- Email: [email protected]
proton-exchange membrane electrolyser system
international journal of hydrogen energy 34 (2009) 6589–6595
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
An experimental and modelling study of a photovoltaic/ proton-exchange membrane electrolyser system Ozcan Atlam* _ Kocaeli University, Technical Education Faculty, Electrical Department, Umuttepe 41380, Izmit, Kocaeli, Turkey
article info
abstract
Article history:
An experimental model of a photovoltaic (PV) module-proton exchange membrane (PEM)
Received 13 August 2008
electrolyser system has been built. A model has been developed for each device separately
Received in revised form
based on the experimental results. Output current–voltage (I–V) characteristics of the PV
16 February 2009
module are modelled in respect to different irradiance and temperature conditions by
Accepted 29 May 2009
experimental tests. Similarly, input I–V characteristic and hydrogen formation character-
Available online 2 July 2009
istic of the PEM electrolyser are measured and modelled. After these studies, combined PV module–PEM electrolyser system model is defined. There is a good agreement between
Keywords:
model predictions and measurements. At 18–100% irradiance interval, operating points of
Photovoltaic
PEM electrolyser on the PV module are predicted with relative errors of 0.1–0.8%.
Hydrogen
Furthermore, the study shows that these simple model system devices can easily be
PEM electrolyser
defined in MATLAB/Simulink and used to model similar systems of different size. ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Recently, the problems such as global warming, greenhouse effect, and global and regional pollution, have caused increased interest in renewable energy systems (solar, wind, etc.). Hydrogen, which is a versatile and clean energy carrier, can be produced from electrical energy in these renewable energy systems using water electrolysis. Electrolyser is a device that is used to produce hydrogen from water via electrolysis. In return, fuel cells convert stored hydrogen and oxygen or air to electricity directly. Hence, renewable energy and hydrogen systems are employed in an integrated form [1–5]. Additionally, polymer electrolyte membrane (or proton exchange membrane or PEM) electrolysers are becoming a new subject of research and development for solar hydrogen systems [6–9]. A PEM type device also can be used as fuel cell generator (reversible device), when stored hydrogen and oxygen (or oxygen from air) gases are applied to the device.
Modelling of such PV module–PEM electrolyser hydrogen systems is important for their planning and control strategies in practical applications. In general, reported models are complex and they use so many various specific parameters based on both theoretical and experimental data. In this paper, more simple models are developed for both PV module and PEM electrolyser based on experimental observations.
2.
Experimental setup
The experimental setup consists of a PV module, PEM electrolyser, an external adjustable dc power source (0–12 V, 20 W), thermometers, and multi-meters to measure current and voltage. The PV module can deliver current approximately 0.7 A at 2 V and under 45 C during a typical sunlight test conditions. Open circuit voltage (Voc) is about 3–3.5 V. The PEM
* Tel.: þ90 262 3032250. E-mail address: [email protected] 0360-3199/$ – see front matter ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.05.147
6590
international journal of hydrogen energy 34 (2009) 6589–6595
Nomenclature A dVt I Imax1 Isc Isc1 Isc2 k Kp KH Ns Np ns np
the PV module area, m2 the voltage coefficient per temperature variation, V/ C current, A the current at maximum power under reference irradiance, A short circuit current of PV module, A short circuit current of PV module at the highest irradiance level test, A short circuit current of PV module at the lowest irradiance level test, A the curve fitting coefficient in Isc versus Voc, V the coefficient of PV module model the power coefficient for rate of hydrogen formation, ml min1 W1 number of PV modules in series number of parallel strings of serially connected PV modules number of PEM electrolyser cells connected in series number of parallel strings of serially connected PEM electrolyser cells
P PH2 PEM PV T Tref DT V Vmax1 Voc Voc1 Voc2 DVoc vH vm Wi hH2
power, W the chemical energy of the produced hydrogen per second, W polymer electrolytic membrane photovoltaic temperature, C reference temperature, C change of temperature, C voltage, V the voltage at maximum power under reference irradiance, V open circuit voltage of PV module, V open circuit voltage of PV module at the highest irradiance level test, V open circuit voltage of PV module at the lowest irradiance level test, V change of open circuit voltage of PV module rate of hydrogen formation, ml min1 molar volume, ml mol1 the irradiance level, W m2 the overall system efficiency
electrolyser is a single cell with maximum current of 1 A at 2 V. A tungsten type lamp with 100 W incandescent bulb is used as a solar simulator. The Lutron LX-101 digital lux meter with a precision selenium photovoltaic cell is calibrated to incoming radiation of about 800 W/m2 on clear winter midday. For the indoor test, distance between the lamp and the PV module is adjusted until the rate of short circuit currents of the PV module and the rate of LX-101 device data measured under the sunlight and lamp light are approximately same. In this condition, the highest irradiance level is obtained as 460 W/m2. Also, the irradiance level of the lamp is calibrated with the book value of the short circuit current of PV where the irradiance level is determined as 460 W/m2. The irradiance level for solar system can be changed by varying distance (or angle) between the PV module and the lamp. Thermometer is used to measure PV module temperature. In order to measure hydrogen formation, oxygen and hydrogen tanks are scaled. Output I–V characteristics of PV module can be defined using a variable resistive load bank with 2–1000 ohm.
given in Fig. 1. The experimental and modelling stage involves following three tests.
3.
3.2.
