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Dynamic modeling of a photovoltaic hydrogen fuel cell hybrid system
international journal of hydrogen energy 34 (2009) 9531–9542
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Dynamic modeling of a photovoltaic hydrogen fuel cell hybrid system J.J. Hwang a,*, L.K. Lai a, W. Wu b, W.R. Chang c a
Department of Greenergy, National University of Tainan, Tainan 700, Taiwan Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Yunlin 640, Taiwan c Department of Landscape Architecture, Fu Jen Catholic University, Taipei 242, Taiwan b
article info
abstract
Article history:
The objective of this paper is to mathematically model a stand-alone renewable power
Received 15 April 2008
system, referred to as ‘‘Photovoltaic–Fuel Cell (PVFC) hybrid system’’, which maximizes the
Received in revised form
use of a renewable energy source. It comprises a photovoltaic generator (PV), a water
20 September 2009
electrolyzer, a hydrogen tank, and a proton exchange membrane (PEM) fuel cell generator.
Accepted 26 September 2009
A multi-domain simulation platform Simplorer is employed to model the PVFC hybrid
Available online 22 October 2009
systems. Electrical power from the PV generator meets the user loads when there is sufficient solar radiation. The excess power from the PV generator is then used for water
Keywords:
electrolysis to produce hydrogen. The fuel cell generator works as a backup generator to
Photovoltaic generator
supplement the load demands when the PV energy is deficient during a period of low solar
Proton exchange membrane fuel cell
radiation, which keeps the system’s reliability at the same level as for the conventional
Water electrolyzer
system. Case studies using the present model have shown that the present hybrid system
Hybrid system
has successfully tracked the daily power consumption in a typical family. It also verifies the effectiveness of the proposed management approach for operation of a stand-alone hybrid system, which is essential for determining a control strategy to ensure efficient and reliable operation of each part of the hybrid system. The present model scheme can be helpful in the design and performance analysis of a complex hybrid-power system prior to practical realization. ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Today, most of energy demand in the world relies on fossil fuels such as petroleum, coal and natural gas, which are however being exhausted rapidly. More importantly, one of their combustion products, carbon dioxide, is the major cause of the serious problems of global warming, which are posing great hazard for the entire life on our planet [1]. Renewable energy sources such as solar, wind, biomass, etc. are attracting more attention as an alternative of fossil fuels. Among them, the photovoltaic (PV) generator that directly converts
solar radiation into electricity has been widely utilized in low power applications. It has many significant advantages such as being inexhaustible and carbon free, silent, without moving parts, and with size-independent electric conversion efficiency. However, the fluctuating nature of solar radiation retards the PV generators for off-grid applications. One method to overcome this problem is to integrate the PV generator with other power sources such as diesel, fuel cell, or battery backup [2–4]. The diesel generator has some significant disadvantages such as noise and exhaust gases pollution. In addition, reasonably reliable diesel backup generators are
* Corresponding author. Fax: þ886 422518272. E-mail address: [email protected] (J.J. Hwang). 0360-3199/$ – see front matter ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.09.100
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available only for the power range above about 5 kW, which is too high for a large number of applications [5]. In the middle and small power range, this technology cannot be used in an effective way. In contrast, the fuel cell generator is a good option to integrate with the PV power since it is characterized with many good features such as high efficiency, fast response, modular production, and fuel flexibility [6–9]. Its feasibility in coordination with a PV system has been successfully realized for both grid-connected and stand-alone power applications. Due to the rapid response capability of the fuel cell power system, a photovoltaic–fuel cell (PVFC) hybrid system may be able to solve the photovoltaic’s inherent problem of intermittent power generation. In addition, the fuel cell unlike a secondary battery can produce electricity for unlimited time to support the PV power generator. Therefore, a continuous supply of high quality power generated from the PVFC hybrid system is possible all daylong. Therefore, the fuel cell power system has a great potential for being coordinated with the PV generator to smooth out the photovoltaic power’s fluctuations. The objective of this work is to develop a dynamic model to simulate a stand-alone PVFC hybrid-power system which comprises mainly a photovoltaic generator, an alkaline water electrolyzer, and a PEM fuel cell generator that is intended to be an environmentally friendly solution since it maximizes the use of renewable energy sources. In the present stand-alone power system, the power produced by the PV generator satisfies the requirements of the user loads. Whenever there is more solar radiation, the user loads are powered totally by the PV generator and the excess solar energy is used for water electrolysis to produce hydrogen that subsequently store in the hydrogen tank. If the PV generator energy is deficient during the periods of low solar radiation, the fuel cell works as an auxiliary generator to
supplement the user load demands, which consumes hydrogen produced by the electrolyzer. Several tasks are carried in the present work, first, proper data collecting and/or data synthesizing that describe the system operation and the load profiles; then, deriving mathematical formulations together with proper empirical correlation that develops the subsystem models; moreover, linking all subsystems on the Simplorer platform to create an accurate simulation model that predicts the real dynamic behaviors of the PVFC hybrid system; finally, visualizing and analyzing the system dynamic behaviors using the power trace technique over one-day duration. System design and dynamic analysis achieved by using the present simulation tools prior to practical realization can be beneficial in cost-reduction and timesaving in developing the renewable hybrid-power system.
2.
Simulation model
As shown in Fig. 1, the majority of the PVFC system comprises a solar-cell module, a PEM fuel cell generator, and a water electrolyzer. An integral photovoltaic controller runs the solar cell in vary irradiation while extracting maximum power. In addition, a PEM fuel cell stack consisting of 65 cells connected in series provides output current up to 100 A. The open-circuit voltage of the fuel cell stack is about 60 V. The fuel supply line controllers are deployed if the output voltage of the fuel cell stack drops below 48 V. Controller actions compensate the drop in the fuel cell stack voltage caused by the load current variations. If the solar cell generates more current than the load requires, then the excess current is diverted towards the electrolyzer. The hydrogen is thus produced by the water electrolyzer and is subsequently stored in a tank for later use in the fuel cell stack.
Fig. 1 – Schematic drawing of the PVFC hybrid system.
international journal of hydrogen energy 34 (2009) 9531–9542
2.1.
