Solar Energy Vol. 72, No. 2, pp. 113–128, 20022002 Elsevier Science Ltd

Pergamon PII: S0038 – 092X( 01 )00094 – 9 All rights reserved. Printed in Great Britain0038-092X/02/$ - see front matter

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THE THERMAL AND ELECTRICAL YIELD OF A PV-THERMALCOLLECTOR

† ,* * ** ***H. A. ZONDAG , D. W. DE VRIES , W. G. J. VAN HELDEN , R. J. C. VAN ZOLINGEN*and A. A. VAN STEENHOVEN

*Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands**Energy research Centre of the Netherlands ECN, P.O. Box 1, 1755 ZG Petten, The Netherlands

***Shell Solar Energy B.V, P.O. Box 849, 5700 AV Helmond, The Netherlands

Received 9 May 2000; revised version accepted 28 August 2001

Communicated by BRIAN NORTON

Abstract—Four numerical models have been built for the simulation of the thermal yield of a combinedPV-thermal collector: a 3D dynamical model and three steady state models that are 3D, 2D and 1D. Themodels are explained and the results are compared to experimental results. It is found that all models followthe experiments within 5% accuracy. In addition, for the calculation of the daily yield, the simple 1D steadystate model performs almost as good as the much more time-consuming 3D dynamical model. On the otherhand, the 2D and 3D models are more easily adapted to other configurations and provide more detailedinformation, as required for a further optimization of the collector. The time-dependent model is required foran accurate prediction of the collector yield if the collector temperature at the end of a measurement differsfrom its starting temperature. 2002 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION means of the Hottel–Whillier model, dating backto 1958. Increasingly, the dynamical modelling of

A combined PV-thermal collector – henceforth tothermal collectors has attracted attention. A com-

be called a combi-panel – consists of a photo-parison of three dynamical models has been made

voltaic laminate (a PV-laminate) that functions asby Klein et al. (1974). They identified a storage

the absorber of a thermal collector. In this way, aeffect – lowering the efficiency of the collector

device is created that converts solar energy intoduring the period it is heating up to obtain its

both electrical and thermal energy. The mainworking temperature – and a transient effect due

advantages of a combi-panel are:to the changing weather conditions. Smith (1986)

1. An area covered with combi-panels producescompared dynamical models with an increasing

more electrical and thermal energy than anumber of nodes. From his results it can be

corresponding area covered half with conven-concluded that the modelling of the cover glass

tional PV-panels and half with conventionaldoes not have much impact on the thermal

thermal collectors. This is particularly usefulefficiency, while the temperature difference be-

when the amount of space on a roof is limited.tween the fluid and the tube seems to be im-

2. Combi-panels provide architectural uniformityportant.

on a roof, in contrast to a combination ofThe integration of PV and a thermal collector

separate PV- and thermal systems.into one design fundamentally changes the

3. Depending on the system configuration, thecharacteristics of both. The electrical yield of the

average PV temperature in a PV-thermal col-PV-cells is influenced by the collector inflow

lector might be lower than for a conventionaltemperature and – for the case in which the panel

PV-laminate, thereby increasing its electricalhas an additional glass cover to reduce the heat

performance.loss to the ambient – by the additional reflection

Much is known about the modelling of theat this cover. The thermal yield of the collector is

thermal efficiency of a conventional thermalchanged by the increased heat transfer resistance

collector. A well-known way of modeling it is bybetween the absorber and the fluid, the increasedspecific heat – which approximately trebles due to

† the presence of a PV-laminate – the lower lightAuthor to whom correspondence should be addressed.absorption of the PV-laminate and the absence ofTel.: 131-40-24-72140; fax: 131-40-24-33445;

e-mail: h.a.zondag@wtb.tue.nl a spectrally selective coating.

113

114 H. A. Zondag et al.

In contrast to the situation for conventional The efficiency of the combi-panel has beenthermal systems, the literature on combined measured and has been compared to the efficien-photovoltaic-thermal collector design is not very cies of a conventional sheet-and-tube thermalextensive. In order to optimise the overall design collector and a multi-crystalline silicon PV-panelof the collector, as well as to be able to predict the of the same length and width, which wereeffect of small improvements in the components positioned next to it in the test rig. A photographof the collector, an accurate numerical model is of the test rig is shown in Fig. 2. The originalrequired. However, the effort invested in model- thermal collector surface was somewhat largerling of PV-thermal collectors has been limited. A than the PV-laminate. In order to create similarmodel study was published in which the Hottel– areas for the PV-laminate, the thermal collectorWhillier model was adapted to cover PV-thermal and the combi-panel, the absorbing surfaces of thecollectors as well (Florschuetz, 1979) and several latter two were partly covered with insulation thatresearchers have made simulations in order to had a reflective aluminium top layer. In Fig. 2determine the efficiency of a combi-panel system these covered parts appear as the white areas(Cox and Raghuraman, 1985; Bergene and Løv- around the collector and the combi-panel. The

2vik, 1995). Nevertheless, as far as the present uncovered parts have an area of 0.94 m each.authors are aware, a systematic comparison be- The water was drawn from the tank into thetween various models for combi-panel efficiency thermal collector and the combi-panel by a NKFcalculations has not been published yet. In order Verder ND 300 KT 18 diaphragm pump. Theto obtain more information on the design parame- construction was such that the water heated by theters of combi-panels, several models were built collector was discharged on the sewage system inand compared to experimental results. order to be able to keep the inlet water tempera-

ture at a constant value. The water flow throughthe combi-panel and the conventional thermal

