Optimization of operating parameters in a hybrid wind–hydrogen system using energy and exergy analysis: Modeling and case study

Energy Conversion and Management 106 (2015) 1318–1326

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Optimization of operating parameters in a hybrid wind–hydrogen system using energy and exergy analysis: Modeling and case study Amir Hossein Fakehi a, Somayeh Ahmadi a,⇑, Mohammad Rezaie Mirghaed b a b

Institute of International Energy Studies (IIES), 65, Sayeh St., Vali-e-asr Ave., Tehran 1967743711, Islamic Republic of Iran Energy Engineering Department, Sharif University of Technology, Azadi St., Tehran, Islamic Republic of Iran

a r t i c l e

i n f o

Article history: Received 25 July 2015 Accepted 3 October 2015

Keywords: Exergy analysis Hybrid renewable system Efficiency Wind turbine Fuel cell Electrolyzer

a b s t r a c t In this study, hybrid renewable energy system based on wind/electrolyzer/PEM fuel cell are conceptually modeled, and also, exergy and energy analysis are performed. The energy and exergy flows are investigated by the proposed model for Khaf region-Iran with high average wind speed and monsoon. Exergy and energy analysis framework is made based on thermodynamic, electro-chemical and mechanical model of the different component of hybrid system. Also, the effects of various operating parameters in exergy efficiency are calculated. The results show an optimum wind speed where the exergy efficiency and power coefficient is at maximum level, and also, when the ambient temperature start to be increased in wind turbine, the efficiencies decrease by a great deal for constant wind speeds. Also, the optimum temperature is calculated by exergy analysis in electrolyzer and fuel cell as 353 and the exergy efficiency of electrolyzer decreases by increasing the membrane thickness. Furthermore, pressure changes affect exergy and energy efficiency in PEM fuel cell. Finally, the electrolyzer and fuel cell efficiencies are calculated as 68.5% and 47% respectively. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Availability and environmental hazard of fossil fuel has caused to use resource energy and develop the new technology by human in recent years. Hydrogen is a new environment-friendly energy carrier which is capable of substituting fossil fuels in different applications [1–4]. On the other hand, it can be used in combination with other renewable energy resources, such as wind turbine, to increase reliability [5–7]. As a stand-alone power system, hybrid wind/hydrogen systems have great potentials for contribution in energy markets especially in remote areas [8,9]. In a typical wind/hydrogen hybrid system, hydrogen can be produced by wind power in an electrolyzer and then be consumed by the fuel cells. Among various types of fuel cells, Proton Exchange Membrane (PEM) fuel cells have high efficiency and demonstration level [10]. Since small PEM fuel cell units have been commercially available recently, new opportunities have been created to design hybrid energy systems for remote applications with energy storage in the hydrogen form [11–14]. Thus, hydrogen production can lead to a pathway for electricity generated by wind turbine to store energy for a long time [15,16], and the stored

⇑ Corresponding author. Tel.: +98 21 27644278; fax: +98 2122047188. E-mail address: [email protected] (S. Ahmadi). http://dx.doi.org/10.1016/j.enconman.2015.10.003 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

hydrogen can be used by PEM fuel cell power plants under the low wind speed conditions. Some studies have been reported in the literature that model energy and exergy flow of hybrid systems using wind energy as the energy source. Nfaoui et al. [17] described a model which investigated the feasibility of using a hybrid energy system to provide electricity for an isolated village. They also quantified the optimum wind turbine size and the benefits of a storage system on fuel saving. Ozgnar and Ozgnar [18] studied an exergy and reliability analysis of wind turbine systems. They described if failure rate can be decreased, real availability, capacity factor and exergy efficiency will be improved in the system. Yang and Aydin [19] also carried out theoretical investigations about a hybrid power generation system which utilized wind energy and hydrogen storage. They used a revised wind turbine model to determine the wind power density and the electric output power for hydrogen production. Ni et al. [20] perform energy and exergy analysis to investigate the thermodynamic–electrochemical characteristics of hydrogen production by a PEM electrolyzer plant. They also offered better understanding of the PEM electrolyzer plant characteristics for hydrogen production by renewable energy. In recent years, there have been some studies on fuel cell-wind hybrid systems. Onar et al. [21] described a dynamic model of a wind–fuel cellultra capacitor hybrid system. Their proposed system could tolerate the rapid changes in wind speed and suppress the effects of

