cpc solar mini

8/19/2019 CPC Solar Mini

1/12

Investigation on a mini-CPC hybrid solar thermoelectric generator unit

Y.J. Dai a , *, H.M. Hu a , T.S. Ge a, R.Z. Wang a , Per Kjellsen a, b

a Institute of Refrigeration and Cryogenics, Research Center of Solar Power and Refrigeration, M.O.E, Shanghai Jiao Tong University, Shanghai, Chinab Norwegian University of Science and Technology, Trondheim, Norway

a r t i c l e i n f o

Article history:

Received 31 August 2015

Received in revised form

20 January 2016

Accepted 20 January 2016

Available online xxx

Keywords:

Solar hot water

Thermoelectric generator

Mini-CPC

Ef ciency

a b s t r a c t

A hybrid solar hot water and Bi2Te3-based thermoelectric generator (TEG) unit using a heat pipe evac-

uated tube collector with mini-compound parabolic concentrator (mini-CPC) is proposed. In this unit, theheat from the heat pipe evacuated tube solar collector is transferred to the hot side of TEG. Simulta-

neously, water cooling is used at the cold side to maintain the temperature difference. Electricity is

generated by TEG and the remaining heat is transferred to water at the same time. This paper in-

vestigates how to convert excess solar heat into electricity more effectively. A mathematical model

regarding this unit is developed and validated. It is found that the mini-CPC can signi cantly improve the

electrical ef ciency. The optimal thermal conductance of TEG is determined, which could make the best

use of excess solar heat. The excess solar heat can be effectively converted into electricity when ZT of

Bi2Te3 can be improved from 100 C to 200 C. Using TEG with ZT ¼ 1.0 and a geometrical concentrating

ratio at 0.92, electrical and thermal ef ciencies of this system are predicted to be 3.3% and 48.6% when

solar radiation and water temperature are 800 Wm2 and 20 C, respectively.© 2016 Published by Elsevier Ltd.

1. Introduction

Increasing pressure from environment and energy crisis attracts

the development of solar thermal technologies for industrial and

domestic applications. Operation data in the USA show that water

heating accounts for 20% of household energy use [1]. Flat plate

solar collector and evacuated glass tube solar collector are

commonly used for solar water heating system. In China, evacuated

glass tube collector is more popularly used due to the improved

thermal performance and low cost.

Most of the evacuated glass tube solar collectors are non-

concentrating, and the operation temperature is normally low.

Recently, low concentrating solar evacuated collector has been

developed to be both cheaper and more compact. Li et al. [2]investigated thermal performance of evacuated collectors with

3 and 6 CPC reectors. It is found that thermal ef ciencies (hths)are ashigh as51% and 54% byusing 3 CPC and 6 CPCwhen watertemperature (T w) is150

C.Pei etal. [3] compared the performancesof solar evacuated collectors with and without mini-CPC. It is found

that solar evacuated collector with mini-CPC has a higher thermal

ef ciency than that without mini-CPC at high water temperature.

Zambolin [4] investigated the thermal performances of at plate

and evacuated tube solar collectors with external CPC reectors.

The ef ciency curves in steady-state and quasi-dynamic methods

are obtained. Kossyvakis et al. [5] modeled the solar thermoelectric

generator using ANSYS workbench software. The computational

results reveal that the performance can be signicantly improved

by optical concentrated congurations.

The ef ciencies of evacuated glass tube collectors with and

without low concentrating CPC are normally above 50% and 60%,

respectively, even if the water temperature is up to 90 C. Thetemperature range meets the operational requirement of thermo-

electric generator (TEG). The combined technology of TEG and

evacuated glass tube solar collector has received increasing atten-

tion. Chen et al. [6,7] proposed the concept of thermal concentra-tion to obtain a large temperature drop across thermoelectric (TE)

legs in a very cost-effective way. The experimental results showed

that electrical ef ciency (he) is around 4.6% with solar radiation (G)

at 1000 Wm2 and cold-side temperature of 20 C. However,commercial TEG could not be employed in this system because the

thermal concentration of the commercial TEG is not more than 10

[8], while in that system the thermal concentration is around 200

[7]. McEnaney et al. [9] also extended the concept of thermal

concentration into concentrating solar TEG. The results showed

that he can be 10% when geometric optical concentration ratio is 45

using skutterudite and Bi2Te3 materials. Lesage et al. [10] have* Corresponding author.

E-mail address: [email protected] (Y.J. Dai).

Contents lists available at ScienceDirect

Renewable Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . co m / l o c a t e / r e n e n e

http://dx.doi.org/10.1016/j.renene.2016.01.060

0960-1481/©

2016 Published by Elsevier Ltd.

Renewable Energy 92 (2016) 83e94

mailto:[email protected]://www.sciencedirect.com/science/journal/09601481http://www.elsevier.com/locate/renenehttp://dx.doi.org/10.1016/j.renene.2016.01.060http://dx.doi.org/10.1016/j.renene.2016.01.060http://dx.doi.org/10.1016/j.renene.2016.01.060http://dx.doi.org/10.1016/j.renene.2016.01.060http://dx.doi.org/10.1016/j.renene.2016.01.060http://dx.doi.org/10.1016/j.renene.2016.01.060http://www.elsevier.com/locate/renenehttp://www.sciencedirect.com/science/journal/09601481http://crossmark.crossref.org/dialog/?doi=10.1016/j.renene.2016.01.060&domain=pdfmailto:[email protected]


