Design of a hybrid polygeneration system with solar collectors and a Solid Oxide Fuel Cell: Dynamic simulation and economic assessment

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Design of a hybrid polygeneration system with solar collectors and a Solid Oxide Fuel Cell: Dynamic simulation and economic assessment F. Calise* DETEC e University of Naples Federico II, P.le Tecchio 80, 80125 Naples, Italy

article info

abstract

Article history:

Solid Oxide Fuel Cells (SOFC) are very promising energy conversion devices, producing

Received 14 December 2010

electricity and heat from a fuel directly via electrochemical reactions. The electrical effi-

Received in revised form

ciency of SOFCs is particularly high, so that such systems are very attractive for integration

8 February 2011

in complex polygeneration systems. In this paper, the integration of SOFC systems with

Accepted 10 February 2011

solar thermal collector is investigated seeking to design a novel polygeneration system

Available online 15 March 2011

producing: electricity, space heating and cooling and domestic hot water, for a university building located in Naples (Italy), assumed as case study. The polygeneration system is

Keywords:

based on the following main components: concentrating parabolic through solar collectors,

Solar energy

a double-stage LiBreH2O absorption chiller and an ambient pressure SOFC fuel cell. The

Solar cooling

system also includes a number of additional components required for the balance of plant,

SOFC

such as: storage tanks, heat exchangers, pumps, controllers, cooling tower, etc. The SOFC

Fuel cell

operates at full load, producing electric energy that is in part self-consumed for powering

Polygeneration

building lights and equipments, and in part is used for operating the system itself; the

Optimization

electric energy in excess is eventually released to the grid and sold to the public Company that operates the grid itself. The system was designed and then simulated by means of a zero-dimensional transient simulation model, developed using the TRNSYS software; the investigation of the dynamic behavior of the building is also included. The results of the case study were analyzed for different time bases, from both energetic and economic points of view. Finally, a thermoeconomic optimization is also presented aiming at determining the optimal set of system design parameters. The economic results show that the system under investigation may be profitable, provided that it is properly funded. However, the overall energetic and economic results are more encouraging than those claimed for other similar polygeneration systems in the recent literature. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

In the last few years, a wide research activity in the energy field has been focused on the development of new conversion

systems, which are able to simultaneously reduce the use of fossil fuels and the emissions of pollutants. In this framework, researchers are investigating both high efficiency power plants and renewable energy sources.

* Tel.: þ39 817682301; fax: þ39 812390364. E-mail address: [email protected]. 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.02.057

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Nomenclature Fluid specific heat, kJ/kg K Feed-in tariff, €/kW h Concentrating ratio Natural gas specific cost, €/S m3 Electric energy specific cost, €/kW h Standard Gibbs free energy, kJ/mol Current density, mA/cm2 i i0 Exchange current density, mA/cm2 il Limiting current density, mA/cm2 _ m Mass flow rate, kg/h p Partial pressure, Pa pEE Electric energy price, €/kW h t Temperature,  C TK1 specific volume, summer, L/m2 of SC nTK1,s TK1 specific volume, winter, L/m2 of SC nTK1,w x Molar fraction A Area, m2 ASC Solar collector field area, m2 AF Annuity factor, years DHW production cost, €/year CDHW CDHW,rej Loss of earnings for the dissipated heat, €/year Electric energy cost, € Cel Incomes for electricity selling [€] Cel,þ Cost for electricity purchase, € Cel, Net cost for electricity selling/purchase, € Cel, Operating costs, €/year Cop Total cost, €/year Ctot COP Coefficient of performance Activation energy, kJ/kmol Eact Electric energy for auxiliaries and parasitic loads, Eaux kJ EDHW,rej Thermal energy dissipated, kJ Eel,aux,EHP,RS Electric energy demanded by auxiliaries of EHP of RS, kJ Eel,EHP,RS Electric energy demanded by EHP of RS, kJ Electric energy for building lights and equipments, Eel,b kJ Electric energy produced and sold to the grid, kJ Eel,þ Electric energy purchased from the grid, kJ Eel, Eel,HSSOFC Net electric energy demanded by the HSSOFC, kJ Eel,SOFC Electric energy produced by the SOFC, kJ Nernst Open Circuit Voltage, V ENernst Chemical exergy rate, kW Exch Physical exergy rate, kW Exph F Faraday Constant Solar Fraction Fsol SC loss coefficient FRUL Corrected SC loss coefficient F0 UL H Enthalpy rate, kW Total radiation, W/m2 Itot Ib Beam radiation, W/m2 J Component capital cost, € cf cft cSC cNG cEE g0f

