Transient simulation of polygeneration systems based on PEM fuel cells and solar heating and cooling technologies

Energy 41 (2012) 18e30

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Transient simulation of polygeneration systems based on PEM fuel cells and solar heating and cooling technologies Francesco Calise a, *, Gabriele Ferruzzi a, Laura Vanoli b a b

DETEC e University of Naples Federico II, P.le Tecchio 80 80125 Naples, Italy DIT e University of Naples “Parthenope”, Centro Direzionale IS.5, 80143 Naples, Italy

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 September 2010 Received in revised form 6 May 2011 Accepted 14 May 2011 Available online 17 June 2011

This paper presents a dynamic simulation of an innovative polygeneration system based on solar heating and cooling and PEM fuel cells technologies. The polygeneration system is based on the following main components: evacuated solar collectors, single-stage LiBreH2O absorption chiller and a PEM fuel cell. The fuel cell operates at full load producing electrical energy which is in part consumed by the building lights and equipments. The fuel cell is grid connected in order to perform a convenient net metering. Finally, the system also includes heat exchangers producing domestic hot water in case of scarce space heating/cooling demand. The analysis was carried out by means of a transient simulation model, developed using TRNSYS software and includes the investigation of the dynamic behavior of the building, developed in TRNBUILD. A small university hall, including also a fitness center, was adopted as test case. Energetic and economic models were also developed, in order to assess primary energy savings and the operating and capital costs of the systems under analysis. The results of the case study were analyzed on monthly and yearly basis, paying special attention to the energetic and monetary flows. The results are excellent from the energy saving point of view. On the other hand, the pay back periods can be profitable for the final user only in case of significant public funding. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Solar energy Fuel cell Polygeneration

1. Introduction The well known growth in world energy demand and population is forcing research toward more efficient energy conversion devices. A strong impulse to this scope has been given by new emerging energy-efficient technologies and by regulatory incentives related to energy production from renewable sources and environmental friendly systems [1]. In this framework, polygeneration technologies show a significant potential in terms of energy savings and reduction of CO2 emissions, due to their implicit peculiarities, such as: maximum utilization of energy and natural resources, reduction of unit cost of products and reduction of environmental burden [2]. Polygeneration, or multi-generation, is usually defined as the combined production of multiple energy vectors (e.g. electricity, cool, heat, etc) and/or products (e.g. hydrogen, methanol, etc) using natural resources (fossil fuels, wood, etc) and/or renewable energy sources (solar, wind, biomass, etc). Hence, the simplest example of polygeneration is combined heat and power generation, CHP, also called cogeneration. In the case of combined heat, cool and * Corresponding author. Tel.: þ39 817682301; fax: þ39 812390364. E-mail address: [email protected] (F. Calise). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.05.027

electricity production, polygeneration devices are defined as trigeneration systems. Cogeneration and trigeneration technologies are well known and widely adopted for industrial, residential and commercial applications [1,2]. In particular, very promising is also the small-scale cogeneration (micro-cogeneration) for residential applications. In fact, when micro-cogeneration is based on efficient energy conversion devices (such as fuel cells) and the demand of thermal energy is significant, the energy and monetary savings may be very high [3,4]. An additional impulse regarding the analysis of polygeneration systems is also given by the studies concerning distributed generation. In fact, several papers available in the literature [1] assess that small scale (below 1 MWe) distributed polygeneration systems are useful since they: i) promote energy efficiency and renewable sources; ii) can defer investments on large power plants; iii) promote the use of local energy resources, reducing energy dependency and increasing the reliability of the electrical systems; iv) contribute to reduce the impact of fuel supply infrastructures also reducing transmission losses; v) bring into play the local emission problem. Usually, polygeneration systems e adopted in distributed generation e are classified on the basis of: i) engine technology (reciprocating engines, micro gas turbines, fuel cells); ii) bottoming

F. Calise et al. / Energy 41 (2012) 18e30

Nomenclature

Lowercase roman Letters Concentration c* Natural Gas cost [V/Sm3] cNG Electrical Energy cost [V/kWh] cEE i Current density [mA/cm2] l Cell Thickness[cm] Partial pressure [Pa] p* Electrical Energy price [V/kWh] pEE t temperature [ C] Uppercase roman Letters A Area [m2] Solar Collector Field Area [m2] ASC Total PEM thermal capacity [kJ/K] Ct Operating Costs [V/year] Cop COP Coefficient of Performance Electrical energy for auxiliaries [kWh] Eaux Electrical energy for building lights and equipments Eel,b [kWh] Electrical energy produced and sold to the grid [kWh] Eel,þ Electrical energy purchased from the grid [kWh] Eel, Electrical energy produced by the PEM [kWh] Eel,PEM Nernst Open Circuit Voltage [V] ENernst Solar Fraction Fsol Total radiation [W/m2] IT J Capital cost [V]

devices (absorption or electrical chillers); iii) auxiliary devices (heaters, gas-fired absorption chillers or heat pumps, engine-driven chiller); iv) eventual renewable energy source (solar, biomass, wind, hydro); v) eventual products (ethanol, hydrogen, etc). Thus, it is clear that a large number of possible system layouts of polygeneration systems can be identified. Among them, this paper is focused on fuel cell technology combined with absorption chiller and the use of solar energy. This kind of system was diffusely investigated in the literature, but from a different point of view with respect to the idea presented in this paper. In fact, in the literature the production of hydrogen using solar energy and its consequent use in fuel cells and/or storage is mainly analyzed [5]. Shapiro et al. designed and built a prototype of a photovoltaic solar-powered regenerative PEM-electrolyzer, demonstrating the system feasibility and characterizing system performance [6]. A similar study was performed by Hedstrom, showing the experimental and numerical performance of a PEM fuel cell fed by hydrogen produced both by photovoltaic cells/electrolyzer and by reformer, fed by biogas [7]. Hence, all the above mentioned papers are focused on the combination of PEM fuel cells and photovoltaic collectors. To the authors’ knowledge, literature did not show any significant paper analyzing the possibility of integrating fuel cells and solar thermal collectors. Thus, this paper aims at covering this lack, developing a transient simulation model of a polygeneration system capable to produce electricity, cool and heat, powered by solar energy and natural gas fueling an externally reformed PEM fuel cell. The concept of the system under investigation comes from the combination of solar heating and cooling (SHC) systems [8e24] e including evacuated tube solar collectors and single stage absorption chillers e and cogenerative PEM fuel cells as auxiliary system. The basic concept of the SHC lies in the possibility of using the solar

