Design of a novel concentrating photovoltaic–thermoelectric system incorporated with phase change materials

Energy Conversion and Management 112 (2016) 49–60

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Design of a novel concentrating photovoltaic–thermoelectric system incorporated with phase change materials Tengfei Cui a, Yimin Xuan a,b,⇑, Qiang Li a a b

School of Energy and Power Engineering, Nanjing University of Science & Technology, China College of Energy and Power Engineering, Nanjing University of Aeronautics & Astronautics, China

a r t i c l e

i n f o

Article history: Received 7 October 2015 Accepted 5 January 2016

Keywords: Solar energy utilization Photovoltaic cells Thermoelectric modules Phase change material PV–PCM–TE system

a b s t r a c t Since the solar irradiance within a day is varying, the temperature of the photovoltaic–thermoelectric (PV–TE) system becomes fluctuant with the change of the incident solar irradiance, which exerts a significant influence on the efficiency of the total system. In this paper, the phase change material (PCM) is introduced into the PV–TE system to construct a novel PV–PCM–TE hybrid system. The purposes of applying PCM are to mitigate the temperature fluctuations of the PV cell and the TE modules and keep the hybrid PV–TE system operating under a fixed operating condition. A theoretical model of evaluating the efficiency of the concentrating PV–PCM–TE hybrid system is presented. The feasibility of the PV–PCM–TE system with four types of PV cells, c-Si, CIGS, single-junction GaAs, and GaInP/InGaAs/Ge (III–V), are investigated. The optimum operating conditions which indicate that the PV–PCM–TE system has the highest total efficiency are discussed to determine the melting temperatures of PCMs. A series of structure parameters are designed to obtain the optimized parameters for the PV–PCM–TE system, and the influences of these parameters on the PV–PCM–TE system are investigated. The results indicate that the performance of the PV–PCM–TE system is superior to single PV cells and/or PV–TE systems. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Solar energy which is currently one of the most renewable and potential energy sources has been widely focused and investigated. However, only a limited solar energy incident on a photovoltaic (PV) cell can be converted into electricity; the remaining absorbed solar energy has to be transformed into heat, which is not only a waste of energy but also an adverse influence factor for the PV cell converting solar energy into electricity [1]. Therefore, reutilization of this part of exhaust heat and further improving the efficiency of utilizing solar energy becomes an attractive problem and receives more and more attentions. Recently, a so-called hybrid photovoltaic–thermoelectric (PV–TE) system has been proposed, which implies enhancement on the total efficiency of utilizing solar energy [2–12]. Wang et al. [6] measured the conversion efficiency of a hybrid PV–TE system which was combined by the series-connected dye-sensitized solar cell (DSSC), a solar selective absorber (SSA), and a TE generator. They found that compared with the referenced efficiency 9.39% of the DSSC, the maximum entire efficiency of the entire PV–TE ⇑ Corresponding author at: School of Energy and Power Engineering, Nanjing University of Science & Technology, China. Tel.: +86 025 84890688. E-mail address: [email protected] (Y. Xuan). http://dx.doi.org/10.1016/j.enconman.2016.01.008 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

system amounted to 13.8%. Hsueh et al. [7] investigated the performance of the PV–TE system formed by the CuInGaSe2 (CIGS) PV cell and a TE generator, the maximum total efficiency of the whole hybrid system increased from 16.5% to 22.02%. Zhang et al. [8] developed a theoretical model of the concentrating PV–TE hybrid system. By using fins as cooling device, the enhancement of 1–8% on the total efficiency of utilizing solar energy was realized compared with the pure PV system. A similar simulation was found in the work of Liao et al. [9], the difference between their work and the studies from Zhang’s group [8] was that the matched load resistances in the PV–TE system were discussed. Moreover, Dallan [10] experimentally investigated the viability of a PV–TE system. The experimental results showed that the output power of the PV–TE system increased up to 39% under the fixed thermal input conditions compared with the PV module’s operating performance in the absence of the TE module. For most of the aforementioned investigations, the PV–TE systems were mostly tested or simulated under the laboratory environment (AM 1.5) which implies a constant solar irradiance 1000 W/m2. At this situation, the operating temperature of the PV–TE system may be kept at a constant value. In fact, the solar irradiance during a day changes along the time and the operating temperature of the PV–TE system varies with the changes of solar irradiance as consequence. Wu et al. [11] studied the performance of a PV–TE system by using the nanofluid as

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T. Cui et al. / Energy Conversion and Management 112 (2016) 49–60

Nomenclature A h l Ac T Twi Two Twm m cp R Rc hw hair 1/hr P t C Cth G J NA ND NC NV I(k) c kB Eg k ni p n Rre RSRH RAug T ZT E H Tm

area (mm2) height (mm) the length of channels (mm) the cross sectional area of channels (mm2) temperature (K) temperature of water at the inlet (K) temperature of water at the outlet (K) mean temperature of the water (K) the number of channels thermal capacity (J/kg K) thermal resistance (mm2 K/W) thermal contact resistance (mm2 K/W) convection heat transfer coefficient of water (W/mm2 K) convection heat transfer coefficient of air (W/mm2 K) radiation thermal resistance (mm2 K/W) power (W) time (s) optical concentrating ratio thermal concentrating ratio optical generation rate current density (mA cm
2) acceptor doping concentration (cm
3) donor doping concentration (cm
3) the effective densities of electrons (cm
3) the effective densities of holes (cm
3) the solar irradiance spectrum (cm2 s
1) speed of light (m/s) Boltzmann constant (1.38  10
23 J K
1) the band-gap energy (eV) thermal conductivity (W/m K) the intrinsic carrier concentration (cm
3) free hole concentration (cm
3) free electron concentration (cm
3) carrier recombination rate (cm
3 s
1) Shockley–Read–Hall recombination Auger recombination temperature (K) the dimensionless thermoelectric coefficient heat absorbed by phase change material the latent heat of phase change material the melting temperature of phase change material

