Dynamic modeling of a solar hydrogen system under leakage conditions

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33 (2008) 3615 – 3624

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journal homepage: www.elsevier.com/locate/he

Dynamic modeling of a solar hydrogen system under leakage conditions J.J. Hwanga,, W.R. Changb, A. Suc a

Graduate Institute of Greenergy Technology, National University of Tainan, Tainan, Taiwan Department of Landscape Architecture, Chung-Hua University, Hsinchu 300, Taiwan c Department of Mechanical Engineering and Fuel Cell Center, Yuan Ze University, Taoyuan, Taiwan b

art i cle info

ab st rac t

Article history:

Dynamic behaviors of an integrated solar hydrogen system have been modeled

Received 13 March 2008

mathematically, which is based on a combination of fundamental theories of thermo-

Received in revised form

dynamics, mass transfer, fluid dynamics, and empirical electrochemical relationships. The

12 April 2008

model considers solar hydrogen system to be composed of three subsystems, i.e., solar

Accepted 13 April 2008

cells, an electrolyzer, and a hydrogen tank. An additional pressure switch model is

Available online 5 June 2008

presented to visualize the hydrogen storage dynamics under a leakage condition.

Keywords: Stand-alone power system Solar cell Hydrogen Electrolyzer

Validation of the solar hydrogen model system is evaluated according to the measured data from the manufacturer’s data. Then, the overall was simulated by using solar irradiation as the primary energy input and hydrogen as energy storage for one-day operation. Finally, electrical characteristics and efficiencies of each subsystem as well as the entire system are presented and discussed. & 2008 Published by Elsevier Ltd. on behalf of International Association for Hydrogen Energy.

1.

Introduction

Hydrogen will play a significant role in the energy supply of a sustainable economy in the future since it can be used as an energy carrier to store intermittent renewable energy sources [1]. Today, the major route of hydrogen production is by reforming natural gas. However, in a sustainable economy, it is necessary to produce the hydrogen by renewable energy sources like hydro, wind, biomass, or solar energy [1,2]. The stand-alone renewable hydrogen systems have been widely investigated around the world over the past decades [3–16]. Most of the previous renewable hydrogen projects have been based on solar energy from solar cells (also known as photovoltaics, PV). Lately, wind energy conversion systems have been considered to be a possible power source as well, particularly for weak-grid applications. In all of the renewable hydrogen studies, the electrolyzer is a crucial part, and the

technical challenge is to make it operate smoothly with intermittent power from renewable energy sources. Until now, most of the R&D on water electrolysis related to renewable hydrogen projects has focused on alkaline systems, although there have been some major research efforts on proton exchange membrane (PEM) electrolyzers as well [17–19]. However, the costs associated with PEM electrolysis are still too high, and the market for small-scale H2-production units is at present day still relatively small. Nowadays, many energy and utility companies are trying to position themselves in the future markets of renewable fuels and distributed power generation. Therefore, they are devoting themselves in developing various renewable power systems. The design of technical systems with the help of simulation is very common in many branches of industry. This is because of an increase in the complexity of designs in addition to the shortening of design cycles of products.

Corresponding author. Tel.: +886 62600321; fax: +886 6260321.

E-mail address: [email protected] (J.J. Hwang). 0360-3199/$ - see front matter & 2008 Published by Elsevier Ltd. on behalf of International Association for Hydrogen Energy. doi:10.1016/j.ijhydene.2008.04.031

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The computation power of modern computers is increasing dramatically and hence the computer-based simulation and optimization have received more and more attention, and becoming an important tool for the design of the power system. Therefore, engineers always rely on an efficient simulation tool to get information before a prototype is built. Moreover, once a design is made, there are many occasions to use simulation technology in further applications. The objective of the present paper is to develop a simulation model that effectively predicts the dynamic behaviors of a solar hydrogen system that comprises subsystems including a PV panel, an electrolyzer, and a hydrogen tank. The integrated model is implemented by using Simplorer simulation platform. A case study that examines the hydrogen leakage effects is carried out to demonstrate the transient dynamic behaviors of the solar hydrogen system. It also verifies the effectiveness of the proposed management approach for operation of the solar hydrogen system. The present model will integrate with fuel cell systems to realize the stand-alone renewable power generator in our future work.