LHV PE Q_ Qc Qh QDHW Qt,PEM Relectronic Rproton Rt T V Vcell

19

Natural gas Lower Heating Value [kWh/Sm3] Primary Energy [kWh] Heat Flow [kW] Space cooling energy [kWh] Space heating energy [kWh] Thermal energy for DHW production [kWh] Thermal energy produced by the PEM [kWh] Electronic Resistance [U] Proton Resistance [U] Total cell thermal resistance [K/W] Temperature [K] Volume [m3] Fuel cell voltage [V]

Greek letters hel,t Conventional electric efficiency hb Boiler efficiency hel,PEM PEM electrical efficiency ht,PEM PEM thermal efficiency hact Activation Overvoltage [V] hohmic Ohmic Overvoltage [V] hconc Concentration Overvoltage [V] hSC Solar Collector efficiency w Time [s] subscripts in inlet amb ambient loss losses to the environment

radiation to provide space heating during the winter and space cooling in the summer, using a heat-driven (absorption, adsorption, etc) chiller. SHC is a very promising technology, especially in summer operation mode, when the maximum demand for cooling coincides with the maximum availability of solar radiation. SHC may significantly contribute to achieve the goals in terms of energy savings, greenhouse gas emissions reductions and increase of use of renewable energy sources, including those stated by the EU Directive 2009/28/EC. Usually, the auxiliary energy, required in case of scarce solar irradiation, is supplied by a gas-fired heater [8,12]. However, such configuration may significantly decrease both energetic and economic performance of the considered system. In fact, several studies showed that the selection of the appropriate auxiliary system is a key point for the development of this technology. In particular, the adoption of different configurations of electric heat pumps, as auxiliary system, can significantly improve system performance [9e11]. Therefore, on the basis of the above mentioned works, the authors here present an additional innovation, aiming at improving the energy and economic profitability of the SHC technology. In particular, in this work, the auxiliary heat is provided by a cogenerative PEM fuel cell, also producing electrical energy for user and electrical grid. This particular layout can be considered very innovative, since the majority of the papers available in literature about this topic, consider traditional auxiliary devices (electric chillers, gas-fired heater, biomass heaters etc) [13,14,22,25,26], and none of them analyzes the possible combination between solar cooling technology and cogenerative fuel cells, under investigation in this paper. The considered system layout was developed and dynamically simulated in TRNSYS environment. The model is partly based on the

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F. Calise et al. / Energy 41 (2012) 18e30

work recently published by one of the authors [10], but it includes some important innovations, as shown in the following sections, such as fuel cell model and net metering models. The model allows one to calculate the time-dependent energy flows and key-point temperatures. It also includes a module which allows one to evaluate the energetic performance and to calculate system economic performance parameters. 2. System layout The system layout considered in this work is based on the combination of well-known SHC and fuel cells technologies. It is capable to produce electricity, space heating or cooling, and domestic hot water all over the year, according to users’ demand. The considered system layout was derived from the one presented in a previous work [10], appropriately modified for the integration to the PEM fuel cell. Regarding SHC technology, several studies showed that the most promising configuration is based on the coupling of evacuated tube solar collectors with single-stage LiBreH2O absorption chillers [2]. Usually, the auxiliary energy to be used in case of scarce solar irradiation is supplied by a gas-fired auxiliary heater. However, as above discussed, the use of low-efficiency auxiliary heaters may significantly decrease system efficiency [9,11]. Thus, in order to maximize system performance, in this work the auxiliary heat was assumed to be provided by a cogenerative fuel cell. In particular a PEM fuel cell was selected since: i) the operating temperature is suitable for the typical operating temperatures of evacuated solar collector and single-stage absorption chillers; ii) it is recognized as the most mature fuel cell technology commercially available. In order to maximize the thermal utilization of the fuel cell, the solar collectors field was designed in order to satisfy only a part (approximately 30%) of the maximum cooling load of the building. In fact, the use of a larger solar field would decrease the amount of heat produced by the fuel cell and effectively used for space heating and cooling. In addition, the operating temperatures of the combination of solar collector, PEM fuel cell and absorption chiller must be accurately evaluated. In fact, a good operation of the absorption chiller can be achieved when the hot fluid inlet temperature is higher than 75  C. On the other hand, PEM operating temperature is usually around 80  C, in order to prevent membrane degradation. Finally, solar collectors outlet temperature is extremely variable but it may be also higher than 90  C. Therefore, for maximizing the utilization of PEM cogeneration heat, a series arrangement between solar collectors, PEM cogenerative heat exchanger and absorption chiller is strictly required. Note also that this arrangement is not expected to reduce solar collector temperature potential. In fact, previous studies [10,11] showed that the set point outlet temperature of the solar collector must be selected as the minimum value required to drive the absorption chiller. In fact, the higher the solar collector temperature, the higher the loss to the environment [10,11]. On the basis of these considerations the layout shown in Fig. 1 was adopted. It consists of 5 different system loops, solar collector water (SCW), hot water (HW), cooling water (CW), domestic hot water (DHW) and chilled/hot water (CHW), respectively. The SHC system consists of the following main components:    

a solar field with evacuated-tube collectors (SC); a hot water inertial storage tank (TK1); a LiBreH2O single stage absorption chiller (ACH); a PEM fuel cell (FC), providing auxiliary heating energy for both cooling and heating needs and simultaneously generating electrical energy for user demands and/or for the electrical grid;

Fig. 1. System Layout.

 a closed circuit cooling tower (CT), providing cooled water to the condenser of ACH;  a fixed-volume pump (P1) for the HW loop, pumping water from TK1 to FC or to the ACH or to the building;  a variable speed pump (P2) for the SCW loop;  a fixed-volume pump (P3) for the CW loop;  a fixed-volume pump (P4) for the CHW loop;  an inertial chilled/hot water storage tank (TK2);  an hydraulic separator (HS), balancing fluid flows between the primary and secondary hydraulic circuits;  a plate-fin heat exchanger producing Domestic Hot Water (HE);  pipes connecting the HS with the fancoils of the zones of the building. Note that the PEM fuel cell is equipped with a complex control system, described in the following section, which manages different diverters and mixers, in order to cool the cell and heat up the HW simultaneously. The control system can also manage eventual DHW in order to supply additional cooling to the cell in case of high temperature of HW entering the cell. The TRNSYS scheme used to simulate the system also includes several additional components (not displayed in Fig. 1), such as: controllers, schedulers, weather database, etc. The basic operating principle of the SHC system is relatively simple: the solar irradiation incident on the SC field increases the SC outlet temperature up to the fixed set point, determining the consequent increase of water temperature in the storage tank TK1. In case of scarce request of building cooling or heating energy (and/ or in case of high solar radiation), the temperature of the fluid exiting the SC may overcome the fixed set point. In this case, the fluid is cooled down to the fixed set point by the heat exchanger HE, which converts this additional SC useful energy to DHW to be used through showers installed in the building. During the summer operation, the hot fluid drawn by P1, from the top of TK1, supplies the ACH, which produces the chilled water (CHW) required for building cooling. The CT provides the cold water required to cool the ACH. The cogenerative PEM fuel cell operates at full load from 8.00 am to 6.00 pm, all year long, except for Sundays. The fuel cell is located upstream of the ACH and provides additional heat in case of scarce solar irradiation. Conversely, when TK1 outlet temperature is higher than the fixed set-points (different values in summer and winter operations are considered, as shown in Table 1), the PEM cogenerative heat exchanger is used to produce additional domestic hot water. During the heating season, the water exiting