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these fluctuations on the equipment side power demand. In the same vein, Kasseris et al. [22] optimized a wind-power fuel-cell hybrid system in an autonomous electrical network environment and concluded that hybridization of wind turbine can increase the plant factor. Kazim presented a comprehensive exergy analysis of a 10 kW PEM fuel cell at variable operating temperatures, pressures, cell voltages and air stoichiometric conditions [23]. Obara et al. investigated the exergy flow and efficiency of a 3 kW proton-exchange-membrane fuel cell and considered the regional characteristic of the distributed energy system [24]. Xydisa et al. analyze exergy concept of wind farms for a case study in Greece, and calculate capacity factor and exergy efficiency [25]. Calderon et al. consider a hybrid wind–solar system with hydrogen storage and simulate the hybrid system for one day, and evaluate performance and exergy efficiency of the whole system [26]. Koroneos and Katopodi assess and maximize wind energy penetration by using hydrogen production. The survey was done using exergy approach and Sankey diagrams [27]. Zafar and Dincer consider energy, exergy and exergoeconomic analysis of electric wind–solar and fuel cell hybrid system. Hydrogen flow rate and the efficiencies were calculated for a constant specification of the system [28]. Baskuta and Ozgener assess exergoeconomic of the wind power plant in the case of Izmir region and calculate exergy loss and costs of the studied plant [29]. Rahimi et al. considered a techno-economic evaluation of wind–hydrogen hybrid system (wind turbine, electrolysis, and PEM fuel cell) in household size [30]. Ludwig et al. utilized the exergy efficiency and cost analyses to compare pathways of hydrogen generation, storage, transportation and utilization [31]. In this paper, the exergy analysis and modeling of a wind turbine and fuel-cell hybrid system is performed. The main objective of this study is to design and develop a model for exergy and energy analysis of a wind hybrid system that uses fuel cell system. The energy and exergy flows are investigated by the proposed model for Khaf region-Iran with high average wind speed and monsoon. Also, this study differs from the previously conducted

ones as follows: (i) exergy and energy analysis in a hybrid wind turbine/electrolyzer/fuel cell system and in each component of system, (ii) investigation of the effects of various operating parameters in exergy efficiency, (iii) comparison of exergy and energy efficiency in each of hybrid system’s components. 2. System configuration The various components used in the developed system include the wind turbines, electrolyzer, hydrogen storage tank, PEM fuel cell. The block diagram of the integrated overall system is shown in Fig. 1. Wind energy is converted to electricity by the wind turbine. The generated electricity may be transmitted to desired places to supply the energy demand. However, continuous power flow to standalone loads cannot be guaranteed due to the lack of energy capacity of storage systems especially under worst climatic conditions. It is possible though to overcome the fluctuations in the output power with an efficient storage technology. Generally, batteries could be used in such systems to eliminate the power fluctuations and improve the operation of the hybrid system. As a promising alternative, the fuel cell can be used as the efficient energy conversion device for the hybrid generation system. In this case, the excess power is transmitted to the electrolyzer and the generated hydrogen is stored in a hydrogen storage tank (Fig. 1a). The fuel cell converts the hydrogen in order to produce electricity and meet the load demand (Fig. 1b). 3. Modeling 3.1. Exergy modeling of system One of the main parameters to achieve in exergy analysis of a system is exergy efficiency. The exergy efficiency of a complicated system can be obtained by dividing useful exergy streams to

air , out air, in

Wind turbine

elec.1

Demand

elec.2 H2O

Electrolyzer

H2

H2 storage

O2 Qloss H2O

Fig. 1a. The block diagram of wind turbine–electrolyzer system.

air air

Wind turbine

elec.

Demand elec. H2 storage

H2

Fuel cell

O2

Qloss air H2O

Fig. 1b. The block diagram of wind turbine–fuel cell system.

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exergy difference between the system input and non-useful output. Therefore, according to Fig. 1 that illustrates condition of hydrogen storage system when charging, the exergy efficiency can be defined as follows. Also, it should be mentioned that the streams which can be used later are not considered in output flows.

w¼

N_ H2 EH2 þ Eelec:1 Eair;in þ EH2 O;in  EO2  EH2 O;out  Eair;out

ð1Þ

In the second state of the hydrogen storage, when discharging, exergy efficiency can be determined by Eq. (2) (as Fig. 1b).

