Marianne Lemoine-Goumard

Marie-Hélène Grondin

Fermi-LAT observations of the Vela X region

Keywords: Gamma-rays, Fermi, Pulsar wind nebulae, Vela X

The Vela supernova remnant (SNR) is the closest SNR to contain a young active pulsar, PSR B0833-45. The remnant spans about 8 • in diameter and contains regions of non-thermal emission in the radio, X-ray and gamma-ray bands, including Vela X, a pulsar wind nebula (PWN) spanning a region of 2 • × 3 • south of the pulsar. With a center offset by about 40' from the pulsar, Vela X served as the first prototype for offset PWN as a result of SNR expansion into an inhomogeneous medium; it emits in the radio, X-ray, and TeV gamma-ray bands. Using recent observations by Fermi-LAT, we have conducted a detailed study of the off-pulse emission in the region of the Vela pulsar. We will describe the Fermi-LAT measurement of this region and discuss the origin of the detected gamma-rays.

I. INTRODUCTION

The region surrounding the Vela SNR (∼ 8 • in diameter) is very well studied across the electromagnetic spectrum and contains a number of complex objects, including the pulsar PSR B0833-45 and the SNR RX J0852.0-4622. Located at a distance of ∼ 290 pc [5], it is the closest SNR to contain an active pulsar, PSR B0833-45, which is bright (S 1.4 GHz ≈ 1.5 Jy), young (characteristic age τ c = P/2 Ṗ = 11 kyr), and energetic ( ĖSD = 6.9×10 36 I 45 ergs/s, for a neutron star moment of inertia 10 45 I 45 g cm 2 ). The SNR contains several regions of non-thermal emission, including those labelled by Risbeth el al. (1958) from radio observations as Vela X, Vela Y and Vela Z [11]. Vela X is the most prominent radio feature with the characteristic of having an almost flat radio spectrum. Further insight into the nature of Vela X was revealed by the detection of a diffuse X-ray emission extending south of the Vela pulsar by ROSAT [10]. This feature was first interpreted as an X-ray jet from the pole of the pulsar along which the pulsar loses energy. However, Chandra observations showed that this X-ray emission (called "cocoon") lies along the extension of the pulsar equator. An alternate explanation for the X-ray filament was then proposed by Gvaramadze (1999) who suggested that this feature represents a projection effect of a Rayleigh-Taylor instability, which is caused by the impact of the SN ejecta with the wind-driven shell from the progenitor [6]. Though the cocoon is no longer considered as a jet, it deserves further investigation and is important in different perspectives. Indeed, a conclusive proof for the existence of relativistic particles in the X-ray cocoon was revealed by H.E.S.S. observations of the Vela region with an integral flux above 1 TeV of ∼50% of that of the Crab Nebula [2]; this places Vela X as one of the best PWN candidate for Fermi. Also, it was the first middleaged pulsar wind nebula (PWN) to be detected and served as the first prototype for offset PWN as a result of SNR expansion into an inhomogeneous medium [3]. With the successful launch of the Fermi Gamma-ray Space Telescope on June 11, 2008, we have a new opportunity to study the Vela X region in the high-energy γ-ray band.

II. Fermi-LAT OBSERVATIONS

The initial observations of the Vela pulsar were based on 35 days of on-orbit verification and the initial ∼ 40 days of the on-going first year sky survey. We report here the results based on these initial observations even though the survey observations keeps increasing the photon statistics accumulated from the Vela region. More details on these observations can be found at [1]. During the initial period of the Launch and Early Orbits Operations, the instrument configuration was being tuned for optimum performance and the results of these studies were used to verify the LAT photon selection, effective area, timing, photon energy measurement and the variation of the Point Spread Function (PSF) with energy.

III. RADIO TIMING

The Vela pulsar is the brightest persistent pointsource in the γ-ray sky with pulsed photons observed up to 17 GeV. The study of Vela X thus imply to assign a phase to the γ-ray photons and select the offpulse ones. Since the Vela pulsar is young and exhibits substantial timing irregularities, it is necessary to have contemporary radio ephemeris. The radio ephemeris is obtained using observations made with the 64-m Parkes radio telescope as part of the overall program for pulsar monitoring in support of the Fermi mission [12]. A total of 27 times-of-arrival (TOAs) were obtained at a frequency of 1.4 GHz over the period of the LAT observations. No large timing irregularities or glitches were detected. An accurate determination of the pulsar's dispersion measure of 67.95±0.03 cm -3 pc was obtained by measuring the delay in the TOAs of the pulse across the 256 MHz bandpass of the 1.4 GHz receiver. This allows extrapolation of the radio ephemeris to infinite frequency with an error of ∼60 µs. Photon arrival times were referred to the Solar-System barycenter and pulse phases were assigned using the standard pulsar timing software TEMPO2 [7].

IV. RESULTS

Using "Diffuse" class events (those reconstructed events having the highest probability of being photons) contained in an energy-dependent region of interest defined by an angle θ < Max[1.6 -3Log 10 (E GeV ), 1.3] deg from the pulsar position, we collect 32, 400 ± 242 pulsed photons and 2, 780 ± 53 background photons with energy > 0.03 GeV. Fig. 1 shows the 0.1-10 GeV pulse profile from this energydependent cut using variable-width bins of 200 counts in order to highlight fine structures. From this pulse profile, we determine the off-pulse region (φ = 0.65 -1.05) and present an inset of this phase interval with 50 counts/bin in Fig. 1. We see that, as for other nonradio Vela pulse profiles, there is a faint tail of pulsed emission in this region, reaching non-detectability only near φ = 0.8 -1.0. We estimate that this 'off pulse' window contains 235±15 pulsed photons (7.3 × 10 -3 of the pulsed flux). It is clear from this Figure that the Vela region is strongly dominated by the pulsed emission except in the off-pulse interval. Figure 2 presents Fermi γ-ray images of the Vela pulsar in three energy bands in the LAT range separated into the on-(φ = 0.05 -0.65) and off-(φ = 0.65 -1.05) pulse phase regions. The images (except for the low count high energy off-pulse frame) are smoothed by Gaussians (with F W HM = 1.2 • , 0.7 • and 0.2 • for the low to high energy images, respectively). The off-pulse images show the bright diagonal band of the Galactic diffuse emission, with appreciable structure. While a clump of extended emission surrounds the pulsar position on the few degree scale, it is at present not possible to associate this flux with known Vela PWN structures (e.g. the Vela-X TeV PWN, contours in the middle energy band). As a first attempt at constraining unpulsed (e.g. PWN) emission from Vela we have attempted to fit for a point source in the off-pulse phase window, fixed at the position of the pulsar. Using 0.1-10 GeV photons in an 8 • ROI in the φ = 0.65 -1.05 phase interval, we derive a 95% CL upper limit on the flux of 1.8×10 -7 γ/cm 2 /s. After subtracting the estimated remnant pulsed flux in this window (0.73% of the phase-averaged flux) and scaling to the full pulse phase, this provides a limit on an unpulsed point source at the position of Vela of 2.8% of the E > 100 MeV pulsed emission count-rate. Additional survey data (September 2008 to May 2009) are currently analysed, especially at higher energy, to search for a resolved PWN correlated with the TeV or radio structures.

V. DISCUSSION AND CONCLUSION Different scenarios have been proposed to interpret the multi-wavelength data accumulated on Vela X. Horns et al. (2006) proposed a hadronic model wherein the γ-ray emission is the result of the decay of neutral pions produced in proton-proton collisions in the cocoon. However, this model requires a density larger than 0.6 cm -3 which seems disfavoured by recent XMM observations [9]. La Massa et al. ( 2008) proposed a leptonic model with radio and X-ray emissions resulting from synchrotron radiation and γ-ray emission arising from Inverse-Compton scattering. In this model, the authors need a 3-component broken power-law to describe the electron population and adequately fit the data [9]. A single break model can also reproduce the multi-wavelength data if a separate electron population produces the radio emission [4]. In this latter case, the morphology of the γ-ray emission observed by Fermi would be very similar to the radio one since it would be produced by the same electron population. Here, we have shown that, in the off-pulse phase, a clump of extended emission surrounds the pulsar position on the few degree scale but it is not possible at this time to firmly associate those photons with Vela X. An upper limit, assuming a point-source at the position of the pulsar, was derived which already constraint the parameters of the emission models cited above, such as the magnetic field or the electron population. The additional survey data whose analysis is still ongoing will allow us to do a complete morphological analysis, thus providing further insights on the electron population.

VI. ACKNOWLEDGMENT

The Fermi-LAT Collaboration acknowledges support from a number of agencies and institutes for both the development and operation of the LAT as well as the scientific data analysis. These include NASA and the DOE in the United States, the CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K.A. Wallenberg Foundation, the Swedish Reseacrh Council and the National Space Board in Sweden. Additional support from INAF in Italy for science analysis during the operations phase is also gratefully acknowledged. The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth Government of operation as a National Facility managed by CSIRO. We thank our colleagues for their assistance with the radio timing observations. Fig. 1: Vela broad band (E = 0.1 -10 GeV) pulse profile for all photons from an energy dependent ROI. Two pulse periods are shown. The peak of the radio pulse is at phase φ = 0. The count rate is shown in variable width phase bins with a constant number of counts. The dashed line shows the background level, as estimated from a surrounding annulus during the off-pulse phase. Insets show the pulse shape near the peaks and in the off-pulse region.

Fig. 2 :

 2 Fig. 2: On-(φ = 0.05 -0.65, top row) and off-(φ = 0.65 -1.05, middle row) pulse phase images in three energy bands. Each panel spans 10 • × 10 • in equatorial coordinates centered on Vela (RA and Dec marked in degrees in the central panel). On-pulse data are dominated by the point source; the panels have a hard square root stretch to show the faint wings of the PSF. The off-pulse images (linear grey scale) are dominated by Galactic diffuse emission; some of the structure is due to limited count statistics. Contours of the point source at 0.5, 0.25 and 0.125 of the peak intensity are shown (red) in each frame. In the middle energy off-pulse image we also show the HESS Vela PWN contours (Aharonian et al. 2006; blue).