F. Calise et al. / Energy 41 (2012) 18e30 Table 1 SHC main design parameters. Parameter

Unit

ASC, Collector area Collector slope TK1 Volume per Collector Area TK1 Volume TK2 Volume P4 Flow rate P2 Flow rate SC outlet winter set point temp. SC outlet summer set point temp. DHW Set point temp. PEM wint. DHW Set point temp. PEM sum. AHP nominal cooling capacity

m2  2

m m3 m3 kg/h kg/h  C  C  C  C kW

200 30 54 l 10.8 2.0 43.0 103 92.1 103 50.0 90.0 45.0 71.5 375

the TK1 e and eventually passing through the PEM fuel cell e is sent directly to the HS. The TRNSYS model also includes a number of components required in order to simulate the control strategies of the components and of the whole system. Some of these innovative control strategies were previously discussed in references [9e11]. In the work here presented, additional control strategies were implemented in order to manage the cogenerative heat exchanger of the fuel cell. In particular, appropriate on/off controllers were used in order to manage mixers and diverters on PEM loop, required in order to activate DHW or HW heating by the cogenerative heat exchanger of the fuel cell. The building considered in the study is a small university hall, consisting of 7 classrooms (A1eA3, C1eC3) and a common area (B1). This building was previously used as test case in reference [10] where details regarding models and parameters are also available. This building is compliant with the requirements of Italian Law (D. Lgs. 311/06) in terms of walls and windows transmittances, system efficiency and primary energy consumption and is located in Naples, South Italy. The building was simulated in TRNSYS environment, using the TRNBUILD application, included in TRNSYS package. The transmittances of walls and windows are largely compliant with the limits of the Italian Law (Ulim). In fact, ground

21

internal wall, external wall and roof transmittances were respectively 0.313 W/m2K, 0.652 W/m2K, 0.339 W/m2K and 0.400 W/m2K. All the windows (transmittance of 1.574 W/m2K) are also provided with shadings, activated or reactivated when the external radiation is respectively 140 W/m2 and 120 W/m2. The occupancy (0.60 person/m2), light (10 W/m2) and the equipment load (5 W/ m2), the mechanical (3.8 Vol/h) and natural (0.30 Vol/h) air change, people sensible (130 kJ/h person and 333 kJ/h person, respectively in summer and winter) and latent (0.080 kg/h person and 0.035 kg/ h person respectively in summer and winter) load of the building is suggested by the Italian Standard (UNI 10339) [10]. Finally, the university hall was also assumed to be placed close to the university fitness center. Thus, the DHW produced by the system can be supplied to those showers all year round. The building electrical demand was simulated on the basis of the experimental load duration curve, measured for a similar existing building and shown in Fig. 2. Note that this Figure shows the electrical demand due only to equipments and lights. It was obtained by the total electrical demand, reduced of the electrical energy required to drive HVAC equipments. The winter set point temperature is established by the Italian Law at 20  C, whereas the summer set-point temperature is not ruled by Law and was arbitrarily set at 26  C. According to the Italian Law, the heating system operates from November 15th to March 31st. As for the summer, the operating period is not fixed by Law, and the interval from May 1st to October 21st was considered. The building was supposed to be occupied all year long, from Monday to Saturday, from 8.00 am to 6.00 pm.

3. Simulation model The model of the layout presented in the previous section can be considered as an improvement of the works previously performed by some of the authors on SHC systems [8e12]. These papers show the simulation models of many of the components included in the system layout presented in this work. Therefore, in the following special attention will be paid only to the new components included in the present layout, whereas only a brief description of the other

Fig. 2. Electrical load duration curve.

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F. Calise et al. / Energy 41 (2012) 18e30

components will be given. In particular, most of the components (SC, P1eP4, TK1, TK2, ACH and CT) of the polygeneration systems previously described were simulated using TRNSYS built-in library [27]. The other components (HS, PEM, fancoils, energy and cost savings), were developed by user-developed models. In particular, in this paper new models are presented for the simulations of: PEM fuel cell, energy savings, economic savings and profitability, electrical net metering. The majority of the simulation models of the components are based on a deterministic approach, calculating the energetic performance of the component on the basis of its geometry/materials and implementing appropriately energy and mass balances. This approach was adopted for important components such as: tanks, building, cooling tower, pumps, hydraulic separator and PEM fuel cell. On the other hand, some other component (e.g.: fancoils and ACH) is simulated using a data lookup approach. Obviously the first approach (deterministic thermodynamic model) is much more complex and computational-intensive with respect to a data lookup approach, based on some performance map of the component. However, the availability of these maps in function of all the required operating variables (e.g.: inlet temperature and flow rates, ambient temperature, etc) is very scarce. Therefore, the simulation of the components by a data lookup approach was limited only to the one whose operational performance data were extensively provided by the manufacturers. In the following, the simulation models are briefly described, paying special attention to the variables used as synthesis/design parameters in the subsequent parametric analysis. 3.1. Evacuated tube solar collectors (SC) The model of the SC is based on Type 71, included in TRNSYS package. Here, the thermal efficiency of the collectors is calculated using the Hottel-Whillier-Bliss equation [28].

hSC



2 tin;SC  tamb tin;SC  tamb ¼ a0  a1  a2 IT IT

(1)

The values of a0, a1 and a2 given in references [9,11]. Correction factors are introduced in the model, in order to account for: series connection, clouds, biaxial Incidence Angle Modifiers (IAM), etc [27]. SC are also equipped with a feedback controller managing a variable flow-rate pump, in order to achieve the desired set point temperature of the stream exiting SC. Further details regarding the proposed control strategies are given in references [9,11].