Eelec:1 þ Eelec:2 w¼ Eair;WTin þ Eair;FCin  EH2 O;out  Eair;WTout  Eair;FCout

ð2Þ

3.2. Wind turbine’s exergy and energy model The electrical energy stored in the wind can be expressed as the kinetic power available in the stream of air multiplied by a Cp factor called power coefficient. Tip speed ratio shows the ratio of the turbine blade-tip linear speed to the wind speed, denoted by k. It can be calculated [32–35] as Eq. (3).

k¼

blade speed xrotor Rrotor ¼ wind speed v wind

ð3Þ

For the wind turbine dynamics, Eqs. (4) and (5) are used to gain C pðk;bÞ based on the turbine model specifications of Onar et al. [21].


 c5  c2 C p ¼ c1  c3 b  c4 e ki þ c6 k ki 1 1 0:035 ¼  ki k þ 0:08b b3 þ 1

ð4Þ ð5Þ

Ultimately, the aerodynamic power on the rotor blades is determined as follows:

Protor ¼ 0:5C p qv 3wind pR2rotor

ð6Þ

Total energy produced annually by a wind turbine can be calculated by summing electrical power produced for all times in a year (Annual Energy Production), where gw is the efficiency of the wind turbine electro-mechanical systems and n is the number of bins for intervals of wind turbine power calculations. n X AEP ¼ Protor ðiÞ  gw

ð7Þ

i¼1

Indeed, there are few researches have focused on wind turbine exergy concepts. However, the exergy of wind can be mostly kinetic although there is thermal exergy in the wind. Dincer [36] has determined the exergy of a wind flow and the related efficiencies. The exergy change for a wind stream can be obtained by Eq. (8).

_ P ðT 2  T 1 Þ þ mT _ at ðC P ln Ex ¼ Egen þ mC



 T2 P2 Q  Rln  loss T1 P1 T at ð8Þ

In the equation, Egen is the electrical generation by wind turbine and Tat is the ambient temperature. The state number 1 and 2 are related to before and after entering the turbine. Temperature, in this equation, is a concept named wind-chill temperature that depends on wind speed and can be calculated by:

  T windch ¼ 35:74 þ 0:6215T air  35:75 V 0:16 þ 0:4274T air ðV 0:16 Þ

ð9Þ

Qloss can be obtained by:

  _ P T at  T av erage Q loss ¼ mC

ð10Þ

Taverage is the mean value of input and output wind chill temperatures. By these equations, the wind turbine exergy efficiency can be calculated. This efficiency is defined as the ratio between the generated electricity (exergy) of the wind turbine and the whole air exergy change toward wind turbine. 3.3. Electrolyzer’s exergy and energy model The block diagram of the PEM electrolyzer plant is presented in Fig. 2. In this electrochemical equipment a DC electric current pass between two electrodes and an electrolyte with good conductivity. By DC current, water decomposed into water and oxygen. The losses of this system are H2O and heat which is given to reference environment. In this section, the performance of the PEM electrolyzer plant for hydrogen production has been done by quantitative energy and exergy analysis [32,36]. In this paper, the performance of the system is calculated in terms of energy efficiency ðgÞ and exergy efficiency ðwÞ. These two efficiencies can be defined as: [37]

g¼

N_ H2 LHV Pelec

ð11Þ

w¼

N_ H2 EH2 Eelec þ EH2 O;in  EO2  EH2 O;out

ð12Þ

The outlet flow rate of H2 can be evaluated by:

J N_ H2 O;reacted ¼ N_ H2 ¼ 2F J N_ O2 ¼ 4F J N_ H2 O;out ¼ N_ H2 O;in  2F

ð13Þ ð14Þ ð15Þ

The exergy of a substance (E) can be obtained by Eq. (16) with ignoring the kinetic and potential exergies of the system [23,36]. ph Ei ¼ Ech i þ Ei