2.

System description

Fig. 1 shows a typical stand-alone power system of PV fuel cell. It consists of a solar cell with maximum power point trackers (MPPT) for solar energy conversion, a pressurized alkaline electrolyzer for H2 production, a pressurized tank for H2 storage, fuel cells for H2 utilization, a secondary battery bank for electricity energy buffer, and a DC/AC inverter for the user load [20–22]. Solar cells convert solar irradiations into

33 (2008) 3615 – 3624

electricity. For the increase in overall system efficiency, the DC/DC converter with MPPT enables the solar cells to work at the maximum power point (MPP) in the highly fluctuated environment. Since the large fluctuations in power are associated with the solar irradiation, a battery bank serves as an instantaneous and daily energy buffer for storing the fluctuating power coming from the solar cells. The battery bank smoothes the solar-cell output and eliminates the intermittence. What is more, the battery bank provides electricity for the daily operation of the control unit and auxiliary devices. For an electrolyzer, the H2 generation rate is proportional to the current into the water electrolysis. For space saving and better system performance, H2 will be produced and stored under high pressure. If neither the PV panel nor the battery can provide sufficient electricity, the fuel cell will utilize H2 to produce electricity for the load. The fuel cell needs a DC/DC converter to transform its output voltage level to the DC bus voltage [23,24]. Since the fuel cell cannot promptly follow a sudden load change and its output voltage changes slowly, it behaves as a constant current/ power source. A microprocessor-based controller is used to monitor the status of all solar hydrogen system devices, control and protect them, and coordinate the overall system operation. The present model is limited to the solar hydrogen subsystem that is shown by a dashed block in Fig. 1. A case study of the leakage effect on the dynamics behaviors of the solar hydrogen subsystem is performed. The solar cell supplies electrical energy demand of the electrolyzer for hydrogen production. The hydrogen is then stored in a pressurized tank before use. A pressure switch ahead of the electrolyzer controls the electrolyzer. If the pressure in the hydrogen tank exceeds the set pressure (threshold value), the

Fig. 1 – Typical stand-alone photovoltaic fuel cell (PVFC) power system.

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electrolyzer is cut off by the pressure switch. When the hydrogen pressure is lower than the set pressure, the pressure switch breaks contact to supply the hydrogen again. In the present simulation, there is a small leakage of hydrogen in pipelines and/or fittings, which reduces the H2 tank pressure. Therefore, the pressure switch is used to control a uniform pressure level in the hydrogen tank.

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3.

Modeling

3.1.

PV model

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Fig. 2(a) shows the equivalent circuit of the one-diode model of PV cell [25,26]. The cell/module is described by cell parameters. No partial shading effects are taken into account by this component. Is and Vs are the terminal current and voltage of the model, respectively. Using Kirchhoff’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. It is modeled as Iph ¼ P1 Es ½1 þ P2 ðEs  E0 Þ þ P3 ðTj  T0 Þ

(2)

where E0 and T0 correspond to a reference solar radiation and a reference temperature, respectively. P1, P2, and P3 are empirical constants. They are given in Table 1. For variations of the ambient temperature and irradiation, the cell temperature Tj can be described with a linear approximation as the following equation: Tj ¼ Ta þ Fig. 2 – (a) Equivalent circuit of the PV cell model, (b) simplified circuit diagram of the water electrolysis cell.