(TK2, modeled by Type 60) is used in the CHW loop to store chilled or hot water, respectively in summer and in winter. Their models are based on the assumption that the tanks can be divided into N fully-mixed equal sub-volumes. The tanks are also equipped with a pressure relief valve, in order to account for boiling effects [27,29]. The TK1 volume is fixed on the basis of the value selected for ASC:

VTK1 ¼

vTK1 ASC 1000

(2)

The TK2 volume is selected on the basis of the value of the building peak cooling load. 3.4. Absorption chiller (ACH) A single-effect hot water LiBreH2O ACH was considered. The component is simulated by the TRNSYS Type 107 which uses a normalized catalog data lookup approach [28]. In fact, some thermodynamic models of the considered absorption chiller are also available in literature [16,21]. However, they are very complex and their implementation would have determined a dramatic increase of the computational time. In addition, such thermodynamic models must be calibrated and validated using experimental data. As a consequence, a data lookup approach was selected since it allows one to achieve both good accuracy and fast calculation time. Here, the performance data were modified in order to comply with the data sheet of a 375 kW single-stage H2OeLiBr hot water driven absorption chiller. The performance data are numerically expressed as a function of CHW, HW, CW inlet water temperatures, CHW outlet set-point temperature and of the cooling ratio factor and the input heat ratio factor, as shown in [28]. The performance data provide a map of the Coefficient of performance (COP) and cooling capacity of the ACH in function of the above mentioned operating parameters. 3.5. Cooling tower (CT) In this paper the TRNSYS Type 510 (closed-circuit cooling tower) was considered. The working fluid (CW) flows in a circuit which is physically separated from the ambient air and process water. The TRNSYS simulation code is based on the model proposed by Zweifel [30] that matches the manufacturers catalog data over a wide range of operating conditions. Cooling tower air mass flow rate, cooling capacity and CW mass flow rate are calculated using the equations reported in [11].

3.2. Pumps (P) 3.6. Heat exchanger The variable flow-rate pump, P2, is modeled on the basis Type 110. The 10 fixed-speed pumps (P1, P3, P4 and 7 zone pumps) are simulated using Type 3. Their simulation models are based on the energy and the mass balances [27]. The mass flow rate for P4 is related to the heating and cooling loads of the building, assuming a nominal temperature difference of 5  C, the nominal mass flow rate for P2 is related to the value selected for the SC surface area, the mass flow rate of P1 depends on the nominal coefficient of performance of the ACH. The same procedure was implemented to set the water flow rate in the CT (pump P3), that has to dissipate the heat produced by the condensing and absorption processes in the ACH.

As above mentioned, the DHW is partly produced by a plate-fin compact heat exchanger, equipped with a control which enables DHW production only when SC outlet temperature overcomes the fixed set point. The HE is equipped with a diverter placed upstream of the DHW inlet, a bypass duct and a mixer downstream the DHW outlet. The diverter and the mixer are managed by the HE control system. The model of this heat exchanger was developed by the authors using a modified version of the e-NTU method [31]. Details regarding the equations adopted to simulate this component are available in reference [10]. 3.7. Hydraulic separator

3.3. Storage tanks (TK) The system layouts under evaluation included two storage tanks, both subjected to thermal stratification. The first tank (TK1, simulated using Type 4) is used in the solar loop; the second one

This device is required in order to balance the flow rates between the primary and secondary loops of the system. In fact, the secondary loop flow rate may significantly vary during the day, depending on the heating/cooling loads of the different thermal

F. Calise et al. / Energy 41 (2012) 18e30

zones. For such device, a new TRNSYS model was introduced, described in detail in reference [10], based on simple energy and mass balances. 3.8. Fan-coil (winter and summer operation) Each zone is equipped with a 2-pipes loop, supplying hot/chilled water to the respective fancoils. In this work, the fan-coil, for both cooling and heating modes is simulated, developing a new TRNSYS type [10], based on a data lookup approach. In fact, TRNSYS library lacks in a fan-coil model, based on manufacturers data, which can operate both in cooling and heating modes. In particular, the data file includes four correction factors, function of: fluid mass flow rate, inlet fluid temperature, air dry and wet bulb temperature, and air flow rate. This approach also allows one to reduce dramatically computational times. In fact, the thermodynamic model of the heating and cooling modes (included separately in TRNSYS library) are very complex (particularly for the calculation of water condensation in cooling mode), requiring a higher computational time. On the other hand, the data lookup approach shows the same flexibility and accuracy of the thermodynamic model, at dramatically shorter computational times. 3.9. Pipe Each zone is hydraulically connected to the system by a supply and return ductwork. This component is simulated on the basis of a non-steady model based on the mass and energy balances (Type 31) [27]. 3.10. Building The building considered in this work was simulated using the TRNBUILD software included in TRNSYS package which provides a very detailed and reliable simulation of the thermo-hygrometric behavior of the building. Here, the building is simulated by means of a non-geometrical balance model with one air node per zone, representing the thermal capacity of the zone air volume and capacities which are closely connected with the air node. The walls are modeled according to the transfer function of Mitialas and Arsenault [27]. The windows are considered as an external wall with no thermal mass, partially transparent to solar, but opaque to the long wave internal gains. Long-wave absorption occurs at the surfaces. The window model also includes a detailed optical and thermal model based on WINDOW 4.1 developed by Lawrence Berkeley Laboratory USA. Finally, the building model also includes detailed effective capacitance humidity, infiltration, ventilation, convective coupling and gain models [27]. 3.11. PEM fuel cell The PEM considered in this study is also equipped with an external reformer, including Steam Methane Reforming (SMR) and shift reactors, converting methane into hydrogen, used to produce both electricity and heat. In this work, a 360 kWe PEM fuel cell was considered, based on the performance data of Ballard PB2 system (Table 2). Unfortunately, these data are not available for all the combinations of operating/boundary conditions (inlet flows and temperatures, ambient temperature, electrical load, etc.). Therefore, the model of the PEM fuel cell was developed on the basis of the thermodynamic/electrochemical equations, describing the phenomena occurring in this component. The model was validated using the available experimental data and subsequently used for whatever combination of operating/boundary conditions.

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Table 2 PEM parameters. Parameter

Unit

Electrical Power Thermal Power Electrical Efficiency Thermal Efficiency Stack temperature Number of cells Cell Current Number of stacks PEM Area MEA thickness PEM thickness

360 305 34 42 80 100 5000 1 10,000 0.010 0.250

kW kW % %  C A cm2 cm cm

The electrochemical and thermodynamic model of the PEM included in this work is based on the model developed by Mann et al. [32] adopting both deterministic and empirical equations for the calculation of cell Nernst voltage and activation, ohmic and concentration overvoltages (both anodic and cathodic). The model is flexible since can be easily adopted for different PEM configuration. It was successfully validated using experimental data of several PEM fuel cells [32]. However, the model of Mann does not implement the cogenerative heat exchangers of the fuel cell, as adopted in this work. Therefore the original model of Mann was here accordingly modified in order to simulate cogeneration. As usual [33e35], the model calculates the cell actual voltage as the difference between Nernst Open Circuit Voltage and ohmic, activation and concentration overvoltages. Such overvoltages are considered losses for the electrochemical process and should be minimized as much as possible.

