy management algorithm has been developed for the studied system. The energy balances are always carried out at the common bus connection of the various energy components of the system. The priority is the supply of the energy demanded by the user from the energy produced by the photovoltaic field. There are two scenarios:
(102)
PauxRP : Power consumed by the auxiliaries of the RP (W); CCauxRP : Constant consumption of auxiliaries of the RP (W); CVauxRP : Variable consumption of the auxiliaries of the RP, depending on the power supplied by it (%).
1. If the power demanded by the load is less than the available solar power, then two sub-cases are presented: a. Either the operating conditions allow the storage of this surplus; b. Either the surplus cannot be stored (consumed neither by the battery nor by the electrolyser) or this causes the increase of the solar field voltage, thus reducing the intensity and the power delivered by the renewable generator. 2. If the power demanded by the load is greater than the available solar power then the additional energy must be provided by the storage. In this case, the solicitation of the storage is then constrained to respect the operating parameters of the components. The actual powers of each component are calculated (see Fig. 35).
As the efficiency of a fuel cell is not perfect, the gases consumed (hydrogen and oxygen) are not entirely converted into electrical power but also into thermal power. This can be defined by the following relation:
PthRP = NCRP (Vth
VRP ) JRP S ARP
(103)
PthRP : Thermal power released by the fuel cell (W); Vth : Thermoneutral voltage of an elementary cell (=1.48 V). 5.3. Energy management and conversion within the system In real systems, the energy produced and consumed by the various components during their operation is usually managed by a central component, to which the devices are connected via various converters. Energy management algorithms are implemented to ensure the autonomy of the system.
' PPV = PPV ×
PV
' PRP
RP
= PRP ×
' PBatt =
PBatt Batt
i. Hybrid system architecture
' PEL =
PEL EL
In any electrical system, the various devices that compose it are generally connected to a network. The type of network (continuous or alternate) depends on its size and the chosen application. In the case of the small isolated system, the DC network or continuous bus architecture can be used. All components are connected as shown in the following figure. Losses in the network are limited because of its size. Moreover, this type of architecture makes it possible to limit the losses due to the inverters, the presence of which is inevitable in the case of the AC-AC network. Here, only the user is connected to the bus via an inverter. The storage components and the PV field are connected to the bus via DC-DC converters which perform better than an inverter (see next paragraph). The bus voltage is maintained by the battery pack, connected in parallel with the DC bus (see Fig. 34).
' Pcharge =
Pcharge charge
• Converters Electronic power converters are used to control the flow of electrical power between an electrical source and a well (usually the load) so that the destination is supplied with the proper current, voltage and/or frequency. This is done with as little power loss as possible occurring on the way or with the greatest possible conversion efficiency. The converters generate energy losses in the system, which translates into a conversion efficiency of less than 1.
ii. Energy Management Algorithm (PMU)
Case#1
The model of the PMU makes it possible to define the powers of the electrolyser, of the fuel cell and of the battery, according to the power delivered by the PV and that demanded by the load. The load to be delivered by the system is the sum of the power demanded by the user
In DC-DC coupling, the PV generator must be designed to cover the DC operating voltage range of the cell. These converters obviously lead to losses of energy in the system, which however remain generally low, the yields generally being between 0.95 and 0.99 [74]. The following values are proposed for the 10% and 100% of Pnom: η10 = 0.92 and η100 = 0.98 ⇒ η0 = 8.58 × 10−3 et m = 11.83 × 10−3. The following figure illustrates the variation in the efficiency of a DC-DC converter as a function of its normalized output power. Case#2 Since the load is supplied with AC power, an inverter is present between the DC bus and the load. Various equations exist to define the efficiency of an inverter as a function of the power delivered [75,76]. The same formula of Macagnan presented previously is used. For the inverter, the values of the 10% and 100% yields of Pnom are: η10 = 0.85 and η100 = 0.96 ⇒ η0 = 17.40 × 10−3 and m = 24.26 × 10−3. This model has the advantage of being simple and faithfully representing the energy losses of a converter. It has been validated in the thesis of Abu El-Maaty (2005) [75].
Fig. 34. diagram of the connection of energy sources and consumers in the PMU: case of the PV-SEH-BATT system. 123
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Fig. 35. PMU diagram: Calculation of the powers of each component on the bus.
5.4. Operation and parameters of the PV-FC system
the fuel cell. It does not correspond to the storage volume because it takes into account the daily consumption of hydrogen. When one increases the intrinsic consumption or the loss in the converters, one directly penalizes the load. In fact, the energy that comes from the PV and the battery does not vary. The storage volume and the quantity of hydrogen produced during the year do not change. The storage volume depends only on the annual profile of the load and the raw energy, i.e. the energy supplied by the PVs and by the fuel cell (dashes). The energy supplied directly by the PV to the load (PV Direct) depends on the load profile. By favoring the direct supply, the gross energy is greatly increased, on the other hand, the daily consumption of hydrogen is reduced. The storage volume increases because the raw energy is more important. When modifying the performance of the electrochemical components, the raw energy is more important. But since the modification of the cells does not lead to a large increase in their average yield, the gross energy is only slightly higher: the storage volume and the daily consumption of hydrogen are therefore slightly greater.
Fig. 36 is a simplified diagram to describe the annual operation of the PV-FC system. The operation of the system and the influence of its parameters described below, come from the analysis of all the simulations carried out. Annual photovoltaic (PV) energy is the total energy that enters the system. Some of this energy is supplied directly to the load (PV Direct). The second part passes through the hydrogen storage system and is reduced by losses in electrochemical cells related to energy and faradic efficiency. The sum of these two energies is further reduced by the loss in the converters and by the loss due to the intrinsic consumption. The efficiency of the system depends on all of these losses. The storage volume (ST H2) is dimensioned so that the energy stored during the favourable months is equal to the energy consumed during the unfavourable months. The white arrow corresponds to the quantity of hydrogen produced by the electrolyser during the year, which is equal to that consumed by
Fig. 36. Operating diagram of the PV-FC system. 124
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EC
IC
Conv
2%
2%
90%
8%
26%
80%
33%
100%
70%
Charge
Battery
16%
60% 50%
18%
18%
38%
38%
40% 30% 20% 10% 0% Pond = 8 kW
Pond = Pcharge
Fig. 37. Distribution of photovoltaic energy during one year of operation of the test bench (Scenario no. 1) - Constant load - Adaptation of the nominal power of the inverter.
• Performance of the test bench
also occurs during sunny days. The energy stored in the battery throughout the year represents 2% of photovoltaic energy or 114 kWh electric per year. The energy available for charging the battery is therefore an average of 313 Wh per day. We do not know for the moment what will be the daily discharge of the battery, used for the help with the PMU transient response. It is possible that this discharge is weak. However, if the battery is at its maximum state of charge, the excess solar energy will not be consumed by the system. The energy stored in the battery therefore represents the maximum loss of solar potential: the use of photovoltaic energy of the PVFC system is equal to or greater than 98%. For these two systems, the required storage volume is 23 m3 of hydrogen and 11.5 m3 of oxygen (storage at 10 bar). This volume represents only 26% of the energy that passes through storage. The consumption of pure water required for autonomy is equal to 43 kg per year. It depends on the amount of hydrogen produced during the year and the faradic efficiency of the electrolyser. It is therefore not a function of the nominal power of the inverter.
Fig. 37 shows the distribution of photovoltaic energy in the load and the different losses of the test stand. The load is a constant power demand. The two studied systems differ in the nominal power of the inverter. The test bench is equipped with an inverter of 8 kW to allow the complete evaluation of its performances. The efficiency of the installation (Charge) is 8%. The loss in the electrochemical components (EC) is the largest (38%). The loss in the converters is also very high (33%). The loss due to intrinsic consumption during a year of operation represents 19% of photovoltaic energy. In an autonomous system, the nominal power of the inverter is adapted to the maximum power demanded by the user. The performance of the test bench equipped with a suitable inverter load, is greatly increased by reducing the loss in the converters. It reaches 26%, a constant load of 168 W. The other losses of the system are not changed. The loss of the system, called “Batt”, is a potential loss related to the use of the safety battery. As known, the battery is mainly charged when the solar excess is lower than the minimum power of the electrolyser. This situation usually occurs twice a day at sunrise and sunset. It
• Modification of the hydrogen storage system Fig. 38 shows the influence of the optimization of the hydrogen
140% 120%
EC
19%
100% 80% 60% 40% 20%
26%
IC
Conv
Charge
14%
2%
41%
47%
Battery
15% 19%
15% 4%
38%
38%
35%
scenario 1
scenario 2
scenario 3
14% 2%
0% Fig. 38. Influence of the scenario on the distribution of photovoltaic energy during a year of operation of the PV-FC system. 125
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where oxygen is not used, the consumption of pure water is important (97 kg/year). It thus appears that the faradic efficiency of the electrolyser has a greater influence than the oxygen partial pressure of the cell. A system that does not use the oxygen produced by the electrolyser is therefore efficient but its autonomy is limited by a large consumption of pure water.
Table 5 Influence of faradic efficiency of the electrolyser and the oxygen partial pressure of the cell on the performance of the test bench and its water consumption. Yes
Yes
No
Faradic yield (EL)% Partial oxygen pressure (FC) bar Efficiency of the PV-FC system% Pure water consumption kg/year
93 1.5 25.7 43
99 0.6 27.6 97
99 1.5 28 0
• Thermal production In all previous tests, the system does not produce heat. The thermal losses of the electrochemical components allow only the raising of their operating temperature. For the electrolyser, the maximum temperature reached is 65 °C, lower than the maximum temperature (72 °C). A heat exchanger is not necessary for this component. It also implies that no cogeneration is possible. For the fuel cell, the module selected for the test bench has a large thermal capacity (45 kJ·K−1 or about 1 kJ·kg−1·K−1). The new battery generations have much higher power densities (multiplied by 5), which leads to a decrease in their thermal capacity. A current module of 4 kW must therefore have a thermal capacity 5 times smaller than that of the test bench. Simulations were performed by modifying the thermal capacity of the fuel cell. The results show that the decrease of the heat capacity makes it possible to increase the production of heat of the system but this becomes important only if the coefficient of exchange with the outside is decreased. This is achievable for the battery thermal insulation device system. When the coefficient is decreased by a factor of 15 or 3.2 W·K−1 instead of 48 W·K−1, the annual heat output of the test bench is 350 kWh. The efficiency of the system increases by 6% thanks to the thermal production. The different charges are described previously. They are differentiated by their daily, seasonal profile and by their correlation with sunshine, characterized by the PLM (PV- Load Meet) criterion. Fig. 39 shows the evolution of system performance and storage volume versus PLM. The name of the profile is specified in the figure. The modelled system is the modified test stand at the fuel cell cells to increase heat output. The nominal power of the inverter is equal to the maximum power demanded by the load. The efficiency of the system increases when the profile of the load is in phase with the sunshine because the power of the user is mainly delivered by the solar field. The direct supply of photovoltaic energy to the load is high efficiency (85%). When the energy is converted to gas before being returned to the load, the efficiency is much lower (33%). The volume of hydrogen increases with the PLM because the raw energy is more important. It is much more important for the profile having an annual variation of the load (St Pierre). In this figure, a variable load
storage system on the different losses during a year of operation. The load is a constant demand for power. The inverter is adapted to the power delivered by the system. With regard to the intrinsic consumption (IC), there is a 15% decrease in the loss between the scenario no. 1 and no. 2, which is to say thanks to the reduction of the intrinsic consumption of the solenoid valves. The loss in the converters is also slightly reduced because the energy converted to power the peripherals is decreased. When, in addition, the fuel cell recirculation engine is eliminated (scenario no. 3), the loss is further reduced to 2%. For scenario # 3, the faradic efficiency of the electrolyser is increased by the on-line measurement of the purity of oxygen. In addition, the fuel cell is supplied with pure oxygen. These two modifications lead to an increase in the average efficiency of the electrochemical cells from 47.2% to 50.1%. This increase is related to the efficiency of the electrolyser (increase from 77% to 82%). The average cell yield is slightly decreased (from 61% to 60.8%), although the oxygen partial pressure is higher. This stems from the fact that the power delivered by the battery is greater in the case of scenario # 3. The improved performance of the electrochemical cells increases the overall efficiency of the system by 3%. The volume of hydrogen is a little larger (+0.6 m3 compared to Scenario # 1 and # 2). Table 5 makes it possible to compare the performance of the test bench in three cases differing in the faradic efficiency of the electrolyser and the partial pressure of oxygen. The inverter of the system is adapted to the power of the load. The results of the test bench (Scenario # 1) are in the first column. The second system is the test bench in the case where the oxygen is not stored. In the last column, the test bench is equipped with an electrolyser of faradic efficiency of 99%. By comparing the first and the third column, it is observed that the improvement of the faradic efficiency of the electrolyser makes it possible to increase the yield of the PV-FC system by 2.3% and especially to reduce to zero the consumption of pure water. . Between the second and third columns, the increase in oxygen partial pressure improves the overall efficiency of the installation by 0.4%. In the case 50.00%
22%
System performance (%)
45.00%
22%
40.00%
22%
35.00% 30.00%
22%
25.00% 21%
20.00% 15.00%
21%
10.00%
21%
5.00% 0.00%
21% 0%
10%
20%
30%
40%
50%
60%
70%
PLM (PV- Load Meet) % Fig. 39. Influence of PLM on System Efficiency and Volume of Hydrogen Required - Scenario # 1.