Es ðNOCT  20Þ 800

(3)

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 concentrations Series resistance Parallel resistance Ideality factor Normal operating cell temperature

Symbol

Value

Unit

T0 E0 k Eg P1 P2 P3 P4 Rs Rsh af NOCT

298.15 1000 1.3854  1023 1.12 2.96 8.6  104 0.0037 1272.3 1.29 154.1 1 43

K W/m2 J/K eV A m2/W m2/W 1/K A/K3 O O – 1C

Table 2 – 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 Cathodic standard exchange current density

Symbol

Value

Unit

Ns Ac de fair ref

30 150 0.0003 44.5 0.12  103

– cm2 cm – A/cm2

jo;c

Anodic standard exchange current density

jo;a

ref

0.12  106

A/cm2

Cathodic transfer coefficient Anodic transfer coefficient

ac aa

0.5 0.3

– –

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NOCT (normal operating cell temperature) is the temperature at which the cells operated under standard operating conditions (SOC), i.e., irradiance of 0.8 kW/m2, 20 1C ambient temperature, and average windspeed of 1 m/s. Eq. (3) is widely used to estimate in a simple way cell temperature along the year [27,28], although it is only valid for open rack systems. The diode loss current Id due to charge carrier recombination is given by " ! # e0 Vs þ Rs Is Id ¼ Isat exp 1 (4) af Ns k Tj where Isat is the saturated current, af, the ideality factor of the PV array, Ns, the number of cells in series, and, k, Boltzmann’s constant, respectively. The saturated current can be represented by ! Eg 3 (5) Isat ¼ P4 Tj exp  kTj

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behavior of the electrolyzer is Vactual ¼ VOCV þ Zanode þ Zcathode þ Zohm

(8)

The overpotentials represent here the surplus of electrical voltages necessary to activate 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 of the fuel cell. Fig. 2(b) shows the simplified circuit diagram of an alkaline water electrolyzer cell according to Eq. (8). The following equation expresses the theoretical equilibrium cell voltage VOCV of the alkaline water electrolyzer under the effective working conditions, such as temperature and pressure: " !#  RT pH2  pH2 O 3=2 pH2 O;r (9) VOCV ¼ V0 þ 2F p0 pH2 O where V0 is the reversible cell voltage at standard conditions, pH2 ; the operating pressure of hydrogen, and pH2 O ; the water vapor partial pressure.

where Eg is gap energy. Finally, the shunt current Ish is calculated from Ish ¼

V s þ R s Is Rsh

(6)

where Rsh is shunt resistance. From the above reduction, the relations between input and output variables are Is ¼ P1 Es ½1 þ P2 ðEs  E0 Þ þ P3 ðTj  T0 Þ !" ! # Eg e0 Vs þ Rs Is exp 1  P4 T3j exp  kTj af Ns k Tj 

Vs þ Rs Is Rsh

(7)

where the empirical constants P1, P2, P3, and P4 are given in Table 1.

3.2.

Electrolyzer model

An alkaline water electrolyzer consists of several electrolyzer cells connected in series. The electrolyzer model [29–32] considered 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 found by multiplying by the number of series cells. The equation that describes the

Table 3 – Electrical characteristics of the PV panel (Sharp NE-80EJEA) Cell

Polycrystalline silicon

No. of cells and connections Open circuit voltage (Voc) Maximum power voltage (Vpm) Short circuit current (Isc) Maximum power current (Ipm) Maximum power (Pmax)* Module efficiency Maximum system voltage Series fuse rating

36 in series 21.6 V 17.3 V 5.16 A 4.63 A 80 W (+10% / 5%) 12.40% 600 VDC 10 A

*Standard Test Conditions (STC): 25 1C, 1 kW/m2, AM 1.5.

Fig. 3 – Control strategy of the pressure switch.