Vcell ¼ ENernst þ hact þ hohmic þ hconc

(3)

In the case of PEM fuel cells, operating at low-medium current density, the concentration overvoltage may be neglected [35]. As regards the Nernst potential, it could be calculated using thermodynamic calculations [36]. However, this procedure is very intensive from the computational point of view. Thus, in order to improve computational velocity, Nernst potential was calculated using the following correlation [32]:

ENernst ¼ 1:229  8:5$104 ðT  298:15Þ þ 4:308$105 T   ln p*H2 þ 0:50 ln p*O2

ð4Þ

The activation overvoltage should be rigorously calculated using the ButlereVolmer equation [35]. However, this equation can be evaluated only implicitly, which is a procedure not compatible with the calculation times required for a dynamic simulation. Therefore, the explicit procedure proposed by Mann [32] is much more suitable for the simulations to be performed in this paper. Mann et al. showed that the activation overvoltage can be approximated using the following simple equations, where the coefficients can be found by simple experiments on the fuel cells [32].





hact ¼ x1 þ x2 T þ x3 Tln c*O2 þ x4 T lnðiÞ

(5)

Finally, the ohmic voltage was calculated implementing the following semi-empirical approach [32].



hOhmic ¼ i Relectronic þ RProton



(6)

The electronic resistance can be considered constant and can be experimentally calculated. The proton resistance depends on several parameters, as follows:

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F. Calise et al. / Energy 41 (2012) 18e30

  2:5 #  i T 2 i 181:6 1 þ 0:03 þ 0:062 þ A 303 A l ¼   A   4:18 T303 i T l  0:634  3 e A "

RProton

(7)

Hydrogen and oxygen partial pressures at the Three Phase Boundary can be calculated using the empirical equations given in references [37e39].

 pH2 ¼ pH2 e

 1:653i 1:334 TPEM

  0:50pH2 Osat


 pO2 ¼ pair;in 1  xH2 Osat  xN2

(8) (9)

Hydrogen and oxygen inlet and consumed flow rates are calculated by simple stoichiometric balances [35]. The previous equations show that the electrochemical performance of a PEM fuel cell dramatically depends on its operating temperature. In fact, the higher the operating temperature is, the lower both activation and ohmic overvoltages are. Therefore, it may be concluded that this temperature should be as high as possible. However, the operating temperature of a PEM is limited by the materials of its membrane that require for a safe operation a maximum operating temperature around 80  C. Ongoing research projects are also developing high temperature PEM fuel cell, aiming at improving its efficiency. However, such devices are far from a commercial availability and consequently they are not considered in the present study. The model also allows one to calculate: heat generated from reaction [35] and evaporative losses due to water evaporation at cathode side [37,38]. The model also calculates the heat losses to the environment, considering the thermal resistance of the fuel cell.

T  Tamb Q_ loss;FC ¼ FC Rt

(10)

Note that this term is usually marginal since the operating temperature of the cell is low (around 80  C) and the insulation of its case is good. Finally, the energy balance can be written as follows:

Ct

vTFC ¼ Q_ gen  Q_ loss  Q_ cool  Q_ evap vw

(11)

In the previous equations the thermodynamic properties of the air and hydrogen are calculated using the assumptions of ideal gas, whereas water properties are calculated taking into account specific correlations, as shown in reference [36]. The cooling power is provided by the cogenerative heat exchangers included in the stack, which were simulated using the well-known e-NTU method [31]. In fact, the stack is equipped with an internal heat exchanger in which flows the water required to cool the membrane. However, from the system point of view, the main scope of the cogenerative heat exchanger is to heat the stream exiting TK1 up to desired set point temperature. As above mentioned, the PEM operates at full load. Therefore, except for the start up and shut down periods, the electrical energy produced and the demanded cooling power are constant. However, the cooling power, which should be provided by the HW entering the PEM, is extremely variable in function of radiation. Therefore a complex control strategy, based on the use of different diverters and mixers, has been implemented in order to achieve simultaneously cogeneration heat and PEM cooling. In particular, HW flow rate entering PEM subsystem is constant, since

P1 is a fixed-speed pump. On the other hand, the temperature of this stream continuously varies in function of solar radiation. Therefore a controller measures the temperature of the stream exiting P1 and the temperature of the stream exiting the cell. This controller manages a diverter placed upstream of the PEM. Here, part of HW stream is eventually bypassed in order to achieve the desired fuel cell operating temperature. However, it may happen that this stream is completely bypassed by the controller when HW is not able to cool the stack. In this case, another valve opens the way coming from cold domestic water and closes the way corresponding to the HW loop. Hence, in this case DHW is produced. The values of temperatures corresponding to a complete bypass of the HW loop were calculated, using energy and mass balances, and fixed among the controller parameters. Such calculations were performed assuming that the PEM operates at 80  C and the maximum temperature of the stream exiting the cogenerative heat exchangers is 75 C. These data were taken from Ballard datasheets. In conclusion, the calculated set point temperatures are shown in Table 1, in which it is shown that DHW enters the cogenerative heat exchanger of the PEM when HW inlet temperature is higher than 45  C or 71.5  C, respectively in winter and summer seasons. The Ballard datasheet was also used in order to evaluate the total parasitic electrical power due to the fans and pumps included in the fuel cell and the steam methane reforming system. The nominal value of this parasitic electrical power was 15.3 kW. This power decreases at partial load according to the same algorithm (power curve) discussed for the pumps [27]. Finally, details regarding the steam methane reforming model are given in TRNSYS documentation [27]. 3.12. Overall energy consumption The energy analysis of the systems under evaluation requires the calculation of the non-renewable primary energy required to operate it; in this way, the primary energy savings of the polygeneration system with respect to a traditional HVAC system assumed as a reference (RS) can be evaluated, too. To this scope, a reference system was also implemented and simulated in TRNSYS, using the same building. In the case study presented in the paper, an air-to-water electric driven heat pump (EHPRS) was considered as the reference system, producing hot water during the winter and refrigerated water during the summer. The nominal COP of the EHPRS in heating mode is 3.0 whereas the nominal COP in cooling mode is 2.5. Such values are often taken as reference in Mediterranean Climates [11]. The RS also includes a gas-fired heater, for DHW production. In fact, the heat pump used for space heating and cooling cannot produce simultaneously DHW. Alternatively, DHW could be more efficiently produced by a dedicated heat pump operating at higher condenser pressures. However, this technology is scarcely adopted due to its higher capital costs. In summary, the RS consists of the following equipments: i) air-to-water electrical heat pump for space heating and cooling; ii) gas-fired heater for DHW; iii) grid electrical energy supplying all the electrical devices (heat pump, lights, equipments, etc.). This system is commonly considered the reference system for Mediterranean climates, since it is the most common configuration for these climates [11]. However, the considered polygeneration system may be compared also with other alternative energy-saving technologies (ground heat pump, free cooling, etc), but this is beyond the scope of this work which is focused only on PEM and SHC technologies. Thus, the primary energy consumed by the RS is calculated by the TRNSYS simulation and then used in polygeneration simulation in order to evaluate primary energy savings. The primary energy consumed by the reference system is mainly due to the electrical energy consumed by the building (lights and equipments) and the one