Jtot LHV NTU NPV PE Pel Pel PSOFC Q_ Q Qc Qh QDHW PI PLR R SPB S_ T UA V Vcell

System capital cost, € Natural gas Lower Heating Value, kW h/S m3 Number of Thermal Units Net Present Value, € Primary Energy consumption, kW h Electrical power, kJ/h Electrical power required by auxiliaries, kJ/h SOFC electrical power, kJ/h Thermal energy flow rate, kW Thermal energy, kJ Cooling energy, kJ Heating energy, kJ Thermal energy for DHW production, kJ Profit Index Part load ratio Gas Constant, kJ/mol K Simple Pay Back, years Entropy rate, kW/K Temperature, K Heat transfer coefficient, kJ/h K Volume, m3 Fuel cell voltage, V

Symbols d 3 hel,t hAH hb hcomb hel,SOFC hact hU hconc hSC j 4P2 (as)n

Cell thickness, m Heat exchanger efficiency Conventional thermoelectric efficiency AH overall efficiency RS boiler efficiency AH combustion efficiency SOFC electrical efficiency Activation Overvoltage, V Ohmic Overvoltage, V Concentration Overvoltage, V Solar collector efficiency Capital contribution rate P2 specific flow rate, kg/h m2 of SC Normal transmittance-absorbance

Subscript

A C NG amb c cc ext f ft h in n out req set

Anode Cathode Natural Gas Ambient Cooling Capital cost incentive External Fluid Feed-in tariff Heating Inlet Nominal Outlet Required Set point

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As for the high efficiency conversion devices, fuel cells are probably the most promising technology due to their high electrical efficiency, modularity and low pollutant emissions [1]. Among the different types of fuel cells commercially available, Polymeric Electrolyte Membrane (PEM) and Solid Oxide Fuel Cells (SOFC) are presently considered as the most promising technologies. PEM fuel cells are much more commercially mature than SOFCs and they are also widely adopted in several applications (vehicles, cogeneration, power productions, etc) [1,2]. The capital cost of PEM fuel cells is relatively low, but this technology suffers from the constraint to be fed by pure hydrogen. Therefore, when fueled by conventional fuels (methane, natural gas, etc), an external reformer is required, dramatically increasing system complexity and decreasing the overall electrical efficiency. In fact, the reforming process is endothermic and requires an additional amount of heat (produced burning additional fuel). As a consequence, the electrical efficiency of PEM drops from about 50% (when fed by hydrogen) down to 35% (when fed by methane) [1,2]. On the other hand, SOFC systems are still in a pre-commercial stage and their costs are significantly higher than PEM ones. However, due to their high operating temperature, SOFCs can convert hydrocarbons into hydrogen internally, showing global electrical efficiencies approximately of 46% even when fed by methane [1e3]. Such efficiency can be further increased when SOFCs are coupled with gas turbines in hybrid cycles [2,4e6]. SOFCs are also considered as one of the most promising candidate for a future high efficiency decentralized energy conversion model. Due to their high operating temperature and modularity, SOFCs can be easily integrated into cogeneration power plants, producing electricity, heat and cooling energy, when combined with absorption chillers. Studies on this topic showed that such systems could result in a potential CO2 reduction of about 45% [7]. With regard to renewable energy sources, a number of innovative renewable technologies are emerging. For example, new building-integrated wind turbines [8], cogenerative solar photovoltaic collectors [9], solar heating and cooling systems [10e14] are currently under investigation both by industry and academia. Among these emerging technologies, solar heating and cooling (SHC) is probably one of the best choices. A great advantage of such technology lies in the possibility of using solar radiation to provide space heating during the winter and space cooling in the summer, by using a heat-driven chiller (absorption, adsorption, etc.). SHC systems are very profitable, particularly 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 goals stated by EU in the Directive 2009/28/EC [11,12,15e18]. The majority of the SHC systems investigated in literature are based on the combination of evacuated tube solar collectors and single-stage absorption chillers [10e13,15e26]. However, in the last few years, the combination of concentrating solar collectors and doublestage chillers is becoming more and more attractive [27e32]. Usually, the auxiliary thermal energy, required in case of scarce solar irradiation, is supplied by a gas-fired heater