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The ohmic overpotential can be represented by Zohm ¼ I  Rel

(10)

where Rel is the internal resistance of the electrolyzer and given by [17], and de sk  Ac

(11)

The electrical conductivity sk of the electrolyte KOH is given by sk ¼ 2:62  CKOH þ 0:067CKOH ðT  273:15Þ  4:8  C2KOH  0:088 

C2KOH ðT

 273:15Þ

(12)

where CKOH is the mass concentration of potassium hydroxide. According to the partial reactions during the electrolysis of an alkaline solution at the cathode and the anode, the total

current density j consists of two parts, the cathodic and anodic parts. j ¼ ja þ jc

(13)

The activation overpotentials at the cathode and the anode in the electrolyzer are calculated using the Butler–Volmer equations: h i ð2ac F=RTÞZact;c (14)  eð2ð1ac ÞF=RTÞZact;c jc ¼ jref o;c e h i ð2aa F=RTÞZact;a ja ¼ jref  eð2ð1aa ÞF=RTÞZact;a o;a e

_ O2 ¼ Ns  F _ H2 ¼ 2m m

I 2F

(16)

Fig. 4 – Validation of the present model by comparison of the manufacturers’ data.

Irradiance (W/m2)

MPP POWER (W)

Irradiance(W/m2)

2000

2000

1800

1800

1600

1600

1400

1400

1200

1200

1000

1000

800

800

600

600

400

400

200

200 0

0 0

(15)

_ O2 Þ in _ H2 Þ and oxygen ðm The production rates of hydrogen ðm an electrolyzer cell can be calculated by

MPP Power (W)

Rel ¼

3619

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10000 20000 30000 40000 50000 60000 70000 80000 Time (s)

Fig. 5 – Typical daily solar irradiation and corresponding maximum power of the solar cells.

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where eF and NS are Faraday’s efficiency and number of series cells, respectively. The operational parameters for the above electrolyzer are given in Table 2.

0.98 MPa, the pressure switch breaks contact to electrolyzer which produces the hydrogen.

3.4.

Model platform

Pressure switch model In this work, a multi-domain simulation program Simplorer is employed to model the solar hydrogen system. It is a quasisteady simulation tool with a modular structure and can offer a wide variety of algorithms to determine characteristic values, such as average and RMS values or rise and fall time during a transient simulation. Besides classic gradient-based algorithms, it also offers a sophisticated genetic optimizer. Conventional manual optimization (trial and error) can handle only a small number of parameter variations and is useful for two- or three-dimensional parameter spaces. In contrast, Simplorer can handle higher order problems by

Voltage at MPP (V)

Voltage at MPP (V)

Current at MPP (A)

50

50

45

45

40

40

35

35

30

30

25

25

20

20

15

15

10

10

5

5

0

Current at MPP (A)

In the present system, a normal closed contact switch is employed to switch the electrolyzer on (signal 0) and off (signal 1) depending on the hydrogen pressure in the tank. Fig. 3 shows the control strategy of the pressure switch. For stability, a two-point regulation method is employed to control the pressure switch. The threshold pressure and its corresponding hysteresis are 1.0 and 0.02 MPa, respectively. That is, when the hydrogen pressure in the tank exceeds 1.0 MPa, the electrolyzer is switched off to stop producing hydrogen. If the hydrogen pressure in the tank is lower than

0 0

20000

40000 Time (s)

60000

80000

Fig. 6 – Voltage and current distributions of the solar cells at MPP. Solar Cell Efficiency (%)

16

Junction Temperature (deg C) 60

14 Solar Cell Efficiency (%)

50 12 40

10 8

30

6

20

4

Junction Temperature (°C)

3.3.

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10

2

0

0 0

20000

40000 Time (s)

60000

80000

Fig. 7 – Dynamic trends of the efficiency and junction temperature of the solar cells.

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using automated optimization algorithm. Therefore, a wide range of influences can be taken into account. In addition, it is composed of linked modules and can be integrated into other simulation programs (e.g., MATLAB Simulink).

Results and discussion

4.1.