Tests on the PV module and modelling
The output I–V characteristic of a PV module is non-linear and changes with irradiance and temperature T. Short circuit current (Isc) of the PV module is proportional to irradiance. The open circuit voltage (Voc) is more affected than Isc by the temperature. The Voc increases with irradiance, however, it decreases with the temperature [10,11]. The connection schema of the experiment for the PV module characteristics is
3.1. Measurements of T–Voc variations at the same irradiance (or same Isc) In this stage, the Isc is a constant value approximately. For a given constant irradiance level (or same value of Isc), the Voc values are measured at different PV module temperatures and values are noted. The resulted variation of Voc with temperature is observed as shown in Fig. 2 for Isc ¼ 0.230 A. The variation of T–Voc is linear. The slope of this characteristic yields a voltage coefficient of temperature variation dVt (V/ C). According to T–Voc test, the dVt (V/ C) is obtained approximately 0.014 V/ C as shown in Fig. 2. Hence, the change of Voc (DVoc) due to temperature change with respect to a reference temperature (Tref), can be formulated by Eq. (1). DVoc ¼ dVt$DT ¼ 0:014 T Tref
(1)
The Tref ¼ 37 C is assigned in the modelling study. The Eq. (1) is valid only for 35 C < T < 60 C.
Measurements of Isc–Voc variations at a constant T
Under a constant temperature, values of Isc and Voc are measured for different irradiance levels. To hold the temperature, T, constant, the PV module can be cooled by a fan if necessary. The variation of Isc–Voc is a logarithmic function as shown in Fig. 3. The temperature T is 37 C. This characteristic can be modelled by the following expressions for the sample PV module.
international journal of hydrogen energy 34 (2009) 6589–6595
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Fig. 1 – The experiment schema for PV module characteristics.
3.3. Measurements of I–V characteristics under different irradiance
Isc–Voc relationship is approximated by Eq. (2). Isc : Voc ðIsc Þ ¼ Voc1 þ kln Isc1
(2)
Voc1 and Isc1 are values of open circuit voltage and short circuit current, respectively, at the highest irradiance level during test. The coefficient k is another curve fitting parameter and it can be defined by Eq. (3). Voc2 Voc1 : k¼ Isc2 ln Isc1
Kp
(3)
Voc2 and Isc2 are a pair of minimal values measured at the lowest irradiance level during the test, namely: Voc1 ¼ 3.27 V, Isc1 ¼ 0.258 A, Voc2 ¼ 2.990 V and Isc2 ¼ 0.049 A. The coefficient k is then found to be 0.168. Using a curve fitting, variation of Isc– Voc at the constant Tref of 37 C is modelled by Eq. (4). Isc Voc ðIsc Þ ¼ 3:27 þ 0:168ln 0:258
(4)
The Isc–Voc curve of the model calculated by Eq. (4) is also shown in Fig. 3. When the effect of temperature on Voc is added to the Eq. (4), the term Voc can be defined as the function of both Isc and T as given by Eq. (5). Voc ðIsc ; TÞ ¼ Voc ðIsc Þ þ DVoc Isc 0:014ðT 37Þ ¼ 3:27 þ 0:168ln 0:258
Fig. 2 – T–Voc variation at Isc [ 0.230 A.
The output I–V characteristics of the PV module are measured under the different irradiance conditions. The I–V characteristic of the PV module can be modelled by Eq. (6) for given Isc and T values. In Eq. (6), the Voc is defined previously by Eq. (5).
(5)
I ¼ Isc Isc e
ðVV
Þ
1
oc
(6)
Kp is a coefficient that enables the characteristic of the model to draw near to maximum power region in the measured I–V curve under the highest irradiance level. This irradiance is taken as reference. In the reference irradiance, Isc ¼ 0.258 A, Voc ¼ 3.27 V and T ¼ 37 C. The reference irradiance corresponds to 460 W/m2. The coefficient Kp can be calculated by Eq. (7). hI I i sc1 max1 ln Isc1 Kp ¼ : Vmax1 1 Voc1
(7)
In Eq. (7), Imax1 and Vmax1 are values of current and voltage at maximum power in reference irradiance, respectively. These values are measured as Imax1 ¼ 0.234 A, Vmax1 ¼ 2.670 V under reference irradiance. For different irradiance levels (or different Isc values) and temperatures, the Kp stays at constant value in the modelling. In this study, the Kp equals to 12.943 for
Fig. 3 – Isc–Voc curves of measurement and model at T [ 37 8C.
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Fig. 4 – I–V curves of measurement and model for PV module.
the PV panel used. The second term of Eq. (6) represents the form of forwardly biased diode current at junction in PV modules. In general, this term consists of some complex and specific parameters which are related to semiconductor physics. In Eq. (6), I equals to zero when the V equals to Voc, and V equals to zero when I equals to approximately Isc. The output I–V curves are non-linear. In the modelling, Isc and T are used as input values of Eqs. (5) and (6). Fig. 4 shows the resulting I–V curves and their maximum power points (MPPs) of the PV module both measured and modelled under different irradiance levels at T ¼ 37 C as a sample. Model estimations match the measurements very closely.
Fig. 6 – Input I–V characteristics of the PEM electrolyser for measurement and model.