2/12


3/12

Fig. 2 show the specication and schematic of heat pipe evacuatedglass tube solar collector with mini-CPC. The prototype of SHTG is

mounted facing south and inclined at 30 from the horizon using asupport. The angle of inclination for SHTG is nearly identical with

latitude of Shanghai (latitude 31.14) in order to obtain largestannual solar gain [13]. According to the study of Mills [14], the

geometrical concentration ratio (C ) can be dened as:

C ¼ W CPC pDi

(1)

3. Mathematical model

3.1. Optical analysis

In order to evaluate the performance of SHTG, a three dimen-

sional ray tracing program Tracepro (Lambda Research Corporation,

Littleton, MA) is employed to determine angular acceptance of

mini-CPC reector. The transversal projection angle of the rays is

varied in steps of 10 from 70 to þ70. As shown in Fig. 3, it canbe noted that the longitudinal projection angle of the rays is

changed from þ60 to 0 to þ60 in the whole day. So the longi-tudinal projection angle of the rays is varied in the steps of 10 from0 to þ60 .

The angular acceptance at a given incident angle can be calcu-

lated by Ref. [2]:

haðqÞ ¼ hað0; 0ÞhaðqT ; 0Þhað0; 0Þ

hað0; qLÞhað0; 0Þ

(2)

Fig. 4 shows the variation of the angular acceptances at any

given incident angle. It is noted that there exists a drop at qT ¼ ±60 , because part of incident rays reected by reector cannot reachthe absorber. It is also found that averageha ismore than84% at any

given incident angle in the whole day. It indicates that ha can

remain at a very high value without tracking system.

3.2. Thermal performance modeling

One-dimensional analytical mathematical model of SHTG is

established. The following assumptions have been made without

losing signicant accuracy:

(1) Heat transfer is assumed to be steady state.

(2) Thermal resistance along the heat pipe is neglected.

(3) Thermal properties of selective coating are constant.

Fig. 1. A general view of SHTG.

Fig. 2. Construction of heat pipe collector with mini-CPC.

Table 1

The specication of heat pipe collector with mini-CPC.

ai εi ao ¼ εo to Do (mm) Di (mm) L tube (m) L cpc (m) Wcpc (mm)0.86 0.10 0.80 0.90 47 58 1.75 1.75 136

South North

East

West

θ

30o

SHTG

θT

Fig. 3. Position of SHTG.

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e94 85


4/12

(4) The Thomson effect of TEG is neglected.

(5) Heat transfers of the air gap inside TEG module are

neglected.

Fig. 5 shows the thermal network of SHTG. The mini-CPC

reector concentrates solar energy onto the selective coating and

then the thermal energy (S ) is produced, which contains useful

energy (Q U ) and thermal loss (Q L). Q U is the thermal energy

absorbed on the hot side of TEG. Based on the energy balance for

the TEG, Q U converts into electrical energy (P ) by TEG and the

remaining Q U is absorbed by hot water. So Q U contains electrical

energy (P ) and thermal energy (Q th).

3.2.1. Thermal loss coef cient

It is found that Q U can be expressed as [15]:

Q U ¼ S Q L ¼ GCAihref hatoai Q L (1)where G is the solar irradiance, C is the concentration ratio, Ai is the

area of the inner glass tube and a i is the absorptance of the inner

glass tube. The thermal loss can be expressed as [16]:

Q L ¼ U L AiðT i T aÞ (2)

where U L, T i and T a are the thermal loss coef cient, the temperature

of the inner glass tube and the ambient temperature. Then, the

thermal loss coef cient can be expressed as [16]:

U L ¼ 1

Ai

1

hi;o Aiþ 1

ho;a þ ho;s Ao!1

(3)

where hi,o is the radiation heat transfer coef cient between the

inner tube and outer glass tube. ho,a is the convection heat transfer

coef cient between outer glass tube and ambient, and ho,s is the

radiation heat transfer coef cient between outer glass tube andsky.

Ao is the surface area of outer glass tube.

hi,o can be expressed as [16]:

hi;o ¼s

T 2

i þ T 2o

ðT i þ T oÞ

1εi

þ A i Ao

1εo

1 (4)

where T o is the temperature of outer glass tube. s is the Ste-

faneBoltzmann constant. εi and εo are the emittances of the

absorber tube and outer glass tube, respectively.ho,s can be expressed as [16]:

ho;s ¼ sεo

T 2o þ T 2sky

T 2o þ T 2sky

(5)

where T sky is the temperature of the sky, T sky ¼ 0.0522T1:5a .ho,a can be expressed as [16]:

ho;a ¼ 5:7 þ 3:8v (6)

where v is the wind speed.

As shown in Fig. 5, the energy balance of the outer glass tube can

be expressed as:

GCAihref haao þ hi;o AiðT i T oÞ ¼ Aoho;sT o T skyþ ho;aðT o T aÞ

(7)

where ao is the absorptance of the outer glass tube. T i is assumed to

be T h here, thus U L can be obtained from Eq. (3) to Eq. (7).

3.2.2. Useful ef ciency

As shown in Fig. 5, the useful energy contains the electric energy

and thermal energy. It can be expressed as:

Q U ¼ P þ Q th (8)As shown in Appendix B, the ef ciencyof useful energy, which is

de

ned as useful ef

ciency (hU ), can be expressed as:

Fig. 4. The optical results of mini-CPC: a) the illustration ray tracing program for the

mini-CPC and b) variations of ha (0, qL ) and ha (0, qT) with longitudinal projection angleand longitudinal projection angle.

Fig. 5. Thermal network of SHTG.