Photovoltaic cell model
Fig. 2(a) shows the equivalent circuit of the one-diode model of PV cell. The four variables generating this model are the two input variables, solar radiation Eo and ambient temperature To, as well as the two output terminal variables, PV cell current Is and terminal voltage Us . Using the Kirchoff’s current law the terminal current through the PV cell can be expressed as: Is ¼ Iph Id Ish
(1)
where Iph is the photocurrent, Id, the diode loss current, and Ish, the shunt current, respectively. Iph is directly dependent on the solar radiation Es and the cell junction temperature Tj. A detailed approach to PV cell module or array modeling based on a mathematical description of the equivalent electrical circuit of a PV cell is given in [10,11]. It is modeled as: Iph ¼ P1 Es 1 þ P2 ðEs Eo Þ þ P3 Tj To
(2)
where P1, P2 and P3 are empirical constants. P1 means the ratio of the production of photocurrent to the solar irradiation. The last two terms of Eq (2) represent the corrections of the photocurrent due to the departures of the irradiation and
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temperature between the solar-cell surface and the ambient environment, respectively. The cell junction temperature Tj can be described as the following equation. Tj ¼ Ta þ
Es ðNOCT 20Þ 800
(3)
where Ta is the ambient temperature and NOCT is the normal operating cell temperature. The diode loss current Id due to charge carrier recombination is given by: eo Us þ Rs Is 1 (4) Id ¼ Isat $ exp $ af Ns k Tj where Isat is the saturated current, af, is the ideality factor of the photovoltaic array, Ns, is the number of cells in series, and, k, is the Boltzmann’s constant, respectively. The saturated current can be represented by Eg (5) Isat ¼ P4 T3j exp kTj where Eg is gap energy. Finally, the shunt current Ish is calculated from: Us þ Rs Is Rsh where Rsh is shunt resistance.
Ish ¼
Fig. 2 – (a) Equivalent circuit of the PV cell model, (b) simplified circuit diagram of the PEM fuel cell, (c) simplified circuit diagram of the water electrolysis cell.
(6)
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From the above reduction, the relations between input and output variables are: Eg Is ¼ P1 Es 1 þ P2 ðEs Eo Þ þ P3 Tj To P4 T3j exp kTj eo Us þ Rs Is Us þ Rs Is 1 exp $ af Ns k Tj Rsh
(7)
In the present PV model, the empirical parameters P1, P2, P3, and P4 used are fitted with a commercial PV module (Sharp NE-80EJEA) [12]. It is interested to note that the above empirical parameters are also valid for the PV module (BPX 47-451A) [13,14].
2.2.
PEM fuel cell model
As shown in Fig. 2(b), the actual voltage UFC is lower than its open-circuit voltage UOCV in an operating fuel cell due to various irreversible loss mechanisms. These losses originate primarily from three sources, i.e., activation overpotential hact, concentration overpotential hconc, and Ohmic overpotential hohm, respectively. Thus, the actual cell voltage can be represented by Ref. [15] UFC ¼ UOCV hact hconc hohm
(8)
The open-circuit voltage can be expressed also as a change in Gibbs free energy for the reaction of hydrogen and oxygen. At conditions different from the standard conditions, it is given by: UOCV
pH2 pO1=2 DSo RT 2 þ ln ¼ 1:2297 þ ðT 298:15Þ 2F 2F po3=2
! (9)
The activation overpotential of a fuel cell is related to the slowness of the reactions that take place on the surface of the electrodes. The electrode activation of a fuel cell can be described by the Butler–Volmer Equation [16]: j ¼ jo eð2aF=RTÞhact eð2ð1aÞF=RTÞhact
hohm;e ¼ I Rec
(14)
where I is the current density flowing through the cell and Rec is the equivalent electrical resistance of cell. As for the Ohmic loss due to the transport of the protons in the electrolyte membrane, its overpotential (hohm) can be also calculated by: hohm; m ¼ I Ric
(15)
where n is the number of the cells in the fuel cell stack. Ric is the ionic resistance electrolyte membrane, which is calculated from: Ric ¼
de s m Ac
(16)
where de is electrode gap width, Ac cross section area of the electrolyte body, and sm ionic conductivity of the electrolyte membrane. The ionic conductivity of the electrolyte membrane is calculated by [20,21]: 1 1 sm ¼ ð0:005139l 0:00326Þ exp 1268 303 T
(17)
where the water content is l ¼ 0:043 þ 17:8f 39:85f2 þ 36:0f3 Thus, the total Ohmic overpotential in the fuel cell can be represented by hohm ¼ hohm;e þ hohm;m
2.3.
(18)
Water electrolysis model
(10)
where jo is the exchange current density on the catalytic surfaces. It closely related to the operation temperature and the reactant concentration [17,18], i.e., a 1a ðDG=RÞ=½ð1=TÞð1=298:15Þ e CH2 O jo ¼ jref o z CO2
The Ohmic losses occurring in a fuel cell stack include the resistance due to the flow of protons (ionic current) in the electrolyte membrane and the resistance due to the flow of electrons (electrical current) through the electrical conductors (such as GDL, bipolar plate, etc) [19]. Therefore, the total Ohmic resistance is a combination of the electronic and ionic resistances. The Ohmic losses due to the transport of electrons obey the Ohm’s law:
(11)
The concentration loss is related to the reduction of the reactant’s concentration in the gas channels. The fuel and oxidant are used at the surface of the electrodes. The incoming gas must then take the place of the used reactant. The concentration of fuel and oxidant is reduced at the various points in the fuel cell gas channels and is less than the concentration at the inlet valve of the stack. This loss becomes significant at higher currents when the fuel and oxidant are used at higher rates and the concentration in the gas channel is at its minimum. hconc; a ¼
RT ja ln 1 jL 2F
(12)
hconc; c ¼
RT jc ln 1 jL 4F
(13)
An alkaline water electrolyzer consists of a number of electrolyzer cells connected in series. The electrolyzer model discussed here is based on the characteristics of individual cells. The calculations of the required operation voltage and the mass flow rates of hydrogen and oxygen are all done on a per cell basis, while the corresponding values for the whole electrolyzer unit are simply by multiplying by the number of series cells. This method is also used with the PEM fuel cell model. The equation that describes the behavior of the electrolyzer is: Uactual ¼ UOCV þ hanode þ hcathode þ hohm
(19)
It is the same form as for fuel cell, while the overpotentials represent here the surplus of electrical voltages necessary to make active the electrode reactions and to overcome the concentration gradients. All of the overpotentials depend on the current density and are calculated by the same manner for the fuel cell. Fig. 4 shows the simplified circuit diagram of an alkaline water electrolyzer cell according to Eq. (19). The following equation expresses the theoretical equilibrium cell voltage UOCV of the alkaline water electrolyzer under the effective working conditions, such as temperature and pressure:
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UOCV ¼ Uo þ
RT 2F
!# " 3=2 pH2 pH2 O pH2 O;r po pH2 O
(20)
where Uo is the reversible cell voltage at standard conditions, pH2 , the operation pressure of hydrogen, and, pH2 O , the water vapor partial pressure. Again, the Ohmic overpotential can be represented by hohm ¼ I Rel
(21)
where Rel is the internal resistance of the electrolyzer, and given by Ref. [21] Rel ¼
de sk Ac
(22)
The electrical conductivity sk of the electrolyte (potassium hydroxide) is given by Ref. [22]
Table 2 – Operational parameters and electrode properties of the PEM fuel cell model Parameters Number of cells Fuel cell temperature Cross section area of the electrolyte Distance between electrodes (electrode gap) Internal current density Symmetric factor at the anode Symmetric factor at the cathode Anodic standard exchange current density Cathode standard exchange current density
Symbol
Value
Unit
Ns T Ac
65 52 126
– C cm2
de
6.0 103
cm
jn aa ac jref o;a
9.8 103 0.5 0.25 0.5 103
A/cm2 – – A/cm2
jref o;c
0.4 106
A/cm2
sk ¼ 2:62 CKOH þ 0:067CKOH ðT 273:15Þ 4:8 C2KOH 0:088 C2KOH ðT 273:15Þ
(23)
where CKOH is the mass concentration of potassium hydroxide. According to the partial reactions during the electrolysis of an alkaline (KOH) solution at the cathode and the anode, the total current density j consists of two parts, j ¼ j a þ jc
(24)
The activation overpotentials at the cathode and the anode in the electrolyzer are calculated using the Butler–Volmer equations: 2ð1 ac ÞF h 2ac Fh hact;c i act;c RT RT e jc ¼ jref e o;c
(25-1)
2ð1 aa ÞF h 2aa Fh hact;a i RT act;a e RT ja ¼ jref o;a e
(25-2)
_ O2 Þ in _ H2 Þ and oxygen ðm The production rates of hydrogen ðm an electrolyzer cell can be calculated by: _ H2 ¼ 2m _ O2 ¼ Ns 3F m
I 2F
(26)
where 3F and NS are the Faradic efficiency and number of series cells, respectively. The operational parameters for the PV module, fuel cell module, and electrolyzer are given in Tables 1–3, respectively.