the coolant in the PV–TE system under a daily changed solar irradiance. The results showed that compared with the forced air cooling method, cooling the PV–TE system with the nanofluid can significantly improve the efficiencies of the PV–TE system. However, the efficiency and the temperature of the PV–TE system were still fluctuant due to the changes of solar irradiance, which induced a series of questions related to the practical applications of the PV–TE system in a realistic situation, such as the designs of structure sizes of the PV–TE systems, the matching of the load resistance [12], and the controls of the cooling system of the PV–TE system [11]. Therefore, it is necessary to weaken the influence of fluctuant solar irradiance on the PV–TE system, and make sure that the PV–TE system operates under the optimal operating status. To suppress the temperature fluctuation of a PV–TE system induced by the fluctuant solar irradiance, one of alternative methods is using phase change materials (PCM). This is because that PCM can absorb a large amount of energy as latent heat at a constant phase transition temperature, and thus be widely used for

Nu Re Pr Dh f Rq u, v, w x, y, z

Nusselt number Reynolds number Prandtl number the hydraulic diameter of channels (mm) friction factor root mean square roughness of the channels (lm) velocity (m/s) coordinate (m)

Greek letters ⁄ Planck constant (6.63  10
34 J s) a(k) absorption coefficient (m
1) b temperature coefficient (K
1) dSB Stefan–Boltzmann constant (5.67  10
8 W m2 K4) e dielectric constant (F m
1) g efficiency (%) k wavelength of photon (lm) ln carrier mobility (cm2 V
1 s
1) / electrostatic potential (V) s relaxation time (s) l viscosity (mm2/s) q density (kg/m3) Subscripts lens Fresnel lens PV photovoltaic cell PCM phase change material TE thermoelectric generators hs heat sink pump pump n electron or the n-type material p hole or the p-type material w water air air r radiation L liquid phase of phase change material S solid phase of phase change material up up side surface down down side surface

passive heat storage and temperature control of electronics [13]. Recently, PCMs are more and more incorporated with photovoltaic devices to improve their conversion performance. Huang et al. [14–16], Maiti et al. [17] and Aelenei et al. [18] numerically and experimentally investigated the performance of a PV–PCM system. All these efforts indicated that using PCM can maintain the system operating under a steady-state and low temperature fluctuation during the day time, and then generate a greater electrical power output. In addition, Malvi et al. [19] proposed the concept of a combined photovoltaic thermal (PVT)–PCM system. By using water cooling, they found that the PCM further mitigated the temperature rise of the PV cell, so that the PV cell operated at a steadystate temperature during a day. Therefore, in order to eliminate the influence induced by the fluctuant solar irradiance on the PV–TE system, PCM is introduced into the PV–TE system in this paper to construct a novel hybrid PV–PCM–TE system. A theoretical model of the PV–PCM–TE hybrid system is presented to evaluate its performances under different conditions. The feasibility of a PV–PCM–TE system operating under

T. Cui et al. / Energy Conversion and Management 112 (2016) 49–60

a real fluctuant solar irradiance is investigated, and the design parameters of the PV–PCM–TE system are optimized. The purpose of this work is to design the PV–PCM–TE system that is able to operate under the realistic situation in the near future. 2. The theoretical model of PV–PCM–TE system 2.1. The geometric structure of the PV–PCM–TE hybrid system One integrated PV–PCM–TE hybrid system is mainly composed of the following components such as an optical concentrator, a PV cell, a container filled with PCM, TE modules, and a cooling system (as shown in Fig. 1). A commercially available Fresnel lens with a high optical transmittance of 98% is selected as the optical concentrator to concentrate solar radiation upon the PV cell. The optical concentration ratio C is defined as the ratio of the area Alens of Fresnel lens to the area APV of the PV cell. The distance between the Fresnel lens and the PV cell is determined by the optical concentration C and the focal length of the Fresnel lens. By considering the fact that the concentration of Fresnel lens may lead to a high temperature of the PV cell, the PCM container is directly attached below the PV cell via thermal interface materials to reduce the thermal contact resistance and the temperature difference between PV cell and PCM. The area APCM of PCM container is set to the same as the Alens. In the PCM container, several fins are designed to enhance the heat transfer between the container and PCM, and reduce the thermal resistance between the PV cell and the TE modules. The container and fins are all made by copper material, the thicknesses of fins and the container are all set to 1 mm, the separation distance between fins is 10 mm, the height of the fins is equal to the height of the container, and the length of fins is 20 mm shorter than the length of container. Since the operating temperature of a PV cell is commonly controlled under 200 °C, bismuth telluride (Bi2Te3) is chosen as the material of the TE modules. The height of the Bi2Te3 is 2 mm and the thicknesses of the ceramic insulation layers below and over Bi2Te3 are 1 mm. For the sake of simplicity, the total area of n-type and p-type thermocouples is considered to be equal to the area of the ceramic plates which is defined as the area ATE of TE modules. The numbers of the n-type and p-type thermocouples are determined by the area of TE modules. At the bottom of the TE modules, a heat sink is employed as a cold source for the TE modules. The area Ahs of the heat sink is the same as the ATE. Small channels with the height