F. Calise et al. / Energy 41 (2012) 18e30

used for the EHP and for the pumps of the primary and secondary water loops. Note also that a correct energy comparison between the two investigated systems must be performed considering the same amount of energy produced by the two systems. In this case, the system installed in the RS produces a lower amount of energy with respect to the polygeneration system. In fact, although the two considered systems provide the same amount of space heating and cooling and electricity (lights and equipments) to the building, the polygeneration system also produces DHW and the exceeding electrical energy sold to the grid. Therefore, in order to perform a correct energetic comparison, it is here assumed that the RS also uses an additional amount of a primary energy to produce: i) the same amount of DHW produced by the polygeneration system; ii) the electrical energy produced by the PEM and sold to the grid (Eel,þ). Therefore, considering the sum over all the time-steps, the RS primary energy is:

PERS ¼

1 X

hel;t

i

þ Eel;þ;i

!

Qh;i Qc;i þ þ Eaux;RS;i þ Eel;b;i COPEHP;RS;i COPEHP;RS;i þ

X QDHW;i

hb;i

i

(12)

The primary energy required by the polygeneration system, in terms of non-renewable sources, is only due to the yearly natural gas volume (VNG) consumed by the fuel cell and to the fossil fuel consumed by the thermal power plant (average efficiency, hel,t¼0.461) in order to supply the auxiliary electrical energy (Eel,,i) required by the building and system and not supplied by the PEM. Therefore the polygeneration primary energy is:

PEpoly ¼ VNG LHV þ

Eel;;i

hel;t

(13)

In fact, the simulation model presented in this paper also includes a module for the calculation of the electricity balances. The model includes a data reader which obtains, from an external file, the electrical energy demand (Eel,b), due to equipments and light, for each time step. Simultaneously, the model also calculates the amount of electricity produced by the fuel cell (Eel,PEM) and the one consumed by the auxiliary devices (pumps, fans, etc) included in the system (Eaux). Thus, for each time step, the model performs the following simple algorithm.


 if Eel;PEM > Eaux þ Eel;b
 Eel;þ ¼ Eel;PEM  Eaux þ Eel;b Eel; ¼ 0
 else if Eel;PEM < Eaux þ Eel;b

(14)

Eel;þ ¼ 0
 Eel; ¼ Eaux þ Eel;b  Eel;PEM

PES ¼

PERS  PEpolygeneration PERS

were neglected. The components capital costs (Ji) were reported on a yearly base by means of an annuity factor (AF), depending on the expected life of the system and the discount rate. So, the total cost (owning and operating) of the polygeneration was expressed as:

P Ctot ¼

Ji

i

þ Cop

AF

(15)

3.13. Economic model A detailed cost model was also implemented in the simulation tool, calculating both operating and owning costs. The equations used for the cost functions of the components are shown in references [9,11]. The operating costs due to natural gas and electrical energy consumptions were evaluated, whereas maintenance costs

(16)

The operating cost, Cop, is mainly due only to the natural gas consumption required to supply the PEM fuel cell. The operating costs are calculated taking into account the electrical net metering. In fact, in this calculation the model considers the eventual purchase/selling from/to the grid at the actual (for the considered hour of the year) price (pEE) or cost (cEE). In fact, according to the algorithm shown in Eq. (14), the model evaluates for each time step the eventual amount of energy purchased or sold. Then, another algorithm evaluates which are the actual costs/prices for the considered time steps, taking into an account that a timedependent electrical tariff is considered. Thus, the model is capable to evaluate the economic value of the electrical energy sold or purchased taking into account the periods in which this energy is purchased or sold:

Cop ¼

X

VNG;i cNG  Eel;þ;i pEE;i þ Eel;;i cEE;i



(17)

i

The cost of natural gas supplying the PEM was fixed at 0.35 V/ Sm3. Note that in Italy, the electrical costs are time-dependent in function of the specific hour of the year. In particular, three different timeframes are established, F1, F2, F3, corresponding respectively to high, medium and low electrical energy demands. Typically, F1 occurs during the working days between 8.00 am and 6.00 pm, F2 is typical of the daylight of Saturday and late evening, F3 is typical of Sundays and nights. Detailed maps of these time-dependent costs are available from Italian Government website (www.autorita. energia.it). The purchase costs in the three considered timeframes are respectively 0.13 V/kWh, 0.10 V/kWh and 0.056 V/kWh. The selling prices in the three considered timeframes are respectively 0.09134 V/kWh, 0.070 V/kWh and 0.049 V/kWh. The Capital costs were estimated by introducing a cost function for each component, obtained by regression of manufacturers data, as described in [8e12]. PEM cost was estimated at 1500 V/kW, which is the goal to be achieved by manufacturers in the next years [35]. As regards the reference System (RS), its operating costs are due to electricity (for the EHP and auxiliaries and for building lights and equipments) and natural gas (required to drive the DHW heater). Thus, the annual RS operating cost is:

Cop;RS ¼

X
  Eel;aux;EHP;RS;i þ Eel;EHP;RS;i þ Eel;b;i cEE;i i

Finally, the overall energy saving is calculated using the Primary Energy Saving (PES):

25

X QDHW;i cNG;i þ LHVhb;i i

! (18)

Finally, the economic performance of the SHC system can be calculated using the Simple Pay Back period (SPB) both with and without public contributions. In particular a possible public funding, presently adopted for solar systems in Italy, consists in a funding of 55% of capital costs of SC and ACH. In this case the Simple Pay Back period is indicated as SPB2. 4. Results and discussion The polygeneration system under investigation was simulated using the set of main design parameters shown in Table 1. However, the complete set of input parameters to be assigned for the