Input currents of the PEM electrolyser are measured at different applied voltages (0–2 V). The characteristic curve is given in Fig. 6 and it looks like a typical diode characteristic. In the characteristic curve, there is a critical voltage at which the current flow starts. The current flow section of the curve can be approximated as linear. The slope of this characteristic corresponds to the internal electrical resistivity of the PEM electrolyser system during electrolysis. According to this test, input characteristic of the PEM electrolyser may be modelled by Eq. (8). I¼
0 V 1:476 3:064ðV 1:476Þ V > 1:476
(8)
The photo of the apparatus used in PV/PEM system is given in Fig. 5. The PEM electrolyser is connected to an adjustable power source, in order to obtain its response characteristics (I–V).
Input I–V characteristic of the model based on Eq. (8) is plotted in Fig. 6. The rate of hydrogen formation (ml/min) is measured and recorded as function of input power, and the results are shown in Fig. 7. Of course, hydrogen production rate is theoretically proportional to current in accordance with the Faraday Law:
Fig. 5 – Picture of the apparatus used in PV/PEM system.
Fig. 7 – Input power versus the rate of hydrogen formation.
4.
Tests on PEM electrolyser and modelling
international journal of hydrogen energy 34 (2009) 6589–6595
Fig. 8 – PV module – PEM electrolyser system.
I 1 1 60 s min mol s1 vm ml mol 2F 1 ¼ 7:5 ml min A1
vH ¼
(9)
However, for the sake of model simplicity the hydrogen production rate may be approximated by a linear relationship to input power: vH ¼ KH P:
(10)
In the study, the coefficient KH is found to be 4.10 ml min1 W1. Even if voltage–current relationship is approximated as linear (Eq. (8)), the resulting P–vH curve cannot be linear, however, an error resulting from linear relationship seems to be negligible, as shown below.
5. Operation of the PEM electrolyser with the PV module The PV module is connected to the PEM electrolyser as shown in Fig. 8. Operating points of the PEM electrolyser are measured and also can be predicted by general system modelling for different irradiance conditions. The PEM electrolyser operates at intersection points between the output I–V curves of the PV module and the input I–V characteristic of the PEM electrolyser for a given irradiance condition. Therefore, operating points occur at the expression in Eq. (11). Ouput f ðI; VÞðPV moduleÞ ¼ Input f ðI; VÞðPEM electrolyserÞ :
(11)
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If operating points seemingly exist in linear characteristic regions of each device, the calculation would be simple. However, the output I–V characteristics of the PV module are non-linear. In order to analyse the operating points of the combined system, an iterative computing is required. This can be achieved by MATLAB/Simulink. The equality in the Eq. (11) can be provided by MATLAB/Simulink model. For generalisation, model equations of PV module and PEM electrolyser are defined in MATLAB/Simulink program for prediction analysis in this study. Fig. 9 shows the resulting MATLAB/Simulink model for PV module–PEM electrolyser system. For example, both of measured and predicted operating points are given in Fig. 10 for PV module–PEM electrolyser system under different irradiance and 37 C. Irradiance interval is taken as 18–100% in respect to the highest irradiance 460 W/m2. The characteristics in Fig. 10 agree with the characteristics given in literature [6–8]. In this study, the operating points of the system occur at constant current regions of the PV module under different irradiance levels. However, for different number of single PV– PEM electrolyser units connected in parallel and/or in series, the operating points may occur near the open circuit regions of the PV module characteristic. Fig. 10 also shows that the operating points of the electrolyser match the electrolyser input characteristic which is measured previously (in Fig. 6). By means of these operating points, the rate of hydrogen formation given in Eq. (10) can be calculated for each irradiance level. By using Eq. (12), the relative errors between the measured and model values are determined and are given in Table 1.
relative error ¼
valuemeasured valuemodel : valuemeasured
(12)
The modelling can be also adapted to the systems with different size of each PV module and PEM electrolyser. It is assumed that Ns is the number of the PV modules in series and the Np is the number of parallel strings of PV modules in series. A larger PV system can be modelled by Eq. (13). Similarly when ns is the number of the PEM electrolyser cells in series and np is the number of parallel strings of PEM electrolyser cells in series. The resulting PEM electrolyser system can be modelled by Eq. (14). In these models, the connection losses are considered to be negligible.
Fig. 9 – PV module – PEM electrolyser system in the MATLAB/Simulink.
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international journal of hydrogen energy 34 (2009) 6589–6595
Fig. 10 – Operating points of the PEM electrolyser on the PV module.
"
Kp
I ¼ Np Isc Isc e I ¼ np
ðN VV Þ #: 1
oc
(13)
0 V 1:476ns : V 3:064 ns 1:476 V > 1:476ns
(14)
s
Eqs. (13) and (14) can easily be programmed in MATLAB/ Simulink. For example, Fig. 11 shows characteristics of systems with different number of both PV modules and PEM electrolyser cells. The I–V curves of the PV systems are given for same irradiance but different temperatures (25 C and 45 C). Additionally, in Fig. 11, the values of Voc decrease with temperature. The slope (conductivity) of PEM electrolyser I–V characteristic with ns ¼ 6, np ¼ 1, is smaller than that of the single PEM electrolyser cell. Intersection points between curves represent the operating points of PV module–PEM electrolyser systems. In order to determine overall efficiency (light energy in hydrogen chemical energy out) of PV/PEM system, Eq. (15) is used in the study.