Y.J. Dai et al. / Renewable Energy 92 (2016) 83e9486


5/12

hU ¼ Q U GCAi

¼ F 0href haaito

U LGC

ðT h T aÞ

(9)

It is noted that C is WCPC/pDi, namely, 1/p for non-concentrating

evacuated collector. F0 is the collector ef ciency factor in Eq. (9). Itcan be expressed as [16]:

F 0 ¼ 1=U LW

" 1

WFU Lþ Lb

k find finþ LtubeRhp

# (10)

where W is the circumferential distance of the inner tube, Lb is the

average length of the bond, Ltube is the length of the tube, F is the n

ef ciency of straight n and Rhp is the resistance from n tohotside

of TEG. W is about pDi/2. R hp is the thermal resistance of the heat

pipe. It is given in Appendix A. F can be expressed as [16]:

F ¼ tanh½mW =2mW =2

(11)

where m is expressed as:

m ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

U Lk find fin

s (12)

where k n and d n are the thermal conductivity and the thickness of

the n. The details of the derivation of the heat transfer model for

this n-type heat pipe are given in Appendix B.

(1). Maximum electrical ef ciency of SHTG

The energy balance equation of the hot side of TEG can be

expressed as:

GCAihU ¼ nateIT h þ kte AteLte ðT h T c Þ 1

2I 2

rte

Lte

Ate

(13)

where n is the number of thermoelectric legs. Ate and Lte are the

cross area and the length of TE legs. ate, kte and rte are the Seebeck

coef cient, thermal conductivity and electrical resistivity of TE legs,

respectively. In the present study, the TE legs are composed by the

Bi2Te3-based TE material. The properties of the TE material are

temperature dependent. Properties of Bi2Te3 are tted in Fig. 6

based on the experimental data from Ferrotec Company [17]. And

it is found that the ZT of commercial TEG available is around 0.59 at

the room temperature, which is far less than that discussed in the

previous studies (ZT ¼ 1) [12].

ate ¼

0:004111T 2m þ 2:84T m 272:2

106

VK 1

(14)

rte ¼

8:735 105T 2m þ 0:1241T m 15:85

106 ðUmÞ(15)

kte ¼ 6:954 105T 2m 0:03767T m þ 6:491

WK 1m1

(16)

where T m is (T h þ T c )/2.The electrical power produced by TEG is [18]:

P ¼ nateðT h T c Þnrte

Lte Ate

þ RL R2L ¼ n

ateI ðT h T c Þ I 2rte Lte Ate

(17)

where RL is the electrical resistance of the external load.

Thus, the electrical ef ciency of SHTG is:

he ¼ P

GCAi(18)

According to the study of solar thermoelectric generator from

Chen [6,7], the optimal current (I opt ) or optimal load (RL,opt ), leading

to maximum electrical ef ciency of the system, are found to be:

I opt ¼ ateðT h T c Þ1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ZT mp rte Lte Ate (19)

RL;opt ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 þ ZT mp

rteLte

Ate(20)

where Z ¼ a2te=ðkterteÞ. We substitute Eq. (19) to Eq. (13) and it isfound that:

280 320 360 400 440190

200

210

220

measured

fit of

ρ measured

fit of ρk measured

fit of k

T/K

S / V K - 1

ρ / Ω m

k / W m - 1 K - 1

12

15

18

21

1.2

1.6

2.0

2.4

2.8

280 320 360 400 4400.2

0.3

0.4

0.5

0.6

0.7

ZT measured

ZT= 2

T/(k ρ)

Z T

T/K

Fig. 6. Experimental data and

tted curve of properties of TE material.



6/12

nkte AteLte ¼ K TEG ¼ GCAihU

,ðT h T c Þ24 ZT h

1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ZT mp þ 1 1

2

Z ðT h T c Þ1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ZT mp 2

35

(21)

where K TEG is the thermal conductance of TEG in SHTG. It is found

that K TEG is related to the structure parameters of lowconcentrating

solar evacuated collector such as Ai and C , and is also related to

operating parameters including G and T c . More importantly, some

manufactures (Marlow, Ferrotec and Kryotherm) have already

given the thermal conductance of TEG. So the suitable TEG can be

directly obtained based on K TEG.

So Eq. (13) can be expressed as:

GCAihU ¼ K TEGðT h T c Þ0@ ZT h

1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ZT mp þ 1

12

Z ðT h T c Þ1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ZT mp 2

1A (22)

Substituting Eqs. (17), (19) and (21) to Eq. (18), the maximum

electrical ef ciency of SHTG can be expressed as:

he ¼ hU ðT h T c Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ ZT m

p 1T h ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 þ ZT mp þ T c =T h

¼ hU hTEG (23)

where the electrical ef

ciency of SHTG is the useful ef

ciency (hU )

of SHTG multiplied by the maximum electrical ef ciency (hTEG) of

TEG. It can be noted that the maximum he can be obtained at theK TEG and I opt or RL,opt, respectively.

(2) Thermal ef ciency of SHTG.

The energy balance on the cold side of TEG can be expressed as

[18]:

T c T wRw

¼ n

ateIT c þ kte AteLte

ðT h T c Þ þ1

2I 2rte

Lte Ate

(24)

where T w and Rw are the temperature of water and the thermal

resistance between cold side and water, respectively. Rw is

approximated to be 0.026 KW1 in this system [19].