Luca Cecchinato

Marco Corradi

Silvia Minetto
email: silvia.minetto@unipd.it

Energy performance of supermarket refrigeration and air conditioning integrated systems

Keywords: Display cabinet, Efficiency, Heat recovery, Heat pump, Supermarket, Water chiller

The electricity consumption for air conditioning and refrigerated cases in large supermarkets represents a substantial share of the total electricity consumption.

The energy efficiency of supermarkets can be improved by optimising components design, recovering thermal and refrigerating energy, adopting innovative technology solutions, integrating the HVAC system with medium temperature and low temperature refrigeration plants and, finally, reducing thermal loads on refrigerated cases. This study is aimed at investigating the performance of different lay-out and technological solutions and at finding the potential for improving energy efficiency over the traditional systems in different climates. In the analysis chillers and heat pumps working with R410A, medium temperature systems working with R404A and low temperature systems

x specific humidity ratio [-] Greek letters

α heat transfer coefficient [W m -2 K -1 ] ∆ difference [-]
η el electric efficiency [-] η is isentropic efficiency [-] η

Introduction

Energy saving and F-gas emission reduction have been top issues for the last two decades. Energy production and use have undergone a rationalisation process in almost all application fields. In particular, since in many countries the structure of energy consumption by different consumer groups is characterised by a high share of the residential and tertiary sector, which is very often responsible for about 40% of the total final energy demand, a great research effort is taking place to minimise their direct and indirect contribution to greenhouse effect. European Comunity Directive 2002/91/CE [START_REF]European Comunity Directive 2002/91/CE, Energy performance in buildings[END_REF] proposes important guidelines for the improvement of building energy efficiency;

in Italy the Directive was applied by the national regulation DL 192/05, issued in 2005 [START_REF]Italian Legislative Decree DL 192/05, Attuazione della direttiva 2002/91/CE relativa al rendimento energetico nell'edilizia[END_REF]. Data supplied by the main Italian energy distribution Company [START_REF] Terna | Energy consumption in Italy-General data[END_REF] show that 25% of the Italian energy consumption is related to commercial

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services and, amongst them, supermarkets are the main consumers. It is therefore of the greatest importance to propose new technologies that can improve energy efficiency in supermarkets and that can represent an acceptable trade off between installation and running costs.

The analysis of each contribution to the total energy bill of supermarkets is the first step towards energy efficiency improvement. According to the Canadian Energy Efficiency Office [START_REF]Canada, Commercial and Institutional Retrofits-Guide-Saving Energy Dollars in Stores[END_REF], food preservation contributes for about one third to the total energy consumption of supermarkets, while lighting and air conditioning account for 25% and 20% respectively. Efficient design of refrigeration plants is mandatory for energy saving in supermarkets. Proposed technical solutions include the adoption of evaporative condensing [START_REF] Kenbel | Evaporative condensing minimizes system power requirements[END_REF], the application of heat recovery and floating condensation [START_REF] Arias | Heat recovery and floating condensing in supermarkets[END_REF] and mechanical subcooling of low-temperature systems [START_REF] Couvillion | Analysis of a vaporcompression refrigeration system with mechanical subcooling[END_REF][START_REF] Thornton | Dedicated mechanical subcooling design strategies for supermarket applications[END_REF][START_REF] Khattar | Experiences with modeling supermarket energy use and performance[END_REF].

Cogeneration and trigeneration have been recently proposed as feasible solutions for supermarket applications to produce electricity and to make cooling capacity available by means of an absorbtion unit. Maidment and Tozer [START_REF] Maidment | Combined cooling heat and power in supermarkets[END_REF] review a number of combined cooling heat and power (CCHP) options involving the use of different cooling and engine technologies. The pay-back time for a CCHP system applied to a supermarket has been estimated to be around 9-10 years by Arteconi et al. [START_REF] Arteconi | Distributed generation and trigeneration: energy saving opportunities in Italian supermarket sector[END_REF].

When air conditioning and space heating are demanded to liquid chillers and heat pumps, there is a real possibility of integrating vapour compression cycles operating at different temperature levels and of recovering waste heat deriving from refrigeration plants [START_REF] Arias | Heat recovery and floating condensing in supermarkets[END_REF][START_REF] Baxter | Advanced supermarket refrigeration/heat recovery systems[END_REF]. As in supermarket there are normally vapour

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compression cycles operating at three different temperature levels, corresponding to air-conditioning units, medium and low temperature refrigeration plants respectively, it is possible to concatenate the systems according to a cascade lay-out, where the unit operating at the lower temperature level rejects the condensation or subcooling heat to the system at the higher temperature level [START_REF] Arias | Innovative system design in supermarkets for the 21 st century[END_REF][START_REF] Arias | Modeling and experimental validation of advanced refrigeration systems in supermarkets[END_REF]. The integration may be operated directly, i.e. coupling evaporators, condensers and liquid subcoolers of different units, either using a secondary fluid.

Gianni and Oliva [START_REF] Gianni | Water loop heat pump system integrated with heat recovery system. Technical and economical comparison with a traditional system[END_REF] suggested the adoption of a water loop heat pump system integrated with a heat recovery system for air conditioning in shopping centres.

The authors presented a technical and economical comparison of this system with a traditional one, based on experimentation, reporting a 28% energy saving over the total air-conditioning costs. Yang and Zhang [START_REF] Yang | Analysis on energy saving potential of integrated supermarket HVAC and refrigeration systems using multiple subcoolers[END_REF] analyse the energy saving potential of integrated supermarket HVAC and refrigeration systems using three subcoolers. The subcoolers are placed between the refrigeration medium and low temperature systems and between the air-conditioning system and the medium and low temperature plants. The energy saving associated to the proposed solution is strictly dependent on the air-conditioning and refrigeration load ratio. The authors pointed out an energy saving equal to 15.6 and 6.5% with a ratio of 1 and 10 respectively. Even though Yang and Zhang In this paper a seasonal dynamic building energy simulation is carried out to compare different plant solutions integrating air-conditioning liquid chillers and heat pumps with refrigeration units in the climates of Treviso (Northen Italy), Stockholm and Singapore. In order to evaluate the different systems energy consumption, a mathematical model providing an accurate estimation of refrigeration and air conditioning units cooling or heating capacity and power consumption out of nominal rating conditions was developed. R410A was chosen as the working fluid for air-conditioning systems; refrigeration units for medium temperature applications were assumed to use R404A, while for freezers units both R404A and R744 were considered.

PLANT OPTIONS

The different plant options are presented in the following. The baseline plant, System 0 (Figure 1), does not include any integration between air conditioning and refrigeration units. Two independent direct expansion refrigeration machines for medium temperature (MT) and low temperature (LT) applications are used; the refrigerant is R404A. An air condensed heat pump provides cold/hot water to the air handling unit (AHU) of the building variable air volume (VAV) air conditioning system. System 1 (Figure 2) provides the simplest level of integration between refrigeration units. Saturated liquid out of the condenser of the LT refrigeration unit is subcooled by means of the evaporation of a certain amount of refrigerant in the MT refrigeration unit.

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System 2 introduces the integration between the air conditioning system and the refrigeration units; during summertime, the liquid chiller, beyond providing the air conditioning unit with cold water, subcools liquid out of both MT and LT condensers (Figure 3). During winter, MT and LT condensation waste heat is completely recovered for supplying the AHU hot coil with water at 45 °C. Excess heat is rejected using a finned coil condenser. A heat pump, in parallel with the heat recovery system, provides the additional heat, whenever necessary (Figure 4). System 2 includes also the subcooling of the LT refrigeration unit by the MT refrigeration unit, as described for System 1.

System 3 consists in a typical cascade system, where the LT refrigeration unit rejects the condenser heat to the MT refrigeration unit. The MT unit is operated on R404A, while the LT unit uses R744. In summertime, the chiller provides the MT unit with cold water for refrigerant subcooling, while feeding the AHU cold coil (Figure 5). In wintertime, total heat recovery is applied to MT refrigeration unit for direct heating service; the heat pump supplies the system with the additional heat (Figure 6).

System 4 during summer overlaps system 2. In wintertime, the waste heat from the condensers of MT and LT refrigeration units is recovered in a water loop working as the heat source of the water/water heat pump (HP 1). Additional heat, if need be, is supplied by the air/water heat pump (HP 2) (Figure 7).

System 5 during summer overlaps system 3, except for being R744 the working fluid in the LT refrigeration unit. In wintertime, the waste heat from the MT refrigeration unit condenser is recovered in a water loop working as the heat source of the water/water heat pump (HP 1). Additional heat, if need be, is

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supplied by the air/water heat pump (HP 2) (Figure 8).

Building simulation

A single-floor building with a total area of 3620 m 2 was simulated. Its height is 5 m. The longest dimension is south-north oriented. The total area is divided into three parts: the supermarket area is 3019 m 1.

The supermarket was considered to be located on a flat ground, without obstacles to the direct solar radiation, such as trees or buildings, and the ground reflection coefficient was assumed equal to 0.2. i.e. 25°C and 60% relative humidity.The reference c ode identifies the cabinets according to ISO 23953 [START_REF]Standard ISO 23953, Refrigerated display cabinets --Part 2: Classification, requirements and test condition[END_REF].

The contribution to internal thermal loads related to lighting, equipment and people are detailed in Table 3. For the bakery area (51.6 m 2 ), which is included in the supermarket, the internal load due to equipment was assumed to be The air conditioning plant was assumed to be active 14 hours per day (from 6.00 a.m. to 8.00 p.m.), six days per week. In summertime, the air conditioning set point is 26°C, while in the wintertime the set point for ambient heating is 20°C. During the opening hours, the maximum relativ e humidity is set to 60%: above this limit, dehumidification is activated. Air change rate is assumed to be 10 -2 m 3 s -1 per person in the cafeteria, 1.2 10 -3 m 3 s -1 per m 2 of shops area and 8 10 -3 m 3 s -1 per person in the supermarket.

Air infiltration was considered negligible in the building air-conditioned spaces because of the presence of door air curtains. The AHU is equipped with a 60% effective heat recovery system and an economizer which is active from 11°C to 25°C external air temperature. An economizer is a d amper opening that draws up to 100% outside air when the outside air is cooler than the temperature inside the building, thereby providing free cooling. The design AHU flow rate is 8.47 m 3 s -1 . The supermarket was simulated with EnergyPlus [START_REF]Energy Plus-version 4.0.0[END_REF] to calculate at hourly intervals the thermo-hygrometric variables and the thermal energy exchanged.