51

of 8 mm and width of 3 mm are designed in the heat sink and the separation distance between channels is 1 mm. Water is used as the coolant. Some more details of the parameters of the PV–PCM–TE hybrid system can be found in Table 1. 2.2. The energy transfer network of the PV–PCM–TE system As shown in Fig. 2, the energy transfer across the PV–PCM–TE system can be considered as a set of elements connected together by a thermal resistance network, each with a temperature and capacitance. Once the solar energy irradiates on the PV cell, a part of the solar energy is converted into electricity PPV by the PV cell, which is determined by the efficiency of the PV cell. The rest solar energy is converted to the heat and transferred from the PV cell to the PCM, which leads to the temperature rise and phase change of the PCM. The parameter E is the heat absorbed by the PCM, which can be released when the solar irradiance is reduced. Subsequently, the remaining heat is transferred into the TE modules to generate electricity PTE. Finally, the exhaust heat which is transferred from the TE modules into the heat sink is taken away by water. In the thermal resistance network of the PV–PCM–TE system, each component has its internal thermal resistance, and is connected with others through a thermal contact resistance. Due to the fact that the thermal contact resistance extremely impedes heat transfer across the interface, some suitable thermal interface materials are usually used between two adjacent contact surfaces in the practicality. When thermal interface materials are used, the thermal contact resistance is usually between 20 mm2 K/W and 100 mm2 K/W [20,21]. The governing equations for energy transfer processes in the PV–PCM–TE system are as following [7,16–18]:

8 CGAPV ¼ APV ðT PV-up
T PV-down Þ=RPV > > > > > > þP PV þ APV ðT PV-up
T amb Þhr ðT PV-up Þ þ APV hair ðT PV-up
T amb Þ > > > > > > A > PV ðT PV-down
T PCM-up Þ=Rc 1 ¼ APCM ðT PCM-up
T PCM-down Þ=RPCM > > > > > þEPCM þ ðAPCM
APV ÞðT PCM-up
T amb Þðhr ðT PCM-up Þ þ hair Þ > > > > > > < APCM ðT PCM-up
T PCM-down Þ=RPCM ¼ ATE ðT PCM-down
T TE-up Þ=Rc 2

þðAPCM
ATE ÞðT PCM-down
T amb Þðhr ðT PCM-down Þ þ hair Þ > > > > > > ATE ðT PCM-down
T TE-up Þ=Rc 2 ¼ ATE ðT TE-up
T TE-down Þ=RTE þ PTE > > > > > A ðT > TE > TE-down
T hs-up Þ=Rc 3 ¼ Ahs ðT hs-up
T hs-down Þ=Rhs > > > > > ¼ hw ðT hs-down
T wm Þð2a þ 2bÞlm ¼ qw cp
water uw mAc ðT wo
T wi Þ > > >
 > > > : hr ðTÞ ¼ ePV r T 2 þ T 2amb ðT þ T amb Þ ð1Þ The time-dependent conversion efficiency of the PV–PCM–TE system is

gðtÞ ¼ ðP PV ðtÞ þ P TE ðtÞ
P pump ðtÞÞ=CGðtÞAPV

ð2Þ

The daily total efficiency of the PV–PCM–TE system is defined as

g¼

P ðPPV ðtÞ þ PTE ðtÞ
Ppump ðtÞÞDt P CGðtÞAPV Dt

ð3Þ

2.3. The electricity output of PV cells

Fig. 1. The proposed PV–PCM–TE hybrid system diagram.

The numerical simulation of PV cell is mainly based on the semiconductor equations [22,23]. According to the different structures, materials, and doping density of PV cells, different I–V curves of PV cells with different temperatures can be obtained. Thus, the electricity output power and the efficiencies of PV cells can be calculated from the I–V curves. Generally, the semiconductor equations [22,23] can be expressed as:

52

T. Cui et al. / Energy Conversion and Management 112 (2016) 49–60 Table 1 The initial values of the parameters of the PV–PCM–TE hybrid system for application. Parameters

Symbol

Value

Ambient temperature (K) Emission of the PV The area of the PV (mm2) The height of the PV (mm) The area of the PCM (mm2) The height of the PCM (mm) The thickness of the shell of the PCM container (mm) The thickness of the fin in the PCM container (mm) The length of the fin in the PCM container (mm) The height of the fin in the PCM container (mm) Thermal conductivity of copper (W m
1 K
1) The area of TE (mm2) The height of ceramic (mm) Thermal conductivity of ceramic (W m
1 K
1) Thermal conductivity of n-type material in TE (W m
1 K
1) Thermal conductivity of p-type material in TE (W m
1 K
1) The height of the TE leg (mm) The area of the heat sink (mm2) The height of the heat sink (mm) The height of the channels (mm) The width of the channels (mm) The distances between two channels (mm) The channels’ hydraulic diameter (mm) The length and width of heat sink (mm) Water temperature at the inlet (K) Number of the channels Flow rate of water (m/s) Density of water (kg/m3) Thermal capacity of water (J kg
1 K
1) Kinematic viscosity of water (m2/s) Thermal conductivity of water (W m
1 K
1) Natural convection heat transfer coefficient (W K
1 m
2) Thermal contact resistance (mm2 K/W) The root mean square roughness factor (lm)

Tair

300 0.7 10 ⁄ 10 0.3 C ⁄ APV 10 1 1 (C ⁄ APV)0.5
20 =hPCM 398 40 ⁄ 40 1 30 2 1 2 =ATE 10 8 3 1 2ab/(a + b) (Ahest sink)0.5 293 l/(a + 1) 0.01 998.2 4183 1.006  10
6 0.599 5 20 3

ePV APV hPV APCM hPCM

ATE

kn kp hTE Ahs hhs b a Dh l T wi m uw

qw cp-water

lw kw hair Rc Rq

Fig. 2. The energy transfer network of the PV–PCM–TE hybrid system.