[16,18]. However, such configuration may significantly decrease both energetic and economic performance of the considered system. In fact, several studies, also performed by the author, showed that the selection of the appropriate auxiliary system is a key point for the development of this technology [11,12,17]. A further technique for energy savings consists of maximizing the usage of all the energetic and material by-products of whatever energy system. This can be accomplished by multi-generation (or polygeneration) systems. 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) by using fossil and/or renewable energy sources. A strong impulse to this field has been given by new emerging energyefficient technologies and by regulatory incentives related to energy production from renewable sources and environmental friendly systems [33]. 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 [34]. An additional impulse to polygeneration systems is also given by the studies concerning the decentralized generation. In fact, several papers available in literature [33] assess that small scale distributed polygeneration systems (below 1 MWe) are useful since they: i) promote energy efficiency and renewable sources; ii) can defer investments for large power plants; iii) promote the use of local energy resources, reducing energy dependency and increasing the reliability of the electric 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 often adopted in the decentralized generation e are classified on the basis of: i) engine technology (reciprocating engines, micro gas turbines, fuel cells); ii) bottoming devices (absorption or electric chillers); iii) auxiliary devices (heaters, gas-fired absorption chillers or heat pumps, engine-driven chiller); iv) eventual renewable energy source (solar, biomass, wind, hydroelectric); and v) eventual materials produced (ethanol, hydrogen, etc). Thus, a large number of possible layouts can be identified for polygeneration systems. Among these possible selections, the layouts including fuel cells are particularly interesting, due to a wide range of possible hybrid configurations, including hydrogen, renewable energy, gas cycles, etc [35]. In particular, the present paper is focused on the combination of SOFC fuel cells with solar energy systems. This kind of system was diffusely investigated in literature, but from a different point of view with respect to the idea presented in this paper. In fact, in literature the production of hydrogen using solar energy is widely investigated [36] and its consequent use in fuel cells and/or storage is also often analyzed [37]. Shapiro et al. designed and built a prototype of a photovoltaic solar-powered regenerative PEM-electrolyzer, demonstrating the system feasibility and characterizing system performance [38]. A similar study was performed by Hedstrom, showing the experimental and numerical performance of a PEM fuel cell fed by hydrogen produced both by

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photovoltaic cells/electrolyzer and by reformer, fed by biogas [39]. Hence, the combination of fuel cells and renewable energy is often considered. However, the integration of fuel cells with solar thermal collector is scarcely investigated. A first work on this topic was recently presented by the author [40]. In this paper, the author developed 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 idea of such system was based on the combination of solar heating and cooling (SHC) systems [11e14,16e18,20e26,30,41,42] e including evacuated tube solar collectors and single-stage absorption chillers and cogenerative PEM fuel cell as auxiliary system. The results of that work validated the theoretical feasibility of the system also emphasizing that the selected plant layout suffered of the low operating temperature of the PEM. In that study, authors concluded that the system layout might be improved by including: concentrating solar collectors, double-stage absorption chiller and high temperature fuel cells. Such improvements have been accomplished in the present study where an innovative solar polygeneration layout is presented. The system includes: parabolic through collectors, a double-stage LiBreH2O absorption chiller and an SOFC fuel cell stack. The paper aims at showing the techno-economic feasibility of the innovative SOFC-solar polygeneration system, overcoming the problems arisen in case of PEM-solar polygeneration system. The layout considered in this paper is significantly original with respect to the one presented in the previous study [40]: it is based on a high temperature solar heating and cooling system combined with an ambient pressure SOFC. In particular, a first work on high temperature SHC has been recently presented by the author [29], showing an innovative SHC layout based on a Parabolic-Trough Solar Collectors (PTC) field, a two-stage absorption chiller and a biomass-fired auxiliary heater. The layout presented in that work has been here taken as a reference and implemented in order to model the polygeneration system under consideration. In particular, the auxiliary biomass heater has been here replaced by a cogenerative SOFC. The SOFC was simulated using an appropriately modified version of the model presented in Refs. [5,43], as discussed in the appendix of the paper. In addition, the work presented in the paper also includes several new models for SOFC, domestic hot water demand, economics, SOFC cogenerative equipments, etc. The system layout proposed was developed and dynamically simulated in TRNSYS environment [44]. The model allows one to calculate the time-dependent energy flows and key-points temperatures, as well as the parameters needed to evaluate the overall energy and economic performance of the system.