A particular effort was spent taken to modelise the interacton between the display cases and the surrounding ambient. Thermal loads of display cases and

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11 cold rooms depend on the supermarket air thermoigrometrical conditions, T A and RH A . In particular, in the surroundings of vertical open cabinets, the cold air leakage creates the so-called cold aisle effect, where temperature T A,C and relative humidity RH A,C can be very different from the average supermarket air thermoigrometrical conditions. Orphelin et al. [START_REF] Orphelin | Are there optimum temperature and humidity set points for supermarket?[END_REF] show the dependence of cold aisle temperature from the average ambient temperature and humidity.

Equations (1) were obtained from Orphelin et al. [START_REF] Orphelin | Are there optimum temperature and humidity set points for supermarket?[END_REF] data. The influence of the other cabinets on the surrounding ambient temperature and relative humidity was neglected.

( ) ( )

3 1.473 0.6067 , , , , , , 6.5 10
,

A C A C A A A A A C A C A C A T T T RH T RH RH RH T x -  = = ⋅ ⋅ ⋅   =   (1)
To correctly evaluate the display cases thermal load, corrective factors were

HER HER A C A C A C A C A C F F T RH a RH T a T a RH a = = ⋅ ⋅ + ⋅ + ⋅ + 1 , 2 , 3 , 4 ( , )

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Table 4 summarises the coefficients of equation ( 2) for the considered cabinets.

In the case of closed cabinets (VF4), ambient relative humidity does not influence HER.

The required HER of each cabinet can be calculated by multiplying the nominal HER by the corrective factor F HER , as expressed in equation ( 3):

N HER HER HER F = ⋅ (3)
During the closing hours, night blinds reduce the HER of vertical multi-deck cabinets by 45%. The HER of each cabinet, expressed as a function of the local thermal hygrometic variables, contributes to the energy conservation equation of each building zone in the simulation. According to Orphelin et al. [START_REF] Orphelin | Are there optimum temperature and humidity set points for supermarket?[END_REF], only 80% of display cabinets HER contributes to the building energy equation, beeing 20% of the HER related to cabinet internal gains (lighting, fans, heaters, etc). The average temperature and humidity of specific zones depend on many variables (conduction through the walls, air supply, radiative loads, internal loads and display cases HER). The cold aisle phenomenon was not considered in the calculation of thermal load from the walls.

Simulations exhibit a maximum heating demand of 207.2, 238.7 and 86.9 kW in Treviso, Stockholm and Singapore respectively. The cooling peak is 69.3, 50.0 and 158.9 kW in the three cities respectively. In Table 1 the maximum LT system load resulting from building simulation is reported together with the peak load ratios of the MT and of the AHU to the LT system (R MT-LT , R AHUc-LT , R AHUh- LT ). It appears that Stockholm loads are similar to Treviso ones but the R AHUh-LT ratio is higher because of the colder climate. Singapore is characterised by a

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13 much lower R AHUh-LT ratio and a more than double R AHUc-LT ratio. This is due to the hotter and more humid climatic conditions.

Air conditioning and refrigeration unit design

The peak value of heating and cooling loads, as resulting from the simulation which is described in the previous section, was considered for the design of the air conditioning and refrigeration units. The evaporation temperatures of the MT and LT refrigeration units were considered to be respectively -10°C and -35°C.

Superheat was set to 5°C for all evaporators, while no subcooling was assumed at the condensers exit. During heating operations, water set point was 45°C, while it was 7°C when cooling is required. Tables 5 and6 summarise the design conditions for refrigeration and air conditioning units. In the case of cascade systems (System 3 and 5), evaporation temperature and superheat of the MT refrigeration units are respectevly T sf,in and ∆T sf , as listed in Table 5. 5 and6, considering the same compressors isentropic and volumetric efficiencies curves.

T c is condensation temperature, T c,sf,
The design conditions for heat exchangers water/refrigerant SR1 (Figures 3 and5), MT refrigerant/LT refrigerant SR2 (Figures 2-4 and7) are presented in Table 7 where T r,in is the refrigerant inlet temperature, T sf,in the secondary fluid inlet temperature, ∆Tapproach is the minimum temperature approach between the fluids, T LT,in and T LT,out are respectevly the inlet and outlet temperatures of the LT refrigerant and T MT,in e T MT,out the inlet and outlet temperatures of the MT refrigerant.

The possibility of varying the chiller/heat pump water delivery temperature according to the actual cooling/heating load was introduced. It has been widely demonstrated in the technical literature [START_REF]ASHRAE Handbook -HVAC Applications[END_REF] that the modulation of the water temperature can lead to relevant energy saving. During summertime the water temperature can vary in the range 7-16°C, if the re quired cooling capacity is inside the interval 20-100% of the design value, while it stays at 16°C under 20%. In the case of Systems 2-5, the total cooling load includes also the subcooling demand of the refrigeration units. Contrary to Yang and Zhang [START_REF] Yang | Analysis on energy saving potential of integrated supermarket HVAC and refrigeration systems using multiple subcoolers[END_REF] approach, the chiller always operates the MT and/or LT plants subcooling even without AHU cooling demand.

During winter, the water delivery temperature is modulated between 45°C and 30°C in the 20-100% interval of the design heating capacity, and never drops below 30°C.

M A N U S C R I P T

A C C E P T E D

Air conditioning and refrigeration units simulation

In order to evaluate the energy consumption of refrigeration and air conditioning units a mathematical model providing an accurate estimation of refrigeration and air conditioning units cooling or heating capacity and power consumption out of nominal rating conditions was developed. The proposed procedure corrects the design transmittance taking into account the heat transfers coefficients variations associated to refrigerant and secondary fluid mass flow rates variations.

For a set refrigerating unit, the numerical procedure can be outlined with the following steps:

A. Determination of design heat exchangers transmittances

A.1 input data gathering;

A.2 calculation of design condensation and evaporation temperatures; "B" steps should be iterated for each different working condition to be considered. The numerical procedure steps are detailed in the following.

A.1 Input Data gathering

The following data are required for the model application to a given refrigeration unit:

• the refrigerant fluid and the secondary fluids at evaporator and condenser;

• for a refrigerating unit, the rated cooling capacity,Q e,D , and compressor power consumption, P k,D (or design efficiency, EER ) in design conditions;

• for an heating unit, the rated heating capacity, Q c,D , and compressor power consumption, P k,D (or efficiency,COP) in design conditions;

• design refrigerant evaporator outlet superheat and condenser outlet subcooling values, ∆T SH,D e ∆T SC,D ;

• compressor coefficients with reference to the EN 12900 [START_REF]European Directive EN 12900[END_REF] polynomial equations;

•

A.2 Calculation of design condensation and evaporation temperatures

Considering the single stage vapour compression cycle shown in Figure 9 p-h diagram, the thermodynamic properties of points 1, 2s, 3 and 4 can now be determined in design conditions. The process undergone by the refrigerant inside the compressor is described by an adiabatic compression (1-2) and an

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18 isobaric process (2-2d) which accounts for heat transfer phenomena between the compressor and the environment. The thermodynamic properties associated to points 2 and 2d depend on the compressor characteristics. In fact, 2s is the discharge point corresponding to an isentropic compression process, while 2 and 2d refer respectively to the end of an adiabatic compression process and to the compressor discharge, taking into account both the compression irreversibility and compressor heat dissipation. With reference to EN 12900 superheat and subcooling standard values [START_REF]European Directive EN 12900[END_REF], it is possible to express the cooling capacity, the power consumption and the refrigerant mass flow rate with the following polynomial equations:

Q a a T a T a T a T T a T a T a T T a T T a T

= + ⋅ + ⋅ + ⋅ + ⋅ ⋅ + ⋅ + + ⋅ + ⋅ ⋅ + ⋅ ⋅ + ⋅ , (4)
= + ⋅ + ⋅ + ⋅ + ⋅ ⋅ + ⋅ + + ⋅ + ⋅ ⋅ + ⋅ ⋅ + ⋅ , ( 5
) 4 1 ˆê Q m h h = - & , (6)
Considering equations (4-6) and the EN 12900 [START_REF]European Directive EN 12900[END_REF], superheat and subcooling values, the compressor volumetric and isentropic efficiencies can be thus easily expressed as:

1 v m V η ρ = ⋅ & & , (7)
M A N U S C R I P T A C C E P T E D ( ) 2 1 ˆˆŝ is k m h h P η ⋅ - = & . ( 8
)
In the hypothesis that these efficiencies values doesn't depend on the refrigerant superheat at the compressor suction, the refrigerant mass flow rate, the cooling capacity and the power consumption can be calculated with reference to Figure 9 cycle:

1 v m V η ρ = ⋅ ⋅ & & , (9)
( )

4 1 e Q m h h = - & , (10)
( )

2 1 k P m h h = - & , (11)
h 2 , being the refrigerant enthalpy at the end of the adiabatic compression process, is determined by:

2 1 2 1 s is h h h h η - = + . ( 12
)
The compressor discharge enthalpy, h 2d , can be defined as a function of the compressor heat dissipation factor, h d :

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 20 2 2 k d P hd h h m ⋅ = -& . ( 13
)
Through equations ( 12) and ( 13), the thermal power to be dissipated in the condenser can be calculated as:

( )

2 1 4 4 2 1 s k c d is h h P hd Q m h h m h h m η                 - ⋅ = - = + - - & & & . ( 14
)
The vapour compression system energy efficiency is obtained with the following two expressions, for a refrigerating and a heating unit respectively:

, 0

e D c D D k e D c D k D Q T T Q P T T P      - = - = , ( 17
)
where Q represent the cooling or the heating capacity for a refrigerating and a heating unit respectively.