126
hydrogen storage volume (10 bar) m3
Use of product oxygen
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45.00% 40.00%
loss in the system (%)
35.00% 30.00% 25.00%
EC
20.00%
IC
15.00%
Conv
10.00%
Ba
y
5.00% 0.00% 0%
10%
20%
30%
40%
50%
60%
PLM (PV- Load Meet) % Fig. 40. Influence of PLM on Annual Loss in Electrochemical Components (EC) and in Converters – Scenario # 1 - Rated Power for the Load. Table 6 Average power demand relative to the nominal power of the inverter, average and theoretical efficiency of the inverter – Scenario # 1 – Rated power equal to the maximum power of the load. Profile type
Paverage
Constant Variable Cosine Constant with annual variation
100% 11% 50% 55%
power / Pnominal power
Average efficiency of the inverter
Theoretical efficiency of the inverter
95% 79% 86% 94%
95% 85% 94% 94%
The current system does not produce heat due to the low power density of the fuel cell cells of the test stand. The use of cells with current performance, would increase the efficiency of the system by 6% through the production of thermal energy. The alkaline electrolyser because of its high energy efficiency, does not allow the generation of heat. A membrane electrolyser with lower energy performance may be a better candidate for cogeneration. The operating times of the electrochemical components are evaluated at 2400 h per year for the electrolyser and at 5800 h per year for the fuel cell. The life of the electrolyzers is very important, perfectly adapted to the application. However, the life of fuel cells is currently very low. To homogenize the lifetimes of all the main components of the PV-FC system, the life of the fuel cell should reach 145,000 h (25 years). Due to the limited life of the fuel cell and the current efficiency of the storage system, battery disposal is currently not an option.
profile (PLM = 33%) results in a different performance of the complete system. Fig. 40 shows the influence of PLM on different system losses. Increasing PLM results in lower losses in electrochemical components because less energy is converted to hydrogen. The loss due to intrinsic consumption and the amount of energy delivered to the battery are not influenced by the charge profile. The loss in the converters varies between 14% and 19% depending on the load profile. For the variable load profile, the lower efficiency of the system is due to the greater loss in the electrical conversion equipment. In fact, as this profile has a peak power, the inverter needed for this profile has a large power rating. During the day, the average power consumed by the load is equal to 11% of the nominal power of the inverter. Table 6 shows the average power consumed by the user and the average and theoretical efficiencies of the inverter as a function of the load profile. For constant profiles, the value of the average efficiency of the inverter corresponds to its theoretical value. On the other hand, for the other two profiles, the average yield is lower than the theoretical yield. For these last two profiles, the requested power has a very important amplitude (from 0% to 100% for the cosine type profiles). Therefore, the average efficiency of the inverter depends on the average power demanded but also on the load amplitude. The current efficiency of the installation is between 21% and 30% depending on the load profile, if the inverter is perfectly sized for consumption. The improvement of the hydrogen storage system would increase the operating efficiency of the installation by 21%, or reach 47%. Reducing intrinsic device consumption would improve performance by 17%. The modification of the oxygen purity measurement system would increase the efficiency by 2.3% but especially reduce to zero the consumption of pure water. The influence of the oxygen partial pressure of the fuel cell is low, but the elimination of the oxygen storage induces a large consumption of pure water of the PV-FC system.
6. Conclusion The present work concerns the study of the hydrogen produced from a direct coupling of a PV generator and a PEM type electrolyzer. The polymer membrane electrolyzer is considered by many to be a future technology because it can benefit from many developments on PEM fuel cells, as well as the associated cost savings, and this technology is still little in global hydrogen production. This justifies the pursuit of research, and the overall objective of this work is to study a PV system to produce the maximum amount of hydrogen by water electrolysis. The production of electrical energy is ensured by the PV panels and with the use of climatic data from Suez city, Egypt. This work models the constituents of the solar hydrogen production system, such as the PVG, the electrolyzer, and a directly coupled PV-electrolyzer, and simulates the different solar radiation intensities and temperatures as well as the different combinations of electrolyzer cells. To study the performance of the module, the global solar radiation was varied with a fixed 127
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temperature (T = 25 °C). The results obtained from the model showed that the I-V characteristic depends on solar radiation. The current delivered by the PVG and the increase in voltage with solar radiation, and consequently the power produced by the PVG, is increased. The second parameter that has a direct influence on the I-V characteristic of the PVG is temperature. The increase in temperature increases the current and decreases the voltage, although the short circuit current varies little with the temperature while the no-load voltage is influenced much more. The temperature therefore has a significant influence on the power of the PVG, where a decrease in power is noticeable when the temperature increases. These results make it possible to see, in the first instance of direct coupling between the PVG and the electrolyzer of a single cell, that the volume of hydrogen produced is very low and is a mismatch between the PVG and the electrolyzer. Therefore, to increase the volume of hydrogen produced and improve the degree of adaptation between the elements of the system, a new dimension for the electrolyzer by changing the number of the electrolyzer cells used was simulated. The results obtained show considerable approximation between the points of maximum power of the PVG and the system operating points, and a significant improvement in system performance that signifies an increase in the volume of hydrogen produced by the system. To put this in perspective, we consider that a study of complete system of electric power production because the modelling tool we developed allows the simulation of directly coupled PVG-Electrolyzers. This tool could be developed to simulate the complete operation of a PVG-Electrolyzer and fuel cell system. The modelling of the system has given the use of empirical and semi-empirical equations, some results of previous work, the software Matlab®-Simulink R2012a and some data of the manufacturer such as the curve of polarization, the surface of an elementary cell, the coefficient related to the operating threshold, the consumption parameters of the auxiliaries and the stoichiometry's of the gases. All these allowed us to build under Matlab® Simulink, the block photovoltaic panels (PV), the battery pack, the fuel cell block, the block electrolyser and all the curves representing the different powers produced or consumed and the different gases products or consumed.
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Using MATLAB to model and simulate a photovoltaic system to produce hydrogen
T
Tamer M. Ismaila, , Khaled Ramzya, , Basem E. Elnaghib, M.N. Abelwhabb, M. Abd El-Salamc ⁎
⁎
a
Department of Mechanical Engineering, Suez Canal University, Ismailia, Egypt Department of Electrical Power and Machines, Suez Canal University, Ismailia, Egypt c Department of Basic Science, Cairo University, Giza, Egypt b
ARTICLE INFO
ABSTRACT
Keywords: Hydrogen PEM electrolyzer Photovoltaic MATLAB Solar radiation
Energy is currently the basis for development in different areas worldwide. Traditional sources of energy such as coal, oil, and nuclear energy have serious repercussions on the environment and are non-renewable energies. Therefore, renewable energy, like solar, wind, and marine energy, are alternatives. Egypt is considered an important country that has climatic averages allowing the exploitation of renewable energy. Solar energy is available in Egypt, especially in Upper Egypt, throughout the year. Different models have been created to estimate and predict the global solar radiation intensity due to the shortage of measuring stations. This study presents a mathematical model to estimate and predict the global solar radiation intensity in Egypt. This model is compared and validated against published measurements of global solar radiation intensity. Furthermore, this study introduces a hybrid system used to produce hydrogen (photovoltaic generator–PEM electrolyzer). Modelling and simulating methods is done by running a flowchart in MATLAB to minimize the losses in the system and increase the quantity of hydrogen produced. The simulation includes the global solar radiation estimation and the photovoltaic generator–PEM electrolyzer. The experiment was conducted in March in Suez city, Egypt. The results obtained showed that the model of global solar radiation gives a good prediction for estimating the intensity of global solar radiation in Egypt. Furthermore, they concluded that there is a significant improvement in system performance that signifies an increase in the volume of hydrogen produced by the system. The whole model is simulated, and the simulation results fit the experimental data very well. The electrolyzer is powered by a PV panel and is modelled, sized, and experimentally validated.
1. Introduction Renewable energy uses natural elements that are renewed faster than they are consumed. Thus, solar, hydro, geothermal, and wind energy are renewable and environmentally friendly. The use of renewable and environmentally friendly energies is one of the best alternatives to fossil fuels, especially after Fukushima nuclear disaster in Japan. Although much research has already done in this field, the research effort has intensified so that future energy sources will be as green as possible. Energy production will be a challenge of great importance in the coming years as the energy needs of industrialized societies are increasing. However, developing countries will increasingly need energy to achieve development, and much of the world’s energy comes from fossil fuels. Today, renewable energies are gradually becoming energies full share, competing with fossil fuels in terms of cost and production
⁎
performance. However, their energy-to-electricity conversion systems often suffer from a lack of optimization that still makes them expensive, with significant inefficiencies in performance and reliability [1]. Solar energy has a great potential for the future. It is free and widely available. The sun generates energy through a thermonuclear process that converts about 650 × 106 tons of hydrogen into helium per second [2]. This process creates electromagnetic radiation that spreads into space, travelling at a speed of 300 × 103 km/s in all directions [2]. The sun is considered the main source of energy worldwide. Solar energy is used in many applications such as water heating, power generation, and heating or cooling. Furthermore, the electricity consumed globally in recent decades is strongly linked to the development of industry, transport, and communications. Today, much of the electricity produced is produced from non-renewable resources such as coal, natural gas, oil, and uranium. Their regeneration rate is extremely slow on a human scale. Solar radiation data are not available for large areas due
Corresponding authors. E-mail addresses: [email protected], [email protected] (T.M. Ismail), [email protected], [email protected] (K. Ramzy).