(SHC) and cogenerative SOFC technologies. Both SOFC and SHC were diffusely investigated by the author during the last few years. In particular, the author developed 0-D and 1-D models of a tubular SOFC fed by methane, paying special attention to the thermodynamic and thermoeconomic optimization of the device [4,5,43,45e47]. Similarly, the author also performed several simulation studies concerning SHC technology, aiming at determining the best configuration from the energetic and economic points of views. The majority of these studies investigated the combination of evacuated tube solar collectors and single-stage absorption chiller. The results showed that the economic profitability of SHC systems dramatically depends on the selection of the auxiliary heating and cooling device, and the studies concluded that an electric-driven vapor compression chiller was often more profitable than the traditional gas-fired heater, specially for Mediterranean climates [11,12,15e18]. On the other hand, a recent study showed that, in case of High Temperature Concentrating Solar Heating and Cooling (CSHC) systems, even a gas-fired heater can be considered as an efficient auxiliary system, due to the use of a double-effect absorption chiller [29]. The combination of low-temperature fuel cells (PEM) and low-temperature SHC was also studied [40], showing some severe issues regarding the thermal balance of such systems. In fact, PEM operating temperature is relatively low to drive the absorption chiller. Therefore, the system could be improved using a different type of fuel cell, operating at higher temperatures. However, the use of a high temperature fuel cell (e.g. SOFC or MCFC, respectively operating at 1000  C and 650  C) to heat-up a stream at 80  C would determine a dramatic exergy destruction in the system, also reducing its overall efficiency. Therefore, in order to avoid excessive thermal irreversibilities in the system, it is here introduced a novel polygeneration layout integrating both high temperature fuel cell (SOFC) and high temperature Concentrating SHC (CSHC). In fact, such system is capable to maximize the “quality” of the cogenerative heat produced by the fuel cell, reducing the temperature difference between cogenerative hot and cold streams. In addition, the idea of integrating CSHC with SOFC was encouraged by the positive energetic and economic results achieved in the recent study regarding CSHC [29]. So, the layout presented in this work is a somewhat natural development of the CSHC system analyzed in Ref. [29], in which the biomass heater was replaced by the SOFC subsystem. Obviously, such modification also required to implement new models for: exchanges of electric energy with the public grid, energy and economic savings, control strategies, etc. Such new models will be discussed in detail in the following sections.

2.2.

2.

System description

2.1.

Concept idea

The Hybrid Solar SOFC (HSSOFC) polygeneration system investigated is a combination of Solar Heating and Cooling

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Operating principle

The system layout is schematically shown in Fig. 1. Five different loops are shown, for the following fluids: the Solar Collector Fluid, SCF (diathermic oil); the High Temperature Fluid, HF (diathermic oil); the Hot Water, HW; the Cooling Water, CW; the Domestic Hot Water, DHW; the Chilled or Hot

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Fig. 1 e HSSOFC system layout.

Water, CHW. The system includes the following main components:  the Solar Collector field, SC, consisting of small newgeneration horizontal Parabolic-Trough Collectors, PTC (e.g. Solitem PTC 1800 [48]), equipped with a single axis (NS oriented) tracking mechanism, and using diathermic oil as High Temperature Fluid (HF);  a Thermal Storage system (TK1), consisting of a set of two vertical hot storage tanks, equipped with mixers, diverters and a controller; the subsystem consists of two tanks e the first big and the second small e managed by the controller which may enable the first, the second or both, according to the thermal storage demand;  a LiBreH2O double-effect absorption chiller (ACH), whose generator is fed by the hot diathermic oil (HF), heated up by the solar field; the condenser and the absorber of the ACH are cooled by the cooling water loop (CW) provided by the cooling tower;  a closed-circuit Cooling Tower (CT), providing cooled water (CW) to the condenser and absorber of ACH;  a cogenerative internally reformed Solid Oxide Fuel Cell (SOFC), fed by methane, providing both electric energy and heat for DHW, space heating and cooling purposes;  a gas-fired Auxiliary Heater (AH), providing auxiliary thermal energy;  a fixed-volume pump (P1) for the HW loop;  a variable-speed pump (P2) for the SCF 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), adopted in order to reduce the number of start-up and shut-down events for the absorption chiller ACH;  a hydraulic separator (HS), balancing the flows between the primary and secondary hydraulic circuits;  a plate-fin heat exchanger in the solar loop, used to produce Domestic Hot Water (HE1) when the solar irradiation is higher than ACH (or HE2) thermal demand;

