Scholarly article on topic 'Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors'

Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors Academic research paper on "Earth and related environmental sciences"

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{"Photovoltaic/thermal systems" / "Hybrid PVT" / "Solar collectors" / "System performance" / "Domestic energy demand"}

Abstract of research paper on Earth and related environmental sciences, author of scientific article — Ilaria Guarracino, Christos N. Markides, Alexander Mellor, Nicholas J. Ekins-Daukes

Abstract In this paper we present a dynamic model of a hybrid photovoltaic/thermal (PVT) collector with a sheet-and-tube thermal absorber. The model is used in order to evaluate the annual generation of electrical energy along with the provision of domestic hot-water (DHW) from the thermal energy output, by using real climate-data at high temporal resolution. The model considers the effect of a non-uniform temperature distribution on the surface of the solar cell on its electrical power output. An unsteady 3-dimensional numerical model is developed to estimate the performance of such a collector. The model allows key design parameters of the PVT collector to vary so that the influence of each parameter on the system performance can be studied at steady state and at varying operating and atmospheric conditions. A key parameter considered in this paper is the number of glass covers used in the PVT collector. The results show that while the thermal efficiency increases with the additional glazing, the electrical efficiency deteriorates due to the higher temperature of the fluid and increased optical losses, as expected. This paper also shows that the use of a dynamic model and of real climate-data at high resolution is of fundamental importance when evaluating the yearly performance of the system. The results of the dynamic simulation with 1-min input data show that the thermal output of the system is highly dependent on the choice of the control parameters (pump operation, differential thermostat controller, choice of flow rate etc.) in response to the varying weather conditions. The effect of the control parameters on the system's annual performance can be captured and understood only if a dynamic modelling approach is used. The paper also discusses the use of solar cells with modified optical properties (specifically, reduced absorptivity/emissivity) in the infrared spectrum, which would reduce the thermal losses of the PVT collector at the cost of only a small loss in electrical output when the selective coating is applied.

Academic research paper on topic "Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors"

Applied

Thermal

Engineering

Accepted Manuscript

Title: Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors

Author: Ilaria Guarracino, Christos N. Markides, Alexander Mellor, Nicholas J. Ekins-Daukes

PII: S1359-4311(16)30199-5

DOI: http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.056

Reference: ATE 7785

To appear in: Applied Thermal Engineering

Received date: 26-11-2015 Accepted date: 20-2-2016

Please cite this article as: Ilaria Guarracino, Christos N. Markides, Alexander Mellor, Nicholas J. Ekins-Daukes, Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.056.

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DYNAMIC COUPLED THERMAL-AND-ELECTRICAL MODELLING OF SHEET-AND-TUBE HYBRID PHOTOVOLTAIC/THERMAL (PVT) COLLECTORS

Ilaria Guarracino1, Christos N. Markides1*, Alexander Mellor2, Nicholas J. Ekins-Daukes2

1 Clean Energy Processes (CEP) Laboratory, Department of Chemical Engineering, Imperial College London,

South Kensington Campus, London SW7 2AZ, U.K.

2 Blackett Laboratory, Department of Physics, Imperial College London, South Kensington Campus, London

SW7 2AZ, U.K.

* Corresponding author: c.markides@imperial.ac. uk; +44 (0)20 759 41601

Research Highlights

• A fully dynamic, 3-D numerical model of a PVT collector is presented.

• High-resolution weather data and hot-water demand data are used in the simulation.

• The use of PV cells with reduced emissivity for PVT applications is introduced. Abstract

In this paper we present a dynamic model of a hybrid photovoltaic/thermal (PVT) collector with a sheet-and-tube thermal absorber. The model is used in order to evaluate the annual generation of electrical energy along with the provision of domestic hot-water (DHW) from the thermal energy output, by using real climate-data at high temporal resolution. The model considers the effect of a non-uniform temperature distribution on the surface of the solar cell on its electrical power output. An unsteady 3-dimensional numerical model is developed to estimate the performance of such a collector. The model allows key design parameters of the PVT collector to vary so that the influence of each parameter on the system performance can be studied at steady state and at varying operating and atmospheric conditions. A key parameter considered in this paper is the number of glass covers used in the PVT collector. The results show that while the thermal efficiency increases with the additional glazing, the electrical efficiency deteriorates due to the higher temperature of the fluid and increased optical losses, as expected. This paper also shows that the use of a dynamic model and of real climate-data at high resolution is of fundamental importance when evaluating the yearly performance of the system. The results of the dynamic simulation with 1-min input data show that the thermal output of the system is highly dependent on the choice of the control parameters (pump operation, differential thermostat controller, choice of flow rate etc.) in response to the varying weather conditions. The effect of the control parameters on the system's annual performance can be captured and understood only if a dynamic modelling approach is used. The paper also discusses the use of solar cells with modified optical properties (reduced absorptivity/emissivity) in the infrared spectrum, which would reduce the thermal losses of the PVT collector at the cost of only a small loss in electrical output, providing the electrical performance does not deteriorate when the selective coating is applied.

1 Keywords

2 Photovoltaic/thermal systems, Hybrid PVT, Solar collectors, System performance, Domestic energy demand

4 Nomenclature

Abbreviations

Symbol

hfree ftgap hlt K

k kA h

Mono-crystalline Domestic hot water Hot water Photovoltaic

Hybrid photovoltaic and thermal collector

Area (m2)

Absorber area (m2)

Aperture area (m2)

Gross area (m2)

Surface area (m2)

Storage tank surface area (m2)

Specific heat capacity (J/kg K)

Specific heat capacity of the absorber (J/kg K)

Specific heat capacity of the fluid (J/kg K)

Specific heat capacity of the glass cover (J/kg K)

Specific heat capacity of the solar cell (J/kg K)

Diameter (m)

Riser external diameter (m) Hydraulic diameter (m) Electricity (W) Fraction

Fraction of the demand of electricity covered by the PVT system Fraction of the demand of hot water covered by the PVT system Irradiance (W/m2) Gravity (m/s2)

Convection heat transfer coefficient

Convective heat transfer coefficient in the pipe (W/m2 K)

Heat transfer coefficient due to free convection (W/m2 K)

Heat transfer coefficient due to convection in the enclosed space between the glass cover and the solar cell (W/m2 K)

Heat transfer coefficient due to convection at the storage tank (W/m2 K)

Forced convection wind heat transfer coefficient (W/m2 K)

Top convective heat transfer coefficient (glass to ambient) due to free and forced

convection (W/m2 K)

Solar irradiance spectrum (W/m3)

Thermal conductivity (W/m K)

Thermal conductivity of the absorber (W/m K)

Thermal conductivity of the air (W/m K)

Thermal conductivity of the encapsulant (W/m K)

Thermal conductivity of the bond (W/m K)

fcf Thermal conductivity of the fluid (W/m K)

kg Thermal conductivity of the glass cover (W/m K)

kgl Thermal conductivity of the adhesive (W/m K)

ki Thermal conductivity of the insulation (W/m K)

kPV Thermal conductivity of the solar cell (W/m K)

^TED Thermal conductivity of the Tedlar (W/m K)

L Length (m)

M Mass (kg)

MA Mass of the absorber (kg)

Mf Mass of the fluid (kg)

Mg Mass of the cover glass (kg)

MPV Mass of the solar cell (kg)

rhf Mass flow rate (kg/s)

NP Number of pipes

Nx,Ny Nodes on x, y direction

Pel Electrical energy generated (W)

Pel(T) Electrical energy generated over the period of time T (J)

¿ELd Demand of electricity (J)

Pr Prandtl number, pcp/k

Q Heat (W)

Qa-cd Heat transfer in the absorber between two adjacent nodes due to conduction (W)

Qcoll Heat addition from the PVT collector to the storage tank through the heat exchanger (W)

Qf Heat addition to the fluid from the absorber due to convection (W)

Qg-cd Heat transfer in the glass cover between two adjacent nodes due to conduction (W)

<2g,a-CV Heat losses from the glass cover to the ambient due to convection (W)

<3g,a-RD Heat losses from the glass cover to the ambient due to radiation (W)

Qg,pv-cv Heat addition to the glass cover from the solar cell due to convection (W)

Qg, PV-RD Heat addition to the glass cover from the solar cell due to radiation (W)

Cg-AB Fraction of the incident irradiance absorbed by the glass cover (W)

<2i Enthalpy drop of the storage tank due to the flow of domestic hot water (W)

(3it Heat losses from the storage tank due to convection (W)

@loss Heat loss from the rear layer of the PVT collector (W)

C?PV-CD Heat transfer in the solar cell between two adjacent nodes due to conduction (W)

Qpv-a Heat addition to the absorber from the solar cell due to conduction (W)

Qpv-ab Fraction of the incident irradiance absorbed by the solar cell (W)

QTU Thermal energy generated (J)

R Thermal resistance (K m2/W)