26

F. Calise et al. / Energy 41 (2012) 18e30

simulations is much more extensive. Details regarding these parameters and their design criteria are given in reference [10] and here omitted for brevity. It is noteworthy that SC field area was designed in order to cover approximately 30% of the peak cooling load, in order to maximize PEM contribution to the overall production of cooling and heating energies. The simulation tool presented in this paper allows one to calculate energetic and economic parameters, using different time horizons. These parameters are evaluated on a yearly basis in order to determine the overall system performance, using a time step of 0.040 h. Such value is very small in order to get convergence in the capacitive components (building and tanks) and in order to achieve a more realistic simulation of the controllers. In addition, a monthly analysis is often useful in order to evaluate the variations of the parameters during the year. Shorter time horizons (weeks or days) are also returned by the simulation code. However, such analysis would be less interesting due to the significant variability of the parameters under investigation. Finally, the tool also provides data and plots of temperatures and heat flows all over the year. Thus, the user, for whatever period (day, hours, etc) can analyze temperatures and heat flows variations. In the following, the analysis is presented on yearly basis in order to evaluate the overall energetic and economic performance of the system. Then, a monthly analysis is also presented aiming at evaluating the sources of the seasonal variations of the investigated parameters. Finally, the hourly analysis is here omitted for brevity since it is also partly presented in reference [10]. The yearly energetic and economic results are summarized in Table 1. Here, it is clearly shown that the building under investigation is dominated by internal loads, determining a winter heating demand dramatically lower than the cooling one. This is due to the combination of the high internal gains and wall insulation, as discussed in reference [10]. Note that in this previous reference, the building electrical energy demand was not analyzed nor a timedependent energy cost was implemented. On the other hand, on the basis of the duration curve displayed in Fig. 2 and using the results of the simulation of the RS, it is possible to analyze in detail the electrical energy consumption of the building. The total electrical energy demand for building equipments and light is 6.68 108 kJ/year. This energy is mainly demanded in F1 (92.7%); the amount of this energy required in F3 is negligible (0.11%). In fact, the building operates mainly in F1 (working days) and partly in F2 (Saturdays). Similarly, the electrical energy necessary for HVAC equipments is mainly required in F1. In fact, considering the RS, the total electrical energy required for space heating and cooling is 2.44 108 kJ/year. The corresponding percentages in F1, F2 and F3 are respectively 81.3%, 17.2% and 1.49%. Consequently, 84.9% of the electrical cost for space heating and cooling occurs in F1. In this framework, the profitability of the considered polygeneration system is maximized. In fact, a significant part of the energy produced by the polygeneration system in F1, is supplied by the sun, determining significant savings due to the lower amount of energy demanded in the most expensive hours. On the other hand, it must be pointed out that the considered polygeneration system is much more expensive than the traditional electric heat pump installed in the RS. In fact, the system capital cost (1.07 MV) is one order of magnitude higher than RS corresponding cost (80 kV). However, the savings in terms of operating costs are also significant (69.2%), as clearly shown in Table 3. Such savings are mainly due to the production of thermal energy for DHW. A significant contribution is also given by the reduction of electrical energy demand in F1, as discussed above. Therefore, this result shows that the optimal use of energy available from cogeneration is a key point for the profitability of the systems. In fact, as shown in Table 3, the thermal energy produced by the PEM and

Table 3 yearly simulation results. Parameter

Unit

Qh Qc Eel,þ,i Eel,PEM Qt,PEM QDHW,SC QDHW,PEM Qaux QSC VNG PE PERS SPB SPB2 DPB DPB2 P pi Eel;þ;i

kJ kJ kJ kJ kJ kJ kJ kJ kJ Sm3 kJ kJ years years years years V

I0 Cop,RS Cop

V V V

i

7.33107 6.42108 2.76109 3.44109 4.24109 2.51108 3.54109 5.91107 5.92108 2.97105 1.031010 1.271010 12.9 10.3 14.8 21.2 71,213 1,073,352 110,929 34,210

used for space heating and cooling is only a small amount of the total thermal energy available from the cogenerative heat exchanger. Therefore, the large amount of DHW request, typical of the considered building, is crucial in order to maximize system energetic and economic performance. In the considered configuration, the payback periods are acceptable, especially in the framework of renewable energy sources. Considering the present Italian public funding of 55% of capital costs of SC and ACH, the pay back period is slightly higher than 10 years (SPB2 in Table 3). Taking into account an actualization factor of 5% and an operating life of 15 years, the system is economically acceptable in case of public funding, showing a Discounted Pay Back period (DPB) of 14.8 years. In the other case, without funding, the DPB would be 21.2 years. Thus, it may be concluded that a significant public funding strategy is crucial in order to promote this renewable technology. In addition, further improvements may be achieved optimizing PEM size. In fact, the electricity produced by the fuel cell is mainly sold to the grid since PEM size (designed on thermal demand) is overestimated for building electrical energy demand. Furthermore, Table 4 shows some important annual parameters. Here, the overall solar fraction is noteworthy, i.e. the ratio of the amount of cooling/heating energy produced by the sun is 30%, whereas the PES is lower than 20%. This is due to the overall electrical efficiency of the PEM which is significantly lower than the average electric efficiency. On the other hand, the effective thermal efficiency of the PEM is very close to the nominal value. Therefore, such circumstance is due to the huge amount of DHW demand typical of the considered building. Finally, the same table shows the very high efficiency of the SC, in accordance with the results obtained in previous studies [8e12]. Conversely, the calculated COP of the absorption chiller is lower than expected. This circumstance is due to the fact that HW temperature entering the ACH, during the summer, is always around 75  C. Such range is lower than 80  C, used in previous works [8e12]. Table 4 Energetic performance parameters. Parameter Fsol

hSC he,PEM ht,PEM COPACH PES

0.30 0.47 0.33 0.41 0.71 0.19

F. Calise et al. / Energy 41 (2012) 18e30

27

Fig. 3. Monthly thermal energy.