2. EXPERIMENTAL SET-UPcollector have been measured independently with

In order to quantify the efficiency of a combi- two rotary piston KENT PSM-LT PL 10 waterpanel, an experimental prototype was built at the volume meters. The volume flow was measuredEindhoven University of Technology (de Vries, by dividing the counted amount of litres by the1998; de Vries et al., 1999). This was a non- measuring time. The wind speed has been mea-optimised first prototype, which was built in order sured with an EKOPOWER MAXIMUM cupto be able to validate the simulated values gener- anemometer. The irradiation has been measuredated by the models under study. The prototype with a Kipp & Zonen CM 11 pyranometer. Thewas constructed by connecting a conventional temperatures of the PV-laminate, the combi-panelPV-laminate, containing multi-crystalline silicon laminate and the collector absorber as well as thecells, to the absorber plate of a conventional in- and outflow temperatures of the collector andglass-covered sheet-and-tube collector, as shown the combi-panel have been measured with ther-in Fig. 1. The panel was then integrated into a test mocouples type K, which were calibrated to anrig on the roof of the department of Mechanical accuracy of 0.2 K. The thermocouples, theEngineering at the Eindhoven University of Tech- pyranometer, the anemometer, the two waternology. meters and the electrical output of the combi-

Fig. 1. The combi-panel.

The thermal and electrical yield of a PV-thermal collector 115

Fig. 2. Left: the test rig. (Left to right: a conventional thermal collector, the combi-panel and a conventional PV-laminate). Right:the insulation versus the location of the tubes.

Table 1. Characteristic system dimensions The encapsulated cell efficiency under standard2 2A Absorber area 1.12 mabs conditions (1000 W/m , 258C) is typically 13%.2A PV panel area 0.94 mPV The laminate efficiency at 258C is 9.7%. TheB Bond width 0.01 m

D Outer diameter tube 0.01 m thermal absorber is a standard ZEN thermalD Inner diameter tube 0.008 minner collector: a sheet-and-tube absorber in which aH Height insulating air layer 0.02 m

copper spiral is soldered to a copper sheet. TheL Length tube segment 0.724 mL Length of collector surface 1.776 m distance between two neighbouring tubes isc

W Tube spacing 0.095 m 10 cm, the tube diameter is 1 cm. Since thed Thickness absorber 0.0002 mabs absorber was covered with the PV-laminate, thed Thickness PV glass 0.003 mPVglass

d Thickness silicon cell 0.00035 m spectral selectivity of the collector surface wascell

d Thickness cover glass 0.0032 mtopglass destroyed. The length scales used in the calcula-tions correspond to the experimental set-up andare given in Table 1.

panel and the PV-panel were read out by aDORIC digitrend 220 datalogger. The time be-tween two measurements was typically 11 s. The

3. MODEL DESCRIPTIONPV-laminate was a standard Shell Solar PV-lami-

2nate consisting of 72 10 3 10 cm EVA encapsu- 3.1. Introductionlated multi-crystalline silicon cells with a low-iron The heat flows through the combi-panel areglass front and an PE/Al / tedlar film at the back. indicated in Fig. 3. Four numerical models have

Fig. 3. Cross section of the combi panel. The material layers in the combi-panel are indicated, as well as the temperatures and thevarious heat fluxes. The dashed line shows the temperature distribution over the surface of the panel.

116 H. A. Zondag et al.

been developed that calculate these heat flows for thermal efficiency is calculated from the effectivethe determination of the daily yield of the combi- transmission–absorption factor by subtracting thepanel. These models require a decreasing amount electrical efficiency from t , according to t 5a a,eff

of computation time at the cost of less detailed t 2 th . Here, t represents the transmissivityh ja el

information and an increased reliance on empiri- of the glass cover, which equals 92%. In this waycal correlations. one obtains the amount of absorbed solar energy

The results of the measurements and the calcu- that contributes to the thermal yield.lations are the yield and the efficiency of the With respect to the thermal model, the model-collector. The yield of the collector is defined as ing is simplified by regarding the serpentine-likethe amount of useful energy produced by it, while tube as a long straight tube, ignoring the effectsthe efficiency is defined as the yield divided by related to the bends, which are assumed to be ofthe amount of solar energy received by the secondary importance. In this way, two effects arecollector. Both an electrical and a thermal ef- ignored:ficiency are defined. 1. Additional mixing in the tube due to the bends,

leading to a smaller heat resistance betweenV IMPP MPP tube wall and fluid.]]]h ; (1)el GAPV 2. Variations in the area that supplies its heat to a

certain tube section.~mc T 2 Ts dp out in]]]]]h ; (2) In order to estimate these effects, simulationsth GAPV were carried out. An increase of 20% in heat

The four models have in common the way the transfer between tube and tube wall indicated leadoptical and electrical parts are calculated. The to an increase in thermal efficiency of less thanelectrical efficiency, which is a function of tem- 0.1%. Furthermore, the simulations showed that aperature, is given by 20% increase in fin area results in a reduction in

thermal efficiency of slightly less than 1%. Inh 5h 1 2 0.0045 T 2 258C (3)s f gdel 0 cell addition, in the present experimental configura-The transmission–absorption factor t of the tion, the width of the serpentine is approximatelya

combi-panel has been calculated with an optical the same as the width of the PV-laminate, asmodel. The optical model calculated the coeffi- shown in Fig. 2. This reduces these effects evencients of reflection at each material within the further. It is concluded that these 3D effects arePV-laminate, using the Fresnel equations. The small.solar radiation was assumed to have no nett The thermal resistances of the different layerspolarisation, so the incoming light was split in of material between the solar cells and the copper50% parallel and 50% transverse polarization. absorber sheet have been lumped together into theNext, t was determined for each mode separately heat transfer coefficient h , which has beena ca