vH
ml
103
l 1 min 237; 200 J ml 60 s 22:4 l Wi mW2 Aðm2 Þ
min PH2 ¼ Wi A ml min vH min 0:176 Jml vH 0:176 0:176KH P S ¼ ¼ : ¼ Wi AðWÞ Wi A Wi A
hH2 ¼
(15)
In Eq. (15), the overall system efficiency is hH2 , the PH2 is chemical energy (lower heating value) of the hydrogen produced per second (W), the Wi is irradiance level (W/m2), the A is PV module area (m2). The A is 0.011 m2 in this study. For a given input power of the PEM and irradiance level, the term of vH is determined by Eq. (10) and then it is applied to Eq. (15). In Fig. 12, variation of overall efficiency is given under different irradiance levels. Also Fig. 12 shows the PV module maximum efficiencies and its efficiencies when connected to the PEM electrolyser. These efficiencies are calculated using the maximum power of the PV module and input power of the PEM electrolyser divided by input light power (WiA) which comes to the PV module area. According to characteristics in Fig. 12, the maximum efficiencies of the PV module were about 11–12%. Efficiencies of the PV module connected to the PEM electrolyser were about 7.5%. This difference is due to mismatch between the operating point and the maximum power point of the PV module. The PEM utilized the maximum power of PV module with an efficiency of 64–70%. This ratio of the actual efficiency and the maximum efficiency is called the utilization efficiency. The efficiency of the PEM electrolyser, defined as a ratio between the chemical energy (lower heating value) of the hydrogen produced per second (W) and electrical power fed to the electrolyser, was about 70%. The overall system efficiencies, hH2 were between 5.1 and 5.4% under different irradiances in this study. In general, the electrolyser I–V characteristics should be as close as possible to the PV module MPP trajectory, so that the PV/PEM system attains the high efficiency. In order to increase the overall system efficiency, a PV module type with high efficiency can be selected for the PEM electrolyser system as explained in [8], a controller system can be used to match the voltage and maximum power output of the PV module to operating voltage of PEM as in [7,12–14]. In these cases, maximum utilization efficiency of the PEM from the PV system are developed about 95%. In this study, none of these methods has been used since the goal of the study was not to increase the efficiency. However, the system efficiency achieved by directly coupled PV/PEM system used in this study is normal value for a non-optimized system (w70%) as stated in [12]. It is clear that, the system efficiency, hH2 , of a PV/PEM hydrogen production system is largely limited by the maximum efficiency of the PV module used. Also, the maximum power transfer between module and PEM electrolyser should be provided either by closely matching the PV and electrolyser I–V characteristics or by applying a controller as described in [7–9,12–14] to match the electrolyser and PV curves as close as possible at any irradiance and temperature.
Table 1 – Operating points and relative errors between the measurement and model. Irradiance (W/m2) 460 356 271 178 87
Vmeasured (V)
Vmodel (V)
Imeasured (A)
Imodel (A)
Relative error – V
Relative error – I
1.570 1.550 1.530 1.510 1.480
1.561 1.542 1.526 1.510 1.493
0.258 0.200 0.152 0.100 0.049
0.257 0.199 0.151 0.099 0.048
0.005 0.005 0.002 0.000 0.008
0.001 0.001 0.001 0.001 0.001
international journal of hydrogen energy 34 (2009) 6589–6595
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single exponent diode model is used to form a PV model, however, the model in this study does not need the reverse saturation current, diode factor, internal parallel and serial resistances of the PV module junction. Furthermore, the PEM electrolyser system model is composed of reversible potential and a single term of over-potential due to electrode kinetics and internal resistance. Therefore, this makes the model simple and practical in use. Moreover, the introduced model approach can be applied to similar systems with different sizes of PV modules and electrolyser cells and different number of PV modules and electrolyser cells connected in various parallel/series combinations.
references
Fig. 11 – PV module and PEM electrolyser curves with different size at same irradiance.
Fig. 12 – Efficiencies versus irradiance.
6.
Conclusions
An experimental model study for a PV/PEM electrolyser system is developed. Each device is mathematically modelled separately using the experimental data. The models developed have simple structure and predict the operating points by using MATLAB/Simulink. The irradiance interval is taken as 18–100% of the highest reference irradiance of 460 W/m2. Results taken from the model are compared with the measurement data. Comparison results show that the operating points of PV/PEM electrolyser system are predicted by model in the range of 0.1–0.8% relative errors. In general,
[1] Kolhe M, Agbossou K, Hamelin J, Bose TK. Analytical model for predicting the performance of photovoltaic array coupled with a wind turbine in a stand-alone renewable energy system based on hydrogen. Renewable Energy 2003;28: 727–42. [2] Nelson DB, Nehrir MH, Wang C. Unit and cost analysis of stand-alone hybrid wind/PV/fuel cell power generation systems. Renewable Energy 2006;31:1641–56. [3] Santarelli M, Cali M, Macagno S. Design and analysis of stand-alone hydrogen energy systems with different renewable sources. Int J Hydrogen Energy 2004;29:1571–86. [4] Kasseris E, Samaras Z, Zafeiris D. Optimization of a windpower fuel-cell hybrid system in an autonomous electrical network environment. Renewable Energy 2007;32:57–79. [5] El-Shater TF, Eskander MN, El-Hagry MT. Energy flow and management of a hybrid wind/PV/fuel cell generation system. Energy Convers Manag 2006;47:1264–80. [6] Shapiro D, Duffy J, Kimble M, Pien M. Solar powered regenerative PEM electrolyser/fuel cell system. Sol Energy 2005;79:544–50. [7] Paul B, Andrews J. Optimal coupling of PV arrays to PEM electrolysers in solar–hydrogen systems for remote area power supply. Int J Hydrogen Energy 2008;33:490–8. [8] Peharz G, Dimroth F, Wittstadt U. Solar hydrogen production by water splitting with a conversion efficiency of 18%. Int J Hydrogen Energy 2007;32:3248–52. [9] Gorgun H. Dynamic modelling of a proton exchange membrane (PEM) electrolyser. Int J Hydrogen Energy 2006; 31(1):29–38. [10] Treble FC. Generating electricity from the Sun. Oxford, New York, Seoul, Tokyo: Pergamon Press; 1991. [11] Goswami DY, Kreith F, Kreider JF. Principles of solar engineering. UK: CRC Press, ISBN 1-56032-714-6; 1999. [12] Gibson TL, Kelly NA. Optimization of solar powered hydrogen production using photovoltaic electrolysis device. Int J Hydrogen Energy 2008;33:5931–40. [13] Garsia-Valverde R, Miguel C, Martinez-Bejar R, Urbina A. Optimized photovoltaic generator – water electrolyser coupling through a controlled DC-DC converter. Int J Hydrogen Energy 2008;33:5352–62. [14] Contreras A, Guirado R, Veziroglu TN. Design and simulation of power control system of a plant for the generation of hydrogen via electrolysis, using photovoltaic solar energy. Int J Hydrogen Energy 2007;32:4635–40.