https://doi.org/10.1016/j.enconman.2019.01.108 Received 25 September 2018; Accepted 30 January 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
I0 ID Iel Nc Pr Q H2 Uc Utn Utno xn x n+ 1 A E Eh G ICC If Igen Ilight IPV k KT m n Ncell NOCT Np Ns P
p PEM PN PVG q R RS
diode saturation current (temperature dependent) reverse current of diode the current of electrolyzer (A) number of cells in an electrolyzer stack power required by the electrolyzer (W) hydrogen gas flow rate (Nm3·h−1) actual voltage of the cell (V) thermoneutral potential (V) standard thermoneutral potential (V) the present iteration the next iteration ideality factor global solar radiation (W/m2) the operating point current daily mean global irradiance on a horizontal surface, kWh/m2 an operational short circuit the voltage of the operating point the current delivered by the generator current photo, depending on the intensity of the irradiation cell current Boltzmann constant the clarity index, or the relationship between ground and extra-terrestrial radiation material index (1 or 2 depending on the technology used) number of electrons transferred per hydrogen molecule (n = 2) number of electrolyzer cells nominal solar cell operating temperature number of parallel modules in the photovoltaic field number series module in the photovoltaic field atmospheric pressure
RSH s S Sc T Tamb. Tcell Tel V Vf VOC VPV Z
F T e m s u , s
s
Ho H
to the low number of solar stations especially in remote locations. Thus, using the simulation models to predict the global and diffused solar radiation data is essential for many solar energy systems. These models depend on different parameters such as temperature, sunshine hour data, latitude angles, hour angles, site location and attitude angle such as Chandel et al. [3]; Gueymard [4] ASHRAE [5]; Iqbal [6]; Gueymard [7]. This will lead to a more or less short-term, non-zero risk of depletion of these resources. Although photovoltaic energy has been known for many years as being capable of producing electricity ranging from a few mill watts to a megawatt, it is also an attractive alternative to replace electricity supplied by conventional sources because it has many advantages, as follows:
number of parallel electrolyzer cells proton exchange membrane positive negative photovoltaic generator charge of the electron perfect gas constant resistance in series, modelling ohm losses of material and contacts parallel resistance, representing the parallel admittance of the current generator number of series electrolyzer cells generator surface Solar constant (1353 W/m2 = 4.8708 MJ/h·m2) temperature (K) ambient temperature cell temperature electrolyzer temperature volume of hydrogen produced (mL) the derivative of the function open circuit voltage voltage at the cell terminals number of electrons required to release a molecule angle of inclination, voltage temperature factor current temperature factor ground albedo faradic efficiency energy or thermal efficiency the efficiency of the electrolyzer photovoltaic module performance the overall performance the adaptation performance the time angle of the sunset on the inclined plane the time angle of the sunset on the horizontal plane standard enthalpy of formation (J·mol−1) change in enthalpy of formation (J·mol−1)
hydrogen to ensure the continuity of electricity production. Several hydrogen production techniques exist; some of these have reached commercial maturity while others are still experimental. The catalytic decomposition of natural gas, partial oxidation of heavy oils, gasification of coal, and water electrolysis are among the hydrogen production processes that have been industrialized [8]. However, pure and hybrid thermochemical cycles are at the research and development stage, while photochemical and photo-biological processes are still in the early stages of research. The electrolysis of water for hydrogen production is the most popular process. The use of solar energy in electrolysis processes is the most cost-effective and environmentally friendly method [9]. Hydrogen is considered a potential future energy carrier. Solar hydrogen is produced using renewable energies, especially solar energy, and hydrogen has a definite future in the field of energy. Therefore, the possibilities for its production on a large scale will be study. In large-scale production, consideration must be given to yields and economic opportunities. As part of the study, it is found that hydrogen has major advantages that ensure it has a bright future as an intermediate energy vector. Indeed, its applications cover a wide range of human energy needs; it can be used in the fields of transport and in stationary and portable applications and it also has a high energy efficiency. In addition, it is a clean if its production is based on a non-polluting energy such as solar radiation. This advantage is crucial because of recent controversies over the greenhouse effect. The photovoltaic conversion of global solar radiation into electricity is one way to exploit solar deposits using solar cells. A system coupling a photovoltaic field and an electrolyzer makes it possible to store the electricity in the form
1. Producing this renewable electricity does not emit greenhouse gases; however, the environmental impact of manufacturing the system must be reduced. 2. Photovoltaic energy is exploitable both in mountainous regions, remote villages, and in the center of a big city, in southern and northern regions, because sunlight is available everywhere and almost inexhaustible. Photovoltaic electricity can be produced as close as possible to where it will be consumed, in a decentralized manner, and directly by the user, making it accessible to a large part of the global population. However, in the field of renewable energy, especially photovoltaics, there is a problem of continued electricity production in the night or on cloudy days. To manage that, a techniques is used such as batteries and 102
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of a gas (hydrogen). As a substitute for fossil fuels, hydrogen has excellent physicochemical and thermal properties that give it the quality of a universal fuel. This energy vector is the only one that can be produced from water and several renewable energy sources and can then be used without being detrimental to the environment [10]. Several numerical and experimental studies have been done on hydrogen production facilities that use renewable energies. Chen [11] studied the configuration of hybrid power systems (solar-hydrogen fuel cells) to supply electric vehicles; the electricity from photovoltaic cells placed on the roof was converted to hydrogen through electrolysis. Fuel cells are used to power electric vehicles. Yunez-Cano et al. [12] studied the feasibility of integrating hybrid photovoltaic/hydrogen (PV/H2) systems into houses in Mexico. The PV/H2 system supplies the load, with electricity generated by the main source (PV), excess energy is electrolyzed to produce hydrogen, and the fuel cell provides a backup in case of insufficient energy. Kely et al. [13] studied the application of high-pressure hydrogen produced by water electrolysis in fuel cell motor. However, further studies have shown that hydrogen can be used in other regions without the use of fuel cells. Topriska et al. [14] describe the development of semi-empirical numerical models for solar hydrogen systems; these consist of proton exchange membrane (PEM) electrolysis by photovoltaic panels to produce hydrogen as fuel for cooking applications. Pedrazzi et al. [15] developed a mathematical model and software for solar hydrogen hybrid system. The results showed that the virtual hybrid system can bring about complete grid independence and the hydrogen production balance is positive after a year’s operation with a system efficiency of 7%. Ohta [16] revealed the feasibility of using hydrogen in treatment strategies. Ahmadi et al. [17] analyzed the model system using MATLAB simulations to calculate the hydrogen production, exergy damage, and exergy efficiency of hydrogen production based on an ocean thermal energy conversion system. The system was coupled with a solar enhanced PEM electrolyzer. Bousquet et al. [18] developed an empirical method to simulate the generation of electrolytic or fuel cells. A dynamic model for PEM electrolysis was proposed and evaluated by Gorgun [19]. Onda [20] developed a two-dimensional mathematical model for analyzing PEM electrolytes. Ulleberg [21] demonstrated an alkaline electrolytic cell model based on thermodynamics and heat transfer theory. Recently in renewable energy systems research, Kélouwani et al. [22] developed and demonstrated an independent renewable energy system with hydrogen storage. Khan et al. [23] modelled a small wind-fuel cell hybrid energy system. Assaf and Shabani [24] used the MATLAB to simulate a solar-hydrogen combined heat and power system integrated with solar-thermal collectors to supply power and heat to the applications. From the results they concluded that the maximum thermal reliability that could be obtained is around 96%. It is in this context of announced crisis that renewable resources, varied and inexhaustible, can become an alternative to fossil resources. Their conversion into thermal, chemical, or electrical energy does not present any danger to humans, any more than ecological danger. The production of energy can be centralized or decentralized, allowing the development of a local economic fabric. As energies from renewable primary sources such as solar, wind, and hydro cannot be stored directly, it is necessary to develop a new energy vectors, such as hydrogen, to promote the development of renewable primary sources. PV hydrogen is a renewable source for producing clean fuel and electricity [25]. Wang et al. [26] studied the characteristics of single-stage photovoltaic grid-connected/hydrogen production multi-inverter system using modal analysis. The results showed that the simulation results verified the correctness and effectiveness of the modal analysis. MATLAB/Simulink of a PEM electrolyzer powered by a solar panel was developed by Albarghot and Rolland [27]. They concluded that the experimental and simulated results were matched. Several PV-hydrogen plants are operated in countries such as Finland [28], Germany [29], Italy [30], Japan [31], Spain [32], Saudi Arabia [33], Switzerland [34], and the United States [35,36]. Most of these facilities are demonstration
units managed by public bodies. What motivates us to do this work which studied the production of hydrogen by a hybrid system (photovoltaic generator - PEM electrolyzer), with the aim of minimizing the losses in the system, by the modeling of the system elements and the simulation of operation by executing a flowchart under MATLAB. To increase the amount of hydrogen produced and make this solution cost-effective compared to other solutions, in order to facilitate the use of hydrogen as a storage element of electricity by use of fuel cells, based on their physical and chemical characteristics. Therefore, the main aim of the present research is to contribute to understanding a new technology for the production and storage of clean energy. This study is designed to stimulate future work in this area. In this study, a simulation of a PV system to produce hydrogen by water electrolysis is presented; the photovoltaic panels ensure the production of electrical energy, and climate data for the month of March in Suez, Egypt is used. In most studies and researches the global solar radiation is measured and used in the simulation method as a measured values, but in this study the global solar radiation was modelled using MATLAB and matched with the PV system model to produce hydrogen. So a simulated model was built, validated, and compared with published data due to the importance of estimating the global solar radiation intensity. This model is used to estimate the global solar radiation intensity during the year at any location. Furthermore, system elements were modelled and a flowchart for simulating system performance was run in MATLAB to determine the most favorable conditions for improved hydrogen production. Mathematical models that describe the electrical behavior of the photovoltaic panel and the electrolyzer are presented. The simulation concerns the direct coupling of the hydrogen production system by directly coupling the photovoltaic generator and the PEM electrolyzer. The results obtained show that it is possible to choose an appropriate hydrogen production system. 2. Global solar radiation modelling Global solar radiation data are required for many applications and many areas of research. Most of the energy produced from the sun is transmitted radially as electromagnetic waves called global solar radiation (energy). Solar energy can also be converted to useful forms such as thermal and electrical energy. As global solar radiation passes through the atmosphere, some of it is absorbed, scattered, and reflected by air molecules, water vapor, clouds, dust, and pollutants. The scattered and reflected part returns to the Earth as diffuse solar radiation. The global solar radiation that reaches the surface of the earth without being depleted or diffused is called direct (beam) solar radiation. Global or total global solar radiation is the sum of the diffuse and direct solar radiation. Several models have been developed to predict global solar radiation in many different countries. In Egypt, the solar energy incident on land has a magnitude of 12–30 MJ/m2/day, and the duration of sunshine ranges from 3500 to 4500 h per year [37]. Furthermore, in Egypt, there are few meteorological stations that measure components of global solar radiation. Therefore, some empirical models have been developed to calculate global solar radiation over different sites in Egypt. Morcos [38] developed a mathematical model to calculate the total radiation on a tilted surface in Assiut, Egypt. This model depends on a study by Liu and Jordan [39], in which radiation on a tilted surface consists of three components: beam solar radiation, diffuse radiation, and global solar radiation reflected from the ground, buildings, and trees. The total global solar radiation on the tilted surface E, is the sum of the three terms and given as:
E = Eb Rb +
Ed (1 + cos ) + 2
g (Eb
+ Ed )(1 2
cos ) (1)
where Eb and Ed are beam and diffuse global solar radiation intensities on horizontal surfaces and g is the diffuse ground reflectance. The 103
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geometric factor Rb is the ratio of the beam radiation on the tilted surface to that on a horizontal surface and it is given as
horizontal surface is given by
cos Rb = cos z
The standard clear day radiation is determined from the following relationship:
Ed = Ion d cos
(2)
where
cos = sin sin cos
E = Ion
sin cos sin cos + cos cos cos cos
b cos
(12)
z
+
d cos z
(1 + cos ) + 2
g( b
+
d ) cos z (1
cos )
2
(3)
(13)
On the other hand, Z is the zenith angle that depends on the latitude of the location and the solar hour angle . The last is given as:
The fact that both the theoretical curves and experimental points in Morcos [38] show that the values of d correspond to a fixed value of d depend only very moderately upon the air mass. This indicates that, for the degree of accuracy sough here, a relationship independent of the air mass is adequate. For Eq. (11), a straight line obtained using the least squares method, is the best fit for the experimental points. In this work, the model was simulated and a sub-routine built in MATLAB to investigate the global solar radiation. This model was checked, compared with published measured global solar radiation over different cities in Egypt, and validated. The model described previously was evaluated based on the coefficient of determination R2. This value can be used to test the linear relationship between calculated and measured values; its value should be as close to unity as possible and is given by the following equation [40]:
+ cos sin sin cos cos
cos
Z
= cos cos cos
+ cos sin sin sin
(4)
+ sin sin
where is solar declination angle, , is the tilt angle, and is the surface azimuth angle. The hour angle is equivalent to 15° per hour, with a positive value in the morning and a negative value in the afternoon, is determined using the following:
=
360 × (t 24
12)
(5) (6)
= 23.45sin [(360/365) × (284 + N )]
where t is the hour of the day and N is the day number, beginning with January first. The value of the diffuse ground reflectance is 0.2 [38] when there is no snow cover. The beam and diffuse radiation on a horizontal surface, Eb and Ed, are determined using standard clear sky conditions. The beam global solar radiation on a horizontal surface for clear sky hours is given by
Eb = Ion b cos
R2 = 1
(14)
b
= a o + a1 e
360N 360
E¯ m =
(8)
where Sc is the solar constant. The constants ao, a1, and k are determined according to the correction factors of Eq. (10) as below:
ao = 0.4237
0.00821(6
a1 = 0.5055 + 0.00595(6.5 k = 0.2711 + 0.01858(2.5
AL ) 2 AL )2 AL ) 2
(10)
where AL is the altitude of the observer in kilometers. For changes in climate, correction factors are applied to ao*, a1*, and k*. These correction factors are ro = ao /ao*, r1 = a1/a1*, and rk = k/k*; these are given in Table 1. To estimate the clear sky diffuse radiation on a horizontal surface, Morcos [38] used the following empirical correlations for beam and diffuse radiation for clear sky: d
= 0.2710
0.2939
(11)
b
where d is the ratio of clear sky diffuse radiation to the extraterrestrial radiation on a horizontal plane and. The clear sky diffuse radiation on a
np i=1
ro
r1
rk
Tropical Mid-latitude summer Sub-arctic summer Mid-latitude winter
0.95 0.97 0.99 1.03
0.98 0.99 0.99 1.01
1.02 1.02 1.01 1.00
(15)
Em (16)
np
Tcell = Tamb +
Table 1 Correction factors for climate types [38]. Climate Type
Ec E¯ m )
where np is the number of experimental points. Temperature T and irradiation G have a direct impact on the performance of a photovoltaic cell. When the cell temperature increases the open circuit voltage decreases substantially while the short circuit current increases slightly. Then it can be noticed that the PV cells have better performance in a cold environment with clear sky, unlike a warm environment. For crystalline silicon cells, Voc drops by about 0.37% for each additional degree Celsius, Icc increases by 0.05% for the same conditions. The temperature of the PVG depends not only on the ambient temperature but also on the effects of the irradiation of the cell. Since only a small fraction of the insolation that affects the module is converted into electricity, most of the incident energy is absorbed and converted into heat [31]. To help system designers take into account variations in cell performance with temperature, manufacturers often provide an indicator called NOCT. The temperature of the NOCT cell is in a module when the ambient temperature is 20 °C, solar radiation equal to 0.8 kW/m2, and wind speed at 1 m/s. To account for other environmental conditions, the following expression may be used:
(9)
k / cos z
)2
where Em and Ec are the measured and calculated global solar radiation, respectively. The term E¯ m in Eq. (15) is the average measured global solar radiation and can be defined as follows [40]:
where Ion is the hourly extra-terrestrial radiation, measured on the plane normal to the radiation (MJ/m2) and b is the atmospheric transmittance for beam radiation. Ion and b are calculated from the following equations:
Ion = Sc 1 + 0.033cos
( Em ( Em
R2 = 1
(7)
z
Error between experimental and predicted results Experimental result deviation
NOCT
20 °C ×G 0.8
(17)
where Tcell, Tamb is the Cell temperature and ambient temperature, respectively, G is the solar irradiation (kW/m2). 3. Modelling and simulation of direct coupling PVG-Electrolyzer In this section, a study of a solar hydrogen production system is 104
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presented based on the direct coupling between a photovoltaic generator (PVG) and a PEM electrolyzer. For this study, the PVG, the electrolyzer, and the simulation of the direct coupling were modelled.