2and the results were added. The calculation was measured to be 4563.3 W/m K for our ex-based on the assumption of specular reflection, so perimental set-up. The value of h has beenca

diffuse reflection was not taken into account. A determined by measuring the temperature differ-further complication was presented by the fact ence between the glass surface of the PV and thethat a PV-laminate does not present a homoge- absorber and inserting the results into the formulaneous surface but consists of different parts for h indicated below. It is assumed that the heatca

(active PV-area, the top grid and the spacing loss to the ambient through the back of thebetween the cells). For each part the value for t collector is negligible, as well as the temperaturea

has been calculated separately and then t of the difference between the glass and the cells.a

entire combi-panel has been determined by taking~cm T 2 Ts dout inthe average of these values, weighed with the ]]]]]h 5 (4)ca A T 2 Ts dPV cell absrespective surface areas. This method results in a

slight underestimation of t due to the fact that noa 3.2. Dynamical and steady state 3D modelexchange of light between the different materialsurfaces is possible: light reflected by the top grid The first model that has been built is a fullyarea cannot be reflected back by the glass on the time-dependent quasi 3D model. It has been builtPV area in our model. The average value of t , in order to be able to simulate the time-dependenta

which was found to be 0.74, was then inserted behaviour of the combi-panel. The model is quasiinto the thermal-yield models. In the models that 3D since the absorber plate and the PV-laminatewill be described in the following paragraphs, the are segmented in both the directions perpendicular

The thermal and electrical yield of a PV-thermal collector 117

to the flow (x-direction) and along the flow ( y- pDinner]]direction), but the top layer is only segmented in q y 5 h T 7, y 2 T ( y)s d s ds dtube tube abs wB

the direction along the flow.pkSince the heat stored in the combi-panel can ]5 Nu T 7, y 2 T y (9)s d s ds dtube abs wBchange over time, Eqs. (5) to (8) below describe

4 4the time dependency of the heat flows through the q y 5 F e s T y 2 T ys d s d s ds dsky,rad sky topglass topglass skycombi-panel (see Fig. 3):4 4

1 F e s T y 2 Ts ds dearth topglass topglass a≠T (x, y)lam]]] (10)r d clam lam lam ≠t

5 t 2 th G 2 q x, y 2 q x, ys d s ds da el air,rad air,conv q y 5 h T y 2 Ts d s ds dsky,conv wind topglass a

2 q x, y 1 k ds dca lam lam Nu kwind]]]2 2 5 T y 2 T (11)s ds dtopglass a≠ T (x, y) ≠ T (x, y) Llam lam c]]]] ]]]]3 1 (5)S D2 2

≠x ≠yq x, ys dair,rad

e e≠T (x, y) topglass lamvabs 4]]] ]]]]]]]]A r d c 5 s T x, ys dsabs abs abs abs lam≠t e 1 e 2 e etopglass lam topglass lam

5 q (x, y)A 2 q x, y A 4s dca PV ba abs 2 T y (12)s ddtopglass2 2

≠ T x, y ≠ T x, ys d s dabs abs]]]] ]]]]1 k d 1 AS Dabs abs 2 2 PV q x, y 5 h T x, y 2 T ys d s d s ds dair,conv c lam topglass≠x ≠y

Nu k(6) air]]5 T x, y 2 T ys d s ds dlam topglassH

in which r d c is defined as r d c 1lam lam lam cell cell cell (13)r d c . In the model, a slightly sim-glass PVglass glass

plified set of equations is used since the secondq x, y 5 h T x, y 2 T x, y (14)s d s d s ds dca ca lam absorder differentiations with respect to x are ig-

nored, which is allowed since the change in theq x, y 5 h T x, y 2 T (15)s d s ds dba ba abs ax-direction (along the flow) is almost linear and

therefore substantially smaller than the differen-For the Nusselt relations see Appendix A. Thetiation with respect to y. In Eq. (6) the respective

vertical temperature gradient over the glass on topareas are also indicated in order to account for theof the PV-laminate is not calculated; the prop-absorber area that is covered by the insulation (seeerties of the glass and the silicon are lumpedphotograph in Fig. 2). A is equal to A plusabs PVtogether within Eq. (6). The equations for qthe additional area covered by the insulation. The air,rad

and q (Eqs. (12) and (13)) are averaged in xchanging temperatures of the glass cover and the air,conv

and the result is inserted into Eq. (7).tube are calculated fromThe steady state 3D model is exactly the same

≠T ys dtopglass as the dynamical model, except for the fact that in]]]]r d cglass topglass glass ≠t Eqs. (5) to (8) the derivations with respect to time

have been set to zero. For example, Eq. (5)¯ ¯5 q y 1 q y 2 q y 2 q ys d s d s d s dair,rad air,conv sky,rad sky,convchanges into

(7)0 5

≠T1 1 tube2 2 2 t 2th G2q x, y 2q x, y 2q x, ys d s d s ds da el air,rad air,conv ca] ] ]]S DpD rLc 1 p D 2 D Lcs dinner w inner tube4 4 ≠t2 2

≠ T (x, y) ≠ T (x, y)lam lam~5 q LB 2 mc T ( y 2 1) 2 T ( y) (8)f gtube w w w ]]]] ]]]]1k d 1 (16)S Dlam lam 2 2≠x ≠y

in which L represents the length of a segment inFor the simulation of the equations presentedthe y-direction and B represents the contact width

above, the derivations have been discretized asbetween the sheet and the tube. The seven heatshown below:fluxes appearing in Eqs. (5) to (8) are determined

from the following relations (the tube is located at Q 2 Q≠Q n11 nU] ]]]t5n 5 (17)segment x57):≠t Dt