Model validation

provided by the manufacturer (Sharp NE-80EJEA), as shown in Table 3. The data given by the manufacture under standard test conditions are shown by open circles in Fig. 4, including the open circuit voltage, Voc ¼ 21.6 V, the short circuit current, Isc ¼ 5.16 A, the maximum power delivered, Pmax ¼ 80 W, and the maximum power voltage and current respectively, Vmpp ¼ 17.3 V and Impp ¼ 4.63 A. As for the simulated results, the I–V characteristics of the solar cell for irradiances of 500, 800, and 1000 W/m2 are shown by different curves in Fig. 4. It is seen that the modeled results closely match those provided in the manufacturer’s datasheet.

To validate the present model, the simulated electrical characteristics of a PV panel are compared with those

Electrolyzer Voltage (V)

Electrolyzer Voltage (V)

Electrolyzer Current (A)

35

70

30

60

25

50

20

40

15

30

10

20

5

10

0

Electrolyzer Current (A)

4.

3621

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0 0

20000

40000 Times (s)

60000

80000

Fig. 8 – Voltage and current distributions of the electrolyzer.

Hydrogen Mole Flow Rate (mol/s)

Oxygen Mole Flow Rate (mol/s)

0.006

Mole FLow Rate (mol/s)

0.005

0.004

0.003

0.002

0.001

0 0

20000

40000 Time (s)

60000

80000

Fig. 9 – Mole flow rates of the hydrogen and oxygen produced by the electrolyzer.

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4.2.

PV characteristics

Fig. 5 shows the solar irradiations of a typical sunny day in summer of Taiwan (blue shade) and the corresponding maximum powers delivered by the PV panel (red shade). The electrical characteristics of the PV generator is shown in Figs. 6 and 7. It is seen from Fig. 5 that the distribution of maximum power delivered by the PV panel is largely similar to that of the solar radiation. Fig. 6 further shows the voltage and current distributions of the solar cell at the MPP. It seems that the output voltage should increase as the irradiation increases; however, the distribution of output voltage of the solar cell at the MPP shown in Fig. 6 is inversely related to the daily solar irradiation distribution shown in Fig. 5. As shown by a dashed line in Fig. 7, the cell junction temperature is likely to rise as the irradiation level increases. An increase in cell junction temperature generally leads to a reduction of the output voltage [33]. This makes it imperative to consider the effect of temperature on the cell output voltage. Overall, there is a reduction in the voltage at higher irradiances due to the accompanying higher cell temperature. As for the current distribution at the MPP in Fig. 6, it is largely similar to that of the daily solar irradiance. A small reduction in the terminal voltage in conjunction with a sharp increase in the current leads to an increase in the output power (Fig. 5) since the output power is directly proportional to both the voltage and the current, P ¼ I  V. Fig. 7 further shows the variation of efficiency of the solar cell under the daily irradiant conditions. The efficiency of the solar cell is defined as the ratio of the maximum power output

to the incoming solar irradiation, i.e., P Pmax ns  np  Pmax ¼ ZPV ¼ Es A Es A

(17)

where ns and np are the number of serial cells in a string and the number of parallel strings, respectively. It is seen that the solar-cell efficiency is varied from 8.2% to 13.5%. The lower the solar irradiance the higher the solar-cell efficiency. This is because the solar irradiation increases the operating temperature of the module that causes a reduction in the output voltage and thus the output power of the module. If the temperature rises too much the cell may also be damaged by ‘hot spots’ as well [34].

4.3.

Electrolyzer characteristics

The dynamic behaviours of the electrolyzer and the hydrogen tank are shown in Figs. 8–11. Fig. 8 illustrates the distributions

Hydrogen Tank Pressure (Pa) 1.20E+06 Hydrogen Tank Pressure (Pa)

It is noted also that the short circuit current of the solar cell depends strongly on the solar irradiation while its open circuit voltage is nearly independent of the solar irradiation.

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1.00E+06 8.00E+05 6.00E+05 4.00E+05 2.00E+05 0.00E+00 0

20000

40000 Time (s)

60000

80000

Fig. 11 – Pressure dynamics of hydrogen in the tank.