The current of TEG is xedto be I opt , so Eq. (24) can be expressedas:

T c T wRw

¼ GCAihU ð1 hTEGÞ (25)

Hence, the thermal ef ciency of SHTG is dened as:

hth ¼ T c T w

Rw

GCAi ¼ hU ð1 hTEGÞ (26)

Input structure parameters

and operation parameters

Calculate U L and ηu

Determine T o using Eq.(7)

Guess T i

Guess T c

Calculate ηe and ηth

Determine T c using

Eq.(26)

Find maximum ηe under

T i s

Determine corresponding

T o, ηth, K TEG

Input K TEG

Determine T c using Eq.(22)

Determine T h using Eq.(26)

Determine corresponding ηthand ηe

Variable KTEG Fixed KTEG

Guess T o

Fig. 7. Flowchart of SHTG model.

20 40 60 80 100

160

170

180

190

200

Tw /oC

T h / o C

G=solar constant

C=0.92

Fig. 8. Variations of Th with Tw.

0.2 0.4 0.6 0.8 1.0 1.2

1.0

1.5

2.0

2.5 η

η

η

∆T

C

η

& η

/ %

G=800Wm

T =45 C44

48

52

56

η

/ %

60

80

100

120

∆ T / C

Fig. 9. Variations of he, hTEG, hth and DT with C.



7/12

3.3. Solution

The M language in MATLAB is adopted to establish the mathe-

matic model described above. The owchart of SHTG calculation is

shown in Fig. 7. There are two kinds of calculation processes. One isto obtain maximum electrical ef ciency based on variable K TEG, the

other is to investigate the performance under xed suitable K TEG at

different solar irradiations and water temperatures.

4. Results and discussion

As the two calculation processes discussed in Fig. 7, the calcu-

lation process based on variable K TEG is used to investigate limited

T h of TEG, and effect of concentration ratio (C), operating parame-

ters and ZT of TEG on the performance of SHTG under the

maximum electrical ef ciency condition of SHTG. The calculation

process based on xed KTEG is adopted to investigate performance

of SHTG under different xed KTEGs at different solar irradiations,

which would be discussed in section 4.3. The reference value of solar irradiance is assumed to be 800 Wm2 for common data inShanghai [20]. The experimental validation is discussed in section

4.6.

4.1. Theoretical limits of hot side temperature of TEG

There exists a temperature limit on the hot side of TEG to avoid

melting of the solders, which are used to connect the TE legs to the

electrical connector. Hence, it is important to predict the hot side

temperature of TEG of SHTG in extreme condition.

Fig. 8 shows variations of T h with T w in the extreme condition.

The solar irradiance is set to be solar constant (assumed to be

1368 Wm2) [16]. It can be seen that T h increases with the increase

10 20 30 40 50

0.60

0.65

0.70

T / C

K

/ W K

1.2

1.5

1.8

2.1

2.4

K

η

η

η

/ %

G=800Wm

C=0.92

52

53

54

55

56

57

58

η

/ %

Fig. 10. Variations of KTEG, he and hth with Tw.

0 200 400 600 800 1000

0.2

0.4

0.6

0.8

1.0

K

/ W K

K

η

η

G/Wm

0.5

1.0

1.5

η

/ %

30

35

40

45

50

55

η

/ %

T =45 C

C=0.92

Fig. 11. Variations of KTEG, he and hth with G.

Fig.12. Variations of he and hth with G with respect to different K TEGs: a) he and b) hth.

0 200 400 600 800 1000 1200

80

120

160

200

Th for practical ZT

Th for constant ZT

T h

/ o C

0.2

0.4

0.6

0.8KTEG for constant ZT

KTEG

for practical ZT

K T E G

/ W K - 1

G/Wm-2

Tw=45

oC

C=0.92

Fig. 13. Variations of Th and KTEG for practical ZT and constant ZT with G.



8/12

of T w and the largest value of T h is 201 C when T w is 100 C. The

commercial TEGs of some manufactures (Ferrotec, Marlow) can be

operated steadily below 250 C, so SHTG can work steadily.

4.2. Effect of concentration ratio (C)

Fig. 9 shows the variations of he, hTEG, hth and DT with C when T wis45 C and G is setto be800 W/m2. C increases from 0.32, which isnon-concentrating system, to 1.12. The temperature of 45 C canmeet the needs of domestic hot water [11]. Firstly, it is noted that

hTEG increases from 1.8% to 2.5%. It agrees with the variation of DT

with respect to the commercial TEG. It indicates that hTEG increases

with the increase of C due tothe increase of DT . Secondly, it is found

that hth increases from 45.0% to 56.2%. It is because hU increases

with the increase of C based on Eq. (9). Finally, he increases from

0.8% to 1.4%. It is noted that he increases by more than 50%. It is

because both of hTEG and hU increase with the increase of C. It in-dicates that the low concentrating system can improve hesignicantly.

4.3. Effects of operating parameters (T w and G)

The operating parameters (T w and G) are variable in SHTG. Thus,

the thermal conductance of TEG (K TEG) is variable along the process.

As a result, it is important to investigate the effects of these oper-

ating parameters on K TEG.

Fig. 10 shows the variations of K TEG, he and hth as T w increases

from 10 C to 50 C. he drops from 2.2% to 1.3% and hth drops from57.4% to 53.8% in the process. It is noted thathe drops by nearly 50%,

while hth drops slightly. It indicatesa high electrical ef ciency in the

process of heating watercan be obtained without severely reducingthermal ef ciency. It is also noted that K TEG increases slightly from

0.60 W/K to 0.71 W/K in this process. Thus, the impact of T w on K TEGcan be neglected in the process.

Fig. 11 shows the variations of K TEG, he and hth with G. It is found

that both he and hth increase with the increase of G, because hU increases with increasing of G according to Eq. (9). It is also noted

that he increases more drastically than hth. K TEG increases from 0.15

WK1 to 0.85 WK1 when G increases from 100 Wm2 to1000 Wm2. It implies that K TEG changes dramatically with G.However, variable K TEG could not be employed in SHTG in practice.