118 H. A. Zondag et al.

2 Q 2 2Q 1 Q≠ Q ≠Tn11 n n21]] ]]]]]]x5n 5 (18) U] 5 0 ⇒ T 5 TU2 2 m51 m52≠x x50≠y Dy (19)

≠TU] 5 0 ⇒ T 5 TIn Eqs. (5) to (8) the time step Dt is chosen to m58 m56≠x x50.5Wbe 0.108 s, which is equal to 1 /100 of the timestep between two measurements in the experimen- The treatment of the begin- and end-segmentstal set-up. It was found that a larger step resulted (segment numbers 1 and 6) differs somewhatin an unstable calculation process while a smaller from the middle segments since the sides aretime step did not change the results of the partially covered by the insulation material (ascalculation. shown in the photograph in Fig. 2). Zero heat flux

The PV-laminate and the absorber are sub- is assumed for the outer boundaries, while thedivided into six segments in the y-direction (along discretization is shown in Fig. 4. Since the PV-the flow). For the middle segments (2 to 5) the laminate is somewhat shorter than the coppertemperature profile is assumed to be symmetric absorber, they do not end at the same segmentwith respect to the tube location in its center. The number. The boundary conditions are:segments are subdivided into seven elements inthe x-direction, perpendicular to the flow, as ≠TU] 5 0 ⇒ T 5 Tm53 m54shown in Fig. 4. ≠x x5end laminate (20)In order to obtain the proper temperature ≠TU] 5 0 ⇒ T 5 Tm519 m518gradients at both sides of the domain of the ≠x x5end

calculation, a fake segment is introduced at each≠Tside (for the case of the middle segments at m51 U] 5 0 ⇒ T 5 Tm51 m52and 8; see Fig. 4) and a value is attributed to it ≠x x5end copper≠Tsuch that the boundary condition is satisfied. Both U] 5 0 ⇒ T 5 Tm519 m518for the absorber and the laminate, the boundary ≠x x5end

conditions are provided byFor the calculation, an initial temperature dis-

Fig. 4. The discretisation in the x-direction for the 3D model; upper figure: the middle segments (2 to 5); lower figure: the outersegments (1 and 6).

The thermal and electrical yield of a PV-thermal collector 119

tribution is assumed. The temperature distribution This set of equations contains nine heat fluxes.on subsequent times is determined by integration Of these, seven are provided by the set of Eqs. (9)of Eqs. (5) to (8) with respect to time, using a to (15), although the quantities which in theseRunge–Kutta procedure. Using this model, the equations are functions of x should now betime-dependent calculation of the yield over an replaced by their average value for each layerinterval of 1 h roughly takes 2.5 h of calculation segment in the collector. In particular, Eqs. (14)time on a Pentium 3. and (15) now become

¯q y 5 h T ( y) 2 T ( y) (26)s d s dca ca cell abs3.3. 2D-model

¯To reduce the calculation time required by the q y 5 h T ( y) 2 T (27)s d s dba ba abs amodel, it was decided to remove the time depen-dence of the model and to make a calculation The heat fluxes through the glass cover and thebased on a layer-averaged basis. A new model has PV glass are provided by two additional equa-been built, that solves the heat balance for all the tions:layers in the combi-panel. The model is 2D in the

kglasssense that the collector is segmented in the y- ]]q ( y) 5 T ( y) 2 T ( y) (28)s dPVglass cell PVglassdPVglassdirection (along the flow) and the heat balance isassumed to hold for each segment independently. kglassThe outflow temperature of the first segment is ]]q ( y) 5 T ( y) 2 T ( y)s dtopglass topglass↓ topglass↑dtopglassthe inflow temperature of the next. For each

(29)segment, the set of equations below is solved by amatrix-solving procedure.

A minor modification has been made by taking Finally, an equation is required for the average¯into account the temperature drop over the glass absorber temperature T . The temperature variesabs

front of the PV-laminate and the glass cover. This along the surface as shown in Fig. 3, corre-resulted in three additional equations. In the 3D sponding to the Hottel–Whillier equations for amodel these equations have been left out, since, sheet-and-tube collector (Duffie and Beckman,due to the discretisation, they would add another 1991).50 equations to be solved, while it was found that t 2 th Gs da el

]]]]the effect of the temperature resistance of the T x, y 5 T 1 1 cosh mxs d s da h ( y)lossglass was less than 1% for reduced temperaturesT ( y) 2 T 2 t 2 th G /h ( y)s dless than 0.05. Another modification in the 2D bond a a el loss]]]]]]]]]]3 (30)cosh m W 2 D /2f s d gmodel was to ignore the effect of the edges of the

absorber that were underneath the insulation (see in which the heat loss coefficient was approxi-Fig. 2). This made the area for loss to the rear of mated by:the collector somewhat less, but the difference in

q ( y) 1 q ( y) 1 q ( y)sky,rad sky,conv bacollector performance was not significant. ]]]]]]]]]h ( y) 5 (31)loss T ( y) 2 TThe fact that a temperature gradient now exists PVglass a

over the glass layers means that the temperature21 / 2m 5 h / k d 1 k d (32)s s ddloss abs abs lam lamT appearing in the 3D model now has to betopglass

split up into T and T , while T istopglass↑ topglass↓ lam and the bond temperature is given bysplit up into T and T . The heat balance iscell PVglass