8 rðer/Þ ¼ qe ðp
n þ ND
NA Þ > > > > > > < rJ n ¼
qe ðG
Rre Þ rJp ¼ qe ðG
Rre Þ > > > > J n ¼
qe ln nr/ þ kB T ln rn > > : J p ¼
qe lp pr/
kB T lp rp

The simple Lambert–Beer absorption is used to calculate the optical generation rate [24]:

ð4Þ

SRH

:R

Aug

np
n2

¼ sp ðnþni Þþsni ðpþni Þ ni ¼   2 ¼ ðC n n þ C p pÞ np
ni

hc=Eg

CIAM1:5 ðkÞaðkÞe
aðkÞx dk

ð6Þ

kmin

where the carrier recombination Rre includes the Shockley–Read– Hall recombination (RSRH) and the Auger recombination (RAug), which can be calculated by the following equations [23]:

8
Z Gðx; tÞ ¼

pffiffiffiffiffiffiffiffiffiffiffiffi
Eg Nc NV e 2kT

ð5Þ

where IAM1.5(k) is the global standard solar irradiance spectrum of AM1.5. In order to simplify the simulation model, the efficiency of PV cells is assumed to be dependent upon its type, the structure, and the operating temperature of the PV cell. Therefore, the relationship between efficiency and output power of PV cells is as follows:

PPV ¼ CGAPV gPV ðTÞ

ð7Þ

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T. Cui et al. / Energy Conversion and Management 112 (2016) 49–60

2.4. The electricity output of TE modules The TE modules can convert waste heat into electricity via the Seebeck effect. Therefore, the temperature difference between the two surfaces of TE modules has a great influence on the efficiencies of TE modules. Under the assumption that the heat flux transferred across TE modules is high enough, the optimized efficiency of TE modules can be given by [25]

gTE ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T TE-up
T TE-down 1 þ ZT
1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T T TE-up 1 þ ZT þ TTE-down TE-up

ð8Þ

where TTE-up is higher than TTE-down. The output power of TE modules can be defined as follows:

PTE ¼ gTE ATE ðT PCM-down
T TE-up Þ=Rc2

ð9Þ

The equivalent thermal conductivity of TE modules is

kTE ATE hTE ¼ kp Ap =hp þ kn An =hn

ð10Þ

Because the surface area ATE is different from the area APCM, the ratio of APCM to ATE is defined as the thermal concentration [25]:

Fig. 3. Measured daily irradiation profile of Nanjing (E118°420 /N32°030 ) in 11th of September.

C th ¼ APCM =ATE

the flow velocity of water. The formulas of calculating hw and Ppump are as follows:

ð11Þ

hw ¼ kw Nu=Dh

2.5. The thermal model of the PCM Since the phase change occurs at a set temperature, the temperature field of PCM can be described as

8 > < E=cs T ¼ Tm > : T m þ ðE
HÞ=cL

T < T m ðsolid phaseÞ 0 < E < H; T > T m ðmelt zoneÞ

ð12Þ

E > H; T > T m ðliquid phaseÞ

@t

@x

@y

@z

ð15Þ

When Dh = 1 mm, channels can be considered as macroscopic size channels, the values of Nu and f can be found using the classical correlations of convective heat transfer in a pipe [27]. (

Laminar flow; Re 6 2300 : Nu ¼ 4:364;

f ¼ 64=Re

Turbulent flow; Re > 2300 : Nu ¼ 0:023Re0:8 Pr0:4 ; f ¼ ½1:14 þ 2 logðDh =Rq Þ

During the heat-absorbing process of PCM, when the temperature of PCM is lower than the melting temperature of PCM, PCM is keeping in the solid phase, the absorbed heat is applied to update the temperature of PCM. When the temperature of PCM reaches the melting temperature, the phase change process takes place inside PCM, the temperature of PCM is maintained at a constant value, and a large magnitude of thermal energy is absorbed during the transformation of solid PCM into liquid PCM. Once all of solid PCM is transformed into liquid phase, the temperature of PCM will further increases with the input thermal energy. During the heatreleasing process of PCM, liquid phase PCM is gradually transformed into solid phase PCM. The energy equation and the momentum equations (Navier–Stokes equations) are [14,26]

8 @ðqc TÞ @ðquc TÞ @ðqv c TÞ @ðqwc TÞ p > þ @x p þ @y p þ @z p ¼ rðkrTÞ > > @t > > < q @u þ qu @u þ qv @u þ qw @u ¼ rðlruÞ
@P @t @x @y @z @x @v @v @v @v @P > q þ q u þ q v þ q w ¼ r ð l r v Þ
> @y @t @x @y @z > > > : q @w þ qu @w þ qv @w þ qw @w ¼ rðlrwÞ
@P
qg

Ppump

ð14Þ

l u2 ¼f  w  qw  Ac  uw  m Dh 2


2

ð16Þ

where Re = uwDh/lw is the Reynolds number, Pr = lw/aw = 7 is the Prandtl number of water. 2.7. The irradiance for simulation In order to investigate the practicability of the PV–PCM–TE system in a realistic situation, a measured daily solar irradiance data shown in Fig. 3 is applied as the input solar irradiance for the numerical simulations rather than the AM1.5 incidence. The experimental measurements were recorded during a clear day (September 18th 2014) in Nanjing city, China (Longitude/Latitude: E118°420 /N32°030 ). 3. Results and discussion