3.
Simulation scheme
In the last two decades, several research teams have developed a number of simulation packages for hybrid system, such as INSEL, TRNSYS, and HYBRID2, etc. Most of these software tools simulate a predefined hybrid system based on a mathematical description of the component operation characteristics and system energy flow. In this work, a multidomain simulation program Simplorer is used to model the PVFC hybrid systems. An advanced mathematical model not included in the standard Simplorer library is developed and added to its library. It comprises all models used in PVFC hybrid systems. The main assumptions made in the simulation of the hydrogen PVFC hybrid system are: 1. H2/Air PEM fuel cell is used in the simulated system. Thus, no oxygen purification or storage systems are required. 2. Some hydrogen losses are expected such as hydrogen losses in the electrolyzer or fuel cell during start-up and shut down, hydrogen losses in the gas storage tank, and hydrogen losses in the fuel cell during operation, but these will not be included in the simulation [8].
Table 1 – Parameters of the PV module. Parameters Reference junction temperature Reference solar radiation Boltzmann’s constant Gap energy voltage for Silicon Proportional constant Correction factor of the photoelectric constant Correction factor of the photoelectric constant Coefficient for acceptor and donor concentration Series resistance Parallel resistance Ideality factor Normal operating cell temperature
Symbol
Value
Unit
To Eo k Eg P1 P2
298 1000 1.3854 1023 1.12 2.96 8.6 104
K W/m2 J/K eV Am2/W m2/W
P3
0.0037
1/K
P4
1272.3
A/K3
Rs Rsh af NOCT
1.29 154.1 1 43
U U – C
Table 3 – Parameters and coefficients of the electrolyzer. Parameters Number of cells Cross section area of the electrolyte Distance between electrodes (electrode gap) Surface factor of electrodes Cathode standard exchange current density Anode standard exchange current density Cathode transfer coefficient Anode transfer coefficient Temperature of the electrolyzer
Symbol
Value
Unit
Ns Ac
15 300
– cm2
de
3.0 104
cm
fair jref o;c
44.5 1.0 103
– A/cm2
jref o;a
1.0 106
A/cm2
ac aa T
0.5 0.3 52
– – C
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3. Many parasitic loads are handled by an auxiliary power supply, such as power needed for water cooling pump for the electrolyzer or fuel cell, protective current for the electrolyzer during standby operation, hydrogen purification system, and data acquisition and control system. These parasitic powers are neglected in the simulation of the system. The inclusion of these losses would of course lead to different results, but will not affect on the decisions required from the simulation to operate the system optimally.
Fig. 3 – Comparison of fuel cell polarization curves between the experimental and predicted results.
During the program execution, all necessary system variables needed for a performance analysis are recorded in a simulation output file. For example, hydrogen produced by electrolyzer, hydrogen consumed by fuel cell generator, generated fuel cell energy to cover the deficit energy from the PV generator to satisfy the user load demand, generated PV energy, etc are delivered. Moreover, a 24-h total system energy balance is estimated. These output results can be analyzed to cover all performance aspects of the overall system.
Fig. 4 – Comparison of the predicted and measured power output of the fuel cell power system under the sine-wave current conditions, (a) current extraction, and (b) response of power output.
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Fig. 5 – Variations of solar radiance and ambient temperature in 1 one day.
4.
Results and discussion
Before the discussion of the modeled results of PVFC hybrid systems, it is necessary to validate the subsystem used in present model. The PV model utilized here has been verified in the previous work [12]. The validation of the fuel cell model is shown in Fig. 3 by comparing the polarization curves of the fuel cell stack between the modeled and experimental results. The operational temperature is fixed 52 C. The stoichiometries for the anode and cathode feedings are fixed at 1.5 and 2.5, respectively. It is seen that experimental data almost fall into the modeled polarization curve. In quantity, the maximum deviation between the modeled and measured averaged current density is less than 10%. Fig. 4 further shows a comparison of the predicted and measured dynamics of power output of the fuel cell system under the sine-wave current conditions. Generally, the agreement between the above results is satisfactory.
Two boundary conditions are required for closure of the present hybrid-power model, i.e., the power supply at the upstream site and the power demand at the downstream site. In the present model, the power-supply site includes the photovoltaic power from the solar call modules and the hydrogen energy in the hydrogen tank, while the powerdemand site is the modeled power consumption of a typical family in a daily life. Except for the solar panel characteristics, the amount of solar energy delivered by the solar-cell panel depends on local weather conditions, such as the solar radiation and ambient temperature. Fig. 5 shows the variations of solar radiation and ambient temperature in a typical sunny day in winter of Taiwan. The electrical responses of the present solar-cell panel to the above weather conditions is given in Fig. 6, including the voltage, current, and power at the maximum power point (MPP). It is seen that the MPP voltage is varied from 76 to 93 V. The lowest voltage is located at the maximum power point almost. As for the distribution of maximum
Fig. 6 – Responses of power output at maximum power point (MPP) of the PV cell to the solar radiance and ambient temperature in Fig. 4.