T ( y) 5 T ( y) 1 q ( y) /hbond w w tuberepresented in Fig. 3, which corresponds to thefollowing equations: 5 T ( y) 1 q ( y)W/ pNu k (33)s dw w tube w

with Nu given in Appendix A. Eq. (30) isq ( y) 5 q ( y) 2 q ( y) (21) tubewater ca banumerically integrated with respect to x in orderto provide the average absorber temperature.q ( y) 5 t 2 th G 2 q ( y) (22)s dca a el PVglass The thermal efficiency has been calculated foran increasing number of segments, as shown in

q ( y) 5 q ( y) 1 q ( y) (23)PVglass air,conv air,rad Fig. 5. This figure indicates that for the low flowcase, three segments are enough. For a high flow

q ( y) 1 q ( y) 5 q ( y) (24)air,conv air,rad topglass case, the temperature increase within the collectoris less and a smaller number of segments issufficient.q ( y) 5 q ( y) 1 q ( y) (25)topglass sky,conv sky,rad

120 H. A. Zondag et al.

Fig. 5. Calculated value of the efficiency at zero reduced temperature for an increasing number of segments (2D model) oriterations (1D model).

2The 2D model resulted in a very substantial absorber h the measured value of 45 W/m Kca

reduction in computation time, as it was 25 times was used.as fast as the 3D static model. An iterative procedure is used. For the calcula-

tion, an initial value for the mean plate tempera-3.4. 1D Model ture is assumed and a value is calculated for the

thermal power P produced by the combi-panel.For the computation of the annual yield, the 2DFor each subsequent iteration, a more accuratemodel was still rather time consuming. To reducevalue for the mean plate temperature is deter-the calculation time even further, a 1D model hasmined frombeen built. This 1D model is a Hottel–Whillier

model (Duffie and Beckman, 1991, pp. 253–281). DTcollector]]]T 5 T 1 1 DTThe thermal yield is given by plate in ca2

P 5 A F t 2 th G 2 U T 2 T (34) P Pss d s ddPV R a el loss in a]] ]]5 T 1 1 (39)in ~2mc A hpv cawith F representing the heat removal factor thatR

follows from the Hottel–Whillier equations: This new value for the plate temperature isinserted into the equation for U in Appendix A~mc loss

]]] ~F 5 1 2 exp 2 A U F9 /mc (35)s f gdR PV loss and into Eq. (1) for the electrical efficiency andA UPV lossthe calculation is repeated. The result converges

21F9 5 1/F 1 U /h 1 U W/ pDh (36) very fast (see Fig. 5). It was found that the 1Dh s djt loss ca loss tube

model was roughly 30 times as fast as the 2DD

model.]F 5 1 2 D/W F 1 (37)s dt W

tanh m W 2 D /2f s d g]]]]]F 5 (38) 4. RESULTSm W 2 D /2s d

4.1. Experimental verification of parametersIn Eq. (38), m is again given by Eq. (32). TheMeasurements were carried out on theequations are largely the same as for a conven-

prototype combi-panel to determine the ex-tional thermal collector, apart from the additionalperimental efficiency curves (de Vries, 1998; determ U /h in Eq. (36), representing the heatloss ca

Vries et al., 1997; Zondag et al., 1999). Theresistance between cells and absorber. In order tomeasured efficiency curves for the prototypecalculate the thermal yield, equations are requiredcombi-panel and the thermal collector are shownfor the heat transfer coefficient through the coverin Fig. 6 and the corresponding efficiencies atU and the heat transfer coefficient from theloss

zero reduced temperature are summarized intube to the water h (both given in Appendixtube

Table 2. The thermal efficiency is shown as aA). For the heat transfer coefficient from cells to

The thermal and electrical yield of a PV-thermal collector 121

Table 2. Efficiencies at zero reduced temperature estimated in which F represents the heat removal factorRwith the least square fits on two data sets for each paneland h the loss coefficient. F is typicallyl R

Panel Number of Eta zero 0.8360.01, so the efficiency for zero reduceddata in settemperature and zero electrical efficiency, 0.6,

Thermal collector 22 0.8460.011automatically leads to a t of 0.7260.02, whichCombi-panel without electricity 8 0.5960.015 a

Combi-panel with electricity 12 0.5460.015 corresponds to the calculated value of 0.74 that isused in the models. The loss coefficient equals 5.2

2 2W/m K, which resembles the value of 5.8 W/m Kfunction of reduced temperature, which is defined calculated in the 1D model.as

4.2. Dynamical influencesT ; T 2 T /G (40)s dred in a The dynamical performance of the 3D dynam-The assumption of a linear dependence of the ical model has been tested by simulating the yieldefficiency on the reduced temperature over the of the combi-panel over a day. In order to do so,range of reduced temperatures shown is in accord- the yield of the prototype combi-panel has beenance with the results of the simulations for the measured together with the ambient conditions onpresented design. a day in October. Next, the data collected on the

Fig. 6 can be used to verify several experimen- irradiance and the ambient temperature were usedtal parameters. According to Eq. (34) the ef- as the input data for the simulations. The resultsficiency of a thermal collector can be written as for the 3D model together with the experimentally

measured data are presented in Fig. 7. Accordingh 5 P/GA 5 F t 2 th 2 F U T (41)s dth R a el R loss red to Fig. 7, the 3D model predicts the measured

outflow temperature of the combi-panel very well.In the early hours the match is excellent. The factthat the model slightly underpredicts the ef-ficiency at the end of the day was attributed to thetiles on the roof, which had been heated in thecourse of the day and now increased the ambienttemperature in the direct vicinity of the combi-panel.