A.3 Determination of design heat exchangers transmittances

The evaporator and condenser transmittances in design conditions can be subsequently determined with a logarithmic mean temperature difference approach. If the heat exchanger heat transfer surface is divided into M partitions of equal refrigerant enthalpy difference, its transmittance can be calculated with the following expression in the co-current hypothesis:

( )

1 1, j j j M j m h h UA θ - = ⋅ - = ∑ & , ( 18
)
where θ j is defined as the logarithmic mean temperature difference between the refrigerant and the secondary fluid with reference to the j-th subdivision of the refrigerant enthalpy difference. It can be calculated solving the following algebraic system:

M A N U S C R I P T A C C E P T E D ( ) 1 , , 1 , , , , 0, 1
,

out in j j out in sf j sf j sf p sf j out sf j sf in h h h h M j M m h h T T M m c h h j M T T + +                        - = - = - ⋅ - = - ⋅ ⋅ = = = & & . ( 19
)
For a given refrigerating unit, it is thus possible to calculate the design cycle operative temperature together with the heat exchangers transmittance, For each heat exchanger secondary fluid, the volumetric flow rate is calculated on the basis of the following equation, neglecting mass transfer phenomena:

, sf sf p sf sf Q V c T ρ = ⋅ ⋅ ∆ & , ( 20
)
where Q is the heat exchanger thermal power.

B.1 Calculation of cooling/heating capacity and power consumption

For secondary fluids temperature values different from design conditions, it is possible to determine the refrigeration machine working conditions and energy efficiency based on design data in the following hypotheses:

• constant design evaporator outlet superheat and condenser outlet subcooling values;

     - ⋅ = - ⋅ = , ( 21
)
where the heat exchanger transmittances, UA, are obtained from equations [START_REF]Canada, Commercial and Institutional Retrofits-Guide-Saving Energy Dollars in Stores[END_REF][START_REF] Kenbel | Evaporative condensing minimizes system power requirements[END_REF][START_REF] Arias | Heat recovery and floating condensing in supermarkets[END_REF][START_REF] Couvillion | Analysis of a vaporcompression refrigeration system with mechanical subcooling[END_REF][START_REF] Thornton | Dedicated mechanical subcooling design strategies for supermarket applications[END_REF][START_REF] Khattar | Experiences with modeling supermarket energy use and performance[END_REF][START_REF] Maidment | Combined cooling heat and power in supermarkets[END_REF][START_REF] Arteconi | Distributed generation and trigeneration: energy saving opportunities in Italian supermarket sector[END_REF][START_REF] Baxter | Advanced supermarket refrigeration/heat recovery systems[END_REF][START_REF] Arias | Modeling and experimental validation of advanced refrigeration systems in supermarkets[END_REF] and [START_REF] Stefanutti | Impianti di climatizzazione. Tipologie applicative[END_REF][START_REF]Energy Plus-version 4.0.0[END_REF] that represent the basic equations system of a refrigerating unit for given values of evaporation and condensation temperatures. Instead, the condenser and evaporator transmittance correction coefficients, k , are calculated with the following expression:

1 r fs sf sf r r D D m m sf sf r r D D D D sf r A A k A m m m A m α α α α - -                                     + ⋅ =
where A r and A sf are the heat transfer surface on the refrigerant and secondary fluid side respectively and α r and α sf are the corresponding heat transfer coefficients.

The system of equations is solved using a standard solver based on the MINPACK subroutine HYBRD1, which uses a modification of Powell's hybrid algorithm. This algorithm is a variation of Newton's method, which uses a finitedifference approximation to the Jacobian and takes precautions to avoid large step sizes or increasing residuals [START_REF] Powell | Restart procedures for the conjugate gradient method[END_REF]. The system power consumption, cooling and heating capacity are calculated from system (21) solutions using equations ( 11), [START_REF] Maidment | Combined cooling heat and power in supermarkets[END_REF] and [START_REF] Arias | Modeling and experimental validation of advanced refrigeration systems in supermarkets[END_REF]. The system energy efficiency is obtained according to equations [START_REF] Gianni | Water loop heat pump system integrated with heat recovery system. Technical and economical comparison with a traditional system[END_REF][START_REF] Yang | Analysis on energy saving potential of integrated supermarket HVAC and refrigeration systems using multiple subcoolers[END_REF]. Refrigerant properties were evaluated with NIST Reference Fluid Thermodynamic and Transport Properties -REFPROP, Version 7.0 [START_REF] Lemmon | NIST Reference Fluid Thermodynamic and Transport Properties Refprop 7.0[END_REF].

In presence of systems with cooling or heating capacity control, such as multicompressor scroll chillers, multi-step screw compressor machines or inverter driven units, equations ( 4) and ( 5) can be rewritten as a function of the number of active compressors and of the compressor capacity partialization rate.

If the refrigeration unit has multiple refrigerant or secondary fluids circuits which can be activated as a function of the actual unit working conditions and active compressors, equation [START_REF]ASHRAE Handbook -HVAC Applications[END_REF], expressing the heat exchangers design transmittance correction factor, is corrected. The auxiliaries design power consumption must also be corrected as a function of the secondary fluids active circuits. Further details and equations development can be found in Cecchinato et al. [START_REF] Cecchinato | A simplified method to evaluate the seasonal energy performance of water chillers[END_REF].

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 25

Usually air condensed units for civil and commercial refrigeration are equipped with condensation temperature control systems to assure safe working conditions for the compressor and the expansion valve. These systems regulate the condenser air volumetric flow rate in order to keep or the condensation temperature above a minim value, T c,min , or the pressure difference at the two ends of the throttling valve, above a minim value, ∆p c,min . In this case, the system (21) must be replaced with the following constrained equations system: (

V UA UA k f T V UA UA k T T T T p p        = - ⋅ = = - ⋅ = = = + ∆ & & . (23)
Usually commercial refrigeration plants are equipped with a suction pressure control system to assure stable evaporation temperature to the cabinets.

Parallel compressors are relay controlled in order to keep the evaporation pressure set point value, p e,set . For a given number of active compressors, the system (21) must be replaced with the following constrained equations system:

( ) , , , 0
c e c c c c D e e set f T T UA UA k p p      = - ⋅ = = . ( 24
)

B.2 Part load performance estimation

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

The effect of the part load working of the refrigeration unit, is calculated on the basis of its full load performance and strictly depends on its capacity control system. For single compressor units with simple relay control law, the part load factor, PLF, can be calculated with the equations proposed in the European and

Italian standards [START_REF]prEN 14825, Air conditioners, liquid chilling packages and heat pumps[END_REF][START_REF]Italian standard UNI 10963, Condizionatori d'aria, refrigeratori d'acqua e pompe di calore. Determinazione delle prestazioni a Potenza ridotta[END_REF] as a function of the part load ratio, PLR:

( )

1 c c PLR PLF C PLR C = ⋅ + - , (25)
where C c is a degradation factor associated to the unit cycling operation losses.

The part load ratio is calculated as the ratio between the actual load condition, , or

Q load ,
e c k PL k e PL c PL P PLF P Q PLR Q Q PLR Q = ⋅ = ⋅ = ⋅ . (26)
The system energy efficiency is subsequently obtained according to equations [START_REF] Gianni | Water loop heat pump system integrated with heat recovery system. Technical and economical comparison with a traditional system[END_REF][START_REF] Yang | Analysis on energy saving potential of integrated supermarket HVAC and refrigeration systems using multiple subcoolers[END_REF]. Refrigerating units with multiple compressors or with compressors with different capacity steps, a step capacity control is usually adopted. In this case the full load capacity of each step is determined. It is now possible to determine

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 27
the two steps which mostly approximate the actual load condition, the first one will have a lower capacity, the second one an higher one. The unit part load capacity, power consumption and efficiency are determined by linear interpolation between these two steps performances [START_REF]prEN 14825, Air conditioners, liquid chilling packages and heat pumps[END_REF]. If the unit smallest control step cooling capacity is higher than the required one, the performance data are obtained as detailed for single compressor units, referring the PLR value in equation ( 25) to the unit smallest control step cooling capacity.

Finally, the seasonal energy consumption of the proposed systems has been based on the dynamic building energy load results, as described in section 3;

the average performance of the plant has been calculated with a steady-state approach for each building simulation time step (one hour), as proposed in the standard UNI 11135 (UNI 2003) [START_REF]Italian standard UNI 11135, Efficienza stagionale dei condizionatori, gruppi refrigeratori e pompe di calore-metodo di calcolo[END_REF].

Simulation results

The total annual energy consumption of refrigeration and air conditioning systems, related to the overall supermarket area, is represented in Figure 10 for the considered plant solutions and climates. Treviso monthly results are reported in Tables 8 and9 (constant set point) in Treviso, Stockholm and Singapore respectively. The energy efficiency improvement depends on the climatic conditions and is higher for colder cities. This is related to the higher heat recovery during the heating season.

In general, Systems 2 and 4 show very similar performances; the plant results much simpler in the case of System 2, with lower complexity in the piping integration system and with only one heat pump/chiller. System 3, which has the same integration level between the HVAC unit and the MT refrigeration unit of System 2, while the LT refrigeration unit rejects the condensation heat to the MT refrigeration system in a typical cascade configuration, does not perform as well as System 2, because of the lower cycle efficiency of the cascade system with respect to the LT and MT separate cycles.

In fact, in Treviso design conditions the COP of the System 2 LT unit is 18.5% higher than System 3 one considering the cascade arrangement. For the same reasons, System 5 shows poorer performances than System 3. The energy penalisation of these systems is higher in Treviso than in Stockholm and Singapore. In fact, the energy penalisation of cascade lay-out with respect to single stage one is lower for high compression pressure ratio. This is the case of Stockholm plant operating winter heat recovery for a long time period and of for each system the boiler annual consumption was below 0.3 kWh m -2 and it was not reported in Figure 12.

During wintertime, the integration between the refrigeration units and the HVAC system, resulting from the recovery of the condensation heat, leads to a very low energy consumption for the air/water heat pump. During summertime, Systems 2-5 show higher energy consumption for liquid chillers than that of System 0-1, because of the added heat load coming from the subcooling needs of the refrigeration units.

As for the MT refrigeration unit is concerned: a) the energy consumption of System 2 is higher than that of System 4 in Treviso and Stockholm, because of higher condensation temperature

7.Conclusions

A medium-size supermarket was considered, with respect to the refrigerating machinery for commercial refrigeration and air conditioning/heating system; different levels of integration between the HVAC and the refrigeration units was introduced. A mathematical model providing an accurate estimation of refrigeration and air conditioning units cooling or heating capacity and power consumption out of nominal rating conditions has been developed. The proposed procedure corrects the design transmittance taking into account the heat transfers coefficients variations associated to refrigerant and secondary fluid mass flow rates variations.