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
An experimental and modelling study of a photovoltaic/ proton-exchange membrane electrolyser system Ozcan Atlam* _ Kocaeli University, Technical Education Faculty, Electrical Department, Umuttepe 41380, Izmit, Kocaeli, Turkey
article info
abstract
Article history:
An experimental model of a photovoltaic (PV) module-proton exchange membrane (PEM)
Received 13 August 2008
electrolyser system has been built. A model has been developed for each device separately
Received in revised form
based on the experimental results. Output current–voltage (I–V) characteristics of the PV
16 February 2009
module are modelled in respect to different irradiance and temperature conditions by
Accepted 29 May 2009
experimental tests. Similarly, input I–V characteristic and hydrogen formation character-
Available online 2 July 2009
istic of the PEM electrolyser are measured and modelled. After these studies, combined PV module–PEM electrolyser system model is defined. There is a good agreement between
Keywords:
model predictions and measurements. At 18–100% irradiance interval, operating points of
Photovoltaic
PEM electrolyser on the PV module are predicted with relative errors of 0.1–0.8%.
Hydrogen
Furthermore, the study shows that these simple model system devices can easily be
PEM electrolyser
defined in MATLAB/Simulink and used to model similar systems of different size. ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Recently, the problems such as global warming, greenhouse effect, and global and regional pollution, have caused increased interest in renewable energy systems (solar, wind, etc.). Hydrogen, which is a versatile and clean energy carrier, can be produced from electrical energy in these renewable energy systems using water electrolysis. Electrolyser is a device that is used to produce hydrogen from water via electrolysis. In return, fuel cells convert stored hydrogen and oxygen or air to electricity directly. Hence, renewable energy and hydrogen systems are employed in an integrated form [1–5]. Additionally, polymer electrolyte membrane (or proton exchange membrane or PEM) electrolysers are becoming a new subject of research and development for solar hydrogen systems [6–9]. A PEM type device also can be used as fuel cell generator (reversible device), when stored hydrogen and oxygen (or oxygen from air) gases are applied to the device.
Modelling of such PV module–PEM electrolyser hydrogen systems is important for their planning and control strategies in practical applications. In general, reported models are complex and they use so many various specific parameters based on both theoretical and experimental data. In this paper, more simple models are developed for both PV module and PEM electrolyser based on experimental observations.
2.
Experimental setup
The experimental setup consists of a PV module, PEM electrolyser, an external adjustable dc power source (0–12 V, 20 W), thermometers, and multi-meters to measure current and voltage. The PV module can deliver current approximately 0.7 A at 2 V and under 45 C during a typical sunlight test conditions. Open circuit voltage (Voc) is about 3–3.5 V. The PEM
* Tel.: þ90 262 3032250. E-mail address: [email protected] 0360-3199/$ – see front matter ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.05.147
6590
international journal of hydrogen energy 34 (2009) 6589–6595
Nomenclature A dVt I Imax1 Isc Isc1 Isc2 k Kp KH Ns Np ns np
the PV module area, m2 the voltage coefficient per temperature variation, V/ C current, A the current at maximum power under reference irradiance, A short circuit current of PV module, A short circuit current of PV module at the highest irradiance level test, A short circuit current of PV module at the lowest irradiance level test, A the curve fitting coefficient in Isc versus Voc, V the coefficient of PV module model the power coefficient for rate of hydrogen formation, ml min1 W1 number of PV modules in series number of parallel strings of serially connected PV modules number of PEM electrolyser cells connected in series number of parallel strings of serially connected PEM electrolyser cells
P PH2 PEM PV T Tref DT V Vmax1 Voc Voc1 Voc2 DVoc vH vm Wi hH2
power, W the chemical energy of the produced hydrogen per second, W polymer electrolytic membrane photovoltaic temperature, C reference temperature, C change of temperature, C voltage, V the voltage at maximum power under reference irradiance, V open circuit voltage of PV module, V open circuit voltage of PV module at the highest irradiance level test, V open circuit voltage of PV module at the lowest irradiance level test, V change of open circuit voltage of PV module rate of hydrogen formation, ml min1 molar volume, ml mol1 the irradiance level, W m2 the overall system efficiency
electrolyser is a single cell with maximum current of 1 A at 2 V. A tungsten type lamp with 100 W incandescent bulb is used as a solar simulator. The Lutron LX-101 digital lux meter with a precision selenium photovoltaic cell is calibrated to incoming radiation of about 800 W/m2 on clear winter midday. For the indoor test, distance between the lamp and the PV module is adjusted until the rate of short circuit currents of the PV module and the rate of LX-101 device data measured under the sunlight and lamp light are approximately same. In this condition, the highest irradiance level is obtained as 460 W/m2. Also, the irradiance level of the lamp is calibrated with the book value of the short circuit current of PV where the irradiance level is determined as 460 W/m2. The irradiance level for solar system can be changed by varying distance (or angle) between the PV module and the lamp. Thermometer is used to measure PV module temperature. In order to measure hydrogen formation, oxygen and hydrogen tanks are scaled. Output I–V characteristics of PV module can be defined using a variable resistive load bank with 2–1000 ohm.