If V = 0 (short circuit case):
ICC = IL
3.1. Modelling the photovoltaic generator
0 = IL
ID = Io e
Vth =
IRSh =
I = IL
V + (I . R s ) Vth
1
Io exp
V + (I . RS ) Vth
V + (R S × I ) RSh
1
Io exp
V + (I × RS ) Vth
1
Io exp q
(V + (I × RS )) A × TC × K
0 = IL
Io exp q
Im = IL
Io exp
(21)
Im = ICC 1
(22)
RS =
1
(27)
A TC q
VOC A × TC × K
(Vm + (Im. RS )) A × TC × K
q
1
(30)
VOC C A × TC × K
exp q
(V
exp q K
(29)
VOC + (IRS )) A × TC × K
Vm
(
Im Icc
ln 1
(31) (32)
VOC + (I . RS ) A × TC × K
)+V
(33)
Vm
OC
(34)
Im
To determine the Ideality factor (A):
dP dI dV =0= +I dV dV dI
(35)
q (2Vm
A=
(23)
1
(26)
(28)
I = ICC 1
ns KT
By replacing Vth in the current equation,
I = IL
(Vm + (Im. RS )) A × TC × K
Io exp
Io = ICC exp
A : Ideality factor (between 1 and 2 according to the technology used). For modules supposedly devoid of leaks (infinite Rsh and IRSH 0 ), this relationship is given as follows:
I = IL
1
ICC = IL
(20)
V + (Rs × I ) RSh
(25)
In order to determine the unknown parameters, a simplified explicit method [42] was used and it is suppose that:
(19)
A × Tc × K q
VOC A × TC × K
Io exp q
Im = IL
(18)
IRsh
1
At the maximum power point:
3.1.1. The Current-Voltage (I-V) characteristic simulation models The photovoltaic cell model used in the present work is shown in Fig. 1 as below. Based on the PV cell model circuit, the node law is applied to find the relationship between the current and the voltage [41]:
ID
ICC · RS A × TC × K
If I = 0 (open circuit case):
A PV module converts global solar radiation into electricity directly, and the intensity of global solar radiation and the temperature are essential to its current and output voltage. Thus the predicting the performance of a cell/module/PV generator requires the development of a mathematical model that allows study of its operation (e.g., global solar radiation intensity, temperature) for different meteorological conditions. Many studies focus on the development of mathematical models to simulate current-voltage (I-V) characteristics of a cell/module/PV generator, while others are oriented towards modelling the performance of PV modules in terms of electrical power produced.
I = IL
Io exp q
ISC ICC
Im
VOC )
(
+ ln 1
Lm ICC
)
(36)
ns : The serial cell number (24)
3.1.2. Photovoltaic field
There are four unknown parameters in this equation: IL (photocurrent), Io (saturation current), A (Ideality factor), and Rs (series resistance) There are three remarkable cases in the I-V feature:
Io (gen) = NP × Io (mod)
(37)
Vr (gen) = NS × Vr (mod)
(38)
RS (gen) =
NS NP
RS (mod)
(39)
Therefore, the generator equation takes the following form:
Igen = ICC
Io exp q
Vgen + (Igen· RS (gen) ) A × TC × K
1
NP : number of parallel cells in the photovoltaic field NS : number of serial cells in the photovoltaic field Igen : the current delivered by the generator ICC : Short-circuit current Fig. 1. Equivalent electrical diagram of a photovoltaic cell.
And the V-I relationship can be written as follows: 105
(40)
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Vgen =
Igen + Icc + Io
Igen· RS (gen) + Vth × log
Vthmod =
(41)
Io
TC TC (ref )
Io = Io (ref ) ×
G Gref
G Gref
q 1 × A×K Tcref +
× T
× ICC (ref ) + a × T
Vm = Vm (ref ) +
Im =
× exp E ×
A×K×T G × log q Gref
VOC = VOC (ref ) +
ICC =
3
A
K q
T
× Im (ref ) + a × T
log
1 TC
3.2. Modelling electrolysis An electrolyzer is a device that uses electrical energy to produce chemical reactions. In this study, the electrolyzer was used to perform water electrolysis to produce hydrogen. PEMs are made from pure polymer membranes or composite membranes where the materials form a polymer matrix, and one of the most common materials used is Nafion. Fig. 3 shows the structure of a PEM electrolyzer.
(43)
(44)
3.2.1. Electrolyzer model The water electrolyzer consists of several electrolyzer cells connected in series and in parallel. The electrolyzer model considered here is based on the characteristics of the individual cells. The calculation of the operating voltage required, and the flow rates of hydrogen and oxygen, are all done on a per cell basis, while the corresponding values for the entire electrolysis unit are found simply by multiplying by the number of series and parallel cells. The main inputs and outputs of an
(45)
G Gref
+
T
(48)
Fig. 2 shows the flowchart used in MATLAB simulation with a subroutine to estimate global solar radiation.
(42)
TC (ref )
TC (ref )
α: coefficient of variation of current as a function of temperature β: coefficient of variation of the voltage as a function of the temperature.
3.1.3. Plotting and evolution of the current-voltage (I-V) characteristic The I-V curve of Eq. (40) is an arbitrary reference curve applicable to the global solar radiation intensity and temperature of the cell in particular. For other values of global solar radiation intensity and temperature, the evolution of Eq. (40) is done by the following equations [43]:
T = TC
(Vthmod (ref ) × TC )
(46)
(47)
Fig. 2. Flowchart for the MATLAB program with a subroutine to estimate global solar radiation. 106
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where VNcell is the total voltage of the electrolyzer, Ncell is the number of electrolyzer cells, and Ie is the total current of the electrolyzer. s and p represents the number of cells in the series and parallel, respectively. i. Hydrogen production rate According to the ideal gas law, the volume of gas produced is calculated using the following equation:
Fig. 3. Electrolysis using a proton exchange membrane.
V=
nRT ItRT = = Q H2 × t P ZFP
(52)
n=
I×t Z×F
(53)
Then, by using the trapezium integration method, the volume of hydrogen produced was calculated over a period of time.
Q H2 =
Ncell × R × I f × T Z×F×P
=
Ncell × 8.32 × I f × T
(54)
2 × 96500 × 0.1013
where V: volume of hydrogen produced (ml) Q H2 : hydrogen production rate (ml /s) T : electrolyte temperature R : ideal gas constant Z : number of electrons required to release a molecule Ncells: number of electrolyzer cells (s × p) F: Faraday constant P: atmospheric pressure t: time corresponding to volume produced (V) I f : Electrolyzer operating current ii. Electrolyzer efficiency
Fig. 4. The main inputs and outputs of an electrolyzer.
electrolyzer are shown in Fig. 4. This study used a laboratory-type PEM electrolyzer consisting of a cell with the compound Pt/Nafion/Pt, an EME electrode, and a membrane electrode with a platinum-plated membrane surface [42]. The electrolyzer is a load for the system, with its operating point defined according to its connection with the energy source. The equivalent diagram for the electrolyzer is shown in Fig. 5. The cell voltage of an electrolyzer is expressed in four terms:
Uel = Uth + Uanod + Ucathode + Uohm
The efficiency of electrolyzer is given by the following equation [45]:
(49)
where
el
Uth: Uanode: Ucathode: Uohm:
Theoretical tension Anodic overvoltage (V) Cathode overvoltage (V) Drop in voltage in the internal electrolyzer resistance Rel
Ie p
(55)
3.2.2. The current-voltage of the electrolyzer For the present study, a PEM type electrolyzer is chosen. From the experimental graphs with temperature deflections, the graph of the temperature T equals to 80 °C was chosen and the points (I-V) indicated in Table 2 were determined. Fig. 6 shows the I-V curves of the experimental electrolyzer and those simulated for a Tel of 80 °C.
(50)
The parameters a , b, and c are defined for the particular features (e.g., geometry, membrane, flow, materials, temperature, and pressure) for an electrolyzer cell. According to Eq. (50), the voltage-current relationship based on Tafel’s law for this electrolyzer configuration is given by the following equation [44]:
VNcell = s × a + b × log
1.23 × s VF
VF : The voltage of the operating point s : number of cells in the series
According to Tafel’s law, the cell voltage is expressed as a function of the current density [44]:
Ve = a + b × log(I ) + c × I
=
Table 2 Experimental electrolyzer data extracted from the I-V characteristics [45]. Temperature = 80 °C
(51)
Fig. 5. Equivalent electrical diagram of the electrolyzer according to the electrochemical model. 107
Current (A)
Volt (V)
0.14286 0.28571 0.42857 0.5714 0.85714 1.000 1.285714 1.714285 2.000 2.571428 3.000 4.000 5.000
1.685714 1.733333 1.762069 1.7896552 1.8275862 1.8500 1.873333 1.9066667 1.933333 1.973333 2.0071429 2.0821429 2.1500
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2.5
Volt (V)
2
1.5 Experimental 1
Mathema cal Model
0.5
0 0
1
2
3
4
5
6
Current (A) Fig. 6. The I-V curves of experimental and simulated electrolyzer data for Tel = 80 °C [45].
To determine the factors a , b, and c, three points from the relevant graph of electrolyzer data were chosen and replaced the values of the current and voltage with the points in the equation (50). Thus the following system of equations are obtained:
1.6857143 = a + b × log
( )+c×( ) 1 7
1 7
1.85 = a + b × log(1) + c × (1) 2.15 = a + b × log(5) + c × (5)
(56)
The solution of this system of equations gives the three factors:
a = 1.8018 b = 0.0632 c = 0.0482
(57)
Thus, the model of an electrolyzer cell is written as follows: (58)
V = 1.801 + 0.0632 × log(I ) + 0.0482 × I 3.3. Modelling the coupled PVG-electrolyzer
The directly coupled energy source is the PV generator and the electrolyzer that act as the load in this system. To study this PVGelectrolyzer system, the graphs of the I-V characteristic are coupled to find the point of operation of the electrolyzer because it represents the intersection between the two graphs; this is shown in Fig. 7. The flowchart of the direct coupling organization chart is shown in Fig. 8.
Fig. 7. The operating point of the photovoltaic generator–electrolyzer system.
Eq. (59) is nonlinear. This equation will be solved using the NewtonRaphson method used in [43]:
3.3.1. Calculation of the operating point:
•
+ Vth × log
= xn + 1
(59)
The overall yield is calculated using the following: s
lyzer: Ig = Ie
1.801
0.0632 × log(I )
+ Vth × log
Igen + Icc + Io Io
0.0482 × I =0
is the stopping criterion
ii. The overall efficiency of the system
Igen + Icc + Io
• The current of the generator must be equal to that of the electrof(I ) =
(62)
xn
Such that
I(gen) × Rs (gen) Io
(61)
where f (xn ) is the derivative of the function f (xn) , x n is the present iteration, and xn+1 is the next iteration.
i. Coupling conditions The voltage of the electrolyzer must be equal to that of the PV generator:
1.801 + 0.0632 × log(I ) + 0.0482 × I =
f (x n ) f (x n )
x n+ 1 = xn
=
I f × 1.23 × S E×S
(63)
E: Global solar radiation (W/m2): S generator area (m2) iii. Adaptation performance
I(gen) × Rs (gen) (60)
u
108
=
I f . Vf Im. Vm
(64)
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4.2. Results of simulation with the photovoltaic generator Before executing the steps in the flowchart, the BP 585F type PV cell was chosen [50] with the characteristics for standard conditions (E = 1000 W/m2; ambient temperature for surrounding environment = 25 °C; see Table 3). (a) Results of simulation with an ambient temperature of 25 °C and varying global solar radiation values The simulation results of the I-V characteristic of the photovoltaic generator (PVG) are shown in Fig. 10 for different values of global solar radiation (200, 400, 600, 800, 1000 W/m2) and a constant temperature of 25 °C. According to Fig. 10, the electrical power delivered by the module varies enormously with global solar radiation. As the energy supply for the electron-hole separation is ensured by the light energy, the increase in sunshine automatically leads to an increase in separate electron-hole pairs. The current output IPh (current created by converting light photo-current) is therefore proportional to the amount of sunlight (global solar radiation). Fig. 11 shows the simulation of the power-voltage (P-V) characteristic with different values of global solar radiation at T = 25 °C. The maximum power from the P-V generator can produce a more or less constant voltage that represents the point of maximum power. These results, obtained for the model presented above, show that the I-V characteristic depends on the intensity of the solar radiation. The current delivered by the PV generator and the voltage increase with the global solar radiation; consequently, the power produced by the PV generator increases also. The open circuit voltage is little influenced by the variations in solar radiation, in contrast to the current of the short circuit, which increases in a consistent manner. (b) Results of simulation with fixed global solar radiation E = 1000 W/ m2 and different temperatures The second parameter that has a direct influence on the I-V characteristic of the PV generator is temperature. Simulation results showed that variations in temperature influenced the voltage and the current such that the short-circuit current (Icc) increases slightly with the increase in the temperature, whereas the voltage of the open circuit (Voc) decreases, as shown in Fig. 12. Previous reviews show that the cells are sensitive to temperature variations; the internal resistance of the module increases with the increase in the latter. When the temperature of a cell increases, the current increases slightly but the voltage decreases, reducing the power. Fig. 13 shows that the power variation is opposite to that of the temperature.
Fig. 8. Flowchart of direct coupling organization.
iv. Photovoltaic generator output s
=
I f × Vf E
(65)
(c) Results of simulation using real data from Suez city
4. Results and discussion
To test the module with real data, the variation in global solar radiation and temperatures for the month of March in Suez city in 2016 (Table 4) was used. The global solar radiation and temperatures increased over the course of the day and reached the maximum values from the period 12:00–14:00 before decreasing towards the end of the day. The global solar radiation are at their minimum from 08:00 and 15:00 to 17:00 and reaches its maximum of 790 W/m2 from 12:00 to 13:00, while the temperature reaches its maximum, 41 °C, at 13:00. The measured data was validated using the solar radiation model and the results were obtained using MATLAB. Fig. 14 shows the results of simulating the I-V characteristic with real data from Suez city. The current increases very rapidly when the temperature rises, causing a less pronounced decrease in the open circuit voltage and thus resulting in a relative decrease in the available power.