ð16Þ


Eph i ¼ ðH  H 0 Þ  T ðS  S0 Þ ¼ C P T 0




Ti Ti  1  ln T0 T0




 Pi þ ln P0

i ¼ O2 ; H2 O; out; H2 O; reacted; H2 ð17Þ The electricity’s energy and exergy of this system is equal and can be calculated by Ni’s electro-chemical model [37]:

Eelec ¼ Pelec ¼ JV

ð18Þ

V ¼ V 0 þ V act;a þ V act;c þ V ohmic

ð19Þ

The activation over-potential of Eq. (19) is evaluated by Butlere–Volmer equation for both electrodes as Eq. (20) and describe the anode and cathode kinetics [37,38]:

H2O

H2 PEM Electrolyzer O2

Elec. H2O

Qloss

Fig. 2. The block diagram of the PEM electrolyzer plant.

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V act;i ¼

RT J 1 sinh F 2J 0;i

!

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! RT J J þ þ1 ln ¼ F 2J 0;i 2J 0;i


 Eact;i J0;i ¼ J ref i exp  RT

ð20Þ

ð21Þ

i ¼ anode; cathode Neglecting the electrical resistances of the anode, cathode and bipolar plates, the ohmic over-voltage of PEM electrolyzer is determined by Eq. (22) [37,39].

V ohmic ¼ JRPEM Z L dx RPEM ¼ 0

ð22Þ ð23Þ

rx

w¼

Eelec EH2 þ EO2  EH2 O;out  EAir;out

ð30Þ

The exergy of a substance can be calculated by Eq. (31) with neglecting the kinetic and potential exergies [32,42].

  ph _ i Ech Ei ¼ m i þ Ei

ð31Þ

i ¼ O2 ; H2 O; Air; H2

Physical exergy is obtained with the difference of enthalpy and entropy of the reactants and products in operation and standard temperature and pressure. The physical exergy is evaluated as:




The conductivity of the PEM is described as [40]:




1 1  rx ¼ ½0:5139kðxÞ  0:326 exp 1263 303 T ka  kc x þ kc kðxÞ ¼ L

of reactants and the products. As shown in Fig. 3, in this system the reactants are air (oxygen) and hydrogen and the products are water and air.



ð24Þ

Eph i ¼ ðH  H 0 Þ  T ðS  S0 Þ ¼ C P T 0



 Ti Ti Pi þ ln  1  ln T0 T0 P0

i ¼ O2 ; H2 O; Air; H2

ð25Þ

ð32Þ

The overall thermal energy balance of the electrolyzer system can be shown as Eq. (26) with assuming a lumped thermal capacitance model [37,32].

The mass flow rates of reactants and the products in PEM fuel cell is described by Larminie and Dicks [32,43]. The mass flow rate of hydrogen, water and oxygen can be determined by following equation:

Q_ gen ¼ Q_ loss þ Q_ H2 O;out

ð26Þ

The over-potentials of the PEM electrolyzer operation will result in heat due to entropy generation r. If r P T DS the heat of reaction in PEM electrolyzer is lower of the heat generation due to irreversibilities so Q_ gen ¼ 0. This heat generation is less than

thermal reaction requirement for r < T DS. in this case the heat input of PEM electrolyzer can be determined by Eq. (27) [37].

r ¼ 2FðV act;a þ V act;c þ V ohmic Þ if

r < T DS ! Q_ gen ¼ ½T DS  rN_ H2 O ¼

if

r P T DS ! Eheat ¼ Q_ gen ¼ 0

J ½T DS  r 2F

ð27Þ

The total heat loss to the environment described as [32]:

1 Q_ loss ¼ ðT  T 0 Þ Rt

ð28Þ

Q_ H2 O;out ¼ Q_ gen  Q_ loss ¼ N_ H2 O;out CðT H2 O;out  T 0 Þ

ð29Þ

3.4. Fuel cell’s exergy and energy model The block diagram of PEM fuel cell system is shown in Fig. 3. In this system hydrogen and oxygen reacted and electricity is generated. The losses of this system are water, Air and heat which is given to the reference environment. In this section the performance of the PEM fuel cell system is evaluated by energy and exergy analysis with calculating the exergetic efficiency as the true value of the performance of an energy system [36,42]. The exergetic efficiency of a fuel cell system is described with the ratio of power output and the difference between the exergy H2

elec.