Hence, the optimal value, K TEG, is selected based on the large solar

irradiance and low solar irradiance in the following.

Fig. 12 shows the effect of G on hth and he with respect to

different K TEG including variable K TEG, summer K TEG, winter K TEG and

0 200 400 600 800 1000

0.5

1.0

1.5

2.0

constant ZT

pratical ZT

η e / %

G/Wm-2

constant ZT

Tw=45

oC

C=0.92

30

40

50

60

η t h

/ %

Fig. 14. Variations of he and hth for constant ZT and practical ZT with G. 10 20 30 40 50

2

3

4

5 ZT=0.5

ZT=1.0

ZT=1.5

η e

/ %

Tw

/o

C

C=0.92

G=800Wm-2

a)

10 20 30 40 50

45.0

46.5

48.0

49.5

51.0 ZT=0.5 ZT=1.0

ZT=1.5

η t h

/ %

Tw /

oC

C=0.92

G=800Wm-2

b)

10 20 30 40 50155

160

165

170

175

180

ZT=0.5

ZT=1.0

ZT=1.5

T h

/ o C

Tw

/o

C

C=0.92

G=800Wm-2

c)

Fig. 15. Effect of ZT of TEG on performance of SHTG. a) Variations of he with T w, b)

Variations of hth with T w and c) Variations of T h with T w.



9/12

nonTEG. Summer K TEG and winter K TEG are the K TEG based on high

solar irradiance (1000 Wm2) and poor solar irradiance(100 Wm2), respectively. Variable K TEG is adopted on the basis of avariable solar irradiance, which leads to the largest electrical ef -

ciency under different solar irradiances. NonTEG is just a solar

evacuated heater without TEG. It is noted that hths for variable K TEGand nonTEG increase along with G due to the increase of hU shown

in Eq. (9). hth for variable K TEG is 30%e40% lower than that for

nonTEG. However, hth for summer K TEG increases rstly and then

decreases as G further increases. So there exists a maximum value

(60%) around 300 Wm2

, which is caused by the variation of hU . Asshown in Eq. (9), when G is low, hU can be improved by G. When G is

high, the increase of hL and Th due to the increase of T i leads to the

decrease of hU . Moreover, h th for summer K TEG is close to that for

nonTEG when G is at 300e500 Wm2, while hth for summer K TEG isclose to that for variable K TEG when G is higher than 500 Wm

2.Meanwhile, he for both variable K TEG and summer K TEG increase

with G. However, he for summer K TEG is close to that for variable

K TEG. Furthermore, it is found that hth for winter K TEG decreases with

increasing of G due to small K TEG. Though he for winter K TEG is close

to the maximum he at lower G level, hth for winter K TEG is far lower

than that for nonTEG. It can be seen that the summer K TEG can be

used in SHTG to fully use excess solar heat without reducing

thermal ef ciency when solar radiation is low.

4.4. Effect of temperature dependent properties of TE material

Fig. 13 shows variations of T h and K TEG for practical ZT and

constant ZT (ZT ¼ 0.59) with G. It is noted that T h for constant ZT ishigher than that for practical ZT, especially at large G. When G is

1000 Wm2, T h is 159 C and 192 C for practical and constant ZT,respectively. The reason is that ZT of traditional Bi2Te3 decreases

with the increase of temperature. Further, K TEG for constant ZT is

lower than that for practical ZT, especially at large G. Low T h can be

kept in orderto increasehU when K TEG is high at practical ZT. Thus, it

is effective to increase ZT value at high temperature from 100 C to200 C for Bi2Te3 TE material.

Fig. 14 shows variations of he and hth for constant ZT and prac-

tical ZT with G. Similarly, he for constant ZT is higher than that forpractical ZT while hth for constant ZT is lower than that for practical

ZT, especially at high G. It indicates that TEG cannot effectively

convert solar heat into electricity due to performance degradation

of TE material at high temperature.

4.5. Effect of ZT of TEG

ZT of TEG is the most important parameter to improve the

performance of SHTG. Though practical ZT for traditional Bi2Te3 is

temperature dependent, constant ZT with respect to different

values is adopted to investigate its effect in a straightforward way.

Fig.15 shows the effect of ZTof TEG on the performance of SHTG

under G and C is 800 Wm2 and 0.92, respectively. Recently, ZT

values at 0.5, 1.0 and 1.5 refer to common, good and excellent TEGs,respectively. The TEG, whose ZT is 1.0, can be fabricated by nano-

composites Bi2Te3 TE material and it is available in some manu-

factures [21]. The TEG, of which ZT is 1.5, can be prepared at the

Fig. 16. The experimental test system of SHTG.

Table 2

Specication of the experimental apparatus.

Apparatus Specication Production site Parameter

TEG 9500/127/060 B China L W H (mm): 39.7 39.7 4.1Thermostatic TZL-1015D China Water temperature: 0e100 (oC)

Side rheostat BC1e25 W 10U China Accuracy:0.1U

Temperature sensor PT1000 Germany Accuracy: ±0.15 CPyranometer CM22, Kipp&Zonen Netherlands Accuracy: ±1%

Flowmeter LFS15 China Accuracy: ±2.5%



10/12

laboratory level. As shown in Fig. 15 a), it is noted that he increases

distinctly with the increase of ZT, especially at the low ZT. For

example, hes are 2.0%, 3.3% and 4.3% when ZTs are 0.5, 1.0 and 1.5 at

T w ¼ 20 C, respectively. It implied that the low ZT (ZT ¼ 0.5) valueshould be increased. It suggests that some commercial TE material

should be improved by nanocrystallization and doping [21]. More

importantly, hth could not decrease obviously with the increase of

ZT. As shown in Fig. 15 b), hth is 46.0%, 45.0% and 44.3% when ZT is

0.5, 1.0 and 1.5 when T w ¼ 50 C Fig.15 c) shows the variations of T hwith T w under different ZTs. It can be seen that T h decreases with

the increase of ZT and all of T hs are below 200 C. So in SHTG, highperformance TEG can ensure that T h is lower than melting tem-

perature of solders.

