1、600 2010 ASHRAEABSTRACTOpen-loop building-integrated photovoltaic/thermal(BIPV/T) systems with air as the heat transfer fluid cansupply a substantial portion of the space heating and hotwater needs of residential and commercial buildings in coldclimates. Over the last few years, several customized m
2、athe-matical models for these systems have been developed. Thispaper presents a more general model useful for design orcontrol purposes which allows for steady-state or transientanalysis. Steady state models provide a quick evaluation ofthe energy balance and system performance useful for design.Tra
3、nsient models provide more insight valuable for develop-ment of control algorithms and system design optimization.INTRODUCTIONIn building-integrated photovoltaic (BIPV) systems,photovoltaic modules are installed as functional componentsof the building envelope (typically, replacing cladding onfaades
4、 or shingles on roofs). Since high temperatures aredetrimental to the performance of photovoltaic arrays, thecirculation of a cooling fluid can be used to remove thermalenergy from BIPV systems. The fluid can be used for spaceheating or domestic hot water heating, and in the case of openloop air sys
5、tems the heated air can also be used as fresh air forventilation or for drying clothes. The integrated system iscalled “building integrated photovoltaic/thermal” (BIPV/T).These systems have several advantages. First, the multiplicityof functions significantly reduces costs. Second, the electricaleff
6、iciency of the photovoltaic modules is considerablyimproved. Finally, the proximity to the loads reduces electricaland thermal transmission losses. Properly designed BIPV/Tsystems may even play an aesthetic role, since they can be usedto cover entire roofs, thus allowing seamless integration.In open
7、 loop air systems, outdoor air passes through achannel under the outermost layer of the BIPV/T systemwhich is typically the PV module or metal-roof with directlyattached PV laminates (see Figure 1 for example). Althoughwater or glycol systems have the advantage of a much higherspecific heat, air-bas
8、ed systems have reduced risks such as nopossibility of freezing or damages to the roof due to leaks.Also, less maintenance is required and will last as long as thePV system operates (20 to 50 years).Air-based BIPV/T systems are usually installed in anopen-loop configuration (see Figure 2), in which
9、outdoor airis used to cool the PV modules by convection (commonlyFigure 1 Schematic of a typical air-based open-loop BIPV/T system (Athienitis 2008).Transient and Steady State Models for Open-Loop Air-Based BIPV/T SystemsLuis M. Candanedo Andreas K. Athienitis, PhD, PEng Jos A. CandanedoStudent Memb
10、er ASHRAE Member ASHRAE Student Member ASHRAEWilliam OBrien YuXiang ChenStudent Member ASHRAELuis M. Candanedo, Jos Candanedo, and William OBrien are PhD candidates, and Yu-Xiang Chen is a PhD student at the Departmentof Building, Civil and Environmental Engineering at Concordia University in Montra
11、l, Canada. A.K. Athienitis is a professor in the Depart-ment of Building, Civil and Environmental Engineering, and the scientific director of the Canadian Solar Buildings Research Network.OR-10-064 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org)
12、. Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 601forced convection). The heated air is used to pro
13、vide thermalenergy to one or more functions in the building before beingexhausted to the exterior. Open-loop air systems are normallypreferred over closed loop air systems as the latter wouldlikely lead to overheating of the PV (reducing its durability andpossibly causing delamination) unless fins a
14、re built into the PVdesign. Also, open-loop systems allow for the potential use forfresh air preheating. Since the inlet temperatures are lowerthan in the case of closed-loop systems, the BIPV/T systemnormally operates with higher thermal efficiencies, althoughits air exit temperatures are lower.BIP
15、V/T systems contain several features that complicatetheir study, such as heating asymmetry and a relativelycomplex geometry. Mathematical models of different levels ofcomplexity, emphasizing different phenomena, have beendeveloped over the years (a brief literature review is presentedbelow). This pa
16、per presents a model bringing together some ofthe ideas presented in previous works by the authors, and themost relevant findings obtained from measurements at theexperimental facilities and demonstration projects of theCanadian Solar Buildings Research Network (Athienitis2008). This model could rea
17、dily be adapted as a design tool forair-based open-loop BIPV/T systems in cold climates. Byincorporating meteorological data, this model can be used asa decision-making tool in pre-feasibility studies.LITERATURE REVIEWExisting Numerical ModelsMathematical models for the particular case of forced-con