Fig. 8 shows a close up of Fig. 7. The time lagthat appears in the figure corresponds to approxi-mately 4 min between the increase in the ir-radiance and the increase in the outflow tempera-ture, which is of the same order as the calculatedtheoretical response time of the collector of

Fig. 6. Measured thermal efficiency (x) thermal collector, 3.5 min for a mass flow of 60 l /h. It can be(o, 1) combi-panel either without or with electricity pro-

concluded that the response time is small withduction. The uncertainties (least square fits) in the measure-respect to the duration of a measurement, whichments are presented by the bar lengths.

Fig. 7. Left: calculated (3D dynamical model) and measured outflow temperature for the case without production of electricity~(m561 l /h). The lower line presents the inflow temperature. Right: the corresponding irradiance.

122 H. A. Zondag et al.

Fig. 8. Close up of Fig. 7, illustrating the time lag between the irradiance (left curve) and the outflow temperature (right curve).

typically lasted several hours, but large with model was found to be 11 046 kJ, correspondingrespect to the sampling rate which was typically to 54.4% of the incoming solar energy, whereas10.8 s. the steady model indicated a yield of 11 089 kJ,

Since the calculation of the dynamical effects corresponding to 54.2% of the solar energy. Thetook a lot of calculation time, it was decided to loss caused by ignoring the dynamical effectsestablish the importance of the dynamical effects over the day was therefore only 0.2%. It isfor the calculation of the daily yield. Therefore, important to note, however, that the dynamicalthe value of the daily yield determined from the model gives a lower yield at the beginning of the3D dynamical model has been compared to the day, due to the heating of the combi-panel,value of the daily yield determined from the 3D whereas it predicts a higher efficiency at the endsteady state model. For a first try, the comparison of the day due to the cooling of the collector. Thiswas performed with the data collected on a day in effect is not calculated by the steady state models.August, a clear day without much fluctuation in Therefore, if the yield is calculated over the first 5the irradiance. The data on the ambient conditions h only, the difference between the models iswere measured with an interval of 11 s. At the increased up to 0.8%. It should be concluded thatend of the measurements, the data were averaged the dynamical effects largely cancel during theover the hour and supplied to the model. The day, since the reduced experimental efficiency inresults are shown in Fig. 9. the morning is compensated by the increased

The yield determined from the dynamical 3D experimental efficiency in the afternoon.Next, the calculations were repeated for a day

in September with a strongly fluctuating ir-radiance. The results are shown in Fig. 10. For thecalculation of the yield over the entire day againthe dynamical and the steady state model pro-duced exactly the same value of 45.4%. However,if the calculation was confined to the first 3 h ofthe day, the difference between the dynamical andthe steady state model was increased to 2.3%.

Even with the strongly fluctuating irradiationobserved on this day, the calculation of thedynamical effects does not result in a moreFig. 9. Output temperature of the combi-panel for a day with aaccurate value for the yield over the entire day.constant irradiance, calculated with the 3D dynamical model

(solid line) and the 3D steady model (dashed line). On the basis of these results it has been concluded

The thermal and electrical yield of a PV-thermal collector 123

Fig. 10. Output temperature of the combi-panel for a day witha strongly fluctuating irradiance, calculated with the 3Ddynamical model (solid line) and the 3D steady model (dashed

Fig. 11. Least squares fit of the measurements of the thermalline).efficiency (solid) compared to the results obtained with the 2Dmodel (dashed). Upper line: conventional thermal collector,that for an accurate calculation of the annualmiddle line: combi-panel not producing electricity, lower line:

efficiency for our combi-panel collector, the dy- combi-panel producing electricity.namical effects do not have to be taken intoaccount, even though the specific heat is muchlarger than for the case of a conventional thermal ments is well within the range of the experimentalcollector, as indicated in Table 3. In addition, it data.has been concluded that hourly data are suffi- Next, the thermal efficiency calculated by theciently accurate for the calculation of the daily 1D, 2D, and 3D steady state models has beenyield, which strongly reduced the amount of data compared. The simulations have been carried outto be processed. for the case in which no electricity is produced.

The result is given by Fig. 12. In order to allow a4.3. Steady state performance of the combi- good comparison between the models, curves arepanel shown for the 2D model without temperature

First, a comparison has been made between the gradient over the glass (similar to the 3D model)2D steady state model and the experiments. For and the 3D model with the absorber area equal tothe calculations, the ambient conditions are pre- the PV area, (similar to the 1D and 2D models).sented in Table 4 while the system dimensions The figure shows that the results of the 1D andwere presented in Table 1. The results of the the 2D model differ by roughly 1%. In com-simulation are shown in Fig. 11. The thermal parison to the 2D thermal model, the 3D thermalefficiency was determined as a function of re- model predicts a 2% lower efficiency. However,duced temperature for the 2D steady state model. the figure shows that a large part of the 2%The agreement between the model and the experi- difference between the 2D and the 3D model is

due to the absence of the heat resistance in theTable 3. Specific heat of PV-thermal collector components glass in the 3D model. It should therefore bePV/T Specific heat Component Heat storage concluded that a good correspondence existscomponent (J /kgK) mass (kg) (J /K) between the results of the models.Copper tube 390 3.0 1170Copper sheet 390 2.4 936Water 4180 0.60 2516 5. SIMULATION OF THE DAILY YIELD BYGlass 840 7.23 6080 THE 1D MODELEVA 2300 0.84 1921Silicon 760 0.58 440 As a final test, the thermal yield has beenTotal 14.65 13 063

simulated as a function of reduced temperaturewith the 1D model. The ambient conditionsduring the day were those presented in Fig. 13.Table 4. Standard simulation conditionsThe inlet temperature was kept constant.T 208Ca