ð13Þ

@z

Because the solid phase and the liquid phase of PCM are segregated with each other, thus, it needs to estimate the phase status of each calculation elements according to their temperature levels. If the element is in the solid regions of PCM, l = ls = 1, q = qs. If the element is in the liquid region of PCM, l = lL, q = qL, and the natural convection caused by the temperature gradient in the liquid phase of PCM may take place and needs to be calculated. 2.6. The thermal model of the heat sink The important parameters for a heat sink are thermal convection coefficient hw of water and pump power Ppump, which are mainly determined by the structure parameters of channels and

3.1. The verification of the simulation model In order to verify the accuracy of the simulation model, the present mathematical models are employed to calculate the PV–PCM system in Huang’s work [14] and a TE generator system in AlNimr’s work [5]. The comparison between the results simulated by the present mathematical models and the referenced data is illustrated in Fig. 4. Fig. 4(a) shows the comparison between the calculated PV temperature profiles and the experimental PV temperature data of the Huang’s PV–PCM system [14]. One can find that the simulated data coincide well with the experimental data. The mean deviation between the simulated data and the experimental data is 7%. Fig. 4(b) is the comparison between the calculated efficiencies of a TE generator and the Al-Nimr’s results [5]. The calculated efficiencies by the present model are somewhat higher than the Al-Nimr’s results [5], which is because that heat

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T. Cui et al. / Energy Conversion and Management 112 (2016) 49–60

Fig. 4. The comparisons between the simulated data with (a) the results of Huang’s work; (b) the results of Al-Nimr’s work.

flux is considered to be high enough in the present mathematical model. The max deviation between the simulated efficiencies of the TE generator and the referenced data in Al-Nimr’s work [5] is 9%. Those results indicate that the present model has a high accuracy to be used to simulate energy transfer in the PV–PCM–TE system.

3.2. The evaluation of the PV cells and the TE modules In the hybrid PV–PCM–TE system, electricity is generated from the PV cells and the TE modules. A high temperature gradient can improve the efficiencies of the TE modules, but it may decrease the efficiencies of PV cells. Therefore, in order to make the PV–PCM–TE hybrid system have the maximum entire efficiency of generating electricity, it is highly important to determine the optimized operating temperature of the PV–PCM–TE system. Fig. 5 indicates the influences of temperature and optical concentration on the efficiency of a single PV cell and a PV–TE system deployed with four different types of PV cells (i.e., c-Si, CIGS, single-junction GaAs, and GaInP/InGaAs/Ge). Except for that the efficiencies of the GaInP/InGaAs/Ge (III–V) PV cell are referenced from the literatures [28–30], the efficiencies of c-Si, CIGS, and single-junction GaAs PV cells are calculated from the aforementioned Eqs. (4)–(6) [23,24]. The parameters and the structure models of c-Si, CIGS, and single-junction GaAs cells are all referenced from the literatures [8,31–35]. For a single PV cell, the horizontal coordinate means the temperature of the PV cell and the vertical coordinate indicates

the efficiency of PV cell g ¼ gPV ðTÞ. For the PV–TE system, the horizontal coordinate means the temperature of the hot side of TE modules, the cold side of TE modules is set to 300 K. The vertical coordinate shows the total efficiency of the PV–TE system, which is calculated from the relation g ¼ gPV ðTÞ þ ð1
gPV ðTÞ
gradiation
gconv ection ÞgTE ðTÞ. Here the TE modules with two given ZT are discussed, for that ZT = 0.77 is the value of commercially available products, and ZT = 1.5 is the value of laboratorial products whose manufacturing technology is close to maturity and can be widely used in the future. From the efficiency curves of these four kinds of PV–TE systems, one can find that the hybrid PV–TE system consisting of a singlejunction GaAs PV cell and TE modules shows the best performance. In the c-Si PV–TE system composed of a c-Si PV cell and TE modules, due to the small temperature coefficient which is equal to
0.44% under 1 sun, the improved efficiencies of TE modules cannot offset the decreased efficiency of the c-Si PV cell when the cell temperature increases. The total efficiency of the c-Si PV–TE system always reduces with the increase of temperature no matter whether ZT = 0.77 or ZT = 1.5. The maximum efficiency of the c-Si PV–TE system amounts to 20.1% at 300 K under the optical concentration of 100. Similar finding can be discovered in the III–V PV–TE system. However, the reason for this phenomenon is that the highly effective III–V PV cell has converted most of solar energy into electricity; the rest solar energy is not enough for the TE modules to make a remarkable contribution to the total efficiency of the PV–TE system. The maximum efficiency of the III–V PV–TE system amounts to 38.9% at 300 K under the optical concentration of 500. For the CIGS PV–TE system composed of a CIGS PV cell and TE modules, the participation of TE modules makes great promotions on the total efficiency of the CIGS PV–TE system under high concentration. Nevertheless, the internal resistances of the CIGS PV cell are also increased with the increase of concentrations, which immensely diminishes the efficiency of CIGS PV cell and the total efficiency of the CIGS PV–TE system consequently. Therefore, the maximum efficiency of the CIGS PV–TE system is 20.5 at 300 K without any optical concentration. Being different from the aforementioned three kinds of PV–TE systems, the application of TE modules can significantly augment the total efficiency of the single-junction GaAs PV–TE system, and the TE modules with a higher value of ZT can generate more energy under a high temperature difference. The reasons are the single-junction GaAs has a large temperature coefficient (approximate
0.24% under 1 sun) and a proper photoelectric conversion efficiency. The large temperature coefficient can suppress the efficiency loss when the temperature of GaAs PV cells increases. However, such augment function will be gradually weakened till the maximum total efficiency is reached because the large temperature increases the energy loss caused via radiation and convection to the ambient environment. The maximum efficiency of the GaAs PV–TE system amounts to 28.09% at 425 K with ZT = 1.5 under the optical concentration of 500. Although the maximum efficiency of the GaAs PV–TE system is smaller than the maximum efficiency of the tandem III–V PV–TE system, the market price of single-junction GaAs PV cells is much lower than the price of tandem III–V PV cells. Therefore, by considering the cost and the total efficiencies of these PV–TE systems, single-junction GaAs PV cells are selected to construct the present PV–PCM–TE system in this paper. The maximum efficiency of the GaAs PV–TE systems with different ZT values and optical concentrations are presented in Table 2.