PEM Fuel cell O2 H2O

Air

Qloss

Fig. 3. The block diagram of PEM fuel cell system.

_ H2 ;R ¼ m

J 2F

ð33Þ

J _ air;R  _ air;P ¼ m m 4F J _ H2 O;P ¼ m 2F

ð34Þ ð35Þ

The open circuit voltage of a fuel cell is related to electrochemical reaction of oxygen and other fuels and can be evaluated by Nernst equation [43].

EOCV ¼ EO þ


 PH2 PO2 DS RT J _ H2 O;P ¼ ðT  T 0 Þ þ m ln nF nF 2F P H2 O

ð35Þ

In real, fuel cell systems are operated under situation that varies greatly from the ideal state. The actual output voltage of the cell is calculated with considering the ohmic resistance, mass transport, kinetics and thermodynamics. This voltage can be obtained by following equation.

U ¼ EOCV  U act  U ohmic  U diff

ð36Þ

The ohmic loss is determined by electrical resistance of anode and cathode also ion transportation resistance of electrolyte using Eq. (37).

U ohmic ¼

lm  1  j ð0:005193k  0:00329Þ exp 1268 303  T1

ð37Þ

The activation voltage occurs at the surface of the electrodes and is calculated by Eq. (38):

U act ¼


 RT j ln nF j0

ð38Þ

The diffusion over voltage is obtained by Eq. (39). In PEM fuel cell if the air used as fuel, the oxygen concentration is reduced in the middle operation so mass transport and concentration losses are considerable in this case [39].

U diff ¼ 


 RT j j ln l 2F a jl

ð39Þ

Hence, the operating voltage of PEM fuel cell is evaluated by [43,44]:

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 P H2 P O2 DS RT lm RT j  j ln ln U ¼ EO þ ðT  T 0 Þ þ nF nF nF j0 P H2 O b
 RT j j þ ln l 2F a jl

ð40Þ

The overall thermal energy balance can be expressed as Eq. (41) with assuming a lumped thermal capacitance model [37]:

Q_ gen ¼ Q_ loss þ Q_ H2 O;out

ð41Þ

The thermal power generated by the PEM fuel cell is given as:

_ w _e Q_ gen ¼ nH

ð42Þ

The heat loss to the reference environment is calculated as:

1 Q_ loss ¼ ðT  T 0 Þ Rt

ð43Þ

_ H2 O CðT H2 O;out  T 0 Þ Q_ H2 O;out ¼ m

ð44Þ

Our objective function is to minimize the exergy efficiency, fx; welec:; wFC g, which is defined in Eqs. (8), (12) and (30). Constraints on variable T a has been defined in (3)–(10), and the feasible interval for this variable is between 10 °C and 20 °C. Furthermore, variables Telec. and Lelec. are bounded via Eqs. (11)– (19) and the feasible region for these variables are 300 °K to 350 °K and 50 lm to 200 lm, respectively. Finally, Eqs. (30)–(40) define constraints on variables PFC and TFC. The feasible regions on these variables are 1 atm to 3 atm and 300 °K to 350 °K, respectively. Results has been shown and discussed in this section. It is worth mentioning that because of the extent of the results, we displayed the value of objective function only in few points to represents the amount of changes in exergy efficiency corresponding to changes of each parameter. And the constants used in the modeling are presented in Table 1. The annual energy demand and wind turbine power generation in Khaf region is shown in Fig. 5 If the power generation is higher than demand, the excess power enters in PEM electrolyzer and

4. Results and discussion Table 1 Constants of wind/electrolyzer/fuel cell models.

4.1. Case study

Notation

The Khaf region was selected as a case study in this research. Daily wind speed and monthly average wind speed is shown in Fig. 4. This region has a discrete seasonal wind speed regime because of the wind speed is very low in October to February so in this period fuel cell can provide the daily energy demand. In this case study, from March to Sep, power generated by the wind turbine is capable to supply the entire load directly. The excess power generated in this period will enter to the proposed electrolyzer system for hydrogen production, which is consumed by fuel cell system in the duration of October to February. The used system sizing algorithm in this paper is shown in [35]. According this, the capital cost and capacity of components show in Table 2. 4.2. Modeling results In order to find the optimum point, we develop an algorithm based on pattern search method in MATHLAB 2010, in which the decision variables has been investigated over their feasible region. The decision variables of our optimization procedure are: T a : ambient temperature. T elec: : electrolyzer temperature. Lelec: : electrolyte thickness. PFC : fuel cell pressure. T FC : fuel cell temperature.