18、vection open-loop BIPV/T systems have been developedby Clarke et al. (1997), Eicker and Fux (2000), Bazilian et al.(2001), Bazilian and Prasad (2002), Eicker (2003), and Bloem(2004). However, many other models exist that correspond tosimilar configurations:Models for air hybrid photovoltaic/thermal
19、(PV/T)collectorsnot necessarily installed as a building compo-nenthave been developed by several researchers. Examplesinclude the work of Sopian et al. (1996) (thermal model forsingle and double pass hybrid PV/T air collector); Garg andAdhikari (1997) (hybrid solar air collectors); and Hegazy(2000)
20、(four configurations of hybrid PV/T systems).Models of naturally ventilated BIPV systems. Mosh-fegh and Sandberg (1996) have carried out CFD simulations ofnaturally ventilated PV faades with heating on one side tosimulate solar radiation. Yang et al. (1996) developed anumerical model for a natural v
21、entilated PV roof and faadesystem. The model of Brinkworth et al. (2000) for a naturalventilated PV in a roof included a comparison with experi-mental results. A model of a PV/T air faade was developed inTRNSYS and presented by Bosanac et al. (2003). Mittelmanet al. (2009) developed a natural ventil
22、ated model whereNusselt numbers are also reported.Solar air heaters. Ong (1995) developed a mathematicalmodel and solution procedure for this configuration. Ito et al.(2006) worked on a transient model for a glazed solar airheater.At Concordia University, different BIPV/T numericalmodels have been d
23、eveloped both for research on thesesystems and as design tools for demonstration projects. Thesemodels include the works by Charron (2004), Charron andAthienitis (2006a, 2006b), Athienitis et al. (2005), Liao(2005), Liao et al. (2007), Pantic (2007), Candanedo et al.(2007), Chen et al. (2007b), and
24、Candanedo et al. (2009).The aforementioned models, based on energy balances incontrol volumes, have used different levels of complexity tomodel the energy interactions between the surfaces. Some ofthe most relevant differences in approach are presented below:Common Modelling ApproachesSteady state v
25、s. transient solution. The vast majority ofthe models have relied on a steady state approach, neglectingthe thermal capacitance effects of the PV module. In contrast,Ito et al. (2006) developed a fully-explicit finite differencemodel for a solar air collector. The authors found that the tran-sient m
26、odel is useful to account for the effects of rapid changes(e.g., variable cloudiness, wind speed fluctuations), and there-fore it can be useful for the development of robust control algo-rithms for control of flow rate.Air temperature variation within the control volume.The simplest approach uses a
27、linear approximation to modelthe air temperature variation within the CV (Ong 1995). In thiscase, the average air temperature inside the control volume isthe arithmetic mean of the inlet and outlet temperatures.However, most recent investigations use an exponential airtemperature variation, which is
28、 the exact solution if thetemperatures of the surrounding surfaces are assumed to beuniform inside the CV. The average air temperature (used forthe energy balances) is calculated as Tavg= Tdx/x.Radiative heat transfer. Most investigations have usedthe mean temperature of the surrounding surfaces (Tm
29、) tocalculate a linearization factor (4T3m), as this facilitates thesolution of the equations. The radiative heat transfer coeffi-cient, hr is given then by 4T3m/(1/1 + 1/2 1), assuming aview factor of 1 between the plates. The radiation exchangedifference by using this coefficient assuming two plat
30、es at 350Figure 2 Open and closed loop configurations for solar col-lectors (the heat exchanger may be eliminated inthe open loop configuration). 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, P
31、art 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 602 ASHRAE Transactionsand 273 K is about 1.5% underestimated from the exact valuegiven by the equation (T24 T14)/(1/1 + 1/2
32、 1).Effect of view factors. The majority of the modelsassume, often without stating it explicitly, that the view factorbetween the two surfaces of interest is close to 1. In reality, thisassumption is not always accurate. Charron (2004) took viewfactor calculations for radiative heat transfer modell
33、ing intoaccount.Convective interior heat transfer correlations. Asexplained above, heat transfer in BIPV/T has several particu-larities due to the asymmetric heating (i.e., heat transfer occursmainly through one side of the BIPV/T channel) and the morecomplex geometry. However, most researchers have
34、 usedNusselt number correlations developed for pipes and ductswith uniform boundary conditions for a given cross section,such as the classic correlation by Dittus and Boelter (1930),and the Pethukov equation (Bazilian et al. 2001, Eicker 2003).These correlations tend to underestimate convective heat