PcD Thermal resistance between the solar cell and the absorber (K m2/W)

d gaP Thermal resistance of the air gap between the glass cover and the solar cell (K m2/W)

^loss Thermal resistance to the ambient at the rear layer of the PVT collector (K m2/W)

r Reflectance

rg Glass reflectance

rpv Solar cell reflectance

Rg Top reflected irradiance of a single glazed system

Ra Rayleigh number, gfip2c/kphTL3

Re Reynolds number, pvD^/p

T Temperature (K)

t Time interval (s)

TA Absorber temperature (K)

Ta Ambient temperature (K)

Td Required temperature of the hot water for domestic application (K)

Tf Fluid temperature (K)

7f-in Inlet fluid temperature (K)

Tf-o Outlet fluid temperature (K)

T Glass cover temperature (K)

T- 1 in Inlet temperature (K)

T 1 m Averaged temperature (K) / Mains water temperature (K)

T 1 0 Outlet temperature (K)

Tpy Temperature of the solar cell (K)

T 1 r Reduced temperature (K m2/W)

Trei Reference temperature (K)

^sky Sky temperature (K)

Tt Temperature of the storage tank (K)

v Velocity (m/s)

vw Wind speed (m/s)

W Width (m)

W Nominal power (W)

a Absorption coefficient

«g Glass absorption coefficient

aPV Absorption coefficient of the solar cell

P Temperature expansion coefficient, 1/T (1/K)

A>v Temperature coefficient (1/K)

Y Tilt angle of the collector to the horizontal (rad)

Ô Thickness (m)

Sa Absorber thickness (m)

sb Bond thickness (m)

S eva EVA thickness (m)

¿g Glass cover thickness (m)

<5gi Adhesive thickness (m)

Si Insulation thickness (m)

Spv Solar cell thickness (m)

SjED Tedlar thickness (m)

£ Emissivity

£g Glass emissivity

Heat exchanger effectiveness

£pv Emissivity of the solar cell

V Efficiency

Vrei Solar cell standard electrical efficiency

V7 Electrical efficiency of the solar cell function of the operating temperature

Vel Module electrical efficiency

Vtu Thermal efficiency

V Dynamic viscosity (N s/m2)

P Density (kg/m3)

T Transmittance

Tg Glass transmittance

Tag Glass combined transmission and absorption

TCtpv Solar cell combined transmission and absorption

1. Introduction

Hybrid photovoltaic/thermal (PVT) collectors are devices for the conversion of solar radiation into electrical and thermal energy simultaneously. This solution is particularly interesting in residential applications, where a demand for electricity exists alongside one for low temperature heat. Liquid (water) PVT systems are interesting in cold climate regions such as the UK—the location chosen for this study—where the demand of heating and domestic hot water is almost constant during the year. It is predicted in Refs. [1,2] that a PVT system with a 15 m2 collector area designed for a 3-bedroom house in the UK can cover up to 36% of the demand for hot water and up to 51% of the demand for electricity based on a four-member family.

PVT systems operate mostly under dynamic conditions, particularly where the solar irradiance fluctuates due to cloud coverage. However, most previous studies undertaken with the aims of evaluating the suitability and of assessing the potential of this technology (such as Ref. [1]) were based on quasi-steady approaches, wherein the PVT collector is assumed to operate in steady state, while other system components with a larger thermal mass—such as the hot-water tank—have a dynamic response to the time-varying inputs. A few studies (such as Ref. [3]) did take into account the dynamic response of the collector but did not go as far as estimating the temperature gradients on the PV module and the dynamic analysis is limited to a daily simulation. Similarly, in the studies reported in Refs. [4-6], dynamic analyses of PVT collectors were also preformed but without an accompanying discussion of the interaction of the collector with other system components. Some recent experimental and numerical studies on the dynamic performance of PVT systems for DHW applications can be found in Refs. [7,8] where the demand of hot water was a daily or hourly average input.

Taking the dynamics of the system into account is of fundamental importance when the weather conditions change rapidly. The present paper, in fact, shows that a dynamic model, together with the use of real weather and DHW demand data, is required in order to accurately estimate the energy output of the PVT system. It will be demonstrated, based on both types of models, that quasi-steady solutions deviate significantly from dynamic solutions due to the thermal mass in the system and the inherent variability in the (real) weather data used as inputs to the simulations. Moreover, it will be shown that the use of time-averaged input data leads to an overestimation of the energy generated, as was found in Ref. [9] for a study performed on vacuum tube collectors. A more detailed discussion of these results is reported in Section 4.

In the present study a 3-D PVT collector model is used to estimate the temperature distribution over the PV panel and its influence on the panel's electrical power output. As most of the design parameters can be varied by the user, this numerical model constitutes a tool to optimize the design of sheet-and-tube water collectors focusing on a number of design parameters and operating parameters such as the number of glass covering layers, the material used for glass cover, the spacing between the tubes, the fluid flow-rate and the inlet fluid temperature for various ambient conditions. The numerical model is used to solve an energy balance by taking into account the convective and radiative losses from the collector's top surface and the optical losses due to reflection. The numerical approach is an improvement upon the aforementioned studies in that it takes into consideration the dynamic response of the collector to time-varying climate and demand inputs, and also the 3-D spatial distribution of temperature over the panel. The model can be used to generate results for hourly, daily and

annual performance analyses and provide information on its transient performance. The objective is to propose better designs of this hybrid system by quantifying the influence of important design parameters, while demonstrating that a dynamic model is important for the investigation of control strategies and the interaction of the collector with other system components that require a dynamic description.

The details of the PVT collector and the wider system considered in this study are described in Section 2. This section also discusses the role of the PV module as a thermal absorber as well as an electricity generator and focuses on the emissivity of the solar cell. The numerical model is described in Section 3 and the results are reported in Section 4. The latter also contains a comparison of the annual performance of a PVT collector with standard solar cells and a PVT collector using cells with optimized optical properties.

2. Hybrid PVT Collectors and Systems

The greatest part of the absorbed irradiance in a PV module is converted into heat (about 60% - 70%). This heat is partially rejected to the environment by radiative and convective heat losses, and partially increases the temperature of the solar cell reducing its conversion efficiency [10]. A PVT system aims to improve the overall conversion efficiency of the PV panel by cooling the solar cells. While the rejection of excess heat to the environment is beneficial for a standalone PV module, in a PVT module this low-grade heat is collected by the thermal absorber and recovered by a fluid stream for useful thermally driven processes such as hot water provision, space heating or absorption cooling for domestic and commercial applications.

As mentioned above, the performance of a PV module is strongly dependent on its operating temperature. This introduces additional factors that are in need of consideration. Temperature gradients on the collector surface can significantly affect its electrical efficiency because solar cells operating at higher temperatures generate less power. Therefore, a significant challenge in the design of a PVT collector is in obtaining a uniform temperature distribution over the modules. A sheet-and-tube collector is associated with a non-uniform temperature on its surface during operation. The prediction of this temperature distribution is therefore of crucial importance when selecting the best design and evaluating the thermal and electrical yield of the associated PVT system.

System description: The PVT system modelled in this work is shown in Figure 1. It comprises a sheet-and-tube PVT collector (three configurations were considered: unglazed, single glazed and double glazed), a storage tank with an auxiliary heater, a bypass branch (as implemented in Ref. [11]), a circulation pump and thermally insulated connecting pipes. The system shown in Figure 1 is essentially an indirect solar water-heating system where the fluid heated in the solar collector is circulated in the storage tank trough a heat exchanger. The bypass branch allows for the recirculation of the hot water to the collector during periods of low irradiance. A differential controller regulates the activation of the bypass branch and the circulation pump. The controller monitors the temperature in the storage tank Tt, the temperature at the collector outlet Tf_0 and inlet Tf_in, the incident solar irradiance G, and the ambient temperature Ta. An external auxiliary heater ensures that the temperature of the delivered hot-water to the domestic user reaches the required value of 60 °C [12]. This configuration ensures the maximum utilization of the solar energy stored in the tank [13]. The system is designed for a terraced house in London with 15 m2 roof area available for the installation. The sizing of the system (tank size and array area) was taken from Ref. [1] and the main parameters are reported in Table 1.

Collector description: The modelled collector is a sheet-and-tube PVT/water module for the generation of electricity and domestic hot-water in the UK. The Powertherm collector from Solimpeks® has been chosen as the reference collector for this study (see Table 2 for the collector specification) because of its availability on the UK market. The Powertherm is a single-glazed PVT sheet-and-tube collector with a low-iron glass cover and c-Si solar cells. The copper-sheet thermal absorber has an aperture area of 1.42 m2

and is composed of 14 parallel

pipes. The nominal operating flow rate is 0.02 kg/s

m2, which is the recommended flow rate for standard solar thermal collectors [13,14]. Other than the parameters reported in Table 2, information on the optical and thermal properties of the materials from which the layers of the PVT collector are manufactured (shown in Figure 2) are required in order to fully characterize the collector. These values are listed in Table 3.