25 Daily wind speed Monthly average wind speed

Wind speed (m/s)

    

20 15 10 5 0 0

50

100

150

200

250

300

Days Fig. 4. Daily wind speed and monthly average wind speed.

350

Parameters

Wind turbine Jrotor Rotor inertia Rotor radius Rrotor GR Gear ratio JG Generator inertia P gen Generator power Coefficient c1 c2 Coefficient c3 Coefficient c4 Coefficient c5 Coefficient c6 Coefficient p Generator pole pair Electrolyzer Eact;a Activation energy for anode Activation energy for Eact;c cathode Water content at the anode– ka membrane interface Water content at the kc cathode–membrane interface L Membrane thickness V0 Reversible potential Rt Overall thermal resistance of electrolyzer Exchange current density for Jref a anode Exchange current density for Jref c cathode Oxygen pressure P O2 P H2 Hydrogen pressure Water pressure P H2 O Hydrogen lower heating LHV H2 value Average specific heat of CpH2 hydrogen Average specific heat of CpO2 oxygen Fuel cell T F P O2 P H2 P H2 O lm jl j0  k

Temperature Faraday constant Oxygen pressure Hydrogen pressure Water pressure Membrane length Maximum current Exchanged current Water transport coefficient

Values

Unit

Ref.

4915797.5 35 70 81.2 1500 0.5176 116 0.4 5 21 0.0068 3

kg mm m ... kg mm kW ... ... ... ... ... ... ...

[45] [45] [45] [45] [45] [21] [21] [21] [21] [21] [21] [45]

76 18

kJ mol1 kJ mol1

[46,37] [46,37]

14

...

[47,37]

10

...

[47,37]

50 1.2 0.167

m V °C W1

[48,37] [37] [9]

105

A m2

[37]

10

A m2

[37]

1 1 1 242

atm atm atm kJ/kmol

[49,37] [49,37] [49,37]

14.3

kJ kg1 K1

[23]

1

[23]

1.005

kJ kg

343 96478 0.63 3 1 0.015 1 0.0001 18

K C=mol atm atm atm m A A ...

K



[42] [41,42] [41,42] [41,42] [41,42] [42] [42] [42] [41]

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A.H. Fakehi et al. / Energy Conversion and Management 106 (2015) 1318–1326 Table 2 The size and capital cost of hybrid system’s component. Optimal size

Capital cost

355 kW 3.5 m 224 kW 2000 kW h 2200 kW 800 N m3

1100 $/kW [50] 250 $/m [51] 2000 $/kW [52] 120 $/kW h [52] 1500 $/kW [52] 500 $/kg [52]

Total capital cost for Khaf region:

Exergy Efficiency

Wind turbine Wind tower PEM fuel cell Battery Electrolyzer Hydrogen tank

0.7

T=12 C T=14 C T=18 C

0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

4415.3 MUS$

15

20

25

Wind Speed (m/s) Fig. 7. The wind turbine exergy efficiency in different temperature.

450

Wind turbine power Demand

400 350

0.7

Energy Efficiency

Power (kW)

300 250 200 150 100 50

0.6 0.5 0.4 0.3 0.2 0.1 0

0 0

50

100

150

200

250

300

0

350

50

100

150

200

250

300

350

Days

Days

Fig. 8. The energy efficiency of wind turbine.

Fig. 5. The annual energy demand and wind turbine power generation in Khaf region.

and 9 illustrates the energy and exergy efficiency profile in one year period, respectively. As can be seen, the energy efficiency of a wind turbine cannot exceed the betz law level (wind turbine’s coefficient of Power: about 0.59). Also, exergy efficiency of a specific wind turbine relies on ambient temperature and wind speed in different moments. The hydrogen flow rate produced by electrolyzer is shown in Fig. 10. There is enough H2 reserved throughout the year for the