2G 800 W/m The results of the simulation are presented inV 1 m/swind Figs. 14 and 15. Fig. 14 shows a good corre-T 48Csky spondence between the measurements and the~m 0.020 kg/sT 20–608C simulations, although the calculated values tend toin

w 458 be slightly larger than the measured values,

124 H. A. Zondag et al.

Fig. 12. Comparison between the 1D, 2D and 3D thermal models for the case without production of electricity and h 5ca245 W/m K.

corresponding to the small overprediction of the efficiency could be determined sufficiently accu-efficiency observed in Fig. 11. In addition, it can rately by the 1D model using Eq. (1).be observed that the simulations somewhat over- Fig. 15 shows the measured electrical power ofpredict the measured thermal efficiency in the the system and the temperature difference be-morning and slightly underpredict the measured tween the PV-panel and the PV-laminate that isthermal efficiency in the evening, as can be integrated into the combi-panel. The figure indi-expected from a steady state calculation, since the cates that the electrical efficiency of the PV-panelheat storage effect (Klein et al., 1974) is not taken is slightly smaller than the electrical efficiency ofinto account. the combi-panel. This is due to the lower tempera-

Until now, all attention has been focussed on ture of the cells in the combi-panel for the presentthe thermal efficiency of the system. However, for case in which the inlet temperature was kepta combi-panel also the electrical efficiency should constant at approximately 188C. This implies thatbe determined. It turned out that the electrical the electrical gain due to cooling of the PV by the

Fig. 13. Ambient conditions as a function of time.

The thermal and electrical yield of a PV-thermal collector 125

Fig. 14. Calculated (dashed) and measured (solid) thermal power for the conventional thermal collector and the combi-panel as afunction of time.

water is even larger than the optical loss of the combi-panel for the Dutch meteorological KNMIcombi-panel, that is due to the reflection at the test reference year. The 1D steady model has beenglass cover. This is expected, since additional used to model the case in which two similar

2transmission losses of 8% correspond to a tem- combi-panels with a joined area of 3.5 m and a2perature difference of 168C, while a difference of mass flux of 50 kg/(m /h) have been used to heat

208C is observed. a container of 175 l of water from 10 up to 608C.A boiler unit was assumed to do the remainder ofthe heating required if a temperature level of 608C

6. ANNUAL YIELD OF A COMBI-PANEL IN Acould not be reached by the combi-panel unit

DOMESTIC HOT WATER SYSTEMalone. The pump was assumed to be operated by

Next, simulations have been performed to find an ideal control algorithm, switching it on when-the thermal and electrical yield of the prototype ever a positive yield would occur. The tapping

Fig. 15. Calculated (dashed) and measured (solid) DC electrical power for the PV-panel and for the combi-panel as a function oftime. In addition, the measured temperature of the PV panel and the PV combi laminate are indicated.

126 H. A. Zondag et al.

Table 5. ISSO warm water withdrawal schedule, (2) no withdrawal, (1) 175/8 l withdrawal

Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tapping 2 2 2 2 2 2 2 1 2 2 2 2 1 1 2 2 2 1 1 1 2 1 1 2

Table 6. Advantages of the four models

Model type Characteristics Calculation time

Efficiency curve: Hourly yield

1D Steady model Fast calculation of daily and annually averaged 0.27 s 0.05 syield for sheet-and-tube design

2D Steady model Like 1D steady model but easily adapted to 8.35 s 1.67 sother configurations

3D Steady model Like 2D steady model but also detailed 229.31 s 45.86 sinformation on temperature distribution

3D Dynamical model Like 3D steady model but also calculation of – 2.5 hinstantaneous yield for non-steady conditions

pattern was modelled after the hot water with- error made by ignoring the dynamical effects isdrawal schedule of the ISSO (Institute for Study very small.and Stimulation of Research in the field of heating The 1D steady model was subsequently usedand air conditioning), which is presented in Table for the calculation of the annual yield of a combi-5. For the case in which heat and electrical energy panel design. The thermal and electrical efficien-are produced simultaneously, the thermal ef- cies have been found to be 33 and 6.7% for theficiency has been found to be 33% for the configuration used, as compared to 54% for theconfiguration used, as compared to 54% for the conventional thermal collector and 7.2% for theconventional thermal collector. Taking into ac- conventional PV-laminate under the same con-count low-irradiation loss, electrical loss due to ditions. The advantage of the 1D model is that itthe angle of irradiation, losses due to the inverter is roughly 30 times as fast as the 2D model,(typically 8%) and MPP-tracking losses of 2%, which is about 25 times as fast as the 3D model.the electrical efficiency of the panel was found to Although the 1D model performs just as goodbe 6.7% as compared to 7.2% for the convention- as the 2D model for the cases mentioned above,al PV-laminate under the same conditions. In this the 2D and 3D models have some importantcase, therefore, in contrast to the situation in Fig. advantages over the 1D model since they are15, the additional reflection losses in the PV- more flexible and can easily be adapted to morecombi are not compensated by the cooling of the complicated combi-panel designs. Therefore, thePV. This is due to the higher average inlet 2D and 3D models are very important for furthertemperature of the water, which is heated during optimization of the combi-panel, which is one ofthe course of the day. the main targets in the ongoing research. By

variation of the model parameters information canbe obtained with respect to the effect of further

7. CONCLUSIONSimprovements. Table 6 summarizes the merits of

A dynamic 3D model and steady 3D, 2D and the four models.1D models have been built, together with a firstnon-optimised prototype of the combi-panel. Theefficiency curves determined from the models NOMENCLATUREcorrespond with the experimentally determined