4.1. Validation results of the global solar radiation model The measured and estimated values from a previous model of hourly global solar radiation for Suez, Mansoura, Al Arish, and Al Menia are given in Fig. 9. The predicted values with the measured global solar radiation of Nafey et al. [46] for Suez, Egypt is shown in Fig. 9-a. This figure shows that the present models can be used to estimate the global solar radiation for Suez with an R2 of 0.975. Fig. 9b represents the variations in hourly global measured data for Mansoura, Egypt as reported by Taha [47] with predicted values from the present model. This figure shows that the present models can be used to estimate the global solar radiation for Mansoura with an R2 of 0.978. The results for Al Arish and Al Menia are shown in Fig. 9c and d; again, they showed that the present model results in a good prediction for global solar radiation, with R2 values of 0.945 and 0.973 for data published in Trabea [48] and Shaltout [49], respectively.
(d) Effect of PV surface temperature on the I-V characteristics of a PV panel 109
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Fig. 9. The variation in measured and predicted global solar radiation in different cities in Egypt.
Fig. 15 shows the output power of the PV plate, where the temperature distribution is constant under global solar radiation. In these figures, the curves for I-V and P-V characteristics are based on different PV panel temperatures. Analysis of these two figures, if PV plate temperature, will lead to a gradual decrease in output voltage. However, the output current of PV panels will change only slightly as the temperature increases; when they increase by 10 °C, the output power decreases by about 5%. The minimum output power of the digital PV plates used is 79.5 W and the PV panel temperature is 65 °C; however, when the temperature of PV plate drops to 25 °C, the maximum value of PV plate is 100 W. The potential for ambient temperature to pass through a day usually
Table 3 Photovoltaic cell characteristic type BP 585F [43]. Pm(w)
85
Vco (v) Icc (A) Vm (v) Im (A) α (mA/°C) β (mA/°C) Ns NOCT (°C)
22.03 5 18 4.72 3.2 −80 36 47
6 E=200 (W/m2)
Current (A)
5
E=400 (W/m2) E=600 (W/m2)
4
E=800 (W/m2) 3
E=1000 (W/m2)
2 1 0 0
5
10
15
20
25
Volt (V) Fig. 10. Simulation of the I-V characteristic with different values of global solar radiation (E) for T = 25 °C. 110
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Power (W)
90
E=200 (W/m2)
80
E=400 (W/m2)
70
E=600 (W/m2)
60
E=800 (W/m2)
50
E=1000 (W/m2)
40 30 20 10 0 0
5
10
15
20
25
Volt (V) Fig. 11. Simulation of the P-V characteristic with different values of global solar radiation (E), for T = 25 °C.
depends on changes in global solar radiation intensity. Locations rich in global solar radiation have a high potential for developing PV systems with maximum output. Fig. 16 shows the characteristics of the P-V curve under varying values of global solar radiation at a constant ambient temperature and heat transfer rate. In Eq. (66), the average ambient temperature is assumed to be 25 °C, the equation of the heat transfer coefficient (hc ) is 15 W/m2, and the average wind speed (v) is 2.5 m/s for the PV plate.
temperature on their output performance under different solar radiation intensities. The maximum output power generated by PV panels will be a combination of the high global solar radiation and low temperature. As Fig. 17 shows, the most effective power generation rate for a PV plate is 15.5%, when its temperature is 25 °C and solar radiation intensity is 1000 W/m2. These values are similar to the standard test conditions (STCs) for PV panels. Unfortunately, the efficiency of PV plates decrease when they are exposed to high temperatures; when the latter is 65 °C, the power generation efficiency is 12.27% under the worst conditions. However, when the temperatures of the PV plates are 55 °C, 45 °C, and 35 °C, the efficiencies become 13.1%, 13.8% and 14.7%, respectively.
(66)
hc = 5.7 + 3.8v
An increase in global solar radiation increased the temperature of the PV plates. The maximum temperature was recorded at a maximum global solar radiation of 1000 W/m2, and the lowest temperature of 200 W/m2 was recorded at a low horizontal radiation. The temperature difference between these two values was about 49.5%. Global solar radiation is also a key factor in power generation from PV panels. Fig. 16 shows that the maximum output power increases global solar radiation increases. Unfortunately, the rated power cannot reach 100% due to the rise in the temperature of the PV plate. A worse output power was observed when global solar radiation was low. The payback period of the integrated PV system mainly depended on the effective output power of the PV panel, because the latter are considered the main components of the former. Fig. 17 shows the effect of PV plate
4.3. Results of simulations modelling a coupled PVG-electrolyzer In order to create the coupling flowchart, the global solar radiation E (W/m2) and temperature (T) data were measured and recorded for Suez in 2016. The current results of simulations in which a BP 585F solar panel and a single PEM electrolyzer cell were coupled. After executing the direct coupling flow chart in MATLAB, the following results were obtained:
6
T= 20°C T= 30°C
5
Current (A)
T= 40°C 4
T= 50°C T= 60°C
3 2 1 0 0
5
10
15
20
25
Volt (V) Fig. 12. Simulation of the I-V characteristic at different temperatures, for a global solar radiation value of E = 1000 W/m2. 111
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100 T= 20°C
90
T= 30°C
80
T= 40°C
Power (W)
70
T= 50°C
60
T= 60°C
50 40 30 20 10 0 0
5
10
15
20
25
Volt (V) Fig. 13. Simulation of the P-V characteristic at different temperatures, for a global solar radiation value of E = 1000 W/m2.
(a) The I-V characteristics of the coupling
The efficiency of the electrolyzer varied inversely with the increase in global solar radiation; at 08:00, and from 15:00 to 17:00, the yield values became important. From the interval 12:00 to 13:00 the yield reaches its minimum value. The overall system performance produced low values of between 1% and 1.02%. As shown in Fig. 20, this is because the efficiency of generator use was low, between 12.5% and 15% (non-adaptation) and because the generator yield was also low. Based on the results of this simulation, the efficiency of the utilization (adaptation) and overall system performance appear to be very low. To improve these yields, a new design of the electrolyzer will be proceed. In this system, electrolytes that decompose into hydrogen and oxygen are a key component, and the technical challenge is to make them work despite the irregular electricity from solar energy. Some researchers have numerically analyzed the operation of alkaline water electrolytic cells under static and intermittent conditions [51–54] and photovoltaic conditions [55]. These studies focused mainly on electrolysis in cells with a fluctuating power supply. The reaction of the cell is analyzed by monitoring the voltage, temperature and pressure, current efficiency, time variations in oxygen, and the hydrogen concentration. The power consumption and working voltage of the electrolytic cell are mathematically modelled. The working voltage is considered a function of current density and parameters affecting the cell behavior, such as temperature, pressure, bubbles, and concentration [56]. Instead, other researchers have studied the effect of the structure of AC/DC converters on the thermal properties of alkaline
Fig. 18 shows the I-V characteristics of the PV generator and the electrolyzer when a single cell is used under conditions of different global solar radiation and temperatures. The operation of the electrolyzer is defined by intersections between the I-V curve of the PVG and the electrolyzer. The electrolyzer curve does not pass through the maximum power points of the PV generator throughout the day. The simulation results for the day of March 21, 2016 are given in Table 4. (b) Utilization performance (adaptation) According to Fig. 19, the variation in the yield went through three stages depending on the time of day: i. From 08:00 to 11:00, the utilization efficiency increases to 14.7%. In this period, there was an increase in the coupling voltage Vf and a decrease in maximum power point voltage with a very slight variation in the current, signifying the progression of the coupling power to the maximum PV module power. ii. From 11:00 to 15:00, the operating efficiency reached maximum working value of 14.9%, with a global solar radiation of 790 W/m2 and a temperature of 41 °C. From 15:00 to 17:00, the utilization efficiency decreased to 13%, starting at 13:00. (c) Efficiency of the overall system and electrolysis
Table 4 Characteristics of a coupled electrolytic cell with a module for the data of measured in March in Suez city, Egypt, in 2016. Time
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
E (W/m2) T (°C) Im (A) Vm (V) Icc (A) If (A) Vf (V) Vco (V) Pm (W) Q (ml/s) V (l) ηe (%) ηu (%) ηs (%) ηm (%)
323 29 1.572 15.75 1.663 1.662 1.913 19.78 25.04 0.25 0 64.29 12.70 1.005 1.56
426 31 2.076 15.57 2.20 2.195 1.956 19.6 32.80 0.33 1.043 62.87 13.09 1.006 1.6
569 33 2.773 15.30 2.93 2.932 2.01 19.32 43.24 0.44 2.430 61.18 13.63 1.006 1.64
700 35 3.412 14.97 3.608 3.607 2.056 19 52.34 0.542 4.198 59.82 14.17 1.006 1.68
787 39 3.844 14.53 4.064 0.065 2.086 18.56 57.56 0.610 6.272 58.97 14.72 1.008 1.7
790 40 3.865 14.37 4.086 4.086 2.086 18.39 57.33 0.614 8.476 58.93 14.87 1.009 1.71
724 41 3.543 14.54 3.746 3.746 2.065 18.57 53.06 0.563 10.59 59.56 14.58 1.010 1.69
636 37 3.109 14.9 3.287 3.287 2.035 18.93 47.46 0.494 12.49 60.43 14.09 1.009 1.67
488 37 2.394 15.05 2.53 2.531 1.982 19.08 36.80 0.380 14.07 60.07 13.62 1.012 1.63
364 36 1.706 15.20 1.803 1.803 1.925 19.22 26.37 0.271 15.24 63.89 13.16 1.017 1.59
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4.5
E=323w/m2, T=29°C E=426w/m2, T=31°C E=569w/m2, T=33°C E=700w/m2, T=35°C E=787w/m2, T=39°C E=790w/m2, T=41°C E=724w/m2, T=40°C E=636w/m2, T=37°C E=488w/m2, T=37 °C E=488w/m2, T=37 °C E=364w/m2, T=36 °C
4
Current (A)
3.5 3 2.5 2 1.5 1 0.5 0 0
5
10
15
20
25
Volt (V) Fig. 14. Simulation of the I-V characteristic with real data from Suez city, Egypt.
T=25°C and Pmpp=100W
90
T=35°C and Pmpp=95.0W
80
T=45°C and Pmpp=90.0W
70
T=55°C and Pmpp=84.6W
60
T=65°C and Pmpp=79.5W
Power (W)
100
50 40 30 20 10 0 0
5
10
15
20
25
Volt (V) Fig. 15. The characteristics of a PV panel when E = 1000 W/m2 is constant and PV panel temperatures are different.
E=200 W/m² and T= 45°C
80
E=400 W/m² and T= 56°C
70
E=600 W/m² and T= 67°C
Power (W)
60
E=800 W/m² and T= 78°C
50
E=1000 W/m² and T= 89°C
40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
Volt (V) Fig. 16. P-V characteristics at various temperatures and global solar radiation intensities.
water electrolytic cells [57]. To ensure that the electrolyzer adjusted to the PV generator with a global solar radiation of E = 569 W/m2, the numbers of the series and parallel cells of the electrolyzer were calculated using the following steps. The s and p values were rounded to integers because they were
often decimals. To calculate p and s, the following equation were solved:
Vf = Vmax = s × 1.801 + 0.0632 × log
113
Imax I + 0.0482 × max p p
(67)
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16
Efficiency at output Power [%]
15 14 13
T = 25°C
12
T = 30°C
11
T = 40°C T = 50°C
10
T = 60°C
9 8
0
200
400
600
800
1000
1200
Global solar radiation (W/m²) Fig. 17. The efficiency of output power at various PV panel temperatures and global solar radiation intensities.
4.5 4
MPP
3.5
Current (A)
3 2.5 2 1.5 1
Electrolyzer
0.5 0 0
5
10
15
20
25
Volt (V) Fig. 18. Current-voltage characteristics of a coupled electrolyzer cell and photovoltaic module.
16 14
Usage efficiency (%)
12 10 8 6 4 2 0
0
2
4
6
8
10
12
14
16
Time (hour) Fig. 19. The variation in the usage efficiency of a coupled PV module and electrolyzer cell. 114
18
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Usage of electrolyzer (%)
80
Usage of System (%)
0.8
70
Usage of Electrolyzer (%)
0.7
60
0.6
50
0.5
40
0.4
30
0.3
20
0.2
10
0.1
Usage of system (%)
0.9
90
0
0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 20. The variation in the electricity yields calculated.