4.6. Experimental validation

In order to validate the simulation analysis, experimental setup

is established as shown in Fig.16. Experiments areconducted to test

the electrical and thermal performance of SHTG. The TEG of SHTG is

9500/127/060B from the Ferrotec Company (Hangzhou, China) and

its thermal conductance is about 0.64 W/K, which is K TEG for this

SHTG at 700 Wm2e800 Wm2 of solar irradiance. The specica-tion, mount and inclination of SHTG are described in Section 2. In

this testing system, various inlet water temperatures have been

maintained by using a thermostatic waterbath (Poxiwar China) and

the water is circulated using brushless DC pumps. The slide rheo-

stat (0e10U, 0.1U) is employed as electrical load and connected

with the TEG. The side rheostat is xed at 3.2 Uwhich is around the

optimal value of load (R opt).

he and hth can be measured by:

he ¼ P

GACPC ¼

U 2Load

.RL

GACPC (27)

hth ¼ C pmwðT out T inÞ

GACPC (28)

where ACPC is the area of the CPC, U Load is the voltage of external

load, RL is the resistance of the load, C p is the specic heat of water,

mw is the mass ow rate of water, T in is the inlet water temperature

and T out is the outlet water temperature.

Physical measurement parameters include the water temper-

ature at inlet and outlet of SHTG, the ambient temperature, the

ow rate of water, the incident solar irradiance and electrical

power of SHTG. The temperature sensors (PT1000) were used tomeasure the water temperatures of the inlet and outlet, and

ambient temperature. A pyranometer (CM22, Kipp&Zonen) was

employed to measure the global irradiance on SHTG. The output

voltage was measured by Keithley 2700 directly. The data of

temperatures and solar irradiance were transmitted to a data

logger (Keithley 2700) and then to computer for analysis shown

in Fig. 16. The owmeter (Rotameter) was employed to measure

the water ow rate. The specication of the experimental appa-

ratus is shown in Table 2.

Fig.17 shows the variations of experimental data and simulation

data with T ws when G is around 750Wm2. From Fig. 17 a), the

uctuation of P is small under the variable G due to the thermal

capacity of SHTG. It implies that continuous electricity can be

produced. From Fig. 17 b), it can be seen that the results of themodel agree with that of the experiment. The largest relative errors

of he and hth are 4.5% and 6.0%, respectively. Further, he drops from

1.88% to 1.23% and hth drops from 56.7% to 47.1% when T w increases

from 20 C to 50 C. The he and hth are higher than that predicted byMiao et al. [12], because the mini-CPC and TEG with suitable K TEGare employed in the present study.

Generally, the cost of thermoelectric generator module using in

SHTG is about 4e5 $/piece. This data is from a Chinese largest

online shop (Alibaba) or Amazon. The cost is very low compared to

evacuated tube solar collectors ($830/m2) [22]. In AM1.5G and

Tw ¼ 25 C, he is about 1.9%. As for this SHTG, P is about 4.5 W forone TEG. It indicates that the increased cost is about 1 $/W. This

value is close to that for solar PV.

5. Conclusion

A SHTG using heat pipe evacuated glass tube collector with

mini-CPC has been presented in this study. The following conclu-

sions can be obtained:

(1) ha of mini-CPC is more than 80% from 70 to 70 withouttracking system and the mini-CPC reector can signicantly

improve he.

(2) The optimal KTEG should be determined by high solar irra-

diance and is almost independent on the temperature of the

0 1 2 3 4 5 6 7

700

800

T =30 C

T =20 C

T =50 C

T =40 C

G / W m - 2

t/min

2.4

2.6

2.8

3.0

3.2

3.4

P

/ W

P for T =30 C

P for T =20 C

P for Tw=40 CP for T

w=50

oC

a)

20 25 30 35 40 45 500.0

0.4

0.8

1.2

1.6

2.0

simulation

experiment

η e

/ %

Tw /

oC

45

50

55

60

65

η t h

/ %

b)

Fig. 17. Variations of experimental data and simulation data with T ws, a) experimental

data for P at different Gs, b) variations of he and hth.



11/12

hot water. SHTG with optimal KTEG can effectively convert

the excess solar heat into electricity.

(3) The excess solar heat can be effectively utilized if ZT of Bi2Te3TE material at the temperature from 100 Ce200 C isimproved to a great extent.

(4) he and hth of SHTG are predicted to be 3.3% and 48.6% when C ,

ZT, G and T w are 0.92, 1.0, 800 Wm2 and 20 C, respectively.

Acknowledgments

This work is supported by the National Science and Technology

Support Project of China under the Contract No.2012BAA05B04.

Appendix A. Thermal resistance of heat pipe

R w,E R E R C R w,CR b R con

T b Th

R hp

Fig. 18. Thermal network of the heat pipe.