3.3. The selection of PCM The purpose of introducing PCM is to maintain the hybrid PV–TE system operating at the optimal temperature. Thus the

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T. Cui et al. / Energy Conversion and Management 112 (2016) 49–60

Fig. 5. The influence of temperature on the total efficiencies of PV–TE system with different PV cells: (a) c-Si PV; (b) CIGS PV; (c) single-junction GaAs PV; (d) GaInP/InGaAs/ Ge PV.

Table 2 The maximum efficiencies and related temperatures of GaAs PV hybrid TE system. Concentration

GaAs

PV–TE (ZT = 0.77)

PV–TE (ZT = 1)

PV–TE (ZT = 1.5)

X sun

g (300 K)

T (K)

gmax

T (K)

gmax

T (K)

gmax

1 50 100 500 1000

20.60 25.2 25.7 26.6 26.3

300 300 320 330 335

20.60 25.2 25.73 26.66 26.37

325 345 365 370 375

20.67 25.40 26.02 27.00 26.73

325 410 420 425 430

20.67 26.34 27.06 28.09 27.85

temperature at which the hybrid PV–TE has the maximum total efficiency is a key parameter to select the PCM. In other words, this temperature is selected as the melting temperature of PCM. When the operating temperature of the PV–PCM–TE system is below 375 K, employing paraffin PCM is a proper choice [36]. If the operating temperature of the PV–PCM–TE system surpasses 420 K, the paraffin PCM is no longer valid and the PCM made of NaOH–KOH may be applied. This is because that the melting temperature of

NaOH–KOH PCM can be controlled by changing the ratio of NaOH and KOH [37,38]. The detailed properties of paraffin PCM and NaOH–KOH PCM are provided in Table 3.

3.4. The evaluation of heat sink For evaluating the performance of a heat sink, the convective heat transfer coefficient and pump power are the two crucial parameters which are both determined by the structure parameters of the heat sink and the velocity of the operating fluid. Fig. 6 indicates the relationship among the convective heat transfer coefficient, the pump power, the hydraulic diameter of channels, and the flow velocity of water. Here the hydraulic diameters of the channels Dh = 3.2 mm, Dh = 4.36 mm, and Dh = 6.15 mm respectively indicate that the widths of channels are a = 2 mm, a = 3 mm, and a = 5 mm. The height b of channels is a constant value, 8 mm. One can find that from Fig. 6, with the increase of the channels’ hydraulic diameter, the pump power is reduced and also the heat exchange area between the heat sink and water

Table 3 Thermophysical properties of selected PCMs. Paraffin [31] Melting temperature (K) Heat of fusion (kJ/kg) Specific heat capacity (kJ/kg K) Density solid (kg/m3) Density liquid (kg/m3) Heat conductivity (W/m K) Max operation temperature (K)

320 168 2 880 760 0.2 334

NaOH (24%)–KOH (76%) [32,33] 330,335 152 2 880 780 0.2 358,363

345 182 2 880 770 0.2 373

365–375 200 2 950 850 0.2 393

420 425 205 205 0.435 + 2.451 ⁄ 10
3 ⁄ T (K) 2100 2100 2050 2050 0.6 0.6

430 205 2100 2050 0.6

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Fig. 6. The relationships between the flow velocity of water, the thermal convection coefficient, pump power, and the hydraulic diameter channels.

is lessened. With the increase in the flow velocity of water, the pump power is obviously increased. When Re < 2300, the convective heat transfer coefficient can be approximatively considered as a constant because of the laminar flow pattern; once Re > 2300, the flow pattern becomes turbulent and the convective heat transfer coefficient is remarkably proportional to the flow velocity of water. Synthetically considering the convective heat transfer coefficient, the pump power and the heat exchange area between heat sink and water, the value 3 mm is selected as the width of the channels. Of course, there may have a better structure parameter for the heat sink to balance these influence factors, which is not discussed in this paper for that this needs lots of designs and calculations. 3.5. The comparisons between the single PV, the PV–TE and the PV– PCM–TE system In order to illustrate the superiority of the PV–PCM–TE system, the temperature curves and the efficiencies of a single PV system, a PV–TE system, and a PV–PCM–TE system under the optical concentration of 500 suns are shown in Fig. 7, respectively. The single PV system is constructed by directly attaching a PV cell on a heat sink, and the PV–TE system is composed of a PV cell, a heat sink, and TE modules. The PV cells employed in these three systems are all single-junction GaAs PV cells. The structure parameters of the components of the three systems are all referenced from the initial value shown in Table 1. The thermoelectric coefficient ZT is set to be equal to 1, the area of the TE module is 40 mm ⁄ 40 mm and the thermal concentration Cth is 31.25. The melting temperature Tmelting of PCM is 330 K, the thermophysical properties of PCM are referenced from Table 3. Compared the temperature curves of the PV–PCM–TE system (as shown in Fig. 7(b)) with the temperature curves of the single PV system and the PV–TE system (as shown in Fig. 7(a)), one can easily learn that the temperature of the PV–PCM–TE system experiences a relatively stable value around 330 K from 11 to 17 clock because the phase change of the PCM takes place at 330 K. Whereas, the temperature curves of the single PV system and the PV–TE system are both fluctuant with the solar irradiance. The maximum operating temperatures of the single PV system and the PV–TE system are appeared at the noon time when the solar irradiance is the largest. Meanwhile, one can also find that the deviations between the temperatures of the PV cell, the PCM, and the hot side of TE in the PV–PCM–TE system are not evident. The reasons are (a) the coppery container of PCM can effectively