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Fig. 7 – Power dynamics for PV generator, FC generator and the load requirements.
power delivered by the PV generator, it is largely similar to that of the solar radiance. The modeled trend of the power demands of external loads is shown in Fig. 7, which represents the daily power
consumption in a typical family. From the midnight to early morning (00:00w04:00) all families are sleeping and thus the power requirement is low that keeps the household electronics and appliances, such as refrigerators and safety
Fig. 8 – Electric dynamics of the fuel cell generator, (a) fuel cell current, potential, and power, (b) fuel cell overpotentials.
international journal of hydrogen energy 34 (2009) 9531–9542
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Fig. 9 – Electrical dynamics of the water electrolyzer.
lighting. In the morning (04:00w07:00) and at noon (11:00– w12:00), more power is required for cooking, leisure, etc. From the evening to midnight (16:00w23:00), the consumption of electric power is considerable due to family activities. Fig. 7 further shows the power hybridization of the PV generator and the fuel cell that supports the demands of external loads. From midnight to morning, the fuel cell operates solely to supply to the load demands. After 5:00 AM, the solar power delivered by the PV generator is increased gradually. As long as the solar power is higher than the power demand by the external loads, the PV generator takes charge of the powersupply role for supporting the load demands; meanwhile the fuel cell generator is shut down. During the daytime, the superfluous power is used for water electrolysis to produce hydrogen, which is stored into the hydrogen tank for feeding the fuel cell generator nightly. In the afternoon, the solar power delivered by the PV generator is decreased. If it is lower than the power demands of external loads, the fuel cell generator starts up again to become the majority of power supplier for the external loads.
Fig. 8 shows the dynamics of the electrical behaviors of the PEM fuel cell generator. It is seen from Fig. 8(a) that the current distribution is similar to the load profiles, while the voltage decreases as the current increases. In the daytime, the PEM fuel cell keeps at its open-circuit voltage without any current extracted from the fuel cell stack. Note also that a higher level of current implies lower stack voltage and vice versa. Such changes in fuel cell current cause the stack voltage to vary significantly. Usually, an ultra-capacitor is used in parallel with the fuel cell to avoid a huge variation of stack output. Although it removes the sudden voltage changes to some extent, complete stabilization could not be achieved. Fig. 8(b) shows the dynamics of the overpotential of the PEM fuel cell stack. It is seen that the major losses in the operational fuel cell stack is caused by the cathode activation. Its dynamics dominate the variation of power delivered by the fuel cell stack. Fig. 9 shows the dynamics of current and voltage of the water electrolyzer. The general trend shown in this figure is an increase of current passing through the electrolyzer with
Fig. 10 – Hydrogen flow rate in the hydrogen pipeline.
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Fig. 11 – Hydrogen flow rates and the variation of pressure in the hydrogen tank.
increasing the operational voltage. The difference between the operational voltage and the open-circuit voltage represents the overpotentials in the electrolyzer. The zigzag distributions of current and voltage are caused by the step changes of power requirements at noon (Fig. 7). Fig. 10 shows the hydrogen volume flow rate measured by the flow meters in the hydrogen pipeline. The centerlines are the volume flow rate of hydrogen flowing into the fuel cell generator that is consumed by the PEM fuel cell stack. The dashed lines represent the hydrogen volume flow rate flowing out of the electrolyzer, which is produced by the electrolyzer. It is seen that distributions of the volume flow rates of hydrogen are paralleled to the current distribution of the fuel cell generator and water electrolyzer. Fig. 11 shows the pressure variation and hydrogen mole flow rate in the hydrogen tank. The positive hydrogen flow rate means that the hydrogen flows into the tank, which increases the pressure in the hydrogen tank. While the negative hydrogen flow rate represents the outflow of hydrogen from the tank that reduces the hydrogen tank
pressure. It is further seen that the distribution of hydrogen flow rate in the nighttime is harmonized with that of the power delivery by the fuel cell generator. In the daytime, the rate of hydrogen flowing into the hydrogen tank is coincident with the production rate of the electrolyzer. Fig. 12 illustrates the variation of hydrogen content in the hydrogen tank. The hydrogen tank used here is mainly severed as a buffer to store the fluctuating solar energy. That is the present hybrid-power system produces the hydrogen in the daytime and then is stored in the buffer tank for the energy demands in the nighttime. It is seen that the hydrogen content in the hydrogen tank decreases slightly in the early morning, then increases during the daytime by the surplus power delivered by the PV generator, and drops sharply in the evening due to the considerable family activity. The hydrogen in the tank decreases slightly from 808 mol to 801 mol in 24-h operation. The deficiency of hydrogen means that the solar energy cannot totally support the power requirement of the family. To become a self-sustained power system for the family, it is therefore suggested to enlarge the solar panels to
Fig. 12 – Hydrogen deficiencies for the present stand-alone power system.
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receive more solar energy and/or to enhance the efficiencies of the solar cell, fuel cell, and electrolyzer that reduces the conversion losses.
5.
Conclusions
In the present work, a dynamic model of PVFC power system has been implemented in the Simplorer simulation environment and utilized to predict its operational behaviors through numerical simulation. The system hybridizes photovoltaics and fuel cells to support the power requirement of a typical family in the daily life. Detailed descriptions of the subsystem models required to simulate the hybrid renewable hydrogen system are presented, such as photovoltaic cell, fuel cell, and electrolyzer. These models are mainly based on electrical and electrochemical relations in addition to several empirical relationships for some subsystem models. The results obtained from the present analysis have shown that the present hybrid system has successfully tracked the daily power consumption of a typical family. It also verifies the effectiveness of the proposed management approach for operation of a stand-alone hybrid system that maximizes the use of a renewable energy source. The results obtained by the present work can get better understanding the dynamic behaviors of the each component or subsystem of the hydrogen PVFC system that helps in improving component’s efficiency and utilizing new system concepts. Moreover, system analysis tools provided by the present work have the potential in cost-down and timesaving in the design of a renewable hybrid-power system.
Acknowledgements This research was partly sponsored by the National Science Council of Taiwan under contract no. NSC 92-2212-E-451-002.
Nomenclature
af Eg Eo eo G k NOCT Ns Rsh Rs Ta Tj To jo jref o a Uact n
ideality factor of the photovoltaic array, gap energy, eV reference solar radiation, W/m2 electron charge, C Gibbs free energy [J/mol] Boltzmann’s constant, J/K normal operating cell temperature, K number of cells in series, shunt (parallel) resistance, [U] series resistance, U ambient temperature, K junction temperature, [K] reference junction temperature, K exchange current density, A/cm2 anodic or cathodic standard exchange current density, A/cm2 transfer coefficient activation overpotential, V number of electrons participating,
R T F CH2 O CO2 pH2 pO2 po psat
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universal gas constant, J/K/mol temperature, K Faraday’s constant, C/mol concentration of water vapor, [-] concentration of the oxygen at the cathode, partial pressure of hydrogen, Pa partial pressure of oxygen, Pa operating pressure, Pa Saturated vapor pressure of pure water, Pa
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[20] Hwang JJ. Thermal-electrochemical modeling of a proton exchange membrane fuel cell. Journal of the Electrochemical Society 2006;153(1):A216–24. [21] Wang JT, Savinell RF. Simulation studies on the fuel electrode of a H2-polymer electrolyte fuel cell. Electrochimia Acta 1992;37(15):2737–45. Great Britain. [22] Hoogers G. Fuel cell technology handbook. CRC Press LLC; 2003.