A cross section on the x-z plane of the modelled PVT collector is presented in Figure 2. The collector comprises: one or more glass covering layer(s), a PV module, a thermal absorber (aluminium or copper plate) in thermal contact with copper riser tubes, and a layer of thermal insulation. Amongst the various designs of liquid/water PVT systems, the single-cover sheet-and-tube design appears to be a particularly promising design for domestic applications [17]. The thermal efficiency of a flat-plate water PVT module based on a sheet-and-tube collector design is typically reported as being between 50% and 60% [6,20] at zero reduced temperature, while the annual electrical/photovoltaic efficiency is reported as being 7-15% [20-25].

The thermal and electrical efficiencies of a PVT collector are influenced mainly by the fluid flow-rate, the number of glass covering layers, the type of solar cells used, and the properties of the thermal absorber (material and geometry, e.g.: pipe diameter D, fin-to-pipe diameter ratio W/D) that determine the temperature distribution on the absorber surface. Other than the sheet-and-tube design, a number of alternative designs have been investigated. Zondag et al. [17] analysed seven design concepts for liquid PVT collectors, considering several possible channel designs and also a free-flow design with unrestrained/unconfined fluid flowing above the absorber. All of the channel concepts investigated were found to have a slightly higher electrical efficiency than the sheet-and-tube designs due to a more uniform temperature distribution on the solar cell, while the free-flow panel was found to have a reduced efficiency due to the formation of condensate on top of the glass layer, causing additional reflection losses. On the other hand, simplicity of manufacture and cost are equally important considerations affecting the design selection.

In low temperature applications uncovered designs allow for a higher electrical efficiency (due to reduced optical losses) while single-glazed or double-glazed designs allow for higher thermal efficiencies and higher fluid temperatures (due to reduced convection losses) at the cost of lower electrical efficiencies (due to increased optical losses and reduced PV conversion at the higher temperatures [26]). The presence of a single glass cover reduces the optical efficiency by around 5% as a consequence of reflection and transmission losses at the cover [18]. Thermal losses can also be reduced by the presence of an evacuated layer or a layer filled with a gas (e.g. Argon as discussed in Refs. [27,28]) together with spectrally selective glazing coatings to reduce the infrared radiation losses.

The PV module is composed of a top transparent surface (iron glass), the solar cell (c-Si), an encapsulant (ethyl vinyl acetate (EVA)), and a rear layer (Tedlar). The top glass in a PV module guarantees the required rigidity to the laminate [18]. In a PVT collector the required rigidity is already given by the thermal absorber, thus the top glass is not required, whereas some additional protection covers without mechanical rigidity but with optimal optical properties might be used, as discussed in Ref. [29].

The heat collected by the PV module is transferred to the thermal absorber by conduction, thus a good thermal contact between the PV layer and the absorber is essential. An effective solution is to laminate the whole package of top cover, PV cells and absorber together in one step. In this case an electrically insulating foil can be interposed between the PV cell and the absorber in the lamination process, or an electrically insulating coating can be applied to the absorber top surface [30]. More often a thin layer of thermally conducting and electrically insulating adhesive material is used. Examples of adhesive materials found in the literature are:

1. Silicon adhesive (0.5 mm tick) for application in sheet-and-tube PVT with polymer absorber is used in Ref. [31].

2. Corrugated copper foil is used in Ref. [32] in a PVT with a plastic thermal absorber.

3. Aluminium-oxide-filled two-component epoxy glue was used in Ref. [33] in the construction of a sheet-and-tube PVT collector.

4. Silver-filled glue was used in the work of Ref. [34].

PV radiative losses. The provision of thermal energy for domestic applications can be enhanced if the design and operation of the PVT collector is optimized to maximize heat collection. The PV layer also acts as the thermal absorber, and thus the fraction of solar irradiance converted into thermal energy is related to the absorption factor of the solar cells. However, commercial PV modules are designed to minimize absorption of excess heat in order to maintain a low operating temperature. In fact, mono-crystalline c-Si cells, the type considered in this study and the most commonly used for commercial applications in flat-plate PVT modules, can only absorb and convert to electricity solar irradiance at wavelengths below 1.1 ^m [35].

The thermal efficiency of a PVT collector is limited by the optical properties of the solar cell, as the absorber does not have the same emissivity as a selective absorber typically used in a solar-thermal collector. The thermal efficiency of the PVT collector is expected to be lower than that of a conventional thermal collector due to: (i) the lower absorption factor of the absorber; (ii) the direct conversion of part of the incident solar irradiance into electricity, which reduces the proportion that is available in the form of heat; and (iii) the higher radiative heat losses from the absorber to the glass cover due to a higher emissivity of the solar cell compared to the emissivity of a conventional thermal absorber. The radiative heat losses can be suppressed by using a selective coating with a low emissivity in the infrared spectrum. The radiative heat losses can be suppressed by using a spectrally selective low-emissivity coating. Such a coating must be reflective at wavelengths at which thermal emission occurs (3 - 20 ^m), but transmissive at solar wavelengths (300 - 2500 nm) to allow solar radiation to be efficiently absorbed by the collector. This characteristic behaviour is exhibited by In2O3 : Sn (ITO) films, for example, which are typically used in energy-efficient windows for this purpose [36,37]. An ideal coating would cause the solar absorber to have the absorptivity/emissivity shown in Figure 3, i.e. ex = ax = 1 over the range of solar wavelengths and sx = ax = 0 over the range of emission wavelengths.

A spectrally selective absorber for solar-thermal applications is characterized by a high absorptivity over the visible spectrum and a low emissivity in the infrared and near-infrared spectrum. Such characteristics would

maximize the absorption of the incident irradiance while minimizing the radiative thermal losses. The PV module in a PVT panel has a high absorptivity in the visible and infrared spectra, and a high emissivity in the infrared. Thus high radiative losses from the module enable a lower operating temperature of the solar cell and

higher conversion efficiency. The absorptivity/emissivity reported in Figure 3 has been calculated from experimental measurements of reflection on a commercial solar cell. The emissivity of the solar cell (thick red solid line) in the near infrared spectrum (A > 3 |im) is at least 0.7, if not higher at some wavelengths, while it is

zero for an ideal thermal absorber. The absorption of photons with energy less than the band-gap energy is mainly free carrier absorption, and this absorption coefficient is proportional to the carrier concentration (to the doping of the intrinsic silicon). While the absorption coefficient of the intrinsic silicon would be near zero for energies less than the band gap, this value increases after doping due to the presence of the free carrier [35,38]. The free carrier absorption does not lead to the generation of an electron-hole pair and it constitutes a parasitic absorption process in solar cells that is beneficial for PVT applications [39].

3. Modelling Methodology

The numerical model developed here allows for the evaluation of the thermal and electrical energy generated by the selected PVT system to cover the demands for domestic hot water and electricity of a three-bedroom house in London, UK, and the instantaneous thermal and electrical efficiency of the system. The model uses real weather-data (solar irradiance, ambient temperature and wind speed obtained from a weather station located in London with a 1-min resolution) and a high resolution profile of domestic hot-water demand generated with the software DHWcalc [40]. The use of these high resolution inputs is found to be essential for a correct estimation of the system performance and for the analysis of the response of the system to the control algorithm.

The PVT collector is characterized by its (conventional) thermal-efficiency curve evaluated under steady-state operation and by its time-constant which indicates the response of the collector to a time-varying input. The model of the collector has been validated against experimental data obtained by other authors and against commercially available PVT and thermal collectors.

3.1 Collector Model

Modelling overview: The 3-D thermal model developed here is based on the following assumptions:

1. The thermal properties of all solid materials are constant; variations in the properties of air (as a function of temperature) were calculated by using a polynomial fit according to Ref. [41] while variations in the properties of water with temperature were calculated by using the REFPROP library [42,43] and it was found that these two variations introduced only minor changes to the results of interest here (e.g. <1% in both the outlet fluid temperature and thermal output from the collector).

2. The optical properties of all relevant materials are constant.

3. The edges of the collector are well insulated, thus the edge thermal losses are negligible.

4. The temperature profile between two adjacent pipes is symmetrical, and the temperature has a maximum on the symmetry axis.

5. Water flow-rate is evenly distributed between the pipes and the thermal losses and mixing effects at the inlet and outlet manifolds are negligible [5].

6. The flow is fully developed in the tubes.

7. The effect of the friction in the pipes is neglected when calculating the temperature in the riser pipes.

8. The headers cover a small area of the collector and its effect on the temperature distribution on the absorber can be neglected.

9. The incident irradiance G, the wind speed vw and the ambient temperature T a are uniform boundary conditions at the surface of the PVT collector.