given in Fig. 1. The experimental and modelling stage involves following three tests.
3.
3.2.
Tests on the PV module and modelling
The output I–V characteristic of a PV module is non-linear and changes with irradiance and temperature T. Short circuit current (Isc) of the PV module is proportional to irradiance. The open circuit voltage (Voc) is more affected than Isc by the temperature. The Voc increases with irradiance, however, it decreases with the temperature [10,11]. The connection schema of the experiment for the PV module characteristics is
3.1. Measurements of T–Voc variations at the same irradiance (or same Isc) In this stage, the Isc is a constant value approximately. For a given constant irradiance level (or same value of Isc), the Voc values are measured at different PV module temperatures and values are noted. The resulted variation of Voc with temperature is observed as shown in Fig. 2 for Isc ¼ 0.230 A. The variation of T–Voc is linear. The slope of this characteristic yields a voltage coefficient of temperature variation dVt (V/ C). According to T–Voc test, the dVt (V/ C) is obtained approximately 0.014 V/ C as shown in Fig. 2. Hence, the change of Voc (DVoc) due to temperature change with respect to a reference temperature (Tref), can be formulated by Eq. (1). DVoc ¼ dVt$DT ¼ 0:014 T Tref
(1)
The Tref ¼ 37 C is assigned in the modelling study. The Eq. (1) is valid only for 35 C < T < 60 C.
Measurements of Isc–Voc variations at a constant T
Under a constant temperature, values of Isc and Voc are measured for different irradiance levels. To hold the temperature, T, constant, the PV module can be cooled by a fan if necessary. The variation of Isc–Voc is a logarithmic function as shown in Fig. 3. The temperature T is 37 C. This characteristic can be modelled by the following expressions for the sample PV module.
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Fig. 1 – The experiment schema for PV module characteristics.
3.3. Measurements of I–V characteristics under different irradiance
Isc–Voc relationship is approximated by Eq. (2). Isc : Voc ðIsc Þ ¼ Voc1 þ kln Isc1
(2)
Voc1 and Isc1 are values of open circuit voltage and short circuit current, respectively, at the highest irradiance level during test. The coefficient k is another curve fitting parameter and it can be defined by Eq. (3). Voc2 Voc1 : k¼ Isc2 ln Isc1
Kp
(3)
Voc2 and Isc2 are a pair of minimal values measured at the lowest irradiance level during the test, namely: Voc1 ¼ 3.27 V, Isc1 ¼ 0.258 A, Voc2 ¼ 2.990 V and Isc2 ¼ 0.049 A. The coefficient k is then found to be 0.168. Using a curve fitting, variation of Isc– Voc at the constant Tref of 37 C is modelled by Eq. (4). Isc Voc ðIsc Þ ¼ 3:27 þ 0:168ln 0:258
(4)
The Isc–Voc curve of the model calculated by Eq. (4) is also shown in Fig. 3. When the effect of temperature on Voc is added to the Eq. (4), the term Voc can be defined as the function of both Isc and T as given by Eq. (5). Voc ðIsc ; TÞ ¼ Voc ðIsc Þ þ DVoc Isc 0:014ðT 37Þ ¼ 3:27 þ 0:168ln 0:258
Fig. 2 – T–Voc variation at Isc [ 0.230 A.
The output I–V characteristics of the PV module are measured under the different irradiance conditions. The I–V characteristic of the PV module can be modelled by Eq. (6) for given Isc and T values. In Eq. (6), the Voc is defined previously by Eq. (5).
(5)
I ¼ Isc Isc e
ðVV
Þ
1
oc
(6)
Kp is a coefficient that enables the characteristic of the model to draw near to maximum power region in the measured I–V curve under the highest irradiance level. This irradiance is taken as reference. In the reference irradiance, Isc ¼ 0.258 A, Voc ¼ 3.27 V and T ¼ 37 C. The reference irradiance corresponds to 460 W/m2. The coefficient Kp can be calculated by Eq. (7). hI I i sc1 max1 ln Isc1 Kp ¼ : Vmax1 1 Voc1
(7)
In Eq. (7), Imax1 and Vmax1 are values of current and voltage at maximum power in reference irradiance, respectively. These values are measured as Imax1 ¼ 0.234 A, Vmax1 ¼ 2.670 V under reference irradiance. For different irradiance levels (or different Isc values) and temperatures, the Kp stays at constant value in the modelling. In this study, the Kp equals to 12.943 for
Fig. 3 – Isc–Voc curves of measurement and model at T [ 37 8C.