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Dynamic modeling of a photovoltaic hydrogen fuel cell hybrid system J.J. Hwang a,*, L.K. Lai a, W. Wu b, W.R. Chang c a
Department of Greenergy, National University of Tainan, Tainan 700, Taiwan Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Yunlin 640, Taiwan c Department of Landscape Architecture, Fu Jen Catholic University, Taipei 242, Taiwan b
article info
abstract
Article history:
The objective of this paper is to mathematically model a stand-alone renewable power
Received 15 April 2008
system, referred to as ‘‘Photovoltaic–Fuel Cell (PVFC) hybrid system’’, which maximizes the
Received in revised form
use of a renewable energy source. It comprises a photovoltaic generator (PV), a water
20 September 2009
electrolyzer, a hydrogen tank, and a proton exchange membrane (PEM) fuel cell generator.
Accepted 26 September 2009
A multi-domain simulation platform Simplorer is employed to model the PVFC hybrid
Available online 22 October 2009
systems. Electrical power from the PV generator meets the user loads when there is sufficient solar radiation. The excess power from the PV generator is then used for water
Keywords:
electrolysis to produce hydrogen. The fuel cell generator works as a backup generator to
Photovoltaic generator
supplement the load demands when the PV energy is deficient during a period of low solar
Proton exchange membrane fuel cell
radiation, which keeps the system’s reliability at the same level as for the conventional
Water electrolyzer
system. Case studies using the present model have shown that the present hybrid system
Hybrid system
has successfully tracked the daily power consumption in a typical family. It also verifies the effectiveness of the proposed management approach for operation of a stand-alone hybrid system, which is essential for determining a control strategy to ensure efficient and reliable operation of each part of the hybrid system. The present model scheme can be helpful in the design and performance analysis of a complex hybrid-power system prior to practical realization. ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Today, most of energy demand in the world relies on fossil fuels such as petroleum, coal and natural gas, which are however being exhausted rapidly. More importantly, one of their combustion products, carbon dioxide, is the major cause of the serious problems of global warming, which are posing great hazard for the entire life on our planet [1]. Renewable energy sources such as solar, wind, biomass, etc. are attracting more attention as an alternative of fossil fuels. Among them, the photovoltaic (PV) generator that directly converts
solar radiation into electricity has been widely utilized in low power applications. It has many significant advantages such as being inexhaustible and carbon free, silent, without moving parts, and with size-independent electric conversion efficiency. However, the fluctuating nature of solar radiation retards the PV generators for off-grid applications. One method to overcome this problem is to integrate the PV generator with other power sources such as diesel, fuel cell, or battery backup [2–4]. The diesel generator has some significant disadvantages such as noise and exhaust gases pollution. In addition, reasonably reliable diesel backup generators are
* Corresponding author. Fax: þ886 422518272. E-mail address: [email protected] (J.J. Hwang). 0360-3199/$ – see front matter ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.09.100
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available only for the power range above about 5 kW, which is too high for a large number of applications [5]. In the middle and small power range, this technology cannot be used in an effective way. In contrast, the fuel cell generator is a good option to integrate with the PV power since it is characterized with many good features such as high efficiency, fast response, modular production, and fuel flexibility [6–9]. Its feasibility in coordination with a PV system has been successfully realized for both grid-connected and stand-alone power applications. Due to the rapid response capability of the fuel cell power system, a photovoltaic–fuel cell (PVFC) hybrid system may be able to solve the photovoltaic’s inherent problem of intermittent power generation. In addition, the fuel cell unlike a secondary battery can produce electricity for unlimited time to support the PV power generator. Therefore, a continuous supply of high quality power generated from the PVFC hybrid system is possible all daylong. Therefore, the fuel cell power system has a great potential for being coordinated with the PV generator to smooth out the photovoltaic power’s fluctuations. The objective of this work is to develop a dynamic model to simulate a stand-alone PVFC hybrid-power system which comprises mainly a photovoltaic generator, an alkaline water electrolyzer, and a PEM fuel cell generator that is intended to be an environmentally friendly solution since it maximizes the use of renewable energy sources. In the present stand-alone power system, the power produced by the PV generator satisfies the requirements of the user loads. Whenever there is more solar radiation, the user loads are powered totally by the PV generator and the excess solar energy is used for water electrolysis to produce hydrogen that subsequently store in the hydrogen tank. If the PV generator energy is deficient during the periods of low solar radiation, the fuel cell works as an auxiliary generator to
supplement the user load demands, which consumes hydrogen produced by the electrolyzer. Several tasks are carried in the present work, first, proper data collecting and/or data synthesizing that describe the system operation and the load profiles; then, deriving mathematical formulations together with proper empirical correlation that develops the subsystem models; moreover, linking all subsystems on the Simplorer platform to create an accurate simulation model that predicts the real dynamic behaviors of the PVFC hybrid system; finally, visualizing and analyzing the system dynamic behaviors using the power trace technique over one-day duration. System design and dynamic analysis achieved by using the present simulation tools prior to practical realization can be beneficial in cost-reduction and timesaving in developing the renewable hybrid-power system.
2.
Simulation model
As shown in Fig. 1, the majority of the PVFC system comprises a solar-cell module, a PEM fuel cell generator, and a water electrolyzer. An integral photovoltaic controller runs the solar cell in vary irradiation while extracting maximum power. In addition, a PEM fuel cell stack consisting of 65 cells connected in series provides output current up to 100 A. The open-circuit voltage of the fuel cell stack is about 60 V. The fuel supply line controllers are deployed if the output voltage of the fuel cell stack drops below 48 V. Controller actions compensate the drop in the fuel cell stack voltage caused by the load current variations. If the solar cell generates more current than the load requires, then the excess current is diverted towards the electrolyzer. The hydrogen is thus produced by the water electrolyzer and is subsequently stored in a tank for later use in the fuel cell stack.
Fig. 1 – Schematic drawing of the PVFC hybrid system.
international journal of hydrogen energy 34 (2009) 9531–9542
2.1.