As shown in Fig. 18, thermal resistance of the heat pipe can be

expressed as [23]:

Rhp ¼ Rw;E þ RE þ RC þ Rw;C þ Rcon (29)

where R w,E and R w,C are the wall radial thermal resistances of

evaporation and condensation sections. R E and R C are evaporation

and condensation interfacial thermal resistances. R con is the contact

resistance between the heat pipe and hot side of TEG. R con is

assumed to be 0.02 W K1 [12]. The thermal resistance of the vaporow is negligible.

Rw;E ¼ln

Do;E

Di;E

2pLE kw(30)

RE ¼ 1

pDi;E hE LE (31)

RC ¼ 1

pDi;C hC LC (32)

Rw;C ¼ln

Do;C

Di;C

2pLC kw(33)

The evaporation and condensation heat transfer coef cients can

be expressed as [24,25]:

hE ¼ A"

r21 gh fg k3l

mlðT w:E T sat :E ÞLE

#0:25(34)

A ¼h

0:997 0:334ðcos qÞ0:108i" LE

Di;E

#½0:254ðcos qÞ0:385(35)

hC ¼ 0:943"r1 g cos qðr1 rvÞh fg k3l

mlðT sat :C T w:C ÞLC

#0:25(36)

where q

is the incline angle for the SHTG (30 in this study).

Appendix B. Derivation of heat transfer for n-type heat pipe

Fig. 19. The details of the unfolding n.

Based on Fig. 2, the details of the unfolding n are shown in

Fig. 19. The half of the unfolding n inside of the inner glass tube is

selected due to symmetry.

Fig. 20. Energy balance on the n element.3

As shown in Fig. 20, the element balance on the n element can

be expressed as:

S D x Ai

U LD xð

T

T aÞ þ k find

dT

dx

x

k finddT

dx

xþD x

Ltube

¼ 0 (37)The n is directly connected with the inner glass tube of the

evacuatetube. So the input thermal energy per unit of length due to

solar energy is SDx/Ai. The corresponding output thermal energy

per unit of length is UL Dx (TTa).

Ai ¼ WLtube (38)

W ¼ pDi (39)

Boundary conditions:



12/12

dT

dx

x¼0

¼ 0 (40)

It is insulated when x ¼ 0 due to thermal symmetry.

T j x¼W =2 ¼ T b (41)

The useful energy collected by n can be expressed as:

Q U ¼ F ½S U L AiðT b T aÞ (42)

F ¼ tanh½mW =2mW =2

(43)

The useful energy is transferred to the hot side of TEG. There

exist two thermal resistances: one is the bond resistance, the other

is the thermal resistance of the heat pipe. The useful energy can be

expressed as:

Q U ¼ T b T hRb þ Rhp

(44)

Based on the Eq. (42) and Eq. (44), we can nd that:

Q U ¼ F 0½S U L AiðT h T aÞ (45)

F 0 ¼ 1=U LW

" 1

WFU Lþ Lb

k find þ LtubeRhp

# (46)

References

[1] R. Shukla, K. Sumathy, P. Erickson, J. Gong, Recent advances in the solar waterheating systems: a review, Renew. Sustain. Energy Rev. 19 (2013) 173e190.

[2] X. Li, Y.J. Dai, Y. Li, R.Z. Wang, Comparative study on two novel intermediatetemperature CPC solar collectors with the U-shape evacuated tubularabsorber, Sol. Energy 93 (2013) 220

e234.

[3] G. Pei, G. Li, X. Zhou, J. Ji, Y. Su, Comparative experimental analysis of thethermal performance of evacuated tube solar water heater systems with andwithout a mini-compound parabolic concentrating (CPC) reector (C< 1),Energies 5 (2012) 911e924.

[4] E. Zambolin, D. Del Col, Experimental analysis of thermal performance of atplate and evacuated tube solar collectors in stationary standard and dailyconditions, Sol. Energy 84 (2010) 1382e1396.

[5] C. Shih, G. Liu, Optimal design methodology of plate-n heat sinks for

electronic cooling using entropy generation strategy, Compon. Packag. Tech-nol. IEEE Trans. 27 (2004) 551e559.

[6] D. Kraemer, B. Poudel, H.-P. Feng, J.C. Caylor, B. Yu, X. Yan, Y. Ma, X. Wang,D. Wang, A. Muto, High-performance at-panel solar thermoelectric genera-tors with high thermal concentration, Nat. Mater. 10 (2011) 532e538.

[7] G. Chen, Theoretical ef ciency of solar thermoelectric energy generators, J. Appl. Phys. 109 (2011) 104908.

[8] K. Yazawa, A. Shakouri, Cost-ef ciency trade-off and the design of thermo-electric power generators, Environ. Sci. Technol. 45 (2011) 7548e7553.

[9] K. McEnaney, D. Kraemer, Z. Ren, G. Chen, Modeling of concentrating solar

thermoelectric generators, J. Appl. Phys. 110 (2011) 074502.[10] F.J. Lesage, R. Pelletier, L. Fournier, E.V. Sempels, Optimal electrical load for

peak power of a thermoelectric module with a solar electric application, En-ergy Convers. Manag. 74 (2013) 51e59.

[11] W. He, Y. Su, Y.Q. Wang, S.B. Riffat, J. Ji, A study on incorporation of ther-moelectric modules with evacuated-tube heat-pipe solar collectors, Renew.Energy 37 (2012) 142e149.

[12] M. Zhang, L. Miao, Y.P. Kang, S. Tanemura, C.A.J. Fisher, G. Xu, C.X. Li, G.Z. Fan,Ef cient, low-cost solar thermoelectric cogenerators comprising evacuatedtubular solar collectors and thermoelectric modules, Appl. Energy 109 (2013)51e59.