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Fig. 4 – I–V curves of measurement and model for PV module.
the PV panel used. The second term of Eq. (6) represents the form of forwardly biased diode current at junction in PV modules. In general, this term consists of some complex and specific parameters which are related to semiconductor physics. In Eq. (6), I equals to zero when the V equals to Voc, and V equals to zero when I equals to approximately Isc. The output I–V curves are non-linear. In the modelling, Isc and T are used as input values of Eqs. (5) and (6). Fig. 4 shows the resulting I–V curves and their maximum power points (MPPs) of the PV module both measured and modelled under different irradiance levels at T ¼ 37 C as a sample. Model estimations match the measurements very closely.
Fig. 6 – Input I–V characteristics of the PEM electrolyser for measurement and model.
Input currents of the PEM electrolyser are measured at different applied voltages (0–2 V). The characteristic curve is given in Fig. 6 and it looks like a typical diode characteristic. In the characteristic curve, there is a critical voltage at which the current flow starts. The current flow section of the curve can be approximated as linear. The slope of this characteristic corresponds to the internal electrical resistivity of the PEM electrolyser system during electrolysis. According to this test, input characteristic of the PEM electrolyser may be modelled by Eq. (8). I¼
0 V 1:476 3:064ðV 1:476Þ V > 1:476
(8)
The photo of the apparatus used in PV/PEM system is given in Fig. 5. The PEM electrolyser is connected to an adjustable power source, in order to obtain its response characteristics (I–V).
Input I–V characteristic of the model based on Eq. (8) is plotted in Fig. 6. The rate of hydrogen formation (ml/min) is measured and recorded as function of input power, and the results are shown in Fig. 7. Of course, hydrogen production rate is theoretically proportional to current in accordance with the Faraday Law:
Fig. 5 – Picture of the apparatus used in PV/PEM system.
Fig. 7 – Input power versus the rate of hydrogen formation.
4.
Tests on PEM electrolyser and modelling
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Fig. 8 – PV module – PEM electrolyser system.
I 1 1 60 s min mol s1 vm ml mol 2F 1 ¼ 7:5 ml min A1
vH ¼
(9)
However, for the sake of model simplicity the hydrogen production rate may be approximated by a linear relationship to input power: vH ¼ KH P:
(10)
In the study, the coefficient KH is found to be 4.10 ml min1 W1. Even if voltage–current relationship is approximated as linear (Eq. (8)), the resulting P–vH curve cannot be linear, however, an error resulting from linear relationship seems to be negligible, as shown below.
5. Operation of the PEM electrolyser with the PV module The PV module is connected to the PEM electrolyser as shown in Fig. 8. Operating points of the PEM electrolyser are measured and also can be predicted by general system modelling for different irradiance conditions. The PEM electrolyser operates at intersection points between the output I–V curves of the PV module and the input I–V characteristic of the PEM electrolyser for a given irradiance condition. Therefore, operating points occur at the expression in Eq. (11). Ouput f ðI; VÞðPV moduleÞ ¼ Input f ðI; VÞðPEM electrolyserÞ :
(11)
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If operating points seemingly exist in linear characteristic regions of each device, the calculation would be simple. However, the output I–V characteristics of the PV module are non-linear. In order to analyse the operating points of the combined system, an iterative computing is required. This can be achieved by MATLAB/Simulink. The equality in the Eq. (11) can be provided by MATLAB/Simulink model. For generalisation, model equations of PV module and PEM electrolyser are defined in MATLAB/Simulink program for prediction analysis in this study. Fig. 9 shows the resulting MATLAB/Simulink model for PV module–PEM electrolyser system. For example, both of measured and predicted operating points are given in Fig. 10 for PV module–PEM electrolyser system under different irradiance and 37 C. Irradiance interval is taken as 18–100% in respect to the highest irradiance 460 W/m2. The characteristics in Fig. 10 agree with the characteristics given in literature [6–8]. In this study, the operating points of the system occur at constant current regions of the PV module under different irradiance levels. However, for different number of single PV– PEM electrolyser units connected in parallel and/or in series, the operating points may occur near the open circuit regions of the PV module characteristic. Fig. 10 also shows that the operating points of the electrolyser match the electrolyser input characteristic which is measured previously (in Fig. 6). By means of these operating points, the rate of hydrogen formation given in Eq. (10) can be calculated for each irradiance level. By using Eq. (12), the relative errors between the measured and model values are determined and are given in Table 1.
relative error ¼
valuemeasured valuemodel : valuemeasured
(12)
The modelling can be also adapted to the systems with different size of each PV module and PEM electrolyser. It is assumed that Ns is the number of the PV modules in series and the Np is the number of parallel strings of PV modules in series. A larger PV system can be modelled by Eq. (13). Similarly when ns is the number of the PEM electrolyser cells in series and np is the number of parallel strings of PEM electrolyser cells in series. The resulting PEM electrolyser system can be modelled by Eq. (14). In these models, the connection losses are considered to be negligible.
Fig. 9 – PV module – PEM electrolyser system in the MATLAB/Simulink.