Fig. 7. The performances of single PV system, PV–TE system and PV–PCM–TE system at 500 sun. (a) The temperatures and efficiencies of single PV system and PV–TE system. (b) The temperatures and efficiencies of PV–PCM–TE system. (c) The output power of single PV system and PV–PCM–TE.

transfer heat from the PV cell to the PCM, which is beneficial to eliminate the hot spot in the PV cell and reduce the temperature deviation between the PV cell and the PCM; (b) The large area of PCM can reduce the heat flux density transferred from the PCM to the TE modules, which decreases the temperature deviation between the PCM and the TE. In contrast, the temperature difference between the PV cell and the hot side of the TE modules in the PV–TE system becomes very severe. This is because that the

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ceramic layer upon the TE modules extremely impedes the heat transfer from the PV cell to the TE module for the low thermal conductivity of the ceramic material. From the efficiency curves of the single PV system, the PV–TE system, and the PV–PCM–TE system, one can find that the total efficiency of the PV–PCM–TE system is also different from the fluctuant efficiency of the single PV system and the PV–TE system. In the single PV system and the PV–TE system, the electricity output only occurs when there is solar irradiance. But in the hybrid PV–PCM–TE system, the PCM will store heat when the incident solar irradiance is large, and release it to the TE modules to generate electricity when the incident solar irradiance becomes weaker or none. Therefore, the total efficiency of the PV–PCM–TE has a severe increase nearly the sunset. The timely output power of the single PV system and the PV–PCM–TE system are pictured in Fig. 7(c). The total output power of the PV–PCM–TE system is obviously higher than that of the single PV system. Due to the fact that the melting temperature of PCM is 330 K, the most output power comes from the PV cell which contributes about 98% of the total power of the PV–PCM– TE system, and the output power of TE modules only accounts for 2% of the total power the PV–PCM–TE system. When the flow velocity of water is 0.01 m/s, the pump power is negligible and it is considered to have no influence on the total efficiency of the PV–PCM–TE system. The daily total efficiency of the single PV system is 25.55% and the daily total efficiency of the PV–PCM–TE

Fig. 8. (a) The temperatures and efficiencies of the PV–PCM–TE system with Rc = 40 mm2 K/W. (b) The relationship between the total efficiency of the PV–PCM– TE system with the thermal contact resistance.

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system amounts to 26.57%. The raised efficiency of the PV–PCM– TE system results from the following two parts: one is that the PCM can store thermal energy, control the cell temperature, and keep the PV cell operating with a higher efficiency, and the other is that the thermal energy stored inside the PCM can be released to the TE modules to generate electricity later on when the solar irradiance becomes faint. 3.6. The influence of the thermal contact resistance As shown in Fig. 7, one can discover that the performance of the PV–PCM–TE system do better than the single PV system and the PV–TE system. However, extra thermal contact resistances are brought into the heat transfer network of the PV–PCM–TE system, one can find that there are three types of interfacial thermal contact resistances existing in the PV–PCM–TE system due to the introduction of PCM (as shown in Fig. 2). In order to investigate the effect of thermal contact resistance on the PV–PCM–TE system, the temperature curves and the efficiency curve of the PV–PCM–TE system with the thermal contact resistance of 40 mm2 K/W are presented in Fig. 8(a). Other structure parameters are not changed. One can discover that high thermal contact resistance significantly increases the temperature steps cross the interfaces between different components by comparing Fig. 8(a) with Fig. 7 (b). As shown in Fig. 8(b), it is not hard

Fig. 9. The temperatures and efficiencies of the PV–PCM–TE system after altering parameters (a) Tmelting = 370 K; (b) Tmelting = 370 K and ATE = 20 mm ⁄ 20 mm.

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to find that the efficiency of the PV–PCM–TE system directly decreases with the increase of the thermal contact resistance. Therefore, it is extremely necessary to control the thermal contact resistances in the PV–PCM–TE system. 3.7. The optimization of PV–PCM–TE systems In Fig. 7(b), the melting temperature of PCM for simulation is 330 K, however, when ZT = 1, the maximum efficiency of the PV–PCM–TE system appears at the operating temperature of the PV–PCM–TE is maintained at 370 K. Therefore, without changing other structure parameters of the simulation model, the performance of the PV–PCM–TE system with the melting temperature of PCM of 370 K is simulated, the temperature curves and the efficiency curve of the PV–PCM–TE system are presented in Fig. 9(a), in which the thermal contact resistance is set to be equal to 20 mm2 K/W. One can find that, when the melting temperature of PCM is set to 370 K, the maximum temperature of the PV–PCM–TE system is only 345 K, which is below the melting temperature of 370 K of the paraffin PCM, the PCM’s function of maintaining the temperature of the PV–PCM–TE system is not realized. In such a case, one simple and effective method is to regulate the thermal resistance of the TE modules to regulate the operating temperature of PV–PCM–TE system. Since the height of the TE

modules is fixed in this study, reducing the surface area of the TE modules becomes an effective way to increase the whole thermal resistance of the TE modules. By reducing the surface area of the TE modules to 20 mm ⁄ 20 mm, the simulated temperature curves of the PV–PCM–TE system are presented in Fig. 9(b). The thermal concentration Cth consequently becomes 125. For this situation, due to the larger thermal resistance of the TE modules, the temperature of the PCM module can reach its melting temperature of 370 K. Nevertheless, for the same reason, the large thermal resistance of TE modules also impedes the heat transfer from the PCM to the heat sink. When the detained heat exceeds the total latent heat capacity of the PCM, the temperature of the PV–PCM–TE system will continue rising. As shown in Fig. 9(b), the maximum temperature of the PCM is up to 410 K, which surpasses the allowed maximum operating temperature of the paraffin PCM and results in the invalidation of the PV–PCM–TE system. Therefore, it is crucial to elaborately design the volume quantity of PCM and the thermal resistance of the TE modules. Moreover, a side-effect of reducing the area of TE modules is that a small surface area of TE modules will increase the heat flux density transferred through the TE modules, which increases the temperature differences at the interface between the PCM and the TE modules, and at the interface between the TE modules and the heat sink for the existence of