Calculations show that all the proposed solution offer a benefit in terms of energy efficiency over the reference traditional solution. The integration between the refrigeration units and the HVAC system and their optimal management can produce energy saving up to 15.6, 22. units. The simplest solution, operating the LT unit subcooling by means of the MT plant, allows energy efficiency improvements equal to 6.2%, 5.9 and 7.4%

for Treviso, Stockholm and Singapore respectively. This solution is suitable for hot climates. LT cascade lay-out is not to be adopted in temperate climates (Treviso).

As widely demonstrated in the technical literature, simulations confirm that floating water set point is effective for energy saving.

As a final remark, the integration approach should be proposed also for large supermarkets and hypermarkets, in consideration of their significant energy consumption.

M

[ 16 ]

 16 carried out a model based analysis on the energy saving potential of integrated supermarket HVAC and refrigeration systems using multiple subcoolers, they compared the different solutions considering only two operating conditions, namely 35 and 18.3 °C externa l air temperature.

  W m -2 , as recommended by Stefanutti[START_REF] Stefanutti | Impianti di climatizzazione. Tipologie applicative[END_REF].The resulting nominal display cases and cold rooms contribution to internal thermal loads is respectively -34.1 W m -2 and -26.6 W m -2 , respectively, during opening (Mon-Sat 6 a.m.-8 p.m.) and closing hours (Mon-Sat from 8 p.m. to 6 a.m., Sunday).

  introduced to emend the nominal HER. Such coefficients are dependent, in the case of open cases, on temperature and humidity of the air entering the cabinetwhile they are only a function of average ambient temperature in the case of closed cabinets. The following general equation (2) was derived from technical datasheet of a refrigeration equipment manufacturer [21]. It expresses the corrective factor F HER for the cabinets nominal HER (declared at 25 °C ai r temperature and 60% relative humidity), as a function of ambient temperature T A,C , and relative humidity R HA,C near cabinets. , ,

  in is the temperature of the secondary fluid entering the condenser and ∆T sf is its temperature lift. T e,sf,in is the temperature of the secondary fluid to the evaporator. V & indicates the compressors total swept volume. Stockholm Systems 2-5 HP2 (air/water heat pump) was dimensioned at -3 °C air temperature, suplementary heating is supplied through a condensing boiler of costant 1.1 energy efficiency. For System 0 in Treviso, Bitzer 4CC-6.2Y, Bitzer 6G-30.2Y and Copeland ZP295KCE-TWD compressors were considered for MT, LT and HP1-2 units respectively. Treviso System 3 adopts Bitzer 2EHC-3K in R744 LT plant. For all M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14 other systems and climates, in order to obtain a fair comparison, the swept volume was changed according to Tables

A. 3 16 B. 2

 3162 determination of design heat exchangers transmittances; B. Determination of system performance under different load and secondary fluid temperature operating conditions B.1 calculation of cooling/heating capacity and power consumption based on corrected transmittances as a function of the actual refrigerant and secondary fluid flow rates and of the logic of the unit control system; part load performance estimation.

  secondary fluids design inlet temperature, temperature variations between inlet and outlet and pressure drops,T sf,D , ∆T sf,D (or in alternative , sf D m & ) M A N U S C R I P T A C C E P T E D • heat exchanger pumps or fans power consumption, ratio of refrigerant side to secondary fluid side heat transfer area; heat exchangers design ratio of refrigerant to secondary fluid heat transfer coefficient with reference to the considered heat transfer surface area; refrigerant and secondary fluid circuits pattern; compressors sequencing and inverter management for multi-compressor and inverter driven unit respectively, with reference to cooling capacity control. Refrigerant pressure drops in the heat exchangers data are not required since they are not easily available in manufacturers data sheets. Heat exchangers heat transfer surface areas and heat transfer coefficients, together with condenser air inlet-outlet temperature difference (or mass flow rate), are seldom present in data sheets; nevertheless they can be quite easily obtained from the manufacturer or from open literature correlations or heat exchangers design practice.

  , through equations[START_REF]Canada, Commercial and Institutional Retrofits-Guide-Saving Energy Dollars in Stores[END_REF][START_REF] Kenbel | Evaporative condensing minimizes system power requirements[END_REF][START_REF] Arias | Heat recovery and floating condensing in supermarkets[END_REF][START_REF] Couvillion | Analysis of a vaporcompression refrigeration system with mechanical subcooling[END_REF][START_REF] Thornton | Dedicated mechanical subcooling design strategies for supermarket applications[END_REF][START_REF] Khattar | Experiences with modeling supermarket energy use and performance[END_REF][START_REF] Maidment | Combined cooling heat and power in supermarkets[END_REF][START_REF] Arteconi | Distributed generation and trigeneration: energy saving opportunities in Italian supermarket sector[END_REF][START_REF] Baxter | Advanced supermarket refrigeration/heat recovery systems[END_REF][START_REF] Arias | Innovative system design in supermarkets for the 21 st century[END_REF][START_REF] Arias | Modeling and experimental validation of advanced refrigeration systems in supermarkets[END_REF][START_REF] Gianni | Water loop heat pump system integrated with heat recovery system. Technical and economical comparison with a traditional system[END_REF][START_REF] Yang | Analysis on energy saving potential of integrated supermarket HVAC and refrigeration systems using multiple subcoolers[END_REF][START_REF]Standard ISO 23953, Refrigerated display cabinets --Part 2: Classification, requirements and test condition[END_REF][START_REF] Stefanutti | Impianti di climatizzazione. Tipologie applicative[END_REF][START_REF]Energy Plus-version 4.0.0[END_REF].

23 •

 23 refrigerant pressure drops variations influence is neglected;• constant design heat exchangers secondary fluids volumetric flow rates and pressure drops; • refrigerant and secondary fluids heat transfer coefficient, α proportional to the m-th power of Reynolds number: Re m α ∝ The vapour compression cycle operating temperatures, c T e e T , determination problem can be reduced to the solution of the following non-linear equations system:

  and the unit full load cooling or heating capacity considering the of operative secondary fluids temperature values. For a refrigerating or a heating system, the part load power consumption, cooling or heating capacity, , be thus defined as a function of full load performance: , , ,

  . With reference to System 0 in the case of constant water delivery temperature (constant set pont), System 4 presents the largest energy saving (14.8, 20.5 and 12.9% in Treviso, Stockholm and Singapore respectively), thanks to the integration between the liquid chiller/heat pump and the refrigeration units. The water/water HP of System 4, which uses the recovered heat as heat source, satisfies 89.4, 86.8 and 100% of the heating energy demand in the three climates. System 2, which directly recoveres the M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 28 refrigeration units condensation heat, is slightly penalised by the high condensation temperature in wintertime. But, if the water delivery temperature can vary (floating set point) according to the heating/cooling demand, System 2 operates at lower average winter condensation temperature thus offering the best result, with 15.6, 22.5 and 14.9% energy saving in comparison to System 0

29 Singapore

 29 Figures 11,[START_REF] Baxter | Advanced supermarket refrigeration/heat recovery systems[END_REF] and 13 represent the annual energy consumption related to the

  E P T E Dassociated to winter heat recovery; b) Systems 3 and 5 show the highest energy consumption due to the fact that they have to manage, as an additional load, the condensation heat of the LT R744 units. System 1 is also penalised in Singapore because of the higher load associated to LT unit subcooling.

  5 and 14.9% in comparison with the traditional solution in Treviso, Stockholm and Singapore respectively. The best performance is achieved in the colder climates and its associated to wintertime condensation total heat recovery from the refrigeration M A N U S C R I P T A C C E P T E D

Figure 2 M

 2 Figure 2

Figure 4 M

 4 Figure 4

Figure 6 M

 6 Figure 6

Figure 7 M

 7 Figure 7

Figure 8 M

 8 Figure 8

Figure 10 M

 10 Figure 10

Figure 11 M

 11 Figure 11

Figure 12 M

 12 Figure 12

Figure 13 MFigure 1 .

 131 Figure 13

Figure 2 .

 2 Figure 2. System 1.

Figure 3 .

 3 Figure 3. System 2. Summertime operations.

Figure 4 .

 4 Figure 4. System 2. Wintertime operations.

Figure 5 .Figure 6 .

 56 Figure 5. System 3. Summertime operations

Figure 7 .

 7 Figure 7. System 4. Wintertime operations.

Figure 8 .

 8 Figure 8. System 5. Wintertime operations.

Figure 9 .Figure 10 .

 910 Figure 9. Single stage vapour compression cycle in p-h diagram

Figure 11 .

 11 Figure 11. Annual energy consumption for each unit of the analysed systems in

Figure 12 .

 12 Figure 12. Annual energy consumption for each unit of the analysed systems in

Figure 13 .

 13 Figure 13. Annual energy consumption for each unit of the analysed systems in

Table 2

 2

	summarises the supermarket MT and LT display cases and cold rooms
	main dimensions, their nominal heat extraction rate (HER N ) and the area where
	they are located. Nominal power is related to standard ISO 23953 Class 3 [17],

50 TABLES Table 1 .

 TABLES1 Monthly maximum and minimum mean average temperature, LT design load and MT and AHU load ratios for the different climates.

			ACCEPTED MANUSCRIPT
		Max		Min	Load ratios
	Treviso Stockholm Singapore	T db [°C] 22.6 17.0 28.5	T wb [°C] 17.5 11.6 25.0	T db [°C] 3.32 -3.6 26.3 M Q LT [kW] 26.5 25.5 27.5 A N U S C R I P T R MT-LT R AHUc-LT R AHUh-LT [-] [-] [-] 2.2 2.6 7.8 2.1 2.0 9.3 2.3 5.8 3.2
	A C C E P T E D
					51

Table 2 .