Photovoltaic cell model
Fig. 2(a) shows the equivalent circuit of the one-diode model of PV cell. The four variables generating this model are the two input variables, solar radiation Eo and ambient temperature To, as well as the two output terminal variables, PV cell current Is and terminal voltage Us . Using the Kirchoff’s current law the terminal current through the PV cell can be expressed as: Is ¼ Iph Id Ish
(1)
where Iph is the photocurrent, Id, the diode loss current, and Ish, the shunt current, respectively. Iph is directly dependent on the solar radiation Es and the cell junction temperature Tj. A detailed approach to PV cell module or array modeling based on a mathematical description of the equivalent electrical circuit of a PV cell is given in [10,11]. It is modeled as: Iph ¼ P1 Es 1 þ P2 ðEs Eo Þ þ P3 Tj To
(2)
where P1, P2 and P3 are empirical constants. P1 means the ratio of the production of photocurrent to the solar irradiation. The last two terms of Eq (2) represent the corrections of the photocurrent due to the departures of the irradiation and
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temperature between the solar-cell surface and the ambient environment, respectively. The cell junction temperature Tj can be described as the following equation. Tj ¼ Ta þ
Es ðNOCT 20Þ 800
(3)
where Ta is the ambient temperature and NOCT is the normal operating cell temperature. The diode loss current Id due to charge carrier recombination is given by: eo Us þ Rs Is 1 (4) Id ¼ Isat $ exp $ af Ns k Tj where Isat is the saturated current, af, is the ideality factor of the photovoltaic array, Ns, is the number of cells in series, and, k, is the Boltzmann’s constant, respectively. The saturated current can be represented by Eg (5) Isat ¼ P4 T3j exp kTj where Eg is gap energy. Finally, the shunt current Ish is calculated from: Us þ Rs Is Rsh where Rsh is shunt resistance.
Ish ¼
Fig. 2 – (a) Equivalent circuit of the PV cell model, (b) simplified circuit diagram of the PEM fuel cell, (c) simplified circuit diagram of the water electrolysis cell.
(6)
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From the above reduction, the relations between input and output variables are: Eg Is ¼ P1 Es 1 þ P2 ðEs Eo Þ þ P3 Tj To P4 T3j exp kTj eo Us þ Rs Is Us þ Rs Is 1 exp $ af Ns k Tj Rsh
(7)
In the present PV model, the empirical parameters P1, P2, P3, and P4 used are fitted with a commercial PV module (Sharp NE-80EJEA) [12]. It is interested to note that the above empirical parameters are also valid for the PV module (BPX 47-451A) [13,14].
2.2.
PEM fuel cell model
As shown in Fig. 2(b), the actual voltage UFC is lower than its open-circuit voltage UOCV in an operating fuel cell due to various irreversible loss mechanisms. These losses originate primarily from three sources, i.e., activation overpotential hact, concentration overpotential hconc, and Ohmic overpotential hohm, respectively. Thus, the actual cell voltage can be represented by Ref. [15] UFC ¼ UOCV hact hconc hohm
(8)
The open-circuit voltage can be expressed also as a change in Gibbs free energy for the reaction of hydrogen and oxygen. At conditions different from the standard conditions, it is given by: UOCV
pH2 pO1=2 DSo RT 2 þ ln ¼ 1:2297 þ ðT 298:15Þ 2F 2F po3=2
! (9)
The activation overpotential of a fuel cell is related to the slowness of the reactions that take place on the surface of the electrodes. The electrode activation of a fuel cell can be described by the Butler–Volmer Equation [16]: j ¼ jo eð2aF=RTÞhact eð2ð1aÞF=RTÞhact
hohm;e ¼ I Rec
(14)
where I is the current density flowing through the cell and Rec is the equivalent electrical resistance of cell. As for the Ohmic loss due to the transport of the protons in the electrolyte membrane, its overpotential (hohm) can be also calculated by: hohm; m ¼ I Ric
(15)
where n is the number of the cells in the fuel cell stack. Ric is the ionic resistance electrolyte membrane, which is calculated from: Ric ¼
de s m Ac
(16)
where de is electrode gap width, Ac cross section area of the electrolyte body, and sm ionic conductivity of the electrolyte membrane. The ionic conductivity of the electrolyte membrane is calculated by [20,21]: 1 1 sm ¼ ð0:005139l 0:00326Þ exp 1268 303 T
(17)
where the water content is l ¼ 0:043 þ 17:8f 39:85f2 þ 36:0f3 Thus, the total Ohmic overpotential in the fuel cell can be represented by hohm ¼ hohm;e þ hohm;m
2.3.
(18)
Water electrolysis model
(10)
where jo is the exchange current density on the catalytic surfaces. It closely related to the operation temperature and the reactant concentration [17,18], i.e., a 1a ðDG=RÞ=½ð1=TÞð1=298:15Þ e CH2 O jo ¼ jref o z CO2
The Ohmic losses occurring in a fuel cell stack include the resistance due to the flow of protons (ionic current) in the electrolyte membrane and the resistance due to the flow of electrons (electrical current) through the electrical conductors (such as GDL, bipolar plate, etc) [19]. Therefore, the total Ohmic resistance is a combination of the electronic and ionic resistances. The Ohmic losses due to the transport of electrons obey the Ohm’s law:
(11)
The concentration loss is related to the reduction of the reactant’s concentration in the gas channels. The fuel and oxidant are used at the surface of the electrodes. The incoming gas must then take the place of the used reactant. The concentration of fuel and oxidant is reduced at the various points in the fuel cell gas channels and is less than the concentration at the inlet valve of the stack. This loss becomes significant at higher currents when the fuel and oxidant are used at higher rates and the concentration in the gas channel is at its minimum. hconc; a ¼
RT ja ln 1 jL 2F
(12)
hconc; c ¼
RT jc ln 1 jL 4F
(13)
An alkaline water electrolyzer consists of a number of electrolyzer cells connected in series. The electrolyzer model discussed here is based on the characteristics of individual cells. The calculations of the required operation voltage and the mass flow rates of hydrogen and oxygen are all done on a per cell basis, while the corresponding values for the whole electrolyzer unit are simply by multiplying by the number of series cells. This method is also used with the PEM fuel cell model. The equation that describes the behavior of the electrolyzer is: Uactual ¼ UOCV þ hanode þ hcathode þ hohm
(19)
It is the same form as for fuel cell, while the overpotentials represent here the surplus of electrical voltages necessary to make active the electrode reactions and to overcome the concentration gradients. All of the overpotentials depend on the current density and are calculated by the same manner for the fuel cell. Fig. 4 shows the simplified circuit diagram of an alkaline water electrolyzer cell according to Eq. (19). The following equation expresses the theoretical equilibrium cell voltage UOCV of the alkaline water electrolyzer under the effective working conditions, such as temperature and pressure:
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UOCV ¼ Uo þ
RT 2F
!# " 3=2 pH2 pH2 O pH2 O;r po pH2 O
(20)
where Uo is the reversible cell voltage at standard conditions, pH2 , the operation pressure of hydrogen, and, pH2 O , the water vapor partial pressure. Again, the Ohmic overpotential can be represented by hohm ¼ I Rel
(21)
where Rel is the internal resistance of the electrolyzer, and given by Ref. [21] Rel ¼
de sk Ac
(22)
The electrical conductivity sk of the electrolyte (potassium hydroxide) is given by Ref. [22]
Table 2 – Operational parameters and electrode properties of the PEM fuel cell model Parameters Number of cells Fuel cell temperature Cross section area of the electrolyte Distance between electrodes (electrode gap) Internal current density Symmetric factor at the anode Symmetric factor at the cathode Anodic standard exchange current density Cathode standard exchange current density
Symbol
Value
Unit
Ns T Ac
65 52 126
– C cm2
de
6.0 103
cm
jn aa ac jref o;a
9.8 103 0.5 0.25 0.5 103
A/cm2 – – A/cm2
jref o;c
0.4 106
A/cm2
sk ¼ 2:62 CKOH þ 0:067CKOH ðT 273:15Þ 4:8 C2KOH 0:088 C2KOH ðT 273:15Þ
(23)
where CKOH is the mass concentration of potassium hydroxide. According to the partial reactions during the electrolysis of an alkaline (KOH) solution at the cathode and the anode, the total current density j consists of two parts, j ¼ j a þ jc
(24)
The activation overpotentials at the cathode and the anode in the electrolyzer are calculated using the Butler–Volmer equations: 2ð1 ac ÞF h 2ac Fh hact;c i act;c RT RT e jc ¼ jref e o;c
(25-1)
2ð1 aa ÞF h 2aa Fh hact;a i RT act;a e RT ja ¼ jref o;a e
(25-2)
_ O2 Þ in _ H2 Þ and oxygen ðm The production rates of hydrogen ðm an electrolyzer cell can be calculated by: _ H2 ¼ 2m _ O2 ¼ Ns 3F m
I 2F
(26)
where 3F and NS are the Faradic efficiency and number of series cells, respectively. The operational parameters for the PV module, fuel cell module, and electrolyzer are given in Tables 1–3, respectively.