10. It is assumed that there is no dust or partial shading on the collector.

11. The reflection, absorption and transmission factors are calculated only for the incident solar irradiance [13,29,44].

12. The electrical resistances are neglected when evaluating the electrical energy output and the electrical efficiency.

When the energy balance at the collector is solved in steady-state conditions for different ambient temperatures and incident solar irradiance values, and at a given inlet fluid temperature , the result is the thermal efficiency curve of the collector plotted against the reduced temperature Tr = (Tm — Ta)/ G. In order to estimate the DHW and electricity generated by the system, the model of the PVT collector is integrated within the wider dynamic model of the whole system (Figure 1). The dynamic energy balance takes into account the masses and specific heat-capacities of each layer forming the PV module and of the mass of water stored in the tank.

3.2 PVT unit, thermal model equations

The 3-D dynamic thermal model solves an energy balance equation at each layer of the PVT module. The equations are written for the element (ij). The same equations can be used for the double-glazed and unglazed PVT collectors, and also for the conventional thermal collector. An energy-balance equation is solved numerically along the water-flow direction, y, and in the transverse direction, x, where each layer is discretized respectively into Nx and Ny number of nodes as shown in Figure 4. The energy balance equation is solved at each finite volume having size Axhy S and the solution is a 2-D temperature distribution on the x-y plane over each layer of the PVT module and a 1-D temperature distribution on the x-z plane.

Glass cover energy balance: The energy balance at each node (ij) of the glass cover in Eq. (1) takes into account thermal radiation and convection losses to the ambient, thermal radiation to the PV module, and absorption of the glass cover. d TJi.j)

MgCg-—- = <2g_CD - <2g,a-RD(lJ) - <2g,a-cv0.y) + <3g,PV-RD Oj) + <2g,PV-CvO./) (1)

+ C?g-AB(iJ) ■

The net conductive heat-flux Q£¡__cD ( i,j) at the node (ij) for the layer 'ii' is the sum of the conductive flux in the x direction and they direction, which are expressed as:

k;;8;; Ay

Qii _ c d ,x (ij) = —t[Tn (i + 1 ,j) + Tii (i — 1 ,j) — 2 Tii (i,j) ] ; (2)

knSnAx

Qii_cD,y (i.j) = —t[Tii (i,j + 1) + Tii(i,j — 1) — 2Tii(i,j)] . (3)

The radiative heat losses to the ambient in Eq. (4) are calculated using the sky temperature .

For clear sky conditions the sky temperature is related to the ambient temperature according to Eq. (5) [45]. Other models relate the sky temperature to the dry bulb and dew point temperatures ( and ) and to the time of the day t (in hours) counted from midnight in Eq. (6) [46,47]. For a cloudy sky, other equations are available, which require an estimation of the cloud coverage based on the diffuse irradiance, while for an overcast day the

sky temperature is calculated as in Eq. (7) [48,49]. The value of the collector thermal and electrical output is affected by less than 1% by the correlation chosen for calculating the sky temperature, thus Eq. (5) is chosen in this modelling work as it has been widely used in the literature (such as in Refs. [49-54]) and it requires no knowledge of the dew point temperatures or of the cloud coverage estimation.

<2g,a - RD ( i-y) = A *Ayg a ( Tg4 ( ij) + rs4ky) ; (4)

7sky = 0.0552 Tt5

T' = T

1 sky 1 a

0.711 + 0.0056 7dp + 0.000073 Td2p + 0.013 cos

Tsky Ta

The convective heat losses to the ambient air in Eq. (8) are calculated using the convective heat

transfer coefficient ftt0 P, as expressed in Eq. (9), which takes into account the forced and free convection on top of the panel [55,56]. The forced convection coefficient, ftw, in Eq. (10) varies linearly with wind speed (a review of empirical correlations for is given in Refs. [3,5,7,50-53,55,57-61]). A number of different correlations are available in the literature for the calculation of . These correlations are obtained at various testing conditions and for different geometries and the uncertainty associated to the measured value of the heat transfer coefficient ranges between 6% and 20% [62,63]. This large uncertainty is due to the difficulties of making the measurements involving rapid variations of the wind speed and direction and of the incident radiation. The free convection coefficient, ftfr e e, in Eqs. (11) is a function of Ra (Eq. (13)) calculated on the plate top-surface for the characteristic length and at the mid-temperature between the mean glass temperature and the

ambient A T = 7g - Ta [56,64]:

<2g,a - c v ( ij) = AxAy ftto P (Tg ( i,7') + Ta) ; (8)

^to P = ^ ^w + frfr e e ;

ftw = 2 Vw + 3 . 8 .

The correlation used for external free convection in inclined plates is:

(9) (10)

fyfree

0.68 +■

0.67 Ral

\ Pr )

Ra > 10y

hfree = —NU°

Ra < 10y

(12) (13)

with: R a = (# c o s ^ - y) /?A TL3p 2c) / /c/i .

The radiative and convective heat fluxes between the glass and the solar cells, and

<3g,pv- c v (i,y) , according to Ref. [6], are:

i'g.PV-

rdGJ) = AxAy [ r^—) a(TP4v(i,7) + Tg4) ;

Vg PV /

<2g,pv- c v a;) = AxAy — (Tpv (¿J) + Tg (i) ) . (15)

The thermal resistance Rgap in Eq. (16) accounts for the thin top layers on the top of the PV module (top glass and Tedlar) and for convection in the air gap.

<5eva Sg <5py 8* 1

EVA kg 2/CpV ¿.ng ngap

The convective heat transfer coefficient hgap in enclosed space is expressed in Ref. [65] as:

g P kpVA kCT 2 fcpv 2 ka h.

7 _ "-air

gap — A

/ 1708 \* / 1708(sinl.8y)16\ / /fia cosyy + ' V Racosy) I Ra cosy )+ \ V 5830 /

In Eq. (17):

1. The brackets signified by the superscript '*' go to zero when they are negative.

2. y is the tilt angle of the collector to the horizontal.

3. The thermal conductivity of the air is evaluated at the temperature , where TH is the temperature of the hot surface and A T the temperature difference between the two surfaces.

The solar irradiance absorbed by the glass cover Qg -ab ( ¿J) is: <2g -a b ( ¿j)= T«g CAxAy . (18)

The fraction of the incident irradiance absorbed by the glass cover and by the solar cell and the reflection losses R g are included in Eqs. (19-21) below [45,66]:

rg = rg+t^' (19)

__(l-rpv)Te

ra pv = 7-;s[; (20)

r«g = T-rg-Tg1 - . (21)

PV module energy balance. The energy balance at each node (ij) of the PV module is:

drPV(i,j)

MpyCpy —

= Qpv-cu(iJ) - Qg,pv-RT)(iJ) + Qg,pv-cv(iJ) + Qpv-ab(iJ) - Qpv-a(iJ)

The conduction at node (ij) is calculated as in Eqs. (2) and (3), while <2g,pv- rd and <2g,pv- c v are given in Eqs. (14) and (15), and is the heat transferred by conduction from the solar cell to the thermal absorber

through the layers of EVA, Tedlar and adhesive:

<3pv-a ( ¿j) = AxAy —— ( Tpv(i,y) - ta ( i,y)) ; (23)

rcd=^a + ^ + ^ . (24)

KEVA KTED Kgl

The energy absorbed by the solar cell depends on the absorption coefficient of the cell over the solar spectrum, and on the transmission and reflection at the glass cover. The fraction of the absorbed irradiance that is then converted into electricity is calculated as a linear function of the cell's temperature as in Ref. [67]:

MacA J( — Oa-CD0<y) C?PV-aO>/) QpO-ij*) Qloss (i) ■ (27)

E (i,j) = AxAyGr]T (i, j) . (25)

1 In Eq. (25) the conversion efficiency % of the incident sunlight into electricity is assumed to decrease

2 linearly with increasing cell operating-temperature TPV. This is a typical assumption that is valid in the range of

3 temperatures of operation of PV modules, and the most common expression is [3,5,7,35,36,49,53,59,67-78]:

V7 (UD = Vref [1 - fov (TPV (i,D - Trei)] ■ (26)

4 The conversion efficiency decreases linearly with the operating temperature as a consequence of the linear

5 decrease of the open circuit voltage and of the fill factor with the temperature, while the short-circuit current

6 slightly increases. The temperature coefficient (JPV in Eq. (26) is mainly a material property, having value of

7 about 0.0045 K-1 for crystalline silicon modules [5,6]. T]ref is generally around 0.17 for c-Si cells [5,67].