0.14 0.12

Exergy Efficiency

produce hydrogen. And if the power demand is greater than the wind turbine power generation, the fuel cell supplies the load. The principal exergy model of wind turbine can be based on above relations. The modeling results for the case study Temperature and wind speed profile are obtained. The exergy efficiency and power coefficient for wind turbine in a constant ambient temperature (12 °C) as a function of wind speed is illustrated in Fig. 6. It can be seen that there is an optimum wind speed where the exergy efficiency and power coefficient is at maximum level. Indeed, by increasing wind speed for constant conditions, those efficiencies decrease to about zero. Also, because the thermal and the other types of the exergy of the wind flow cannot be absorbed by the turbine, the exergy efficiency is lower than the power coefficient. Moreover, for different temperatures, the exergy efficiency is calculated and illustrated in Fig. 7 varying wind speed. When the ambient temperature start to be increased, the efficiencies decrease by a great deal for constant wind speeds, because the thermal exergy of the wind flow increase relative to ambient temperature and it can seldom be absorbed by the wind turbine. The energy efficiency of a wind turbine can be considered equivalent to the power coefficient in a short time interval. Thus, the annual energy and exergy efficiency profile is calculated for the studied region and wind speed and temperature profile. Figs. 8

0.1 0.08 0.06 0.04 0.02 0 0

50

100

150

200

250

300

350

300

350

Days Fig. 9. The exergy efficiency of wind turbine.

0.7 Exergy Efficiency Power Coefficient

0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

20

Wind Speed (m/s) Fig. 6. The exergy efficiency and power coefficient of wind turbine.

25

Hydrogen flow rate (mol/s)

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50

100

150

200

250

Days Fig. 10. The hydrogen flow rate produced by electrolyzer.

A.H. Fakehi et al. / Energy Conversion and Management 106 (2015) 1318–1326

74 T=353 K T=323 K T=300 K

70 68 66 64 62 60 58 56 54

10

20

30

40

50

60

Days Fig. 11. The exergy efficiency of PEM electrolyzer at different temperature.

70 68 66 64 62 60 58 56 10

20

30

40

50

60

Days Fig. 13. the energy and exergy efficiency of PEM electrolyzer in optimum values of parameter.

50 45 40 35 30 25 20 15 10 5 0 90

100

110

120

130

140

150

160

170

180

Days Fig. 14. The exergy efficiency of PEM fuel cell at 1 and 3 atm.

pressure variation in cathode and anode. Therefore, pressure changes effect on exergy and energy efficiency in PEM fuel cell. Fig. 15 shows the effect of temperature changing on exergy efficiency of PEM fuel cell in hybrid system. According this figure, the optimum temperature is 353 that related to activation overpotential. Also, a compression between energy and exergy efficiency of PEM fuel cell in this system is illustrated in Fig. 16. The total energy input in wind turbine is 9266 MW h annually in Khaf region and accumulative of energy output in wind turbine is calculate as 3132 MW h/year. So, the energy efficiency in this technology is 33.8. 1401 MW h of energy supply the energy demand after passing from electrical invertor. Also, 1731 MW h excess energy entire to electrolyzer and 1147.6 MW h exit from it. The exergy efficiency of PEM electrolyzer is 68.5%. The fuel cell energy output in case study region is 456.7 MW h/year and exergy efficiency of this is 47%. The energy and exergy analysis result of the case study illustrate in Table 3.

50

72

Exergy efficiency (%)

Energy Exergy

72

L=50 µm L=120 µm L=200 µm

70 68 66 64 62 60 58

45

Exergy efficiency (%)

Exergy efficiency (%)

72

74

Efficiency (%)