Electrolyzer Efficiency (%)

90

Electrolyzer Efficiency (%)

80 70 60 50 40 30 20 10 0 0

20000

40000 Time (s)

60000

Fig. 10 – Dynamic trends of the efflciency of electrolyzer.

80000

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of terminal voltage and current of the electrolyzer. It is seen from this figure that the electrolyzer is active by the solar-cell power when it receives the solar irradiation in the morning. Both the terminal voltage and the current are increased by an increase in the solar irradiation. This also means that both hydrogen and oxygen produced by the electrolyzer are increased (Fig. 9). The flow rate of the hydrogen is double that of the oxygen. When the pressure of the H2 tank reaches its maximum allowed pressure (10 atm), the electrolyzer is automatically switched off. As the time proceeds further, the hydrogen pressure decreases due to the leakage (Fig. 11). The electrolyzer is reactive to produce hydrogen when the the hydrogen pressure in the tank is reduced to 9.98 atm. Such control stratages can keep the pressure of the H2 tank in a relatively uniform level. The efficiency of the electrolyzer shown in Fig. 10 is defined as the ratio of the hydrogen enthalpy flow rate to the power requirement of the electrolyzer, i.e., ZEZR ¼

_ H2  hH2 m PEZR

(18)

Except for the idle conditions, the efficiency of the electrolyzer is ranged from 60% to 76%. It has a lower efficiency at a higher irradiation (power) condition. At higher power conditions, the electrolyzer produces hydrogen with a higher operated voltage (Fig. 8) that reduces the reversibility of the system, hence a reduction in the electrolyzer efficiency. Fig. 11 shows the pressure dynamics of the hydrogen tank. At the initial stage, the pressure decreases gradually due to the leakage. When the solar cell is active by the solar irradiation, the electrolyzer begins to produce hydrogen that increases gradually the hydrogen pressure in the tank. The slight zigzag of pressure distribution reflects the control strategy of the pressure switch mentioned above, which keeps the pressure of the hydrogen tank at 1070.02 MPa.

4.4.

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System efficiency

The efficiency of the solar hydrogen system is defined as the ratio of hydrogen enthalpy flow to the total solar irradiation received by the PV panel, i.e., Zsystem ¼

_ H2  hH2 m Es  A

(19)

Actually, Eq. (19) can be further represented by the production of the solar-cell efficiency and the electrolyzer efficiency, i.e., (20)

Zsystem ¼ ZPV  ZEZR

It is seen from Fig. 12 that the efficiency of the present solar hydrogen system is in the range of 5.5–10%. Under higher irradiation conditions, the solar hydrogen system has a hydrogen-production rate with a lower efficiency.

5.

Conclusions

A dynamic model has been developed by exploiting conservation of mass and energy in a solar hydrogen system. The majority of subsystem includes solar cells, an electrolyzer, and a pressurized hydrogen tank. Special attention has been given to the modeling of subsystems to clearly quantify the dynamic interactions among each part of the solar hydrogen system. The integrated model is implemented by using Simplorer simulation platform. Case studies of examining the hydrogen leakage effects have demonstrated that the model can capture the transient dynamic behaviors of the solar hydrogen system. It also verifies the effectiveness of the proposed management approach for operation of a standalone solar hydrogen system, which is essential for determining control strategy to ensure efficient and reliable operation of each part of the solar hydrogen system. Furthermore, the

System Efficiency 12

System Effeciency (%)

10

8

6

4

2

0 0

20000

3623

40000 Time (s)

60000

Fig. 12 – Efficiency of the solar hydrogen system.

80000

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solar hydrogen dynamic model can be integrated with fuel cell system models to design, analyze, and optimize the sustainable energy systems. The extension of this study will be to fully validate the model in our future work.

Acknowledgments This work was partially funded by National Science of Council of Tainan under the contract number NSC 95-2212-E-006. R E F E R E N C E S

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