Icell =
Imax p
production also increases, reaching the maximum value between 12:00 and 13:00. According to the electrolyzer yield curve, the pace reaches its maximum value from 08:00 to 11:00 and 15:00 to 17:00 and its minimum value from 11:00 to 14:00, because the electrolyzer output varied inversely with voltage (Fig. 23). According to Figs. 25 and 26, the overall system performance varied between 6% and 8% compared to the first case because the utilization yield (adaptation) varied between 92% and 99.7%. The judicious choice of the number of cells s and parallel series p of the electrolyzer improved the system adaptation result such that system operating points would be as close as possible to the maximum power points (MPP) of PVG. From these results from the mathematical models, which describe the behavior of the PV module and the electrolyzer, we became interested in a system consisting of these two elements. The operating points, maximum powers of the module, different yields, and the hydrogen production will be determined. The result of the simulation in the first case (a single celled electrolyzer) showed that the maximum value of the utilization yield was 15% and that of the maximum overall system yield was 1%; these low values are due to the non-adaptation of the system. To improve the system adaptation, the electrolyzer dimensions were changed; the results obtained showed a clear
(68)
The resolution of this system is s = 8; p = 1. 4.4. Results of simulating the electrolysis sizing Fig. 21 represents the I-V characteristic of a PV generator and an electrolyzer when s = 8 and p = 1, the different values of global solar radiation and temperature. A remarkable approximation between the maximum power points and the system operating points were seen, especially for the averages of the global solar radiation. To reduce losses caused by non-adaptation of the system, the I-V coupling characteristics of the new electrolyzer configuration were simulated using the program developed. The results obtained are shown in Figs. 22–25, which indicate that the current variations, hydrogen flows, and power vary proportionately with the global solar radiation. This occurs because the curves of these parameters reach their maximum values between 12:00 and 13:00 and their minimum values at 8:00 and 17:00 and are thus correlated with the evolution of the global solar radiation curve. Further analysis of Figs. 9 and 22–25, show that there is a strong relationship between hydrogen production and the intensity of global solar radiation. As the global solar radiation increases, hydrogen 4.5 4
MPP
3.5
Current (A)
3 2.5 2 1.5 1
electrolyzer
0.5 0 0
5
10
15
20
25
Volt (V) Fig. 21. I-V Characteristics of a coupled photovoltaic generator and an electrolyzer when s = 8, p = 1. 115
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18
6 Volt (V) Current (A)
16
4
Volt (V)
Current (A)
14
12
2
10
8
6
0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 22. Variations in current and voltage as a function of time.
4.5 4
Hydrogen flow rate (ml/s)
3.5 3 2.5 2 1.5 1 0.5 0
0
2
4
6
8
10
12
14
16
18
14
16
18
Time (hour) Fig. 23. Evolution of time-dependent hydrogen flow.
60
Electrolyzer power (W)
50
40
30
20
10
0
0
2
4
6
8
10
12
Time (hour) Fig. 24. Change in electrolyzer power over time. 116
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120
Hydrogen volume (L)
100 80 60 40 20 0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 25. Change in hydrogen volume as a function of time.
80
8 Electrolyzer yield (%)
60
Electrolyzer yield (%)
7
Overall yield (%)
6
50
5
40
4
30
3
20
2
10
1
0
Overall yield (%)
70
0 0
2
4
6
8
10
12
14
16
18
Time (hour) Fig. 26. Change in system and electrolyzer yields as a function of time.
improvement in the power transfer between the PVG and the electrolyzer (see Fig. 27). During the trial experimental period, the electrolyzer produced hydrogen ready to be stored for a period of 180 h at a very unstable production rate, varying from 0.05 Nm3 h−1 to 0.5 Nm3 h−1. Fig. 28 shows the percentage of the electrolyzer working time as a function of the different H2 rates produced. The histogram in Fig. 28 shows that the electrolyzer operated under a fluctuating input current. This occurred because it produced the hydrogen at a very high flow rate (between 0.4 and 0.5 Nm3 h−1) for 33.1% of the time. The standard deviation for the data in Fig. 28 is 3.44%. During the cloudy or partially overcast days, the effectiveness of the electrolyzer was intermittent because it worked in a transient state. These conditions occurred during daylight hours and caused periods of low work. During clear sky days, the electrolyzer worked continuously and the production of hydrogen was affected by the intensity of the solar radiation. Fig. 29 shows that the measured power required increased with the increase in the hydrogen flow rate. The measured power required showed a linear relationship with the hydrogen gas flow rate with a coefficient of determination (R2) of 0.973, and fit these data as a second-degree polynomial as follows:
Pr =
0.0145Q H2 2 + 0.3886Q H2 + 0.2082
equivalent to the electrical current in the circuit. The overall hydrogen production rate Q H2 (Nm3 h−1) in the electrolyzer is based on Nc cells connected in a series. For an ideal gas molar volume of 22.414 × 10 3 m3 mol 1 and a standard temperature of 273 K at pressure of 105 Nm−2 [57,58], the Faradic efficiency F , can be calculated as follows:
Q H2 = 80.69
F
Nc Iel = 80.69 n×F
F
Nc Pr U×n×F
(70)
The power Pr required by the electrolyzer is given as [59]:
Pr = Uc Nc Iel = UIel
(71)
where Pr is the dissipated power required, Iel is the electric current, Uc is the potential difference between the cathode and the anode [59], and U is the voltage supplied to the electrolyzer. The Faradic efficiency is defined as the ratio between the effective and theoretical maximum amount of hydrogen produced in the electrolyzer system; it is a very good way to assess the electrolysis system. The increase in temperature causes a lower Faradic efficiency due to the lowered resistance and increased in parasitic current. The thermal efficiency or energy efficiency T is an expression commonly used to describe the electrolysis system and can be calculated as follows [57]:
(69)
According to Faraday’s law, the hydrogen production rate is directly proportional to the electron transfer rate at the electrodes and
T
117
=
Ho H
(72)
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100 99
Usage efficiency (%)
98 97 96 95 94 93 92 91 90 8
10
12
14
16
18
Time (hour) Fig. 27. Change in usage efficiency as a function of time.
18
Acttual time/ total time (%)
16 14 12 10 8 6 4 2 0
0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 28. The percentage of time that the electrolyzer worked as a function of the different flow rates of the hydrogen gas produced.
3
Required power (kW)
2.5 2 1.5 1 0.5 0 0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 29. The measured power required by the electrolyzer as a function of flow rates of the hydrogen gas produced.
This is defined as the ratio of the enthalpy change based on the thermoneutral potential Utno and the actual potential Uc. In another words, it is calculated as the ratio between the specific energy
consumption (with respect to HHV) and the actual specific energy consumption (MJ·N·m−3). Therefore, for a thermal efficiency of 100%, the electrolyzer would consume 10.58 MJ for each Nm−3 of hydrogen 118
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1.2
Faradic efficiency
1 0.8 0.6 0.4 0.2 0 0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 30. Faradic efficiency of the electrolyzer as a function of the rate of the H2 produced.
Electrolyzer energy efficiency
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.05- 0.1 0.1- 0.15 0.15- 0.2 0.2- 0.25 0.25- 0.3 0.3- 0.35 0.35- 0.4 0.4- 0.45 0.45- 0.5
H2 Production (Nm3/h) Fig. 31. The energy efficiency of the electrolyzer versus hydrogen gas produced.
produced. At a standard pressure and temperature (105N·m−2 and 298 K, respectively), the enthalpy variation H can be evaluated based on pure hydrogen (H2), water (H2O), and oxygen (O2) as follows: H o = 286 kJ mol 1, assuming that oxygen and hydrogen represent ideal gases while water represents an incompressible fluid [21]. The Faradic efficiency F can be calculated from equation (70) and is shown in Fig. 30. The predicted result occurs due to the manner in which the electrolyzer works, as it needs to continuously adjust itself to changes in operating conditions without reaching a steady–state requirement. An analysis of Fig. 30 shows that the Faradic efficiency was higher than 90% when the hydrogen production rate was greater than 0.4 Nm3 h−1 and the power required by the electrolyzer was close to the power rating of 2.5 kW, under the operating conditions shown in Fig. 29. The T of the electrolyzer under experimental conditions was evaluated using Eq. (72) and is shown in Fig. 31. The model of this equation is rough because the H o is evaluated at a standard pressure and temperature and under the assumption that hydrogen is an ideal gas and water is an incompressible fluid. Eq. (72) allows the estimation of the performance of the electrolyzer; the T value of the electrolyzer increased 45% (from 0.46 to 0.67) at a hydrogen flow rate ranging from 0.05 to 0.5 Nm3 h−1. A literature review shows that similar results were obtained when testing hybrid systems that include electrolyzers and PV panel combinations [60]. The average energy efficiency of 5 kW alkaline electrolyzer set up in Zollbruck, Switzerland, inside a domestic system, was
62% after evaluation for three summer days. In clear sky conditions in the morning, cloud cover in the afternoon caused strong variations in the current and thus in the electrolyzer performance [61]. In California, USA, a 9.2 kW PV medium pressure bipolar alkaline PEM electrolyzer hybrid system was built and tested for eleven months. The electrolyzer efficiency was high, at 75%, for more than 70% of the daily averages. The results of a single day of operations showed an average Faraday efficiency of 96% [54]. The test results for the hybrid system providing thermal power and electric energy to the different units showed that when the electrolyzer cycled on and off, the cell electrode catalyst could be degraded. Therefore, an advanced battery should be used to minimize electrolyzer cycling and provide short-term energy storage [62]. Zini and Tartarini [61] discussed and analyzed different case studies and reported that since the electrolyzer was switched on and off frequently if the input current was highly variable, some back-up systems should be considered to stabilize the electrolyzer input power and increase the overall performance of the system. Furthermore, the results acquired showed that the efficiency of the electrolyzer was low because of the irregular solar energy supply, and that this problem did not allow the hydrogen produced to be stored suitably inside the tanks. It is necessary to avoid shutdowns of H2 production as these require the system to have significant idle time before restarting. Little et al. [63] showed that when the electrolyzer is switched off, the hydrogen in the cathode reverses the potential of the cell stack, generating corrosion in the cell 119
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Fig. 32. The modified integrated power system. The battery bank is connected to: (a) the electrolyzer; (b) the fuel cell.
answered storage technology in a stand-alone PV system is that of lead acid. The latter is treated in various articles published in the literature [69–71] the trade-off between the benefits of availability, reliability and cost. This model is based on an electrical diagram. It defines the voltage across the battery according to some parameters such as the imposed current, its state of charge and its temperature. It takes into account the faradic efficiency in charge to calculate the evolution of its state of charge, while integrating the phase of degassing (hydrogen evolution) which is a phenomenon peculiar to lead batteries, causing a significant increase of the voltage in end of charge [72]. The phenomena of self-discharge and aging have not been taken into account. In this model, for nb cells in series, the voltage across the battery is given below:
membranes and reducing the lifetime of the electrolyzer, even if a minimum current is also imposed to maintain the purity of the hydrogen gas. These constraints in the operation of the electrolyzer require some form of short-term energy storage to reduce the short-term fluctuations in electric input. A battery bank can supply 1200 Ah and could be charged using the PV modules or the fuel cell, as shown in Fig. 32. The energy from the PV cells are affected by the intensity of the solar radiation and should be accumulated using the battery bank; therefore, there will be a continuous feed of current to the electrolyzer. Using the connections shown in Fig. 32a, the current from the AC/DC rectifier, affected by change in the PV panel performance, feeds the battery bank which in turn can continuously power the electrolyzer. In this way, the system would operate correctly and a suitable quantity of hydrogen can be produced and stored in the tanks. By employing the arrangement shown in Fig. 32b, a constant current produced by the fuel cells is stored inside the battery bank. This new layout using the battery bank will be adopted in future tests and the performance of the integrated power system will be evaluated. This proposed solution stems from the results of simulations of the electrolyzer on/off cycle and fuel cells in an integrated power system that employed a battery as a short-term energy buffer [64].
Vbat = nb × Eb ± nb × Rbat × Ibat
(73)
where Vbat and Ibat are the voltage and current of the battery (according to the receptor convention), Eb is the emf (electromotive force) of a cell of the battery and Rbat its internal resistance. The description of the behavior of the battery according to the CIEMAT model, requires three equations corresponding to the three modes of operation: the discharge regime, the charging regime and the battery overload regime. All of these equations take into account the standardized expression of the battery capacity Cbat . The SOC state of charge of the battery is a function of the residual charge and the charging or discharging regime.
5. Simulation of hybrid system The investigation of hybrid system is designed and manufacturing for generating, storing and supplying electric power to local loads. The hybrid system is simulated to predict and evaluate its performance before implementation and is often installed in remote and rural areas. Therefore, in the design process it’s important to improve the system configuration, sizes of components and control settings. The design via simulation methods allows studying the different options, considering various influencing variables and effectively fulfils the system/user requirements. Mathematical models of the system components are associated to form a general representation of the system, through a central controller unit that defines the best way in which components interact to simulate the operation of the system. In this section, a hybrid system will be simulated and the components of the system have been modelled and validated with the previous work. The comparison between the different topologies of the system such as DC and AC coupled, with different PCU types at two different locations on the basis of the energy point of view is studied.
• Modelling capacity C
bat
The model of the capacity Cbat gives the quantity of energy that can restore the battery according to the average current of discharge Ibat . This capacity is given by:
Cbat =
1.67C10 1 + 0.67 ×
( )
Ibat 0.9 I10
(1 + 0.005 × T ) (74)
With:
I10 : Nominal battery current (in A) given by the manufacturer; C10 : Nominal capacity of the battery (in Ah) in a constant current discharge regime for 10 h. It is given by the manufacturer and it is such that: Cnom = C10 = 10 × I10
5.1. Modelling the battery storage system
(75)
T : The heating of the battery compared to the ambient temperature of 25 °C. It is assumed to be identical for all elements of the
The storage of energy for an autonomous photovoltaic system has been the subject of several publications [65–68]. Currently, the most 120
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battery. The state of charge of the battery SOC is a function of the capacity Cbat and the amount of charge missing from the battery Qd .