9 Thermal absorber energy balance: The energy balance at each node ij of the thermal absorber is:

dMy) d t

10 Here, the conduction heat flux QA_cD at the node (ij") is calculated as in Eqs. (2) and (3), QPV-A is given in

11 Eq. (23), in Eq. (28) is the heat transferred to the pipe and accounts for the heat losses to the ambient

12 from the rear surface through the insulation. It is assumed that: (i) the pipe wall is at uniform temperature at each

13 node; and (iii) the fluid and the pipe temperatures vary only along the direction of the fluid flow. Qp is given by:

Qp (i,j) = Ax Aykb/Sb ( T a(i,j) - Tp (j)) , (28)

14 where kb and 5b are the bond thermal conductivity and the bond thickness.

15 The heat transfer due to heat losses at the rear of the panel Q\0ss is given by:

Qloss (i.j) = AxAy 1 /Ryoss(Ta(i.j) - Ta) , (29)

16 The thermal resistance Rloss in Eq. (30) takes into account the conduction trough the insulation and the free

17 convection at the rear of the panel calculated by:

Rlo ss=^ + 7— ■ (30)

19 Fluid energy balance. The bulk-fluid temperature T{ is calculated by applying the energy balance equation: MfCf^1 = mcf(Tf_in(j) - Tf_o(j)) + nDAyhf (tp(i,j) - Tf(j)) , (31)

20 where the heat transfer coefficient depends on the flow regime (laminar, or turbulent) [64], according to Eqs.

21 (31) and (32) for natural and for forced circulation. When the pump is not active and the fluid is not circulating

22 in the collector the heat transfer occurs by conduction between the pipe wall and the centre of the pipe and the

23 heat transfer coefficient is given in Eq. (33).

hf = 4 ■ 3 6-1 for R e< 2 3 00 ; (32)

hf = ^-0■ 23 Re08Pr 0A for > 23 00 ; (33)

hf = —- for mf=0 . (34)

24 Pipe energy balance. The pipe temperature is calculated from:

pCp ^¡^ = ^P1 ( rA ( ¿,7) - Tp0') ) - TiDAy hf ( 7p ( 1,7 ) - 7>0') ) - ^ ( 7p 00 - ¡a) . (35)

2 Boundary conditions. The boundary conditions required to solve the energy balance are:

7f- in ( l) = ¡in ; (36)

= 0 ; (37)

x=0,W/2

5y =° ' (38)

* x=0 ,L

4 Thermal and electrical instantaneous efficiency. The instantaneous thermal efficiency, the electrical efficiency

5 and the electrical power output are:

% h ( 0 =-^-; (39)

i=Nx j=Ny

^e l (0 = Wp ^ £ ( ¿,7) ; (40)

i=l 7 = 1

"elW-ts • (4I)

7 3.3 Storage tank energy balance and control

8 The storage tank has been modelled as a fully mixed tank. The tank temperature and the inlet fluid-temperature

9 of the collector are outputs of the energy-balance equation for the storage tank. The energy balance in Eq. (42)

10 accounts for the demand of hot water, the heat losses at the storage tank and the efficiency of the heat exchanger.

11 The temperature at the outlet of the heat exchanger immersed in the storage tank is calculated using Eq. (43) and

12 the energy for supplying domestic hot water is given in Eq. (44), while Eq. (45) is the energy loss to the

13 environment, at room temperature 7\. The demand loop takes water from the top of the tank and replaces it with

14 water at the utility mains temperature of 7m = 12 °C [I], thus C? i is zero when 7t < 7m.

Mt ctdi = Cc ° ii-c-ci ° * * ; (42)

Ci = mi q (7m - 7t) ; (44)

. (45)

15 A discussion of the variations in the results when using fully mixed or stratified designs is included Section 4.4.

17 3.4 Input ambient conditions

18 The ambient conditions appear as inputs to the simulations performed in the present work, which uses

19 measurements of time-varying solar irradiance, ambient temperature and wind-speed. Full information on the

20 fluctuations in the ambient conditions (e.g. of solar irradiance during intermittent cloud cover; see Figure 5)

21 which appear as inputs to the model can only be captured if a low sampling interval A ts is used. In the present

1 case study the smallest sampling interval (highest temporal data resolution) possible was 1-min. The time-

2 resolved data were obtained by the authors over a one-year monitoring period (July 2014 to July 2015) from a

3 weather station located in London, UK. The monitored parameters were measured as follows:

4 1. Wind speed: measured with a solid-state magnetic sensor having an accuracy of 1 m/s and a range of

5 0.5 m/s to 89 m/s.

6 2. Ambient temperature: measured with a PN junction silicon diode, in a range of -40 °C to 65 °C and

7 with an accuracy of 0.5 °C above 20 °C or 1 °C above 20 °C.

8 3. Solar irradiance: measured with a precision of 5% at full scale up to 1800 W/m2. The sensor is mounted

9 on a roof-installed PV system oriented towards the south on the plane of the PV modules.

10 The ambient data-sampling interval of 1-min is also shorter than half of the time constant t c of the single-

11 glazed collector as defined in Eq. (46), which is the shortest of the investigated collectors. In this case, if the

12 fluctuations in the inlet conditions to the model are faster than the system dynamics as characterised by :

A ts<Tr , (46)

13 the response of (and system outputs from) (quasi-)steady state simulations will deviate significantly from results

14 of equivalent fully dynamic simulations of the same system with the same inputs.

15 Time-averaged input data were also used for evaluating the long-term performance of the PVT system (e.g.

16 as is done in Section 4.1; Figure 10). This was done in order to quantify the discrepancy of the outputs from the

17 system from the fully time-resolved result. Specifically, the results of an annual simulation obtained using 1018 year averaged weather-data at a 30-min resolution have been compared with the results of an annual simulation

19 with 1-min resolution datasets and the results are discussed in Section 4.1. The intention here is to quantify the

20 deviations of data resolution and of using a dynamic versus a quasi-steady model. The 10-year averaged

21 weather-data are the result of a 10-year measurement period and are available online at the Photovoltaic

22 Geographical Information System (PVGIS) [79]. The PVGIS data are global irradiance incident on a fixed plane

23 and ambient temperature, provided as average daily profiles for each month of the year that can be used for the

24 estimation of solar-system performance as in the work presented in Ref. [1].

26 3.5 Hot-water demand data

27 A time-varying profile of hot-water consumption is required as an input when predicting the energy demand for

28 hot water. The performance of the solar water-heater is sensitive to the load timing and to the load day-to-day

29 variability, as the temperature of the storage tank varies when a water draw-off event occurs. The key parameters

30 that define the profile of hot-water demand are the average daily volume, the yearly total demand, the draw-off

31 flow rates and the distribution of the drawn hot water during the day. The profile of hot water demand is driven

32 by the number of occupants (which has a linear effect on the total hot water use [80]), by the appliances, and by

33 the ambient conditions. The latter determine seasonal variations of the energy consumption due to variations in

34 the mains temperature. It has been observed that when the mains temperature is higher, in summer, the mixed

35 temperature required for end-uses such as showers, baths and sinks is obtained with a smaller flow rate of hot

36 water. In the UK this translates to a seasonal variability of -16% / +8% of the demand of the energy required for

37 hot water, having a minimum in July and a maximum in December [81].

38 In the present study, a statistically realistic distribution of hot-water consumption was generated with the

39 software DHWcalc [40]. This software is based on a code used for the IEA-SHC Task 26 on solar combi-

1 systems and can be used to evaluate and compare the performance of solar combi-systems from different

2 European countries using realistic time-varying input data [82,83]. DHWcalc generates random event schedules

3 for hot-water consumption based on:

4 I. Daily average consumption (for weekdays and week-end days).

5 2. Seasonal variation of the daily DHW consumption in percentage, described as a sine function of the hot

6 water consumption during the year [40].

7 3. Flow rate, drawn duration and portion of the total daily consumption of 4 different demand types (short

8 load, medium load, bath and shower).

9 4. Household type (single house or multifamily).

10 DHWcalc generates profiles of DHW demand at 60, 6 or I -min resolution, and the event flow-rate varies

11 randomly around an average value based on a standard deviation entered by the user. The parameters used in this

12 study are specific for the UK. A monitoring study on 124 dwellings in the UK found a mean household hot-

13 water consumption of 122 L/day with a 95% confidence interval of 18 L/day [81], and a daily average profile as

14 given in Figure 6 based on the data reported in Ref. [81]. The four load types are characterized as follows:

15 I. Short load (toilet and kitchen sinks): the mean flow rate is 3 L/min [84] and the duration of a single

16 drawn- off is I min, accounting for 30% of the daily load [81].

17 2. Medium load (dishwasher and washing machine): the mean flow rate is 6 L/min and the duration is I0

18 min [80], accounting for I0% of the daily load [8I].

19 3. Bath: the mean flow rate is 8 L/min [84] and the duration is I0 min, accounting for 40% of the daily

20 load [8I].

21 4. Shower: the mean flow rate is 8 L/min [43] and the duration is 9 min, accounting for 20% of the daily

22 load [8I].

23 An example of a three-day profile of DHW for a single family house obtained with DHWcalc using the listed

24 options and at a I -min resolution is shown in Figure 7.