 2 MT and LT display cases. Nominal HER (HER N )

	Display Cabinets	Reference	Lenght	HER N	Area
	MT Cabinet	[-]	[m]	[kW]	[-]
	MT vertical, multi-deck	VC2	40.0	41.1	supermarket
	MT open, wall site	HC3	22.5	10.2	supermarket
	MT open, island	HC4	7.5	3.0	supermarket
	LT open, wall site	HF3	7.5	6.0	supermarket
	LT vertical, glass door	VF4	20.0	20.0	supermarket
	Coold Rooms	Reference [-]	Volume [m 3 ]	HER N [kW]	Area [-]
	MT	-	224.0	33.0	supermarket
	LT	-	30.5	4.0	supermarket
	MT total [kW]		89.3
	LT total [kW]		30.0

Table 4 .

 4 Coefficients used in equation[START_REF]European Comunity Directive 2002/91/CE, Energy performance in buildings[END_REF].

	Cabinet Reference VC2	a 1 5.08 10 -4	a 2 2.46 10 -2	a 3 -2.88 10 -3	a 4 -1.77 10 -1
	HC3, HC4	1.73 10 -4	2.95 10 -2	-3.17 10 -4	3.38 10 -2
	VF4	0	2.40 10 -2	0	4.00 10 -1
	HF3	8.21 10 -5	1.84 10 -2	6.41 10 -5	4.15 10 -1

Table 5 .

 5 design conditions for MT and LT refrigeration units second value refers to Stockholm design conditions. † : for each system the three swept volumes refers to Treviso, Stockholm and Singapore respectively.

				MT unit			LT unit
			T c	T c,sf,in	∆T sf	V & †	T c	T c,sf,in ∆T sf	V & †
	System	Season		[°C]	[K]	[3600 m 3 s -1 ]		[°C]	[K]	[3600 m 3 s -1 ]
	0	winter summer 45/37* 35/27* ---	5	---140 45/37* 35/27* 130 100	5	256 184 265
	1	winter summer 45/37* 35/27* ---	5	---178 45/37* 35/27* 166 128	5	130 109 135
		winter	50	40	5	191	50	40	5	144
	2	summer 45/37* 35/27*	5	178 206	45/37* 35/27*	5	139 149
		winter	50	40	5	216				14
	3	summer 45/37* 35/27*	5	203 231	-7	-10	5	14 15
		winter	20	10	5	90	20	10	5	130
	4	summer 45/37* 35/27*	5	84 97	45/37* 35/27*	5	125 135
		winter	20	10	5	137				14
	5	summer 45/37* 35/27*	5	127 148	-7	-10	5	14 15
	*: the

& & & &

Acknowledgments

This research work is part of the "Supermercato in classe A (Class A Supermarket)" project, carried out by Distretto Veneto del Condizionamento e della Refrigerazione Industriale (District of Venetian Region for AC and Industrial Refrigeration) and financed by Regione Veneto (Venetian Region) with legislative measure DDSE n. 258 on 21/12/2007. The following companies, managed by the above mentioned district, were collaborating on the project : Bluebox Group Srl, Carel SpA, Climaveneta SpA, DGD Srl, Elettromeccanica SpA, Enofrigo Srl, Evco Srl, Ever-est Srl, G. R. Elettronica Srl, Guerrato SpA, La Felsinea Srl, Rhoss SpA, SCM Frigo Srl, Sirman SpA, Studio 54 Srl, Uniflair SpA, Zoppellaro Srl. Finally we would like to thank Dr. Alessio Gastaldello and Mr Sergio Girotto for the management of the project.

Table 3. contributions to internal loads (Stefanutti, 2002)

Area

Lighting Equipment People [W m -2 ] [W m -2 ] [persons m -2


R Mastrullo

C Renno
email: crenno@unisa.it

A thermoeconomic model of a photovoltaic heat pump

Keywords: photovoltaic evaporator, heat pump, modelling, thermoeconomic analysis

In this paper the model of a heat pump whose evaporator operates as a photovoltaic collector, is studied. The energy balance equations have been used for some heat pump components, and for each layer of the photovoltaic evaporator: covering glaze, photovoltaic modules, thermal absorber plate, refrigerant tube and insulator. The model has been solved by means of a program using proper simplifications. The system input is represented by the solar radiation intensity and the environment temperature, that influence the output electric power of the photovoltaic modules and the evaporation power. The model results have been obtained referring to the photovoltaic evaporator and the plant operating as heat pump, in terms of the photovoltaic evaporator layers temperatures, the refrigerant fluid properties values in the cycle fundamental points, the thermal and mechanical powers, the efficiencies that characterize the plant performances from the energy, exergy and economic point of view. This study allows to realize a thermoeconomic comparison between a photovoltaic heat pump and a traditional heat pump under the same working conditions.

Introduction

The direct use of solar energy as primary energy source is interesting because of its universal availability and low environmental impact. Solar heating applications are intuitive; on the contrary, the solar energy use to obtain refrigeration is less intuitive.

Different technologies can be adopted to get refrigeration from solar energy: thermal and electric solar systems, and some new emerging technologies [START_REF] Kim | Solar refrigeration options a state of the art review[END_REF]. The solar thermal systems include absorption [START_REF] Zambranoa | Model development and validation of a solar cooling plant[END_REF], adsorption [START_REF] Hildbrand | A new solar powered adsorption refrigerator with high performance[END_REF], solar ejector [START_REF] Vidal | Modelling and hourly simulation of a solar ejector cooling system[END_REF], thermo-mechanical and regenerative dessicant solutions [START_REF] Henning | Solar-assisted Air-conditioning Handbook in Buildings: A Handbook for Planners[END_REF]. As for the solar electric systems, the photovoltaic solar is the most popular technology. In fact referring to a traditional vapour plant, the compressor motor can be electrically supplied by photovoltaic modules that allow the direct conversion of solar radiation into direct current [START_REF] Kattakayaml | Thermal performance characterization of a photovoltaic driven domestic refrigerator[END_REF]. The PV system is most appropriate for small capacity refrigeration plants used for food or medical applications in areas far from conventional energy sources [START_REF] Cherif | Dynamic modelling and simulation of a photovoltaic refrigeration plant[END_REF], where a high level of solar radiation is present. Moreover, the solar assisted heat pump (SAHP), introduced by [START_REF] Kern | Combined photovoltaic and thermal hybrid collector systems[END_REF], allows improvements in comparison with a traditional heat pump [START_REF] Gorozabel Chata | Analysis of a direct expansion solar assisted heat pump using different refrigerants[END_REF]; in [START_REF] Badescu | First and second law analysis of a solar assisted heat pump based heating system[END_REF][START_REF] Kuang | Experimental study on solar assisted heat pump system for heat supply[END_REF] some experimental and theoretical studies of a SAHP are presented. Lately the solar energy conversion into electricity, by means of photovoltaic modules placed on the house roof, is widely used, but the PV module electric efficiency is about 15% and the greater part of solar radiation is converted into heat. Hence, the hybrid photovoltaic/thermal systems (PV/T) have been designed to recover contemporaneously electrical and thermal energy.

Several experimental and theoretical studies have been realized on the PV/T systems

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

3 [8;12-13]. Moreover, the photovoltaic heat pump is also a promising technology, where the photovoltaic collector is used as evaporator [START_REF] Pei | Performance of a solar assisted heat pump using photovoltaic evaporator[END_REF]; it is possible to use the evaporator refrigeration effect to cool the solar cells with a photovoltaic efficiency increase. The solar radiation is partially transformed into electric energy by photovoltaic modules, while most of it is absorbed from the refrigerant fluid whose values of pressure and temperature rise during the day with a heat pump performances improvement. In cold winter the PV collector protects the evaporator from frosting. This paper aims at studying the dynamic model of a heat pump whose evaporator works as a PV collector.

The model results have been obtained referring to the PV evaporator and the plant operating as heat pump, in terms of evaporator temperatures, refrigerant fluid properties in the cycle fundamental points, thermal and mechanical powers and efficiencies that characterize the plant performances. This analysis allows to compare from the thermoeconomic point of view a PV heat pump with a traditional plant under the same operating conditions.

Description of the photovoltaic heat pump

In the model analysed, the plant works as photovoltaic heat pump (Figure 1) and is mainly made up of a variable speed compressor, an electronic expansion valve, a platetype water condenser, a PV evaporator that works in parallel with an air evaporator; the refrigerant fluid is R22. The main component is the PV evaporator that consists of: covering glaze, photovoltaic modules, thermal absorber plate, refrigerant tubes and insulator. The removable covering glaze allows both to decrease the outward thermal

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dispersions of the collector superior surface and to assure mechanical protection; besides, it operates also as concentrating lens. An air gap allows a good thermal insulation and, instead of air, other insulators could be used. The photovoltaic modules are placed on the absorber plate superior surface, connected by means of gluing with high conductibility resins. The materials used for the photovoltaic cells are mainly the single-crystal silicon, the polycrystalline silicon or the amorphous silicon that differ both in terms of electric performances and manufacture costs. A limited energy conversion is possible, in fact only 5÷15% of the solar radiation incident on the collector is transformed into electric energy according to the material and temperature of the panels and the solar radiation incidence angle. To obtain a high thermal and electric insulation, the modules are laminated and subjected to pressure together with a double layer of TPT, that protects the cells from the weather, and EVA that acts as adhesive between TPT and cells. The thermal absorber plate consists of a thin layer that allows a high solar radiation absorption; the materials more used are aluminium, copper and steel. The refrigerant tubes are usually placed in the photovoltaic modules middle to optimize the thermal exchange. The insulator, placed on the collector inferior surface, aims at decreasing the outward thermal dispersions and avoiding the condensate formation; for this reason materials with a low thermal conductivity are used, as foam polyurethane and polystyrene. The whole collector is assembled in a light loom, generally realized in aluminium, and is placed on a steel frame to fix the position according to the chosen tilt angle to tap the higher sun energy. The dimension of each

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module considered is 1.3 m 2 with a peak power of 0.18 kW p , and the photovoltaic cells total area is about 7.2 m 2 . Photovoltaic cells in single-crystal silicon have been considered with an electric efficiency of about 15%. Moreover, the following working conditions have been used in the model: a removable covering glaze with high transmittance, a thermal absorber plate in aluminium with high absorption coefficient, copper tubes with high conductibility, an insulating layer of foam polyurethane, the tubes pitch equal to 150 mm, tilt angle equal to 30°, south orientation of the panels and environment data related to Southern Italy. The panels electric terminals are linked to an inverter able to transform the direct current available into alternate current at 220 V, that can be either introduced into the grid, with an outlet electricity meter, or used to supply the compressor or stored in a battery where it could be taken overnight or during cloudy days. Generally, when the water cooled condenser operates, the circulating water might support space heating and domestic water heating through specific heat exchange devices that in the model have been simulated by a tank that feeds water to the condenser. The water mass flow rate is about 0.2 kg/s; the water temperature is variable in the range 30÷55°C. When the water temperature changes there is a control that fixes the set point required.