35、transfer coefficients, because several heat-transfer enhancingfactors are not taken into account, such as the presence of theframing structure and surface imperfections (which act asturbulence promoters) and developing flow conditions at theinlet.Convective and radiative exterior heat transfer coef-
36、ficients. The determination of the heat loss to the surroundingshas been carried out through many different approaches. TheMcAdams formula reported by Duffie and Beckman (2006)developed in the 50s, combines radiation and convection intoone coefficient. The McAdams formula has often been used(Ong 199
37、5, Ito et al. 2006). This approach is satisfactory forglazed collectors, since the addition of the glass layer signif-icantly increases the insulation, and the effect of the exteriorheat transfer coefficients becomes less important. Mostresearchers separate exterior heat losses in two components:con
38、vection to the exterior air and radiation to a representativesky temperature. The convective heat transfer correlations byTest (1981) and Sharples and Charlesworth (1998) were devel-oped for roof-mounted flat-plate collector and are preferableto the McAdams formula, as confirmed by the experimentalo
39、bservations mentioned in this paper. Both correlations havebeen used in modelling BIPV/T systems (Chen 2009). TheModel by Berdahl and Martin (1984) presented a simplifiedcalculation for a representative sky temperature, which can beused to calculate radiative heat transfer losses.Incidence angle adj
40、ustments. Few researchers haveaccounted for the effect of the variation of the optical proper-ties (transmittance, reflectance, absorptance) of the significantsurfaces as a function of the angle of incidence. In contrast,incidence angle adjustments has often been considered ininvestigations dealing
41、with the electrical performance of PVand BIPV systems (Fanney et al. 2003, King et al. 2004).Effect of moisture content. Moisture has an importanteffect on the physical characteristics of the fluid, in particularon the effective specific heat of the air, accounting for a 1 to 4%increase with respect
42、 to the specific heat of dry air. This effectis less significant under cold winter conditions.Inlet air temperature effects. In BIPV/T systems, theinlet air temperature is sometimes slightly higher than theexterior air temperature. This is especially true in BIPV/Troofs, where the inlet air has been
43、 warmed by thermal energyreleased by the buildings faade. However, few works haveconsidered this effect in BIPV/T modeling (Saelens et al.2004).Electrical efficiency modeling. Most BIPV/T investiga-tions account for the effect of the PV modules temperature ontheir electrical efficiency with a very s
44、imple linear model(Candanedo et al. 2007).Equations solving method. A common approach hasbeen to linearize all the equations and solve the resulting linearsystem by matrix inversion. Since the system of equations isrelatively robust, it can be solved by the simple method ofassuming guess values and
45、iterating until a convergence crite-rion is met. When the effects of thermal inertia are considered,a transient method, such as the fully explicit finite differencemethod has been used.Pressure drop. The modeling of the pressure drop in theair channel has been largely overlooked in most previouswork
46、. It is worth mentioning, however, that the measured pres-sure drops along BIPV/T roofs and faades is often muchsmaller than the pressure drop along the ducting system. Pres-sure drop is evidently a strong function of the geometricconfiguration of the channel, especially of the framing systemused to
47、 support the BIPV/T. Since the modules repeat them-selves at regular intervals, the air pressure follows a “spatiallyperiodic” variation inside the BIPV/T channel, with an overalllinear trend.EXPERIMENTAL FACILITYThe models developed are mainly based on experimentaldata obtained in a test channel lo
48、cated at Concordia Univer-sity, which is shown in Figure 3. The BIPV/T channel was builtto simulate a section of the roof at the EcoTerra demonstra-tion house (Chen et al. 2007a). It is shorter in length howeverdue to practical construction limitations. The top of the chan-nel consists of an amorpho
49、us PV module, with a 6% efficiencyunder standard test conditions, glued to a 0.02 in. (0.5 mm)stainless steel sheet. The bottom of the channel consists of2 in. of polysterene insulation R-10 (1.76 Km2/W) and 3/8 in.thick plywood board (see Figure 3). There is a 1.57 in.(0.04 m) gap between the PV module and the board (D). Awooden frame keeps the top and bottom parts together. Thechannels length (L) in the flow direction is 112 in. (2.84 m),and its width is 15.23 in. (0.387 m). The channel is orientedwith a due-south azimuth angle and a tilt angle () of 45.T
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