26 After generating the event schedule, the results were compared with the input data to check for consistency

27 and it was concluded that the average hourly flow rate, the daily and the annual water use match well with the

28 user defined input data. The hot-water profile has been generated with a day-to-day standard deviation in the

29 daily consumption of 53.3% over the year. This value can be considered acceptable if compared with the value

30 of 48% reported in Ref. [85] as result of an investigation into daily DHW consumption in 74 dwellings. The

31 seasonal variation of the energy demand of hot water is taken into account as a variation of the water flow rate

32 while the mains temperature is kept constant during the simulation.

34 3.6 Electricity demand

35 The electricity generated by the PVT system is compared with the yearly and monthly demand for electricity.

36 The electricity demand and the electricity generation are independent of each other as a cost analysis is not an

37 objective of this study, thus the instantaneous profiles of electricity demand are not considered here. The yearly

38 and monthly data of electricity demand are taken from the previous study of Ref. [I]. In this paper the model

39 developed by the Centre for Renewable Energy Systems Technology (CREST) was used for the demand profile

1 calculation [86]. The model generated outputs at 1-min resolution for 365 days depending on the user input

2 parameters (occupancy patterns, appliances, annual mean energy demand).

4 3.7 System performance

5 The performance of a PVT system can be assessed in terms of its thermal output (provision of domestic hot-

6 water) and electrical energy output. The instantaneous thermal energy provided by the system to the end-user is

7 given by Eq. (44). Here ^ is zero if there is no consumption of hot water or if the tank temperature is lower than

8 the mains temperature. The second case is not encountered in this specific case because the tank is located

9 indoors and exchanges heat with an environment at a constant temperature of 20 °C. Further, the fluid from the

10 collector is allowed to circulate to the storage tank only if its temperature is higher than the tank temperature.

11 The fraction of the thermal energy demand covered by the PVT system f q is given in Eq. (48) and is

12 calculated as the contribution of the storage tank to the heating/preheating of the hot water supply (as expressed

13 in Eq. (47)) over the total energy demand of hot water at the demand temperature Td of 60 °C:

QTH = 6 O'YjQi (0 i (47)

f = £ IzlQjt) (48)

Ht=0 mwcw(^d - ^m)

14 The total electricity generated over the year is the sum of the generation of electricity at each time interval of

15 60 s (1 min), and is given as:

Pel (T = 6 O-^Pz l (0 . (49)

16 The electricity generated is compared with the energy required by the user and the fraction of the electricity

17 demand covered by the PVT system over the year is:

PEL(T)

fz = . (50)

18 It is interesting to compare the profile of the electricity generated by the PVT system with the profile of the

19 demand for electricity, but an economic analysis is beyond the scope of this study and therefore only the net

20 values of electricity demand and generation are compared.

22 4. Results and Discussion

23 4.1 Model validation

24 The numerical model of the PVT collector was validated against the data published by the Eurofins laboratory in

25 a technical report available online (Ref. [15]). This report presents the results of the steady-state outdoor testing

26 of the Powertherm single glazed PVT collector. The tests were conducted at the nominal flow rate of

27 0.02 kg/s m2 and in steady-state conditions. During the tests the incident irradiance was greater than 850 W/m2,

28 as indicated by the European standards for solar collector testing [6,13,14,87] and the inlet fluid temperature was

29 varied between 15 °C and 54 °C. The experimental results of these steady-state tests are compared directly with

30 the numerical predictions of the present model and the values are shown in Figure 8.

1 The model fits the experimental data within an average discrepancy of 8%. The calculated thermal-efficiency

2 curve based on the aperture area for this PVT single-glazed collector is given in Eq. (5I). This expression can be

3 compared with the efficiency curve obtained by fitting the experimental data in in Eq. (52).

%h = ° .483 -4. 52 8(7m-7a)-°. ° 1 4 G (77m—' (5I)

77Th = ° .486 - 4. ° 2 8(7m-7a)- ° . ° 6 7 G (7m-' (52)

5 The response of the system to a time-varying input was validated against the experimental results of a

6 dynamic test of a PVT collector published by Amrizal et al. [87]. For this purpose, the parameters of the

7 numerical models were changed in order to adapt the model to a configuration of PVT collectors that is different

8 from the Powertherm collector considered so far. Amrizal et al. [87] tested an in-house PVT collector consisting

9 of 2 lines of 26 c-Si cells connected in series, having a glass cover of 4 mm thickness. The dynamic behaviour of

10 the PVT collector can be defined in terms of its time constant, which can be measured by studying the response

11 of the collector to a step variation in solar irradiance. In practice this is achieved by covering the collector with a

12 reflective cover until a steady state at near-zero irradiance is reached, and then uncovering the collector and

13 measuring the response time for the collector to reach a new steady state operating condition. As defined in the

14 EN I2975 [I4], the time constant in Eq. (53) represents the elapsed time the collector needs to reach a A 7 of

15 63.2% (I/e) of its final value from an initial condition. The measurements of the time constant in Ref. [87] were

16 taken according to the procedure described in Refs. [4,I4], with a perpendicular incident irradiance at around

17 solar noon and a constant flow rate of 0.022 kg/s m2. The experimental value of the time constant obtained by

18 Amrizal et al. was 87 ± 5 s, which is matched closely by our numerical result of 88 s.

19 The time constant of the Powertherm solar collector was calculated with the same numerical code and using

20 the same approach as above by changing the geometrical parameters of the collector, resulting in a value of

21 I38 s. The response of the PVT collector to a step change in incident solar irradiance (from 30 W/m2 to

22 900 W/m2) is shown in Figure 9. The outlet fluid temperature of the collector at the steady-state incident

23 irradiance condition of 900 W/m2 is 24.07 °C. The initial outlet fluid temperature of the covered collector

24 (incident irradiance of 30 W/m2) is I8.54 °C, for a constant inlet temperature of I8.50 °C.

26 The importance of using real ambient data at high resolution instead of time-averaged data can be assessed by

27 considering the discrepancy in the results obtained when the same simulation is run with the two input datasets.

28 For an array of single-glazed PVT collectors, the yearly electricity generation is overestimated when using time-

29 averaged input data by 23.4% (the yearly electricity generation calculated with I-min resolution data is I572

30 kWh, and I940 kWh when using time-average data). With regards to the thermal-energy generated, the major

31 discrepancy is obtained in the summer period when the fraction of thermal energy demand covered by the system

32 is overestimated by over 25% (see Figure I0).

34 When solving the energy balance of the system using input data at I -min resolution, a decision has to be

35 made whether a dynamic or quasi-steady model is required. This is related to the value of the collector time-

1 constant. In the present study, a model having a simple control strategy was tested by solving both the quasi-

2 steady and the dynamic problem for the month of July. The results reported in Table 4 show that the quasi-steady

3 solution overestimates the thermal energy-demand coverage fraction by up to 12.3%, while the electricity

4 production is overestimated by 7.0%. As expected, the larger discrepancy is observed for the double-glazed

5 collector, which has a larger thermal mass. This discrepancy can be explained by considering the activation and

6 de-activation of the pump, which is determined by the differential controller set with a specific value of

7 temperature-difference. When the quasi-steady solution is applied, the fluid temperature follows the profile of

8 the solar irradiance and as soon as there is irradiance on the solar collector the temperature reaches the required

9 value to activate the pump. The results show that the pump is running by 57% additional hours in the case of the

10 single-glazed collector for the quasi-steady solution.

12 4.2 Temperature distribution on the PV module

13 The thermal model allows the prediction of the temperature distribution on the solar cell, which is then used as

14 the input to the electrical model. The top surface of the PV module is not isothermal and has a maximum

15 between two adjacent pipes that increases in the flow direction as the coolant collects thermal energy from the

16 absorber, as shown in Figure 11. Knowledge of the temperature distribution on the PV module is of fundamental

17 importance for the correct estimation of the electrical output. This numerical model constitutes a tool that can be

18 used for the investigation of different geometries of the thermal absorber and the solar cells in order to assess the

19 influence of the various design parameters on the temperature distribution on the PV module.

20 4.3 Comparison of unglazed, single-glazed and double-glazed collectors

21 The thermal/electrical performance and the dynamic behaviour of the three configurations of the PVT solar

22 collector (unglazed, single-glazed and double-glazed) are presented in this section. A comparison of the thermal

23 efficiencies of the three configurations is shown in Figure 12 where the efficiency is plotted against the reduced

24 temperature. The thermal efficiency is obtained by using the same geometrical characteristics of the Powertherm

25 collector discussed thus far (pipe diameter over fin width ratio D/ W, pipe diameter, flow rate, pipe length).