[13] R. Tang, Y. Yang, W. Gao, Comparative studies on thermal performance of water-in-glass evacuated tube solar water heaters with different collector tilt-angles, Sol. Energy 85 (2011) 1381e1389.

[14] D. Mills, A. Monger, G. Morrison, Comparison of xed asymmetrical andsymmetrical reectors for evacuated tube solar receivers, Sol. Energy 53(1994) 91e104.

[15] L. Ma, Z. Lu, J. Zhang, R. Liang, Thermal performance analysis of the glassevacuated tube solar collector with U-tube, Build. Environ. 45 (2010)1959

e1967.

[16] J.A. Duf e, W.A. Beckman, Solar Engineering of Thermal Processes, John Wiley& Sons, 2013.

[17] F. Company, Thermoelectric Technical ReferencedMathematical Modeling of TEC Modules in, 2014.

[18] D.M. Rowe, Thermoelectrics Handbook: Macro to Nano, CRC Press, 2005.[19] H.-S. Huang, Y.-C. Weng, Y.-W. Chang, S.-L. Chen, M.-T. Ke, Thermoelectric

water-cooling device applied to electronic equipment, Int. Commun. HeatMass Transf. 37 (2010) 140e146.

[20] L. Miao, M. Zhang, S. Tanemura, T. Tanaka, Y.P. Kang, G. Xu, Feasibility studyon the use of a solar thermoelectric cogenerator comprising a thermoelectricmodule and evacuated tubular collector with parabolic trough concentrator,

J. Electron. Mater. 41 (2012) 1759e1765.[21] A.J. Minnich, M.S. Dresselhaus, Z.F. Ren, G. Chen, Bulk nanostructured ther-

moelectric materials: current research and future prospects, Energy & Envi-ron. Sci. 2 (2009) 466.

[22] Y. Hang, M. Qu, F. Zhao, Economic and environmental life cycle analysis of solar hot water systems in the United States, Energy Build. 45 (2012)

181e

188.[23] F. Jafarkazemi, H. Abdi, Evacuated tube solar heat pipe collector model andassociated tests, J. Renew. Sustain. Energy 4 (2012) 023101 .

[24] N. Miljkovic, E.N. Wang, Modeling and optimization of hybrid solar thermo-electric systems with thermosyphons, Sol. Energy 85 (2011) 2843e2855.

[25] H. Hussein, M. Mohamad, A. El-Asfouri, Theoretical analysis of laminar-lmcondensation heat transfer inside inclined wickless heat pipes at-plate so-lar collector, Renew. Energy 23 (2001) 525e535.

http://refhub.elsevier.com/S0960-1481(16)30060-X/sref1http://refhub.elsevier.com/S0960-1481(16)30060-X/sref1http://refhub.elsevier.com/S0960-1481(16)30060-X/sref1http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref7http://refhub.elsevier.com/S0960-1481(16)30060-X/sref7http://refhub.elsevier.com/S0960-1481(16)30060-X/sref7http://refhub.elsevier.com/S0960-1481(16)30060-X/sref7http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref9http://refhub.elsevier.com/S0960-1481(16)30060-X/sref9http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref16http://refhub.elsevier.com/S0960-1481(16)30060-X/sref16http://refhub.elsevier.com/S0960-1481(16)30060-X/sref16http://refhub.elsevier.com/S0960-1481(16)30060-X/sref16http://refhub.elsevier.com/S0960-1481(16)30060-X/sref17http://refhub.elsevier.com/S0960-1481(16)30060-X/sref17http://refhub.elsevier.com/S0960-1481(16)30060-X/sref17http://refhub.elsevier.com/S0960-1481(16)30060-X/sref18http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref23http://refhub.elsevier.com/S0960-1481(16)30060-X/sref23http://refhub.elsevier.com/S0960-1481(16)30060-X/sref24http://refhub.elsevier.com/S0960-1481(16)30060-X/sref24http://refhub.elsevier.com/S0960-1481(16)30060-X/sref24http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref25http://refhub.elsevier.com/S0960-1481(16)30060-X/sref24http://refhub.elsevier.com/S0960-1481(16)30060-X/sref24http://refhub.elsevier.com/S0960-1481(16)30060-X/sref24http://refhub.elsevier.com/S0960-1481(16)30060-X/sref23http://refhub.elsevier.com/S0960-1481(16)30060-X/sref23http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref22http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref21http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref20http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref19http://refhub.elsevier.com/S0960-1481(16)30060-X/sref18http://refhub.elsevier.com/S0960-1481(16)30060-X/sref17http://refhub.elsevier.com/S0960-1481(16)30060-X/sref17http://refhub.elsevier.com/S0960-1481(16)30060-X/sref17http://refhub.elsevier.com/S0960-1481(16)30060-X/sref16http://refhub.elsevier.com/S0960-1481(16)30060-X/sref16http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref15http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref14http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref13http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref12http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref11http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref10http://refhub.elsevier.com/S0960-1481(16)30060-X/sref9http://refhub.elsevier.com/S0960-1481(16)30060-X/sref9http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref8http://refhub.elsevier.com/S0960-1481(16)30060-X/sref7http://refhub.elsevier.com/S0960-1481(16)30060-X/sref7http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref6http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref5http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref4http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref3http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref2http://refhub.elsevier.com/S0960-1481(16)30060-X/sref1http://refhub.elsevier.com/S0960-1481(16)30060-X/sref1http://refhub.elsevier.com/S0960-1481(16)30060-X/sref1

cpc solar mini

Documents