As above mentioned, a monthly analysis is also useful in order to show the seasonal variability of the considered energetic and economic parameters. This analysis is shown in Figs. 3e5 showing respectively monthly thermal energy, electrical energy and costs. In particular, Fig. 3 shows building cooling (Qc) and heating (Qh) energies, solar field useful energy (QSC), absorption chiller cooling energy (Qc,ACH), PEM cogenerative energy (Qt,PEM) and DHW energy. Here, it is clearly shown that building heating energy demand is negligible if compared with the cooling one (e.g., February vs. June), as discussed in previous studies [10]. This circumstance is basically due to the high occupancy rate and the high wall insulation, typical of the building under investigation. In fact, in such a building, during winter the use of space heating is low since most of the heating is provided by the students occupying the classes. On the other hand, during the summer, the insulation rate of the walls increases the demand of space cooling since the heat generated by the people can hardly leave the building envelope. As a consequence, during the winter the thermal energy produced by the solar field is often higher than building space heating demand, as clearly shown in Fig. 3. This is a surprising result, since in ordinary buildings the energy produced by SC during the winter is significantly lower than space heating demand. Therefore, in the winter and in the middle seasons, most of the PEM cogenerative heat and SC useful gain is not required for space heating and cooling. As a consequence, this large amount of thermal energy is profitably

converted in DHW. This is clear in Fig. 3, where it is clearly shown that both SC and PEM DHW production dramatically decrease during the summer. In fact, during that season the cooling energy demand is very high also determining a high demand of thermal energy to drive the ACH, reducing the amount of energy available for DHW production. Fig. 3 shows that SC thermal energy is lower than ACH thermal energy demand. However, PEM cogenerative heat is high enough to drive the ACH, even in the hottest months (July and August). Fig. 3 also shows that the difference between cooling energy produced by ACH and cooling energy delivered to the building is negligible. Such difference is lost in ducts and tanks included in the systems, which are well insulated. In summary, Fig. 3 clearly shows that the considered system, although optimally balanced for the operation during the hottest months, shows remarkable exceeding thermal energy during the rest of the year. This large amount of energy can be here recovered for DHW production. However, the high request of DHW, considered in this case, is not common in ordinary buildings. Therefore, it may be concluded that the proposed system would be acceptable only when the user is able to consume most of the thermal energy available from PEM and SC, for applications others than space cooling and heating. Fig. 4 shows the monthly flows of electricity. Here, it is clearly shown that the electrical energy produced by the PEM is stable. The related variations are only due to the different lengths of the

Fig. 4. Monthly electrical energy.

28

F. Calise et al. / Energy 41 (2012) 18e30

Fig. 5. Monthly costs.

months. In fact, the PEM operates at full load 10 h per day, 5 days per week, all year long. A better performance would be achieved by a PEM whose load would be adjustable in function of thermal and electrical demand. However, for a safe operation, data from the manufacturer showed that a full load operation is preferable. The consequence of this design selection is a large amount of exceeding electricity (Eel,þ). In fact, the electrical demand of the considered building is not stable and the duration curve rapidly decreases as shown in Fig. 2. On the other hand, the possibility to purchase

electricity by the grid is also rare as shown in Fig. 4. Finally, the electricity required by SHC equipments (auxiliary devices) is negligible for all the months, showing some peaks during the summer, due to the fans of the cooling towers. Fig. 6 shows that the operating costs of the considered polygeneration system are always lower than reference system ones. However the savings are higher in winter and in mid seasons. In fact, during the summer, the incomes due to DHW production are lower, due to the larger amount of cogenerative heat used to drive

Fig. 6. Sensitivity analysis (ASC).

F. Calise et al. / Energy 41 (2012) 18e30

29

Fig. 7. Sensitivity analysis (electricity and natural gas costs).

the absorption chiller. Therefore, it may be concluded that the eventual profitability of the proposed system basically lies in DHW production. An important role in the economic balance is also played by the amount of money earned from the selling of the exceeding electrical energy. In fact, the PEM produces exceeding electrical energy mainly in F1, when the selling prices are very high. This circumstance also balances the low electrical efficiency showed by the PEM. This study was also completed by a sensitivity analysis in which the simulations were iteratively carried out, varying some of the main design parameters. In particular, the following parameters were varied: collector area, TK1 volume, SC outlet set point temperatures and PEM set point temperatures. Among these parameters only the collector field area showed significant influence on the overall system performance. The results were quite insensitive in function of the remaining parameters. Some slight variations are detectable only in case of TK1 volumes. However, the corresponding results are similar to those ones showed in references [10]. Therefore, for sake of brevity, in the following the sole sensitivity analysis regarding collector area (Fig. 6) will be presented. This analysis showed that the efficiencies of the equipments are slightly sensitive to the variations of ASC. This is quite trivial for the case of PEM, in which both thermal and electrical efficiency do not depend on SC size. In the case of SC a slight decrease can be detectable, due to the higher operating temperature achieved for higher SC areas. In fact, it is well known that higher temperatures determine lower efficiency as a consequence of the increase in heat losses. Fig. 6 also shows that both solar fraction and PES increase with ASC. However, it is also noteworthy that the values of PES are significantly lower than the corresponding values of Fsol. In fact, when Fsol approaches the value of 1, almost all the space heating and cooling energies are produced by the sun. However, the electrical efficiency of the PEM is lower than the corresponding efficiency of a thermal power plant, determining the trend of PES showed in Fig. 6. In this Figure, it is also shown that the minimum SPB is achieved at 200 m2, which was the initial guess value adopted in the present simulations. On the other hand, according to SPB2 criteria, a larger SC solar field would determine a better economic performance. Therefore, it may be concluded that

renewable energy may be significantly promoted only in case of public funding. Finally, a sensitivity analysis was also performed with the scope to investigate the variations of the SPB in function of electricity and gas costs/prices, as shown in Fig. 7. In particular, in this study a timedependent electric tariff was considered. Therefore, the same factor e reported on the x-axis of Fig. 7 e was used to multiply both electricity costs and prices in F1, F2 and F3. This analysis shows that the SPB is dramatically sensitive to the costs of the energy vectors, especially with respect to the natural gas. In fact, the system can be economically profitable (at the present electricity costs) only for a natural gas cost lower than 0.35 V/Sm3. Conversely, the higher the increase of electricity costs/prices, the lower the SPB. In fact, for the considered polygeneration system, the electricity produced in excess is dramatically higher than the one bought from the grid. Simultaneously, the higher the cost of electricity, the higher the operating cost of the reference system. Thus, an increase of electricity costs/prices would be extremely profitable. 5. Conclusions The paper presents a dynamic simulation of a novel polygeneration system based on the coupling of a PEM fuel cell and a solar heating and cooling system. The polygeneration system is capable to supply space heating and cooling and domestic hot water all year long. The system is powered by natural gas and solar energy. The dynamic model showed the technical feasibility of such system also providing acceptable economic performance both with and without public funding. The values of the economic parameters were in accordance with those ones found for simple SHC systems in previous studies [8e12]. The authors also concluded that these results can be obtained only in the case of buildings where high DHW volumes are required all year long. The results also showed that the system performance may be improved using fuel cells with higher efficiency and higher operating temperature. In fact, the electrical efficiency of the PEM was significantly lower than the reference electric one. In addition, the maximum operating temperature of 80 C stated by PEM manufacturer is slightly low to drive the ACH, at high COP. Therefore, authors are planning to overcome these problems in

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F. Calise et al. / Energy 41 (2012) 18e30

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