3.
Simulation scheme
In the last two decades, several research teams have developed a number of simulation packages for hybrid system, such as INSEL, TRNSYS, and HYBRID2, etc. Most of these software tools simulate a predefined hybrid system based on a mathematical description of the component operation characteristics and system energy flow. In this work, a multidomain simulation program Simplorer is used to model the PVFC hybrid systems. An advanced mathematical model not included in the standard Simplorer library is developed and added to its library. It comprises all models used in PVFC hybrid systems. The main assumptions made in the simulation of the hydrogen PVFC hybrid system are: 1. H2/Air PEM fuel cell is used in the simulated system. Thus, no oxygen purification or storage systems are required. 2. Some hydrogen losses are expected such as hydrogen losses in the electrolyzer or fuel cell during start-up and shut down, hydrogen losses in the gas storage tank, and hydrogen losses in the fuel cell during operation, but these will not be included in the simulation [8].
Table 1 – Parameters of the PV module. Parameters Reference junction temperature Reference solar radiation Boltzmann’s constant Gap energy voltage for Silicon Proportional constant Correction factor of the photoelectric constant Correction factor of the photoelectric constant Coefficient for acceptor and donor concentration Series resistance Parallel resistance Ideality factor Normal operating cell temperature
Symbol
Value
Unit
To Eo k Eg P1 P2
298 1000 1.3854 1023 1.12 2.96 8.6 104
K W/m2 J/K eV Am2/W m2/W
P3
0.0037
1/K
P4
1272.3
A/K3
Rs Rsh af NOCT
1.29 154.1 1 43
U U – C
Table 3 – Parameters and coefficients of the electrolyzer. Parameters Number of cells Cross section area of the electrolyte Distance between electrodes (electrode gap) Surface factor of electrodes Cathode standard exchange current density Anode standard exchange current density Cathode transfer coefficient Anode transfer coefficient Temperature of the electrolyzer
Symbol
Value
Unit
Ns Ac
15 300
– cm2
de
3.0 104
cm
fair jref o;c
44.5 1.0 103
– A/cm2
jref o;a
1.0 106
A/cm2
ac aa T
0.5 0.3 52
– – C
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3. Many parasitic loads are handled by an auxiliary power supply, such as power needed for water cooling pump for the electrolyzer or fuel cell, protective current for the electrolyzer during standby operation, hydrogen purification system, and data acquisition and control system. These parasitic powers are neglected in the simulation of the system. The inclusion of these losses would of course lead to different results, but will not affect on the decisions required from the simulation to operate the system optimally.
Fig. 3 – Comparison of fuel cell polarization curves between the experimental and predicted results.
During the program execution, all necessary system variables needed for a performance analysis are recorded in a simulation output file. For example, hydrogen produced by electrolyzer, hydrogen consumed by fuel cell generator, generated fuel cell energy to cover the deficit energy from the PV generator to satisfy the user load demand, generated PV energy, etc are delivered. Moreover, a 24-h total system energy balance is estimated. These output results can be analyzed to cover all performance aspects of the overall system.
Fig. 4 – Comparison of the predicted and measured power output of the fuel cell power system under the sine-wave current conditions, (a) current extraction, and (b) response of power output.
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Fig. 5 – Variations of solar radiance and ambient temperature in 1 one day.
4.
Results and discussion
Before the discussion of the modeled results of PVFC hybrid systems, it is necessary to validate the subsystem used in present model. The PV model utilized here has been verified in the previous work [12]. The validation of the fuel cell model is shown in Fig. 3 by comparing the polarization curves of the fuel cell stack between the modeled and experimental results. The operational temperature is fixed 52 C. The stoichiometries for the anode and cathode feedings are fixed at 1.5 and 2.5, respectively. It is seen that experimental data almost fall into the modeled polarization curve. In quantity, the maximum deviation between the modeled and measured averaged current density is less than 10%. Fig. 4 further shows a comparison of the predicted and measured dynamics of power output of the fuel cell system under the sine-wave current conditions. Generally, the agreement between the above results is satisfactory.
Two boundary conditions are required for closure of the present hybrid-power model, i.e., the power supply at the upstream site and the power demand at the downstream site. In the present model, the power-supply site includes the photovoltaic power from the solar call modules and the hydrogen energy in the hydrogen tank, while the powerdemand site is the modeled power consumption of a typical family in a daily life. Except for the solar panel characteristics, the amount of solar energy delivered by the solar-cell panel depends on local weather conditions, such as the solar radiation and ambient temperature. Fig. 5 shows the variations of solar radiation and ambient temperature in a typical sunny day in winter of Taiwan. The electrical responses of the present solar-cell panel to the above weather conditions is given in Fig. 6, including the voltage, current, and power at the maximum power point (MPP). It is seen that the MPP voltage is varied from 76 to 93 V. The lowest voltage is located at the maximum power point almost. As for the distribution of maximum
Fig. 6 – Responses of power output at maximum power point (MPP) of the PV cell to the solar radiance and ambient temperature in Fig. 4.