2A surface area (m )curves well within the range of the experimentalB bond width (m)data. It is concluded that for the determination ofc specific heat (J /kgK)

the efficiency curves and the daily and annual D tube diameter (m)yield the simple steady 1D model performs satis- F view factorfactorily, while the calculation time is substantial- F heat removal factorR

2G irradiation (W/m )ly reduced in comparison to the more complicated2g gravitational acceleration (m/s )models, even for the case of a combi-panel with 2h coefficient of heat transfer (W/m K)

its much larger specific heat in comparison to a H height of insulating air layer (m)conventional thermal collector. In addition, for the I current (A)calculation of the daily yield, it is found that the k thermal conductivity (W/mK)

The thermal and electrical yield of a PV-thermal collector 127

L length tube segment (m) between PV and top cover by Hollands formulaL length collector surface (m)c (Duffie and Beckman, 1991, p. 160)~m mass flow (kg/s)Nu Nusselt number 1.61708 sin 1.8ws dP thermal power generated (W) ]]]]]Nu 5 1 1 1.44 1 2F Gair Ra cos wPr Prandtl number

21q heat flux (W/m ) 1708

]]]Ra Rayleigh number 3 1 2F GRa cos wRe Reynolds number10.333T temperature (K) Ra cos w

2 ]]]FS D G1 2 1 (A.2)T reduced temperature (Km /W)red 58302U overall heat loss coefficient (W/m K)loss

V voltage (V) In Eq. (A.2) the 1 indicates that the term onlyW Tube spacing (m) has the value indicated between the brackets if thex direction perpendicular to flow

latter is positive: it becomes zero if the quantityy direction of flowbetween the brackets is negative.b coefficient of expansion of air

d thickness of layer (m) Heat loss from cover glass to ambient due toe coefficient of emissivity convection (Fujii and Imura, 1972):h electrical efficiency at Standard Conditions0

0.25h electrical efficiencyel Nu 5 0.56 Ra cos ws dwind crit3r density (kg/m )

0.333 0.333s constant of Stefan–Boltzmann 1 0.13 Ra 2 Ra (A.3)s dcritt transmission of glass

3t transmission–absorption factor gb T ( y) 2 T La s dtopglass a c

]]]]]]]Ra 5 Prw collector angle 2nSubscripts

8a ambient Ra 5 10 (A.4)critabs absorberb bond Heat loss at the upper surface (1D model):.ba from back to ambient Formula of Klein (Duffie and Beckman, 1991, p.c collector

260):ca from cells to absorber21conv convection N 1

crit critical ]]]]]] ]]U 5 1eloss ¯ hT 2 Tel electrical C windlam a]] ]]]F G5 6in inflow ¯ N 1 fs dT lamlam laminate

2 2¯ ¯mpp maximum power point s T 1T T 1Ts ds dlam a lam a]]]]]]]]]]]]1rad radiation 2N1f2110.133elam21th thermal ]]]]]e 10.00591Nh 1 2Ns dlam wind etopglassw water

(A.5)

where N5number of glass coversAcknowledgements—Part of the results presented on the 3Ddynamical model were obtained by Ben Ligtvoet, who was a

f 5 1 1 0.089h 2 0.1166h e 1 1 0.07866Ngraduate student at the EUT at the time of this project. s ds dw w p

2C 5 520s1 2 0.000051w d for 08 , w , 708

APPENDIX A. THE HEAT TRANSFER 100]e 5 0.430 1 2S DRELATIONS APPLIED Tpm

2h 5 wind heat transfer coefficient (W/m K)Heat transfer from tube to water. wind

5 2.8 1 3.0 VwindRe , 2300 ⇒ u 5 4.364tube0.8 0.4Re . 2300 ⇒ u 5 0.023Re Pr (A.1)tube The temperatures in Kleins equation are in

(Bejan, 1993) Kelvin.

The Reynolds number is typically equal to 3200throughout the measurements so the flow is in the REFERENCEStransition regime between laminar and turbulent.

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Duffie J. A. and Beckman W. A. (1991). Solar Engineering of model, outdoor experiment. In Proceedings of ISES WorldThermal Processes, 2nd Edition, Wiley, New York. Congress, August 24–30, Taejon, Korea.

Florschuetz L. W. (1979) Extension of the Hottel–Whillier de Vries, D. W., 1998. Design of a PV/ thermal combi panel.model to the analysis of combined photovoltaic / thermal flat PhD Thesis Eindhoven University of Technology, Eind-plate collectors. Solar Energy 22, 361–366. hoven.

Fujii T. and Imura H. (1972) Natural convection heat transfer de Vries, D. W., van Steenhoven, A. A., van Helden, W. G. J.from a plate with arbitrary inclination. Int. J. Heat Mass and van Zolingen, R.J.C., 1999. A panel-shaped, hybridTransfer 15, 755–767. photovoltaic / thermal device. Dutch Patent 1006838.

Klein S. A., Duffie J. A. and Beckman W. A. (1974) Transient Zondag, H. A., de Vries, D. W., van Steenhoven, A. A., vanconsiderations of flat-plate solar collectors. J. Eng. Power Helden, W. G. J. and van Zolingen, R. J. C., 1999. The96, 109–113. efficiency of PV/T-combi energy production. In Proceed-

Smith J. G. (1986) Comparison of transient models for flat- ings of ISES World Congress, Vol. 3, July 4–9, Jerusalem,plates and through concentrators. J. Solar Energy Eng. 108, pp. 96–101.341–344.