Rb
(76)
Qd Cbat
Vbat
(77)
Qt
1
+
charge
× Qech (t )
Qt
1
+
discharge
g
(79)
=1
exp
(80)
20.73 Ibat I10
+ 0.55
(EDC
= 1.965 + 0.12SOC
Rb
discharge
= Rbat =
(81)
0.007 T ) (83)
= nb × Eb
Vbat
discharge
= nb × (2.085 + 0.12(1
discharge
nb × Rb
discharge
× |Ibat |
tg g
(89)
1 + 852 ×
( )
Ibat 1.67 C10
(90)
Ibat × (1 C10
Ibat × (1 C10
0.002 × T )
0.002 × T )
(91) (92)
In the electrolyser and the fuel cell, the same electrochemical reactions take place. The electrical model of these components is identical. The electric model to describe the polarization curve (characteristic in current-voltage of the fuel cell) was chosen, is the model of Kim (J. Kim et al., 1995). This model is semi-empirical, that is, based on theoretical equations but using parameters to fit the model to the experimental data obtained from literature survey.
Hence the expression of the battery voltage, for this discharge regime: discharge
t
• Electric model
(82)
Vbat
exp
Several models are needed to correctly simulate the behavior of the fuel cell. The electrical model calculates the operating point as a function of the requested current, the temperature and the pressure of the gases while the thermal model makes it possible to calculate the evolution of the temperature in the component.
1)
1 4 0.27 + + 0.02 (1 C10 1 + |Ibat |0.3 EDC1.5
Vg ) 1
5.2. Modelling of the fuel cell
In discharge regime, the emf and the internal resistance are determined by the following: discharge
(88)
× Ibat
The different mathematical formulations presented above, allowed us to develop, under the Matlab-Simulink environment, the model of the CIEMAT battery.
• Modelling the discharge of the battery Eb
charge
1.73
Vec = 2.45 + 2.011 × ln 1 +
The Faradic efficiency under load depends on the charge rate, it has a value close to 100% for low load currents and a low state of charge. Then, it gets worse as we approach full load. charge is given by the following relation: charge
nb × Rb
= nb × Vg + nb × (Vec
Vg = 2.24 + 1.97 × ln 1 +
For the CIEMAT model, the Faradic efficiency is taken into account in the case of the load and is assumed equal to 1 in the discharge regime.
= 1(10)
charge
The gassing voltage Vg and the ending charge voltages Vec have the following expression:
• Faradic yield modeling
discharge
overcharge
=
t 0
= nb × Eb
With: tg the moment the “gassing” begins. Thus (t-tg) is the duration during which the gassing takes place. The time constant g is expressed as follows:
(78)
Ibat (t ) dt
charge
Vbat
where the amount of charge exchanged Qech is:
Qech (t ) =
(87)
For this overcharge regime, the expression of the battery voltage is then given by the equation:
if Ibat > 0
× Qech (t ) if Ibat < 0
0.48 + 0.036 (1 EDC )1.2
• Modelling of the battery overcharge
The quantity of charge Qbat at a time t, is obtained as a function of the value of the current Ibat, the Faradic efficiencies ( charge & discharge ) and the state of charge SOC calculated at the previous instant Qt 1 , according to:
Qbat =
1 6 + C10 1 + (Ibat )0.86 (1
Hence the expression of the voltage of the battery before the overload:
where t is the operating time of the battery with a current Ibat . The expression of the state of charge of the battery EDC is given by:
EDC = 1
= Rcharge =
0.025 T )
The time evolution of the latter, depends on the operating mode of the battery, it is defined by:
Qd = Ibat × t
charge
• Voltage
(84)
Ibat C10 (85)
The actual voltage is strictly less than the electromotive force E because of the different voltage drops that occur in any electrochemical generator. It decreases with the current flow. The curve of the voltage V across the terminals of an element is usually plotted as a function of the current density J (see Fig. 33).
In the charging regime and before the appearance of the phenomenon of “Gassing” (gaseous release of hydrogen and oxygen), the emf and the internal resistance are determined by:
where VRP : Tension of an elementary cell of the released power (RP) (V); JRP : current density of an elementary cell of the RP (A·cm−2). Origins of the voltage drop
× (1
0.007 T )
EDC ))
nb ×
• Modelling the battery charge
Eb
charge
= 2 + 0.16EDC
•
(86) 121
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1
VRP (volt)
0.95
0.9
0.85
0.8
0.75
0
0.2
0.4
0.6
0.8
1
1.2
1.4
JRP (A.cm-2) Fig. 33. Curve of the voltage across a fuel cell element as a function of the current density.
As for any electrochemical generator, the voltage drop results essentially from three phenomena is distinguish as follows:
diffusion zone. By cons, it is not usable for a low current density, lower than the exchange current density Jo of the electrode, because of the J term – Aln RP . b
( )
• the activation voltage drop ΔV act; • the resistive voltage drop ΔV ohm; • the concentration voltage drop ΔV conc
• Effect of operating conditions The pressure and the temperature act on both the electromotive force and the voltage drop.
The voltage across an element can be written as:
VRP = ERP
Vact
Vohm
Vconc
(93)
(a) Influence of pressure
With
ERP = ET° +
Vact = Aln
RT ln(PH2 PO1/2 2 ) 2F
(94)
J b
(95)
An increase in pressure causes an increase in the electromotive force. This effect is increased on the voltage because the voltage drop decreases at high pressure. However, the use of the compressor to increase the pressure, it leads to a significant consumption of power. To evaluate the interest of working at high pressure, it is therefore necessary to compare the increase in power due to the increase in voltage with the power loss due to compressor consumption.
(96)
A = Aa + Ac
Coefficients of the Tafel equation at the anode and at the cathode (V);
Vohm = rJ
(97)
(b) Influence of temperature
Vconc = mexp(n × J )
(98)
The increase in temperature leads to a decrease in the electromotive force. This negative effect is counterbalanced by a reduction in voltage drops. Increasing the ionic conductivity of the electrolyte results in a decrease in the resistive voltage drop. On the other hand, a high temperature increases the reaction rate, which reduces the activation voltage drop.
which gives;
VRP = ERP Aa
Aln Ac
bRP = JoaA × JocA
JRP bRP
rRP JRP
mexp(n × J )
(99)
Exchange currents at the anode and at the
cathode (A·cm
2
• Power
(100)
The electric power PRP supplied by a fuel cell formed of N series elements is:
rRP : Specific surface resistance of the membrane (ῼ·cm−2); m (V) and n (cm2/A): Empirical coefficients (parameters related to diffusion); R: constants r of perfect gases; F: number of faradays (96,485 C·mol−1); T: Temperature (K). NB: For a PEMFC fuel cell, RT A = 2F , where is the load transfer coefficient (0 1).
PRP = NCRP VRP IRP = NCRP VRP JRP S ARP
(101)
PRP : Total power supplied by the fuel cell (W) S ARP : Active surface of an elementary cell of the fuel cell (cm2) NCRP : Number of elementary cells in series of the fuel cell (–) IRP : Intensity of the current of a cell of the fuel cell (A). In order for the fuel cell to operate, part of the electrical power released by it must be sent to its auxiliaries (devices that provide cooling of the fuel cell and supply of reagents to the battery and
The parameters of Eq. (98) depend on the temperature, the pressure and the oxygen partial pressure. This model makes it possible to represent all the parts of a polarization curve of a stack, up to the 122
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different sensors and solenoid valves). This power is expressed by the following equation:
PauxRP = CCauxRP + CVauxRP PRP
and the intrinsic power consumption of the system. The present approach method is inspired by the control of the Ulleberg facility [73], an energy management algorithm has been developed for the studied system. The energy balances are always carried out at the common bus connection of the various energy components of the system. The priority is the supply of the energy demanded by the user from the energy produced by the photovoltaic field. There are two scenarios:
(102)
PauxRP : Power consumed by the auxiliaries of the RP (W); CCauxRP : Constant consumption of auxiliaries of the RP (W); CVauxRP : Variable consumption of the auxiliaries of the RP, depending on the power supplied by it (%).
1. If the power demanded by the load is less than the available solar power, then two sub-cases are presented: a. Either the operating conditions allow the storage of this surplus; b. Either the surplus cannot be stored (consumed neither by the battery nor by the electrolyser) or this causes the increase of the solar field voltage, thus reducing the intensity and the power delivered by the renewable generator. 2. If the power demanded by the load is greater than the available solar power then the additional energy must be provided by the storage. In this case, the solicitation of the storage is then constrained to respect the operating parameters of the components. The actual powers of each component are calculated (see Fig. 35).
As the efficiency of a fuel cell is not perfect, the gases consumed (hydrogen and oxygen) are not entirely converted into electrical power but also into thermal power. This can be defined by the following relation:
PthRP = NCRP (Vth
VRP ) JRP S ARP
(103)
PthRP : Thermal power released by the fuel cell (W); Vth : Thermoneutral voltage of an elementary cell (=1.48 V). 5.3. Energy management and conversion within the system In real systems, the energy produced and consumed by the various components during their operation is usually managed by a central component, to which the devices are connected via various converters. Energy management algorithms are implemented to ensure the autonomy of the system.
' PPV = PPV ×
PV
' PRP
RP
= PRP ×
' PBatt =
PBatt Batt
i. Hybrid system architecture
' PEL =
PEL EL
In any electrical system, the various devices that compose it are generally connected to a network. The type of network (continuous or alternate) depends on its size and the chosen application. In the case of the small isolated system, the DC network or continuous bus architecture can be used. All components are connected as shown in the following figure. Losses in the network are limited because of its size. Moreover, this type of architecture makes it possible to limit the losses due to the inverters, the presence of which is inevitable in the case of the AC-AC network. Here, only the user is connected to the bus via an inverter. The storage components and the PV field are connected to the bus via DC-DC converters which perform better than an inverter (see next paragraph). The bus voltage is maintained by the battery pack, connected in parallel with the DC bus (see Fig. 34).
' Pcharge =
Pcharge charge
• Converters Electronic power converters are used to control the flow of electrical power between an electrical source and a well (usually the load) so that the destination is supplied with the proper current, voltage and/or frequency. This is done with as little power loss as possible occurring on the way or with the greatest possible conversion efficiency. The converters generate energy losses in the system, which translates into a conversion efficiency of less than 1.
ii. Energy Management Algorithm (PMU)
Case#1
The model of the PMU makes it possible to define the powers of the electrolyser, of the fuel cell and of the battery, according to the power delivered by the PV and that demanded by the load. The load to be delivered by the system is the sum of the power demanded by the user
In DC-DC coupling, the PV generator must be designed to cover the DC operating voltage range of the cell. These converters obviously lead to losses of energy in the system, which however remain generally low, the yields generally being between 0.95 and 0.99 [74]. The following values are proposed for the 10% and 100% of Pnom: η10 = 0.92 and η100 = 0.98 ⇒ η0 = 8.58 × 10−3 et m = 11.83 × 10−3. The following figure illustrates the variation in the efficiency of a DC-DC converter as a function of its normalized output power. Case#2 Since the load is supplied with AC power, an inverter is present between the DC bus and the load. Various equations exist to define the efficiency of an inverter as a function of the power delivered [75,76]. The same formula of Macagnan presented previously is used. For the inverter, the values of the 10% and 100% yields of Pnom are: η10 = 0.85 and η100 = 0.96 ⇒ η0 = 17.40 × 10−3 and m = 24.26 × 10−3. This model has the advantage of being simple and faithfully representing the energy losses of a converter. It has been validated in the thesis of Abu El-Maaty (2005) [75].
Fig. 34. diagram of the connection of energy sources and consumers in the PMU: case of the PV-SEH-BATT system. 123
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Fig. 35. PMU diagram: Calculation of the powers of each component on the bus.
5.4. Operation and parameters of the PV-FC system
the fuel cell. It does not correspond to the storage volume because it takes into account the daily consumption of hydrogen. When one increases the intrinsic consumption or the loss in the converters, one directly penalizes the load. In fact, the energy that comes from the PV and the battery does not vary. The storage volume and the quantity of hydrogen produced during the year do not change. The storage volume depends only on the annual profile of the load and the raw energy, i.e. the energy supplied by the PVs and by the fuel cell (dashes). The energy supplied directly by the PV to the load (PV Direct) depends on the load profile. By favoring the direct supply, the gross energy is greatly increased, on the other hand, the daily consumption of hydrogen is reduced. The storage volume increases because the raw energy is more important. When modifying the performance of the electrochemical components, the raw energy is more important. But since the modification of the cells does not lead to a large increase in their average yield, the gross energy is only slightly higher: the storage volume and the daily consumption of hydrogen are therefore slightly greater.
Fig. 36 is a simplified diagram to describe the annual operation of the PV-FC system. The operation of the system and the influence of its parameters described below, come from the analysis of all the simulations carried out. Annual photovoltaic (PV) energy is the total energy that enters the system. Some of this energy is supplied directly to the load (PV Direct). The second part passes through the hydrogen storage system and is reduced by losses in electrochemical cells related to energy and faradic efficiency. The sum of these two energies is further reduced by the loss in the converters and by the loss due to the intrinsic consumption. The efficiency of the system depends on all of these losses. The storage volume (ST H2) is dimensioned so that the energy stored during the favourable months is equal to the energy consumed during the unfavourable months. The white arrow corresponds to the quantity of hydrogen produced by the electrolyser during the year, which is equal to that consumed by
Fig. 36. Operating diagram of the PV-FC system. 124
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EC
IC
Conv
2%
2%
90%
8%
26%
80%
33%
100%
70%
Charge
Battery
16%
60% 50%
18%
18%
38%
38%
40% 30% 20% 10% 0% Pond = 8 kW
Pond = Pcharge
Fig. 37. Distribution of photovoltaic energy during one year of operation of the test bench (Scenario no. 1) - Constant load - Adaptation of the nominal power of the inverter.