26 As expected, the double-glazed collector shows a higher thermal efficiency than the other two configurations

27 as the convective thermal losses to the environment are reduced by the presence of the additional glazing. The

28 overall heat transfer coefficient to the environment calculated on the absorber area and at the absorber average

29 temperature is 6.2 W/m2 K for the double-glazed collector, 9.17 W/m2 K for the single-glazed collector, and

30 37.83 W/m2 K for the unglazed collector. This difference is evidenced by the slope of the thermal-efficiency

31 curve. The zero-loss coefficient is reduced with additional glazing due to the reflection losses, as expected.

32 The fraction of incident irradiance that is reflected by the top surface amounts to 21.3% for double glazing,

33 16.2% for single glazing, and 10% for the unglazed collector. As a consequence, the fraction of the incident

34 irradiance that is transmitted from the top glass surface to the PV cell to be absorbed reduces with the number of

35 glazing layers. The fraction of incident irradiance that can be absorbed by the solar cell operating at the reference

36 temperature (calculated from Eq. (20)) is 90% if the cell is exposed directly to the environment, 81.7% if there is

37 a single glass-cover and 74.4% if a second cover is added. This effect is larger than the dependence of the

38 electrical efficiency on the operating temperature (slope of the electrical-efficiency curve) and is reflected in the

39 electrical-efficiency curve which is always higher for an unglazed collector. On the other hand, the electrical

40 efficiency is higher for the unglazed collector when the optical losses due to reflection are reduced.

1 The thermal performance of the unglazed collector can be improved if a selective coating is applied to the

2 solar cell. This reduces the emissivity of the solar cell in the infrared spectrum, thus also reducing the radiative

3 losses as discussed in Section 1. The thermal and electrical efficiencies of the unglazed collector are shown in

4 Figure 13 for an emissivity (also equal to the absorptivity) of the solar cell in the infrared spectrum ranging

5 from 0.9—a typical value for a solar cell—to zero, which is the optimum value of a selective absorber. The

6 thermal efficiency is improved by 10% with ideally no modification of electrical performance.

7 4.4 PVT system operation

8 This section reports the results of the dynamic model showing the predicted daily operation of a PVT system

9 under fluctuating weather conditions and clear sky conditions. An analysis of operation of the PVT collector

10 over day and the operation of the solar system for three typical weather conditions is shown in Figure 14. The

11 circulation of the liquid (water) in the system is determined by the control strategy as described in Section 2.3.

12 The fluid is circulated by the pump when there is an energy gain through the collector, and the circulation is

13 halted otherwise. Moreover, once the pump is activated, the bypass branch is de-activated (=1) and the fluid

14 heats up the tank when the temperature at the collector is sufficiently high. Otherwise the fluid is recirculated to

15 the collector and the bypass is active (=0).

16 The operation of the solar-PVT collector is also influenced by the demand for hot water. When the demand for

17 hot water is high, the temperature in the storage tank drops (as does the temperature of the collector) if the pump is

18 active. On the 1st of September, during a day with a clear sky, the collector fluid circulates in the storage tank for

19 most of the time and the operation is stable. On the 28th of August and 17th of July, which are cloudy and overcast

20 days, the bypass branch is alternately activated and de-activated. Fluid flow to the tank is only activated for a few

21 hours, while (mostly) the fluid is recirculated in the collector in order to increase its temperature/enthalpy. This

22 intermittent behaviour would not be captured if average irradiance data were used. The mean daily temperature of

23 the storage tank operating as fully mixed is also dependent on this pattern and on the ambient conditions. It is

24 generally lower for cloudy days. Furthermore, the temperature of the storage tank is influenced by the profile of

25 domestic hot-water demand. In the morning of the 1st of September, between 6-8 am when the demand of hot water

26 is large, the temperature of the tank and of the collector do not follow the profile of the irradiance.

27 The present work employs a hot-water storage tank with a heat-exchanger (coil) design that promotes mixing,

28 such that the tank is modelled as fully mixed (see Section 3.3). Stratified charging of the hot-water cylinder can

29 also be employed, in which case the stratification of the fluid in the tank will be affected by the design of the coil

30 in the tank, the design of the inlet and outlet ports, the size of the tank, etc. In order to consider the variations in

31 the outputs of interest introduced by the design of the tank (fully mixed or stratified), a 3-node, 1-D stratified

32 tank model with one coil heat exchanger and two ports has been tested together with the fully mixed version of

33 the tank model. The results obtained for 1st September with the two design options are given in Table 5.

35 Given the inherent uncertainty to the design of the hot-water cylinder and the small relative differences in the

36 results, the performance (outputs) of the PVT system with a fully mixed tank discussed in this paper can be

37 considered to extend to an equivalent PVT system featuring a stratified tank. The instantaneous electrical

38 efficiency of the PVT system is shown in Figure 15 along with the temperature of the fluid and of the PV

39 module and the nominal efficiency. The nominal electrical efficiency of a PVT module is the efficiency of the

40 panel operating in steady-state under standard conditions ( = 1000 W/m2 and = 25 °C) and empty of fluid

1 (Ref. [7]). While the nominal electrical efficiency of the PVT module is I2.6% (red dashed line), the

2 instantaneous value is higher than the nominal efficiency during the early morning and in the afternoon due to

3 the low ambient temperature and incident irradiance, while it decreases to I2.2 % when the incident irradiance

4 on the solar collector is around 800 W/m2 due to the increase of the PV cell temperature.

5 The instantaneous generation of electricity over two days of the year is shown in Figure I6. The generated

6 electricity exceeds the demand during the sunny September day, while only a small portion of demand is covered

7 during the cloudy winter day; this significantly affects the economics of the implementation of these systems,

8 since electricity produced during the day is more expensive than the electricity needed during the night.

10 4.5 PVT system monthly and yearly energy yield

11 This section discusses the monthly performance of the PVT system in terms of the fraction of electrical energy

12 demand /E and of the fraction of thermal energy demand /q covered by the system as predicted by the dynamic

13 model presented in this paper. The main results are shown in Figure I7. As expected, the fraction of energy

14 covered by the PVT system is higher during the summer months, for example the monthly generation of

15 electricity exceeds the demand in August if an unglazed collector is installed (as part of the system). A PVT

16 system can cover between 25% and 50% of the total demand of domestic hot water in a UK household

17 depending on the choice of the collector (glazed or unglazed).

18 We can consider now the case of a PVT collector with modified solar-cell optical properties, whose aim is to

19 reduce the radiative losses from the PVT collector. The emissivity of an ideal absorber is considered for the

20 comparison, and e is set to zero. In reality, it is envisaged that a value between 0.9 and the ideal value could be

21 achieved with a selective coating. The results are shown in Figure I8. These show that for all collectors

22 (unglazed, single-glazed and double-glazed) the fraction of thermal energy covered would increase by more than

23 I0%, e.g. for the unglazed collector this increases from 24.3% to 36.2% (i.e. by I2%). Slight differences in the

24 relative improvement arise due to the different fluid temperatures in the different collectors and the operation of

25 the differential controller that regulates the preheating of the storage tank by the collector fluid. In an unglazed

26 collector the system preheats the storage tanks for only few hours each day and the fluid is mainly kept

27 recirculating through the collector so that it can reach the set temperature. On the other hand, the electrical

28 performance is found to deteriorate, as expected, at higher operating temperatures.

29 5. Conclusions

30 This paper describes the development of a detailed 3-D dynamic numerical model of a PVT collector with the

31 aim of estimating the temperature distribution over the surface of the PV module and therefore of estimating the

32 annual thermal and electrical energy outputs generated by the system in a UK domestic installation. The

33 estimation of the temperature distribution on the surface of the PV module is required in order to accurately

34 calculate the electricity generated. The model constitutes a useful tool for the design and optimization of the

35 thermal absorber and for the assessment of different module and system configurations.

36 The model shows that there is a temperature gradient on the PVT collector which results in an efficiency

37 variation due to a non-uniform temperature distribution on the PV cells. The module efficiency drops by only 4%

38 below the nominal value of I2.6%, which is the electrical efficiency of the PVT module at standard conditions and

39 empty of fluid, during the hot hours of the day when the incident irradiance reaches 800 - I000 W/m2. Due to the

40 flow of the cooling liquid (water) the panel operates above its nominal efficiency for the rest of the day.

1 The model uses real weather input-data at high resolution and a high-resolution profile of domestic hot-water

2 demand obtained with the software DHWcalc. One important conclusion concerns the importance of using real

3 input-data at high-resolution for the correct estimation of the yearly and monthly performance of the system, as

4 opposed to averaged data, especially if a novel control strategy that can adjust the system's outputs in response

5 to varying demands is to be designed. In particular, it has been shown that the use of time-averaged climate data

6 results in an overestimation of the thermal production (climate data for the year 2014-2015 are used in the

7 present analysis). This is especially of relevance when doing an economic analysis of the system, which requires

8 a precise knowledge of the instantaneous generation of electricity in relation to the electricity demand during the

9 day. Moreover, when running simulations using high-resolution weather-data, some parameters of the control

10 strategy were found to be critical, namely the cooling flow rate, the operation mode/strategy of the pump, and the

11 temperature of activation/de-activation of the pump and bypass branch.