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Fig. 7 – Power dynamics for PV generator, FC generator and the load requirements.
power delivered by the PV generator, it is largely similar to that of the solar radiance. The modeled trend of the power demands of external loads is shown in Fig. 7, which represents the daily power
consumption in a typical family. From the midnight to early morning (00:00w04:00) all families are sleeping and thus the power requirement is low that keeps the household electronics and appliances, such as refrigerators and safety
Fig. 8 – Electric dynamics of the fuel cell generator, (a) fuel cell current, potential, and power, (b) fuel cell overpotentials.
international journal of hydrogen energy 34 (2009) 9531–9542
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Fig. 9 – Electrical dynamics of the water electrolyzer.
lighting. In the morning (04:00w07:00) and at noon (11:00– w12:00), more power is required for cooking, leisure, etc. From the evening to midnight (16:00w23:00), the consumption of electric power is considerable due to family activities. Fig. 7 further shows the power hybridization of the PV generator and the fuel cell that supports the demands of external loads. From midnight to morning, the fuel cell operates solely to supply to the load demands. After 5:00 AM, the solar power delivered by the PV generator is increased gradually. As long as the solar power is higher than the power demand by the external loads, the PV generator takes charge of the powersupply role for supporting the load demands; meanwhile the fuel cell generator is shut down. During the daytime, the superfluous power is used for water electrolysis to produce hydrogen, which is stored into the hydrogen tank for feeding the fuel cell generator nightly. In the afternoon, the solar power delivered by the PV generator is decreased. If it is lower than the power demands of external loads, the fuel cell generator starts up again to become the majority of power supplier for the external loads.
Fig. 8 shows the dynamics of the electrical behaviors of the PEM fuel cell generator. It is seen from Fig. 8(a) that the current distribution is similar to the load profiles, while the voltage decreases as the current increases. In the daytime, the PEM fuel cell keeps at its open-circuit voltage without any current extracted from the fuel cell stack. Note also that a higher level of current implies lower stack voltage and vice versa. Such changes in fuel cell current cause the stack voltage to vary significantly. Usually, an ultra-capacitor is used in parallel with the fuel cell to avoid a huge variation of stack output. Although it removes the sudden voltage changes to some extent, complete stabilization could not be achieved. Fig. 8(b) shows the dynamics of the overpotential of the PEM fuel cell stack. It is seen that the major losses in the operational fuel cell stack is caused by the cathode activation. Its dynamics dominate the variation of power delivered by the fuel cell stack. Fig. 9 shows the dynamics of current and voltage of the water electrolyzer. The general trend shown in this figure is an increase of current passing through the electrolyzer with
Fig. 10 – Hydrogen flow rate in the hydrogen pipeline.
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Fig. 11 – Hydrogen flow rates and the variation of pressure in the hydrogen tank.
increasing the operational voltage. The difference between the operational voltage and the open-circuit voltage represents the overpotentials in the electrolyzer. The zigzag distributions of current and voltage are caused by the step changes of power requirements at noon (Fig. 7). Fig. 10 shows the hydrogen volume flow rate measured by the flow meters in the hydrogen pipeline. The centerlines are the volume flow rate of hydrogen flowing into the fuel cell generator that is consumed by the PEM fuel cell stack. The dashed lines represent the hydrogen volume flow rate flowing out of the electrolyzer, which is produced by the electrolyzer. It is seen that distributions of the volume flow rates of hydrogen are paralleled to the current distribution of the fuel cell generator and water electrolyzer. Fig. 11 shows the pressure variation and hydrogen mole flow rate in the hydrogen tank. The positive hydrogen flow rate means that the hydrogen flows into the tank, which increases the pressure in the hydrogen tank. While the negative hydrogen flow rate represents the outflow of hydrogen from the tank that reduces the hydrogen tank
pressure. It is further seen that the distribution of hydrogen flow rate in the nighttime is harmonized with that of the power delivery by the fuel cell generator. In the daytime, the rate of hydrogen flowing into the hydrogen tank is coincident with the production rate of the electrolyzer. Fig. 12 illustrates the variation of hydrogen content in the hydrogen tank. The hydrogen tank used here is mainly severed as a buffer to store the fluctuating solar energy. That is the present hybrid-power system produces the hydrogen in the daytime and then is stored in the buffer tank for the energy demands in the nighttime. It is seen that the hydrogen content in the hydrogen tank decreases slightly in the early morning, then increases during the daytime by the surplus power delivered by the PV generator, and drops sharply in the evening due to the considerable family activity. The hydrogen in the tank decreases slightly from 808 mol to 801 mol in 24-h operation. The deficiency of hydrogen means that the solar energy cannot totally support the power requirement of the family. To become a self-sustained power system for the family, it is therefore suggested to enlarge the solar panels to
Fig. 12 – Hydrogen deficiencies for the present stand-alone power system.
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receive more solar energy and/or to enhance the efficiencies of the solar cell, fuel cell, and electrolyzer that reduces the conversion losses.
5.
Conclusions
In the present work, a dynamic model of PVFC power system has been implemented in the Simplorer simulation environment and utilized to predict its operational behaviors through numerical simulation. The system hybridizes photovoltaics and fuel cells to support the power requirement of a typical family in the daily life. Detailed descriptions of the subsystem models required to simulate the hybrid renewable hydrogen system are presented, such as photovoltaic cell, fuel cell, and electrolyzer. These models are mainly based on electrical and electrochemical relations in addition to several empirical relationships for some subsystem models. The results obtained from the present analysis have shown that the present hybrid system has successfully tracked the daily power consumption of a typical family. It also verifies the effectiveness of the proposed management approach for operation of a stand-alone hybrid system that maximizes the use of a renewable energy source. The results obtained by the present work can get better understanding the dynamic behaviors of the each component or subsystem of the hydrogen PVFC system that helps in improving component’s efficiency and utilizing new system concepts. Moreover, system analysis tools provided by the present work have the potential in cost-down and timesaving in the design of a renewable hybrid-power system.
Acknowledgements This research was partly sponsored by the National Science Council of Taiwan under contract no. NSC 92-2212-E-451-002.
Nomenclature
af Eg Eo eo G k NOCT Ns Rsh Rs Ta Tj To jo jref o a Uact n
ideality factor of the photovoltaic array, gap energy, eV reference solar radiation, W/m2 electron charge, C Gibbs free energy [J/mol] Boltzmann’s constant, J/K normal operating cell temperature, K number of cells in series, shunt (parallel) resistance, [U] series resistance, U ambient temperature, K junction temperature, [K] reference junction temperature, K exchange current density, A/cm2 anodic or cathodic standard exchange current density, A/cm2 transfer coefficient activation overpotential, V number of electrons participating,
R T F CH2 O CO2 pH2 pO2 po psat
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universal gas constant, J/K/mol temperature, K Faraday’s constant, C/mol concentration of water vapor, [-] concentration of the oxygen at the cathode, partial pressure of hydrogen, Pa partial pressure of oxygen, Pa operating pressure, Pa Saturated vapor pressure of pure water, Pa
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