• Performance of the test bench
also occurs during sunny days. The energy stored in the battery throughout the year represents 2% of photovoltaic energy or 114 kWh electric per year. The energy available for charging the battery is therefore an average of 313 Wh per day. We do not know for the moment what will be the daily discharge of the battery, used for the help with the PMU transient response. It is possible that this discharge is weak. However, if the battery is at its maximum state of charge, the excess solar energy will not be consumed by the system. The energy stored in the battery therefore represents the maximum loss of solar potential: the use of photovoltaic energy of the PVFC system is equal to or greater than 98%. For these two systems, the required storage volume is 23 m3 of hydrogen and 11.5 m3 of oxygen (storage at 10 bar). This volume represents only 26% of the energy that passes through storage. The consumption of pure water required for autonomy is equal to 43 kg per year. It depends on the amount of hydrogen produced during the year and the faradic efficiency of the electrolyser. It is therefore not a function of the nominal power of the inverter.
Fig. 37 shows the distribution of photovoltaic energy in the load and the different losses of the test stand. The load is a constant power demand. The two studied systems differ in the nominal power of the inverter. The test bench is equipped with an inverter of 8 kW to allow the complete evaluation of its performances. The efficiency of the installation (Charge) is 8%. The loss in the electrochemical components (EC) is the largest (38%). The loss in the converters is also very high (33%). The loss due to intrinsic consumption during a year of operation represents 19% of photovoltaic energy. In an autonomous system, the nominal power of the inverter is adapted to the maximum power demanded by the user. The performance of the test bench equipped with a suitable inverter load, is greatly increased by reducing the loss in the converters. It reaches 26%, a constant load of 168 W. The other losses of the system are not changed. The loss of the system, called “Batt”, is a potential loss related to the use of the safety battery. As known, the battery is mainly charged when the solar excess is lower than the minimum power of the electrolyser. This situation usually occurs twice a day at sunrise and sunset. It
• Modification of the hydrogen storage system Fig. 38 shows the influence of the optimization of the hydrogen
140% 120%
EC
19%
100% 80% 60% 40% 20%
26%
IC
Conv
Charge
14%
2%
41%
47%
Battery
15% 19%
15% 4%
38%
38%
35%
scenario 1
scenario 2
scenario 3
14% 2%
0% Fig. 38. Influence of the scenario on the distribution of photovoltaic energy during a year of operation of the PV-FC system. 125
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where oxygen is not used, the consumption of pure water is important (97 kg/year). It thus appears that the faradic efficiency of the electrolyser has a greater influence than the oxygen partial pressure of the cell. A system that does not use the oxygen produced by the electrolyser is therefore efficient but its autonomy is limited by a large consumption of pure water.
Table 5 Influence of faradic efficiency of the electrolyser and the oxygen partial pressure of the cell on the performance of the test bench and its water consumption. Yes
Yes
No
Faradic yield (EL)% Partial oxygen pressure (FC) bar Efficiency of the PV-FC system% Pure water consumption kg/year
93 1.5 25.7 43
99 0.6 27.6 97
99 1.5 28 0
• Thermal production In all previous tests, the system does not produce heat. The thermal losses of the electrochemical components allow only the raising of their operating temperature. For the electrolyser, the maximum temperature reached is 65 °C, lower than the maximum temperature (72 °C). A heat exchanger is not necessary for this component. It also implies that no cogeneration is possible. For the fuel cell, the module selected for the test bench has a large thermal capacity (45 kJ·K−1 or about 1 kJ·kg−1·K−1). The new battery generations have much higher power densities (multiplied by 5), which leads to a decrease in their thermal capacity. A current module of 4 kW must therefore have a thermal capacity 5 times smaller than that of the test bench. Simulations were performed by modifying the thermal capacity of the fuel cell. The results show that the decrease of the heat capacity makes it possible to increase the production of heat of the system but this becomes important only if the coefficient of exchange with the outside is decreased. This is achievable for the battery thermal insulation device system. When the coefficient is decreased by a factor of 15 or 3.2 W·K−1 instead of 48 W·K−1, the annual heat output of the test bench is 350 kWh. The efficiency of the system increases by 6% thanks to the thermal production. The different charges are described previously. They are differentiated by their daily, seasonal profile and by their correlation with sunshine, characterized by the PLM (PV- Load Meet) criterion. Fig. 39 shows the evolution of system performance and storage volume versus PLM. The name of the profile is specified in the figure. The modelled system is the modified test stand at the fuel cell cells to increase heat output. The nominal power of the inverter is equal to the maximum power demanded by the load. The efficiency of the system increases when the profile of the load is in phase with the sunshine because the power of the user is mainly delivered by the solar field. The direct supply of photovoltaic energy to the load is high efficiency (85%). When the energy is converted to gas before being returned to the load, the efficiency is much lower (33%). The volume of hydrogen increases with the PLM because the raw energy is more important. It is much more important for the profile having an annual variation of the load (St Pierre). In this figure, a variable load
storage system on the different losses during a year of operation. The load is a constant demand for power. The inverter is adapted to the power delivered by the system. With regard to the intrinsic consumption (IC), there is a 15% decrease in the loss between the scenario no. 1 and no. 2, which is to say thanks to the reduction of the intrinsic consumption of the solenoid valves. The loss in the converters is also slightly reduced because the energy converted to power the peripherals is decreased. When, in addition, the fuel cell recirculation engine is eliminated (scenario no. 3), the loss is further reduced to 2%. For scenario # 3, the faradic efficiency of the electrolyser is increased by the on-line measurement of the purity of oxygen. In addition, the fuel cell is supplied with pure oxygen. These two modifications lead to an increase in the average efficiency of the electrochemical cells from 47.2% to 50.1%. This increase is related to the efficiency of the electrolyser (increase from 77% to 82%). The average cell yield is slightly decreased (from 61% to 60.8%), although the oxygen partial pressure is higher. This stems from the fact that the power delivered by the battery is greater in the case of scenario # 3. The improved performance of the electrochemical cells increases the overall efficiency of the system by 3%. The volume of hydrogen is a little larger (+0.6 m3 compared to Scenario # 1 and # 2). Table 5 makes it possible to compare the performance of the test bench in three cases differing in the faradic efficiency of the electrolyser and the partial pressure of oxygen. The inverter of the system is adapted to the power of the load. The results of the test bench (Scenario # 1) are in the first column. The second system is the test bench in the case where the oxygen is not stored. In the last column, the test bench is equipped with an electrolyser of faradic efficiency of 99%. By comparing the first and the third column, it is observed that the improvement of the faradic efficiency of the electrolyser makes it possible to increase the yield of the PV-FC system by 2.3% and especially to reduce to zero the consumption of pure water. . Between the second and third columns, the increase in oxygen partial pressure improves the overall efficiency of the installation by 0.4%. In the case 50.00%
22%
System performance (%)
45.00%
22%
40.00%
22%
35.00% 30.00%
22%
25.00% 21%
20.00% 15.00%
21%
10.00%
21%
5.00% 0.00%
21% 0%
10%
20%
30%
40%
50%
60%
70%
PLM (PV- Load Meet) % Fig. 39. Influence of PLM on System Efficiency and Volume of Hydrogen Required - Scenario # 1.
126
hydrogen storage volume (10 bar) m3
Use of product oxygen
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45.00% 40.00%
loss in the system (%)
35.00% 30.00% 25.00%
EC
20.00%
IC
15.00%
Conv
10.00%
Ba
y
5.00% 0.00% 0%
10%
20%
30%
40%
50%
60%
PLM (PV- Load Meet) % Fig. 40. Influence of PLM on Annual Loss in Electrochemical Components (EC) and in Converters – Scenario # 1 - Rated Power for the Load. Table 6 Average power demand relative to the nominal power of the inverter, average and theoretical efficiency of the inverter – Scenario # 1 – Rated power equal to the maximum power of the load. Profile type
Paverage
Constant Variable Cosine Constant with annual variation
100% 11% 50% 55%
power / Pnominal power
Average efficiency of the inverter
Theoretical efficiency of the inverter
95% 79% 86% 94%
95% 85% 94% 94%
The current system does not produce heat due to the low power density of the fuel cell cells of the test stand. The use of cells with current performance, would increase the efficiency of the system by 6% through the production of thermal energy. The alkaline electrolyser because of its high energy efficiency, does not allow the generation of heat. A membrane electrolyser with lower energy performance may be a better candidate for cogeneration. The operating times of the electrochemical components are evaluated at 2400 h per year for the electrolyser and at 5800 h per year for the fuel cell. The life of the electrolyzers is very important, perfectly adapted to the application. However, the life of fuel cells is currently very low. To homogenize the lifetimes of all the main components of the PV-FC system, the life of the fuel cell should reach 145,000 h (25 years). Due to the limited life of the fuel cell and the current efficiency of the storage system, battery disposal is currently not an option.
profile (PLM = 33%) results in a different performance of the complete system. Fig. 40 shows the influence of PLM on different system losses. Increasing PLM results in lower losses in electrochemical components because less energy is converted to hydrogen. The loss due to intrinsic consumption and the amount of energy delivered to the battery are not influenced by the charge profile. The loss in the converters varies between 14% and 19% depending on the load profile. For the variable load profile, the lower efficiency of the system is due to the greater loss in the electrical conversion equipment. In fact, as this profile has a peak power, the inverter needed for this profile has a large power rating. During the day, the average power consumed by the load is equal to 11% of the nominal power of the inverter. Table 6 shows the average power consumed by the user and the average and theoretical efficiencies of the inverter as a function of the load profile. For constant profiles, the value of the average efficiency of the inverter corresponds to its theoretical value. On the other hand, for the other two profiles, the average yield is lower than the theoretical yield. For these last two profiles, the requested power has a very important amplitude (from 0% to 100% for the cosine type profiles). Therefore, the average efficiency of the inverter depends on the average power demanded but also on the load amplitude. The current efficiency of the installation is between 21% and 30% depending on the load profile, if the inverter is perfectly sized for consumption. The improvement of the hydrogen storage system would increase the operating efficiency of the installation by 21%, or reach 47%. Reducing intrinsic device consumption would improve performance by 17%. The modification of the oxygen purity measurement system would increase the efficiency by 2.3% but especially reduce to zero the consumption of pure water. The influence of the oxygen partial pressure of the fuel cell is low, but the elimination of the oxygen storage induces a large consumption of pure water of the PV-FC system.
6. Conclusion The present work concerns the study of the hydrogen produced from a direct coupling of a PV generator and a PEM type electrolyzer. The polymer membrane electrolyzer is considered by many to be a future technology because it can benefit from many developments on PEM fuel cells, as well as the associated cost savings, and this technology is still little in global hydrogen production. This justifies the pursuit of research, and the overall objective of this work is to study a PV system to produce the maximum amount of hydrogen by water electrolysis. The production of electrical energy is ensured by the PV panels and with the use of climatic data from Suez city, Egypt. This work models the constituents of the solar hydrogen production system, such as the PVG, the electrolyzer, and a directly coupled PV-electrolyzer, and simulates the different solar radiation intensities and temperatures as well as the different combinations of electrolyzer cells. To study the performance of the module, the global solar radiation was varied with a fixed 127
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temperature (T = 25 °C). The results obtained from the model showed that the I-V characteristic depends on solar radiation. The current delivered by the PVG and the increase in voltage with solar radiation, and consequently the power produced by the PVG, is increased. The second parameter that has a direct influence on the I-V characteristic of the PVG is temperature. The increase in temperature increases the current and decreases the voltage, although the short circuit current varies little with the temperature while the no-load voltage is influenced much more. The temperature therefore has a significant influence on the power of the PVG, where a decrease in power is noticeable when the temperature increases. These results make it possible to see, in the first instance of direct coupling between the PVG and the electrolyzer of a single cell, that the volume of hydrogen produced is very low and is a mismatch between the PVG and the electrolyzer. Therefore, to increase the volume of hydrogen produced and improve the degree of adaptation between the elements of the system, a new dimension for the electrolyzer by changing the number of the electrolyzer cells used was simulated. The results obtained show considerable approximation between the points of maximum power of the PVG and the system operating points, and a significant improvement in system performance that signifies an increase in the volume of hydrogen produced by the system. To put this in perspective, we consider that a study of complete system of electric power production because the modelling tool we developed allows the simulation of directly coupled PVG-Electrolyzers. This tool could be developed to simulate the complete operation of a PVG-Electrolyzer and fuel cell system. The modelling of the system has given the use of empirical and semi-empirical equations, some results of previous work, the software Matlab®-Simulink R2012a and some data of the manufacturer such as the curve of polarization, the surface of an elementary cell, the coefficient related to the operating threshold, the consumption parameters of the auxiliaries and the stoichiometry's of the gases. All these allowed us to build under Matlab® Simulink, the block photovoltaic panels (PV), the battery pack, the fuel cell block, the block electrolyser and all the curves representing the different powers produced or consumed and the different gases products or consumed.
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