system to deliver power without interruption. The lowest level is reached in October to February, where prolonged periods of low wind speed almost exhaust H2 reserves. Obviously, one may decide a different power production scheme in actual operation in order to avoid such low H2 levels. A comparison between exergy efficiency of PEM electrolyzer at typical working temperature of 300 K, 320 K and 353 K are shown in Fig. 11. According to results, the exergy efficiency increase with increasing temperature. The increasing of temperature causes to increase the exchange current density and decrease the activation over-potential. On the other hand, because of ionic conductivity and thermal resistance of membrane, the working temperature cannot increase higher than 353. So the optimum temperature is 353. The effect of electrolyte thickness on exergy efficiency is illustrated in Fig. 12. The thickness of the electrolyte can be changed from 50 lm to 200 lm due to the limitations of thermal resistance and mechanical strength of membrane. The exergy efficiency of electrolyzer decrease with increasing the membrane thickness. This is because increase the ohmic over-potential in thicker membrane. So, In order to achieve higher exergy efficiency, the optimum membrane thickness is 50 lm. Fig. 13 also illustrate a comparison between energy and exergy efficiency of electrolyzer in Khaf region. The results show that the difference between energy and exergy efficiency is small in optimum values of membrane thickness and working temperature (50 lm ad 353 K). The changing of exergy efficiency in different pressure is shown in Fig. 14. Pressure changes in each electrode cause the reactant concentration variation. And since the hydrogen transfer in membrane is done by water in PEM fuel cell, so pressure differential has an important factor in PEM fuel cell performance. Also, according to theoretical equation, conductivity change as nonlinear with

Exergy efficiency (%)

1324

40 35 30 25 20 15 10 5

56 10

20

30

40

50

60

Days Fig. 12. The exergy efficiency of electrolyzer at different electrolyte thickness.

0 90

100

110

120

130

140

150

160

170

Days Fig. 15. The fuel cell’s exergy efficiency at 353 and 337 K.

180

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50

Exergy Energy

45

Efficiency (%)

40 35 30 25 20 15 10 5 0 90

100

110

120

130

140

150

160

170

180

Days Fig. 16. The exergy and energy efficiency of PEM fuel cell at optimum parameter.

Table 3 The energy and exergy analysis results. Wind turbine Energy input (MW h) Energy output (MW h) Energy efficiency (%)

9266 3132 33.8

Electrolyzer Energy input (MW h) Energy output (MW h) Energy efficiency (%) Exergy efficiency (%)

1731 1147.6 66.3 68.5

PEM fuel cell Energy input (MW h) Energy output (MW h) Energy efficiency (%) Exergy efficiency (%)

1136 456.7 40.2 47

1325

 The exergy efficiency of electrolyzer decrease with increasing the membrane thickness because of increasing the ohmic over-potential in thicker membrane. So, In order to achieve higher exergy efficiency, the optimum membrane thickness is 50 lm.  Since the hydrogen transfer in membrane is done by water in PEM fuel cell, so pressure differential has an important factor in PEM fuel cell performance. Also, conductivity change as nonlinear with pressure variation in cathode and anode. Therefore, pressure changes effect on exergy and energy efficiency in PEM fuel cell.  The optimum temperature is 353 that related to activation over-potential in PEM fuel cell.  The results showed the electrolyzer and fuel cell have acceptable efficiency as gex;elec: ¼ 68:5% and gex;Fuelcell ¼ 47%. Besides, it is deserved to take further research to do the technoeconomic analysis for the wind turbine/electrolyzer/fuel cell hybrid system also, confirm these results by experimental methods.

References

5. Conclusion In this study we have investigated the energy and exergy analysis of wind/electrolyzer/fuel cell hybrid system. We have presented an aerodynamic/electro-mechanical model for wind turbine and two thermodynamic/electro-chemical models for PEM electrolyzer and fuel cell. And we determined the exergy and energy efficiency of various component of hybrid system in the Khaf region as a monsoon region. Also, we investigated the effects of various operating parameters in exergy efficiency. We have extracted the following conclusions from this research:  An optimum wind speed where the exergy efficiency and power coefficient is at maximum level. And by increasing wind speed for constant conditions, those efficiencies decrease to about zero. Also, the exergy efficiency is lower than the power coefficient, because the thermal and the other types of the exergy of the wind flow cannot be absorbed by the turbine.  When the ambient temperature start to be increased in wind turbine, the efficiencies decrease by a great deal for constant wind speeds, because the thermal exergy of the wind flow increase relative to ambient temperature and it can seldom be absorbed by the wind turbine.  The energy efficiency of a wind turbine cannot exceed the betz law level. Also, exergy efficiency of a specific wind turbine relies on ambient temperature and wind speed in different moments  The increasing of temperature in PEM electrolyzer causes to increase the exchange current density and decrease the activation over-potential. On the other hand, because of ionic conductivity and thermal resistance of membrane, the working temperature cannot increase higher than 353. So the optimum temperature is 353.

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