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Fig. 10 – Operating points of the PEM electrolyser on the PV module.
"
Kp
I ¼ Np Isc Isc e I ¼ np
ðN VV Þ #: 1
oc
(13)
0 V 1:476ns : V 3:064 ns 1:476 V > 1:476ns
(14)
s
Eqs. (13) and (14) can easily be programmed in MATLAB/ Simulink. For example, Fig. 11 shows characteristics of systems with different number of both PV modules and PEM electrolyser cells. The I–V curves of the PV systems are given for same irradiance but different temperatures (25 C and 45 C). Additionally, in Fig. 11, the values of Voc decrease with temperature. The slope (conductivity) of PEM electrolyser I–V characteristic with ns ¼ 6, np ¼ 1, is smaller than that of the single PEM electrolyser cell. Intersection points between curves represent the operating points of PV module–PEM electrolyser systems. In order to determine overall efficiency (light energy in hydrogen chemical energy out) of PV/PEM system, Eq. (15) is used in the study.
vH
ml
103
l 1 min 237; 200 J ml 60 s 22:4 l Wi mW2 Aðm2 Þ
min PH2 ¼ Wi A ml min vH min 0:176 Jml vH 0:176 0:176KH P S ¼ ¼ : ¼ Wi AðWÞ Wi A Wi A
hH2 ¼
(15)
In Eq. (15), the overall system efficiency is hH2 , the PH2 is chemical energy (lower heating value) of the hydrogen produced per second (W), the Wi is irradiance level (W/m2), the A is PV module area (m2). The A is 0.011 m2 in this study. For a given input power of the PEM and irradiance level, the term of vH is determined by Eq. (10) and then it is applied to Eq. (15). In Fig. 12, variation of overall efficiency is given under different irradiance levels. Also Fig. 12 shows the PV module maximum efficiencies and its efficiencies when connected to the PEM electrolyser. These efficiencies are calculated using the maximum power of the PV module and input power of the PEM electrolyser divided by input light power (WiA) which comes to the PV module area. According to characteristics in Fig. 12, the maximum efficiencies of the PV module were about 11–12%. Efficiencies of the PV module connected to the PEM electrolyser were about 7.5%. This difference is due to mismatch between the operating point and the maximum power point of the PV module. The PEM utilized the maximum power of PV module with an efficiency of 64–70%. This ratio of the actual efficiency and the maximum efficiency is called the utilization efficiency. The efficiency of the PEM electrolyser, defined as a ratio between the chemical energy (lower heating value) of the hydrogen produced per second (W) and electrical power fed to the electrolyser, was about 70%. The overall system efficiencies, hH2 were between 5.1 and 5.4% under different irradiances in this study. In general, the electrolyser I–V characteristics should be as close as possible to the PV module MPP trajectory, so that the PV/PEM system attains the high efficiency. In order to increase the overall system efficiency, a PV module type with high efficiency can be selected for the PEM electrolyser system as explained in [8], a controller system can be used to match the voltage and maximum power output of the PV module to operating voltage of PEM as in [7,12–14]. In these cases, maximum utilization efficiency of the PEM from the PV system are developed about 95%. In this study, none of these methods has been used since the goal of the study was not to increase the efficiency. However, the system efficiency achieved by directly coupled PV/PEM system used in this study is normal value for a non-optimized system (w70%) as stated in [12]. It is clear that, the system efficiency, hH2 , of a PV/PEM hydrogen production system is largely limited by the maximum efficiency of the PV module used. Also, the maximum power transfer between module and PEM electrolyser should be provided either by closely matching the PV and electrolyser I–V characteristics or by applying a controller as described in [7–9,12–14] to match the electrolyser and PV curves as close as possible at any irradiance and temperature.
Table 1 – Operating points and relative errors between the measurement and model. Irradiance (W/m2) 460 356 271 178 87
Vmeasured (V)
Vmodel (V)
Imeasured (A)
Imodel (A)
Relative error – V
Relative error – I
1.570 1.550 1.530 1.510 1.480
1.561 1.542 1.526 1.510 1.493
0.258 0.200 0.152 0.100 0.049
0.257 0.199 0.151 0.099 0.048
0.005 0.005 0.002 0.000 0.008
0.001 0.001 0.001 0.001 0.001
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single exponent diode model is used to form a PV model, however, the model in this study does not need the reverse saturation current, diode factor, internal parallel and serial resistances of the PV module junction. Furthermore, the PEM electrolyser system model is composed of reversible potential and a single term of over-potential due to electrode kinetics and internal resistance. Therefore, this makes the model simple and practical in use. Moreover, the introduced model approach can be applied to similar systems with different sizes of PV modules and electrolyser cells and different number of PV modules and electrolyser cells connected in various parallel/series combinations.
references
Fig. 11 – PV module and PEM electrolyser curves with different size at same irradiance.
Fig. 12 – Efficiencies versus irradiance.
6.
Conclusions
An experimental model study for a PV/PEM electrolyser system is developed. Each device is mathematically modelled separately using the experimental data. The models developed have simple structure and predict the operating points by using MATLAB/Simulink. The irradiance interval is taken as 18–100% of the highest reference irradiance of 460 W/m2. Results taken from the model are compared with the measurement data. Comparison results show that the operating points of PV/PEM electrolyser system are predicted by model in the range of 0.1–0.8% relative errors. In general,
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