Fig. 10. The daily total efficiency versus thermal concentration and the velocity of water under different conditions: (a1) C = 100sun, ZT = 0.77, Tmelting = 320 K, hPCM = 10 mm; (a2) C = 100sun, ZT = 1, Tmelting = 365 K, hPCM = 20 mm; (a3) C = 100sun, ZT = 1.5, Tmelting = 420 K, hPCM = 30 mm; (b1) C = 500sun, ZT = 0.77, Tmelting = 330 K, hPCM = 10 mm; (b2) C = 500sun, ZT = 1, Tmelting = 370 K, hPCM = 20 mm; (b3) C = 500sun, ZT = 1.5, Tmelting = 425 K, hPCM = 30 mm; (c1) C = 1000sun, ZT = 0.77, Tmelting = 335 K, hPCM = 10 mm; (c2) C = 1000sun, ZT = 1, Tmelting = 375 K, hPCM = 20 mm; (c3) C = 1000sun, ZT = 1.5, Tmelting = 430 K, hPCM = 30 mm.

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thermal contact resistance. Therefore, a subtle design of the surface area of TE modules (i.e., the thermal concentration ratio) and effective measures of controlling the interfacial thermal resistance are critical for the PV–PCM–TE system. To further investigate the influences of the structure parameters on the PV–PCM–TE system, the relationships between the daily total efficiency of the PV–PCM–TE system, thermal concentration, and flow velocity of water are studied (as shown in Fig. 10). For selecting the thermal concentration, one should take into account the proper operating temperature of the PV–PCM–TE system. In this work, the thermal concentration is adjusted between 1 and 50 when the operating temperature of the PV–PCM–TE system is below 350 K. Similarly, if the operating temperature of the PV– PCM–TE system is between 350 K and 400 K, the thermal concentration is selected to be between 50 and 100. In cases that the operating temperature of the PV–PCM–TE system is larger than 400 K, the thermal concentration is selected to be between 100 and 150. Meanwhile, the quantity of PCM is also regulated according to the thermal concentration and the operating temperature of the PV–PCM–TE system to avoid the failure of the PV–PCM–TE system under high thermal concentrations. When the operating temperature of the PV–PCM–TE system is below 350 K, the height of the PCM layer is designed to be 10 mm. When the operating temperature of the PV–PCM–TE system is between 350 K and 400 K, the height of the PCM layer is set to be 20 mm. When the operating temperature of the PV–PCM–TE system is over 400 K, the height of the PCM layer is selected to be 30 mm. Analyzing the daily total efficiencies of the PV–PCM–TE system with different structure parameters but the same optical concentration, one can find that when the thermal concentration is small, the maximum efficiency of the PV–PCM–TE system appears on a slow flow velocity of water. As the thermal concentration increases, it needs to increase the flow velocity of water to obtain the maximum daily total efficiency. This is because that while the thermal concentration increases, the heat flux transferred from the TE modules to the heat sink is increased, a higher flow velocity of the working fluid is necessary to make sure that the PV–PCM–TE system operates at the optimal temperature point. By analyzing the daily total efficiencies of the PV–PCM–TE system with different structure parameters but the same ZT value, one can learn that the trends of efficiency-curves of the PV–PCM–TE system under different optical concentrations are similar to each other. The reason is that when the value of ZT is fixed, the optimal operating temperature points of the PV–PCM–TE system under different optical concentrations do not greatly deviate from each other. The proper design of the hybrid system makes sure that the surface areas of the TE modules and the heat sinks as well as the volumes of the PCM are all proportional to the optical concentration. Therefore, even the optical concentrations may different from each other in these PV–PCM–TE systems, the operating temperatures of the PV–PCM–TE system exhibit similar change tendencies for the same thermal concentration and the same flow velocity of water.

4. Conclusions A novel PV–PCM–TE hybrid system has been proposed and the detailed performance of such system has been studied. The main findings are as follows: (1) A proper design of a PV–PCM–TE system can effectively promote the conversion efficiency of solar energy. (2) The performance of the GaAs PV–PCM–TE system is superior to the single GaAs PV cell and the GaAs PV–TE system.

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(3) The incorporation of the PCM can suppress the influence of the solar irradiance fluctuation on the PV–PCM–TE system and maintain the PV–PCM–TE system to operate at the optimal operating temperature. (4) A large thermal concentration is beneficial to make the PV–PCM–TE system reach the optimal operating condition. The elaborate design is crucial to determine the suitable volume quantity of PCM, the thermal concentration, and the heat sink. (5) For higher optical concentrations, the side-effects of thermal contact resistances at the interface between the components in the PV–PCM–TE system will significantly emerge. The conversion efficiency of the PV–PCM–TE system will decrease with the increase of the thermal contact resistance. Therefore, it is extremely necessary to control the thermal contact resistances in the PV–PCM–TE system.

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