Model of the photovoltaic evaporator and heat pump

Evaporator

The PV evaporator has been considered as a system that consists of different layers that exchange thermal energy and are identified according to a nodal approach. The energy

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balance equations for each layer are related to: covering glaze node, photovoltaic modules plate node, thermal absorber plate node, refrigerant tube node, refrigerant node and inferior insulator node (Figure 1).

Covering glaze node

1 ε 1 ε 1 ) T (T σA ) T (T A h ) T - T ( A G α ) T (T A h
) m c h A (T T ) h A (T T ) (ατ) G L 1 1 dt 1 ε ε - = - + + - + - + - & & (2)
Thermal absorber plate node

) T (T A h ) T (T A h ) T (T A h dt dT c m b i ib bi b p bp bp b t bt bt b b b - + - + - = (3) Refrigerant tube node ) T (T A h ) T (T A h ) T (T A h ) T (T A h dt dT c m t p pt pt t r rt rt t i it it t b bt bt t t t - + - + - + - = (4) Refrigerant node t t t t,r t,r t r ev dT m c h A (T T ) Q dt = - -+ & (5)
Insulator node

) T (T A h ) T (T A h ) T (T A h dt dT c m i a ai ai i t ti ti i b bi bi i i i - + - + - = (6)
Related to the model equations some terms have been determined:

-                 - - = 2 g 2 1 g g R θ sen 1 Λs exp τ
is the glaze transmittance (Bouguer law) where the glaze extinction coefficient (Λ) is equal to 4, the glaze covering thickness (s g ) is equal to 4mm, θ 1 =45° and R g =1.5÷1.8.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 7 - g pv pv EVA p R ) ( ) ( α - - α τ = ατ 1 1
is the actual absorption coefficient of the photovoltaic modules plate [START_REF] Duffie | Solar Engineering of Thermal Processes[END_REF], where

r 1 r 1 EVA + - = τ
is the EVA transmittance coefficient and

) ( tan ) ( tan ) ( sen ) ( sen r θ - θ =
is the refractive index.

-A ag =A gp =A pb = A ai =A, and the areas A ti , A ib , A bt , A tr of the contact surfaces have been determined in terms of the tube outer diameter (D o ), the A value, the photovoltaic collector width, the tube length.

-m g =48 kg and c g =0.67 kJ/kgK, m p =21 kg and c p =0.71 kJ/kgK, m b =25 kg and c b =0.88kJ/kgK, m t =5.8 kg and c t =0.39 kJ/kgK, m i =6.6 kg and c i =1.4 kJ/kgK.

The unitary conductive conductances of the photovoltaic modules, the absorber, the refrigerant tube and the insulator have been determined in terms of the respective thermal conductivities and thicknesses (s b =2 mm; s p =1.95 mm; s i =20 mm; D i =6 mm; D o =8 mm). As for the heat exchange between covering glaze and insulator with outdoor air, the unitary convective conductances have been determined in terms of air velocity [START_REF] Watmuff | Solar and wind induced external coefficients for solar collectors[END_REF]. The refrigerant fluid at the evaporator outlet, whose temperature depends on the I and T o values variable with the time, is generally considered in the model in superheated vapour conditions, as it absorbs solar energy and fully evaporates in the PV heat exchanger. The evaporation power depends on the daily variation of the solar radiation intensity, the PV evaporator area and the thermal efficiency [START_REF] Pei | Performance of a solar assisted heat pump using photovoltaic evaporator[END_REF].

Condenser

Referring to the condenser, differential equations of the first order have been considered, where the unknowns are the refrigerant and water temperatures at the

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condenser outlet; the first member presents a store term, the second member the input and output thermal fluxes:

tc tc tc tc,r tc,r r tc co dT m c h A (T T ) Q dt = - -& (7)
w,out w w co w w w,out w,in

dT m c Q m c (T T ) dt = - - & & (8)
where co Q & is the condensation power, determined by means of the heat exchanger design equation [START_REF] Fu | Dynamic simulation of air-to-water dualmode heat pump with screw compressor[END_REF], m t,c =13.5 kg and c tc =0.39 kJ/kgK. The refrigerant fluid at the condenser outlet is generally in subcooled liquid conditions.

Compressor and expansion valve

The compressor suction and discharge temperatures are linked by the equation:

ε co 2 1 ev P T =T P       (9)
and the refrigerant mass flow rate is equal to:

1 v nV m v r η = &
. As for the expansion valve the equation considered is:

) p p ( 2ρ A H m ev co 3 va va r - = & (10)
where the evaporation and condensation pressures are obtainable by means of the software Refprop [START_REF]Reference Fluid Thermodynamic and Transport Properties Database (REFPROP): Version 8[END_REF] and H va is the valve characteristic constant.

Thermoeconomic analysis

As for the PV heat pump performances, the daily solar radiation allows an energy and costs saving in comparison with a traditional heat pump working under the same conditions. In particular, the compressor and the evaporator are the PV heat pump components principally influenced by the solar radiation. In order to compare the

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photovoltaic and traditional heat pump performances from the thermoeconomic point of view, it is possible to use the following equation [START_REF] Kotas | The Exergy method of thermal plant analysis[END_REF]: [START_REF] Kuang | Experimental study on solar assisted heat pump system for heat supply[END_REF] where C tot (€/year) is the total cost, x k is the optimization variable (solar radiation), F tot (kW) is the external resource, or fuel, consumed by the system (electric power required by the compressor, whose variation corresponds to the compressor destroyed exergy variation [START_REF] Kotas | The Exergy method of thermal plant analysis[END_REF]), c F (€/kWh) is the fuel cost per unit exergy (unit cost of the compressor electric energy), t (h/year) is the working time, ν (1/year) is the amortization coefficient, C k (€) is the generic component cost. A finite difference form of the Eq. 11 is:

        ∂ ∂ +         ∂ ∂ = ∂ ∂ k k k tot F k tot x C ν t x F c x C
k tot F tot ∆C t ∆F c ∆C ν + = (12)
The Eq. 12 allows to compare from the thermoeconomic point of view the working of the photovoltaic and traditional heat pumps, and then to calculate the economic indexes SPB, DPB and NPV [START_REF] Bejan | Thermal Design and Optimization[END_REF]. Moreover, the heat pump COP, the electric, thermal and global efficiency values of the photovoltaic module are equal to:

cp co hp L Q COP & & = ; c pv el IA L η & = ; c ev t IA Q η & = ; c pv ev tot IA L Q η & & + = (13)
where the electrical efficiency depends on the solar cells efficiency and covering factor values, and the PV plate absorption and transmittance coefficients; the photovoltaic power depends on electrical efficiency, solar radiation intensity and collector area [START_REF] Zondag | The thermal and electrical yield of a PV-thermal collector[END_REF].

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Results and discussion

The PV evaporator model consists of six first order linear differential equations whose unknowns are the layers temperatures. The nodal approach and homogeneous properties for each layer, related to density and temperature, are considered without evaluating the spacial distribution. Each equation has as first member the store term, and then the temperature variation with the time, and as second member the thermal and electrical energy fluxes; the photovoltaic energy terms are only present in the covering glaze and solar cells equations. In order to solve the photovoltaic heat pump dynamic model, a program realized with the Matlab software [START_REF] Matlab | [END_REF] has been used with some simplifying hypotheses; the model flowchart is reported in Figure 2. The system input data are the solar radiation intensity and the environment temperature (Figure 3) that influence the photovoltaic and evaporation powers. These data are related to a typical temperature of the month of November in Southern Italy [START_REF]The Italian National Agency for New Technologies[END_REF], but other values of I and T o can be considered in the model. The evaporator input data are: collector layers thickness (s i ), outside (D o ) and inside (D i ) diameters of the evaporator tube with its pitch (z), tube length (L t ) evaluated in terms of the step with the tubes arrangement in the modules prevalent direction, total and effective areas of the PV collector, mass (m i ) and specific heat (c i ) of the evaporator layers and the condenser tube, tilt and azimuth angles, evaporator components density (ρ i ), conductive conducibility (k i ) and unitary convective conductance (h i ), air velocity (u a ), glaze absorber plate and solar cells emissivity, solar cells efficiency and covering factor (β cf ) values, heat exchangers

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compressor and expansion valve input data. In the simulation the outdoor temperature has been chosen as initial value of the evaporator nodes temperatures, and the superheating and undercooling values are varied until the refrigerant mass flow rate determined by the Eq.10 is equal to the value obtained by the evaporator energy balance. The PV evaporator layers temperatures have been determined (Figure 4) referring to operating hours included among eight in the morning and four in the afternoon, when the gain of electric and thermal energy is possible and larger. In particular, all temperatures follow the parabolic trend of I and T o , and reach the maximum value around noon. In Table 1 the daily variation of the absorber plate temperature according to the photovoltaic cells covering factor (β cf ) value, has been reported. A higher value of β cf results in more solar energy converted into electricity; hence, the mean absorber plate temperature decreases and the PV module electric efficiency increases because of the more favorable temperature conditions. As for the refrigerant fluid operating in the PV heat pump, the properties values are reported in Table 2. It can be observed that the evaporation pressure varies during the day like the evaporation temperature and the solar radiation intensity, and reachs the maximum value around noon. Besides, the thermal energy absorbed from the PV evaporator allows higher condensation power and temperature values. The compression ratio and refrigerant mass flow rate values vary with time, depending on the evaporation and condensation pressures and the water temperature. Hence, the heat pump COP improves when the solar radiation enhances the condenser capacity and the evaporation

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temperature and pressure values; in Figure 5 the values of the compressor input, evaporation and condensation powers and the COP are reported to represent the PV heat pump global performances. It has been useful to validate the system performance by means of experimental data available in literature in order to give greater credibility to the thermoeconomic model described in this paper. In [START_REF] Pei | Performance of a solar assisted heat pump using photovoltaic evaporator[END_REF] an experimental heat pump, whose evaporator works as PV collector, is presented. In particular, in addition to the operating conditions analyzed in this paper, the model has been also made to run under the same working conditions of the experimental tests realized in [START_REF] Pei | Performance of a solar assisted heat pump using photovoltaic evaporator[END_REF] in terms of solar radiation intensity, environment temperature, collector characteristics, water temperature and refrigerant fluid; in [START_REF] Pei | Performance of a solar assisted heat pump using photovoltaic evaporator[END_REF] the water temperature rises to 55°C. By running the model in the same range of water temperatures, average values of the condensation power and the COP have been obtained with a percentage deviation of about 6% from the experimental values [START_REF] Pei | Performance of a solar assisted heat pump using photovoltaic evaporator[END_REF]; the precise comparison also for fixed hours of the day leads to similar percentage deviations.