12 The effect of the emissivity of the solar cell on the thermal output of the PVT panel has also been considered.

13 Solar cells for PVT applications can be specifically designed to increase the thermal performance of the module

14 while maintaining a high electrical efficiency. It has been shown that if the emissivity of the solar cell is reduced,

15 the thermal output of the PVT system can increase by 10% with almost no loss in the electrical output due to the

16 low temperature of operation of the non-concentrated solar-thermal system.

18 Acknowledgement

19 The work described in this paper was partly funded by Climate-KIC <http://www.climate-kic.org/>. All authors

20 gratefully acknowledge this support.

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9 10 11

Auxiliary heater

wt.Tf-t* ~ ^

Figure 1: Schematic diagram of a PVT system for the provision of domestic hot water.

Air gap

Insulation

PV module

Adhesive

Thermal absorber

W/2 <-'-->

Figure 2: Cross section x-z of a single-glazed PVT module showing the pipe diameter D and the distance between two adjacent pipes W.

Black body emission at 400 K Solar specirum

£^ of commercial PV cell (£pv) Ideal e of solar (hernial absorber

1 X turn)

2 Figure 3: Emissivity e PV of a commercial silicon solar cell over the approximate range 0.3 - 20 ^m in the visible

3 to infrared spectrum (thick red solid line) compared with the emissivity of an ideal solar thermal absorber (red

4 dot-dashed line). The emissivity is plotted over the incident solar spectral irradiance / (blue solid line) and the

5 emission of a black body at 400 K (blue dashed line).

6 Figure 4: Sketch of the discretization used for the thermal analysis (left) and network of thermal resistances on

7 the x-z plane between the layers of the PVT module (right).

Figure 5: Solar irradiance G data at 1-min resolution collected in London in 2014. Representing three typical sky conditions: clear-sky (1st September), cloudy day/high intermittence (28th August), overcast day (17th July).

Figure 6: Daily profile of DHW demand for a single family house in the UK [75].\

Figure 7: 3-day demand profile of DHW generated with the software DHWcalc for a single-family house in the UK.

Figure 8(a)-(b): (a) ATf modelled (black squares) and experimental values (red circles) various inlet fluid temperatures Tin; (b) thermal efficiency modelled (black squares) and experimental (red circles). The experimental data are fitted with a 2nd-order polynomial function of the reduced temperature Tr = tm ta, the red line is the efficiency-curve function as published in the test report in Ref. [24].

100 200 300 400 500

Figure 9: Response of the outlet fluid temperature T0 ( t) of the PVT collector (dashed line) to a step variation in the incident solar irradiance (solid line).

0.8 0.6

| Time-averaged input l-min input

Jail Feb Mar Apr May June July Aug Sept Oct Nov Dec

Figure 10: Comparison of the fraction of the covered thermal energy demand evaluated with 1-min resolution input data and with time-averaged input data (over 30-min intervals).

Figure 11: Temperature distribution T over the solar cell between two pipes with G = 1000 W/m , Tf_in = 20 °C and Ta = 20 °C (the geometrical characteristics are from the Powertherm collector). The pipe lies in the y-direction, along the middle of the surface, with the fluid inlet at x = IV/2 and y = 0; here the distance between adjacent pipes is W = 0.1 m.

O 0.005 0.01 0.015 0.02 0.025 0

0.005 0.01 0.015 0.02 0.025

Figure 12: Comparison of the thermal and electrical efficiency for the unglazed collector, single glazed collector and double glazed collector.

0 0.005 0.01 0.015 0.02 0.025 T

0 0.005 0.01 0.015 0.02 0.025 T

Unglazed f-0 Unglazed f=0.9 ■ Single iilazcd i=0.9

Figure 13: Comparison of the thermal and electrical efficiency of the unglazed collector when the solar cells have e = 0 . 9 (dotted line) and e = 0 (dashed line) with the efficiency of the single glazed collector (solid line).

1 September

80 70 60 u 50

h 40 30 20 10

------T I

111 T . k O J M

0 2 4 6 8 10 12 14 16 18 20 22 24 f(h)

28 August

60 in T

/—V y 50 i A A

30 ---fj r* V \

0 2 4 6 8 10 12 14 16 18 20 22 24 f(h)

17 July

70 ______7 t

60 m T

N y 50

K 40 ** i

30 -—A kfy

^0 V--

0 2 4 6 8 10 12 14 16 18 20 22 24 f(h)

......Pump on (l)-o(T(O)

-Flow to tank on (1 VolT (0)

t-T—

0 2 4 6 8 10 12 14 16 18 20 22 24 f(h)

Pump on (l)-orr(O) ■ Flow to tank on (1 )-off (0)

0 2 4 6 8 10 12 14 16 18 20 22 24 f(h)

Pump on (l)-oIT(O) ■ Flow to tank on (1 )-ofl" (0)

0 2 4 6 8 10 12 14 16 18 20 22 24 r(h)

Figure 14: Temperature of the solar collector 7} at the inlet and at the outlet and temperature of the storage tank Tt calculated for three days with different ambient conditions and with the daily profile of hot water demand m;. The figures also show the time of the day for which the circulation pump is on or off, the bypass branch is activated, and the collector fluid is heating the storage tank (flow to tank is on).

0.14 e-

Figure 15: Instantaneous electrical efficiency of the PV module compared with the electrical efficiency at standard conditions rçEL(STC) in relation to the operating temperature of the solar cell 7PV and the incident irradiance G.

1 September

1 January

generated »

Jf ** >. ... i .•.j/.' V VA /

0 2 4 6 8 10 12 14 16 18 20 22 24

60 50 40 30 20 10 0

—V generated

" ...........''el demand jj

k J-< v v '

........'"'J

0 2 4 6 8 10 12 14 16 18 20 22 24

Figure 16: Instantaneous electricity generated PEL compared with the instantaneous demand of electricity during two days of the year.

Figure 17: Fraction of the thermal energy /q and electricity fE demands covered by the PVT system each month.

Figure 18: Fraction of thermal energy generated /q and electricity generated PBL for one year calculated using instantaneous weather data. Here the results are reported for the case of a standard solar cell with e = 0.9 and with solar cells having low emissivity e = 0.

Table 1: Design parameters of the PVT system [1]. Parameter Value

1.9 W/m2 K 150 kg 10

20 °C, 12 °C 0.4

Table 2: Characteristics of the Powertherm PVT collector [15]. Geometrical parameters

¿A Absorber area (m2) 1.427

AC Aperture area (m2) 1.42

AG Gross area (m2) 1.4

D0 Risers external diameter (mm) 8

5g Glass cover thickness (mm) 4

SA Absorber thickness (mm) 0.12

SÍ Insulation thickness and material (mm) 50 (glass-wool), 40 (EPS)

L± Gross length (m) 1.66

l2 Gross width (m) 0.86

Number of pipes 14

PV cell parameters

np Number of cells 72

% Nominal power (W) 180

í7el(STC) Module efficiency (standard conditions) % 12.6

í7ref(STC) Cell efficiency (standard conditions) % 17.8

Thermal characteristics

^th-o Zero loss collector coefficient 0.486

Heat loss coefficient 4.028

a2 Heat loss coefficient 0.067

Table 3: Optical and thermal properties of the layers.

Layer Parameter Value Refs.

Glazing "g 0.01 [16]

g 0.9 [16,17]

Tg 0.95 [16]

Cg 750 J/kg K [16]

feg 18 W/m K [16]

Solar cell aPV 0.93 [16]

pv 0.9 [18]

Cpv 677 W/m [16]

fePV 149 J/kg K [16]

EVA feeva °.35 W/m K [16,17]

Adhesive fegi 0.85 W/m K [1,17]

Tedlar fcted 0.2 W/m K [1,17]

Absorber Ca 385 J/kg K [3]

310 W/m K [19]

Insulation fe 0.035 W/m K [3]

Table 4: Comparison of the dynamic and quasi-steady solutions with the same inputs at 1-min resolution.

/Q Pel (kWh) Pump hours (h)

Double Dynamic 0.95 138.1 364.87

glazed Quasi-steady 1.07 128.4 372.87

Single glazed Dynamic 0.68 166.7 364.53

Quasi-steady 0.73 161.4 573.23

Unglazed Dynamic 0.32 204.6 564.32

Quasi-steady 0.34 203.2 371.93

Table 5: Daily system performance when a fully mixed tank and a stratified tank are employed in the system

Fully mixed tank 3-node, 1-D stratified tank Relative difference [%]

QTH = 7.013 kWh Pel = 7.87 kWh

QTH = 6.76 kWh PEL = 7.96 kWh

3.8 1.1