The main aim is to compare the traditional and PV heat pumps by means of a thermoeconomic analysis; the principal difference between the two systems is represented by the PV evaporator. The PV system is more convenient than the traditional system from the energy point of view, because it can reduce or even eliminate the compressor electrical consumptions both directly and indirectly. In the direct way the compressor is powered by photovoltaic modules independent of the national grid. The solar radiation intensity increase can indirectly improve the

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13 compressor and heat pump performances, by increasing both the condenser capacity and the evaporation temperature that determines a decrease of the compression ratio and the compressor electric consumptions from eight in the morning and noon. It results in a reduction of the compressor destroyed exergy and then of the electric power required by the compressor [START_REF] Kotas | The Exergy method of thermal plant analysis[END_REF]. Referring to a sunny day, in Figure 6 it is shown that the highest exergy losses occur in the PV evaporator and the compressor, followed by the condenser and expansion valve respectively. The components efficiency defects decrease gradually from early in the morning to noon. In particular, the higher I and T o values and the lower set value of the T w are all advantageous for improving the compressor performance. The PV evaporator operating at lower temperatures results in more exergy loss; the higher evaporation temperature is preferable. Hence, the Equations 11 and 12 allow to compare from the thermoeconomic point of view and under the same working conditions, the traditional and photovoltaic heat pumps. The main photovoltaic heat pump components not included in a traditional heat pump are PV evaporator, inverter and accumulator that involve higher initial costs, but allow to use electricity throughout the year. The economic results obtained in this paper take into account the costs deduced by the literature because there is not a mass production of the described system yet. In particular, the overall PV system cost is about 400 €/m 2 [START_REF] Volker | Technical and economical system comparison of photovoltaic and concentrating solar thermal power systems depending on annual global irradiation[END_REF] that takes into account installation and operating costs. The electric power generated by PV panels might be either introduced into the national grid or used to supply the compressor or stored in an accumulator, where it could be taken overnight or during

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ACCEPTED MANUSCRIPT 14 cloudy days. This analysis takes into account the energy incentive proceeds in favour of the photovoltaic systems, provided by [24] and equal to about 0.40 €/kWh el . The PV evaporator of 1 kW p,el , considered in this paper, allows to obtain both electric annual gain and heat gain. The heat gain during the day is fully used in winter for domestic hot water and in summer if the PV evaporator works instead of the air cooling evaporator.

In particular, the heat gain allows during a sunny day, but not at night or when it is cloudy, both an increase of the evaporation and condensation powers and a compressor electrical power decrease. This allows a higher COP and a compressor electric power consumption lower in comparison with a traditional heat pump. Hence, the electricity, that comes from the electric annual gain and the electric power saving obtained from the heat gain, allows both to heat domestic hot water all year and cool in summer without the need of the national grid. In particular, Figure 5 and Table 1 show respectively the values of the compressor power consumption and the photovoltaic power together with the PV evaporator electric and thermal efficiencies values. In particular, the compressor power varies in the range 0.41÷0.46 kW, and the compressor daily electricity consumption is 3.9 kWh el . The PV output power varies in the range 0.25÷0.87 kW and the total daily electricity is 5.3 kWh el,pv ; as every sunny day there is an electricity surplus of about 1.4 kWh el , the system is able to operate in a self-sufficient manner.

Hence, the PV evaporator of 1 kW p,el , considered in this paper, is capable of producing in Southern Italy about 1500 kWh el /year. This is, for example, the average electric energy demand of a traditional heat pump to heat the domestic water and to cool in

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summer, related to a typical Southern Italy house of about 80 m 2 occupied by four people with a demand of about 200 1/day of hot water, whose temperature difference is 30°C, and 400 hours of summer conditioning with a cooling load of about 25 W/m 3 [START_REF]The Italian National Agency for New Technologies[END_REF]. Hence, a PV evaporator of 1 kW p,el allows to meet the demands for domestic hot water and summer cooling, with an air evaporator that works in parallel with the PV evaporator, referring to domestic consumers of Southern Italy where the solar radiation intensity is higher [START_REF]The Italian National Agency for New Technologies[END_REF]. Finally, in the thermoeconomic analysis all the electricity obtained or saved with a PV evaporator of 1 kW p,el , both for heating domestic water and for summer cooling, has been considered. Referring to an amortization coefficient of 0.08 1/year, a discounting back rate of 0.05 and twenty five years the plant life, the economic indexes SPB and DPB have been determined (Figure 7). Under these conditions the cost surplus of the PV heat pump considered in this paper is equal to about 3200 € [START_REF] Volker | Technical and economical system comparison of photovoltaic and concentrating solar thermal power systems depending on annual global irradiation[END_REF], but the PV modules costs are changing and therefore an economic sensitivity analysis has been realized varying the PV system cost between 2800 € and 3600 € (Figure 7). In Figure 8 the NPV values related to a PV system cost of 3200 € are reported. In particular, the NPV is positive after about four years; generally, it depends on the plant location and efficiency.

Conclusions

Aim of this paper has been the study of a photovoltaic heat pump model from the energy, exergy and economic point of view. The analytical model has been solved by means of a program realized with the Matlab software using some simplifications. The

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model results have been obtained related to the PV evaporator and heat pump in terms of the evaporator layers temperatures, the refrigerant fluid properties in the main cycle points, the thermal and mechanical powers and the efficiencies that characterize the plant performances. The theoretical results have been also compared with some experimental values available in literature pointing out a low percent deviation. This PV system could also operate where the electric energy is not available. Moreover, this study has allowed to compare the traditional and photovoltaic heat pumps under the same working conditions; the PV heat pump COP is higher respect to a traditional plant.

In particular, a thermoeconomic analysis has been carried out in terms of exergy destruction rates and economic indexes. Finally, all electricity obtained or saved with a PV evaporator of 1 kW p,el , and used both to heat the domestic water and to cool in summer, has allowed to meet the PV evaporator cost with a SPB of about four years.

Nomenclature

Tables captions

Table 1 Data related to the photovoltaic evaporator

AFigure 1 .Figure 2 .Figure 3 .

 123 Figures captionsFigure1. Heat pump and photovoltaic evaporator scheme

Figure 4 .Figure 5 .Figure 6 .Figure 7 .

 4567 Figure 4. Photovoltaic evaporator temperatures determined by means of the model

Figure 1 .Figure 2 .

 12 Figure 1. Heat pump and photovoltaic evaporator scheme

Figure 3 .Figure 4 .Figure 5 .Figure 8

 3458 Figure 3. Solar radiation intensity and outdoor temperature values

-

Table 2

 2 Properties values of the refrigerant fluid in the main cycle points

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Table 1

 1 Data related to the photovoltaic evaporator

		outdoor conditions	photovoltaic evaporator	adsorber plate temperature
	hour T o (°C) I (W/m²)	η el	η t	L pv (kW) T b (βcf= 0,5) T b (βcf= 0,7) T b (βcf= 0,9)
	8	11,9	250	0,138	0,823	0,248	14,7	14,3	13,8
	9	14,5	480	0,138	0,654	0,476	20,3	19,7	19,3
	10	16,7	674	0,139	0,553	0,674	26,0	25,5	25,1
	11	18,5	804	0,140	0,528	0,810	30,8	30,4	29,9
	12	19,6	850	0,142	0,520	0,868	33,6	33,0	32,6
	13	20,0	807	0,140	0,528	0,813	31,6	31,1	30,7
	14	19,6	677	0,139	0,565	0,677	27,1	26,7	26,1
	15	18,6	483	0,138	0,653	0,479	21,8	21,3	20,7
	16	16,8	253	0,137	0,843	0,249	15,6	15,2	14,7

Table 2

 2 Properties values of the refrigerant fluid in the main cycle points

			refrigerant fluid properties		₄
	hour p ₁ (Mpa) p ₂ (MPa) T				(°C)
	8	0,653	1,29	12,5	51,0	30,2	8,5
	9	0,701	1,55	15,2	58,0	36,0	10,9
	10	0,758	1,81	18,0	64,3	42,3	13,7
	11	0,815	2,00	20,0	68,3	46,3	16,3
	12	0,839	2,06	21,0	69,4	47,4	17,2
	13	0,833	1,97	20,7	67,8	45,8	16,7
	14	0,798	1,75	19,3	62,9	40,9	15,5
	15	0,741	1,53	17,0	57,4	35,4	12,8
	16	0,674	1,32	13,8	51,7	30,1	9,5

₁ (°C) T ₂ (°C) T ₃ (°C) T

Performances evaluation of the heat pump:

  T g , T p ,T b, ,T t ,T i ,T 1 . , p ev , s 1 , s 2 , s 3 , s 4 , h 1 , h 2 , h 3 , h 4 , ex 1 , ex 2 , ex 3 , ex 4 .

				START
				Input data
				ΔT su,i , ΔT un,j
		PV/T evaporator model:
	i=i+1 and/or j=j+1	Condenser model: T 3 , T w . Compressor model: T 2 . Expansion valve model: T 4 .
		p
	no	m 	r	(eq.10)		m ' r 	(		Q ev 	h)  /
						yes
				END

co Q  , pv L  , COP hp , δ k , η ex , SPB, DPB, NPV. co

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