 a plate-fin heat exchanger (HE2) in the HW loop, transferring the heat from the HF (diathermic oil), to the hot water (CHW) to be supplied to the fan-coils during the winter; this component is required in order to avoid to use diathermic oil inside the building;  Balance of the Plant (BOP) equipments (the majority not displayed in Fig. 1, for sake of simplicity), such as pipes, mixers, diverters, valves, and controllers required for the operation of the system. The HSSOFC was dynamically simulated in TRNSYS [44]. The implementation of the above discussed system layout in TRNSYS has been done adopting a number of additional mandatory components (not displayed in Fig. 1) to run the simulations and to process the data, such as: controllers (feedback, proportional and on/off), schedulers (daily and seasonal), weather databases, printers, integrators, etc. The basic operating principle of the HSSOFC system is basically similar to the one presented for the CSHC system [29], with the modification that the auxiliary heat is here partly provided by the SOFC subsystem. In case the SOFC thermal power is lower than the power required to achieve the fixed set point, the eventual additional heat is provided by a gas-fired heater (AH). Therefore, for sake of brevity, the HSSOFC operating principle will be here briefly summarized, since specific details can be found in reference [29]. The variable-speed pump P2 is managed by a feedback controller which varies continuously its flow rate in order to achieve the desired SC outlet temperature. However, when the thermal energy demand is low, this temperature may overcome the set point. In this case, the fluid is cooled down by HE1, producing DHW for the building users. The HF hot stream is stored in TK1. Then, it is pumped by P1 to the cogenerative heat exchanger of the SOFC (and/or to the AH) which provides eventual additional thermal energy in order to achieve the fixed ACH inlet set point temperature. The part of the heat produced by the SOFC, which is not employed to heat-up HF, is used to produce additional DHW. During its

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operation, the fuel cell produces electricity to operate the HSSOFC itself (pumps, CT, ACH, etc.) and for powering the building; eventual electric energy in excess is delivered to the public grid. Then, the HF heats the generator of the ACH in the summer or the primary side of HE2 in the winter. Thus, the produced CHW passes through the TK2 and supplies the fan-coils installed inside the building, providing the demanded space heating or cooling energy. The SOFC subsystem is the main innovation of the layout introduced by this paper. This system was developed on the basis of the studies performed by the author regarding SOFCs during the last few years [5,43]. However, all the works previously performed by the author were focused on hybrid SOFC e Gas Turbine (GT) cogenerative power plants. These systems are very attractive for the significantly high electrical efficiency. Unfortunately, the size of hybrid SOFC-GT power plants is limited by the GT, determining an overall system size reasonably higher than 1 MW [1,3,5,6,49]. This size is not suitable for the university building considered in this work in which both electric [11] and thermal [40,50] loads are significantly lower. On the other hand, simple SOFC systems are available in the range from 1 to 5 kW. Thus, the original SOFC system layout presented in works [5,43] has been here modified in order to pass from the hybrid pressurized SOFC-GT system to a simple ambient pressure SOFC. The result of such modification is shown in Fig. 2, where the SOFC subsystem layout is displayed. Comparing the layout shown in Fig. 2 with the one presented in Refs. [5,43], it is clear that the GT has been eliminated and the two cogenerative parallel heat exchangers have been changed into two series heat exchangers, equipped with by-pass, as discussed in the following. The SOFC subsystem consists of the following main components:  Internally Reformed Solid Oxide Fuel Cell (IRSOFC): tubular SOFC with anode recirculation arrangement fed by methane, internally reformed at the anodic side, after a first external pre-reforming;  Pre-reformer (PR): external tube-in-tube pre-reformer required to crack the higher hydrocarbons included in natural gas and to reform a part of methane into hydrogen.















 

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This component is crucial for the operation of the system since the electrochemical reactions can start from the beginning of the SOFC tube, improving the electrochemical activity of the cell and reducing its longitudinal thermal stresses. The inner tube is filled with the catalyst, required to promote the Steam Reforming Reaction (SMR). The component is also equipped with a heat exchanger section, which is used to reheat the fuel, after the cooling due to the endothermic reforming process; HEC: Heat Exchanger placed on the top of the fuel cell stack, used to pre-heat the air entering the cell. This component is used to model the typical tubular stack configuration, as shown in detail in Refs. [5,43]; C: catalytic combustor which converts the cell exhaust fuel in additional heat, used to pre-heat air and fuel entering the stack; HEA: plate-fin compact heat exchanger, pre-heating the air entering the stack, using the thermal energy of the stack exhaust gases; HEF: plate-fin compact heat exchanger, pre-heating the fuel entering the stack, using the thermal energy of the stack exhaust gases; AC: Air Compressor, providing the additional pressure required to overcome pressure drops in the stack components; FC: Fuel Compressor, providing the additional pressure required to overcome pressure drops in the stack components; HEHF: Cogenerative heat exchanger transferring thermal energy from cell exhaust gases to the HSSOFC Hot Fluid (HF): shell and tube arrangement, 3 shell passes; HEDHW: Cogenerative heat exchanger transferring the residual thermal energy from cell exhaust gases to DHW; BOP: Balance of Plant equipments (valves, mixers, diverters, etc) required for the operation of the system. Note also that the layout is equipped with several by-passes that can be handled in order to achieve the desired plant thermal balances, as discussed in detail in Refs. [5,43].

The operating principle of the SOFC subsystem is significantly changed with respect to the one presented in Refs. [5,43]. Thus, it will be here summarized. Fuel is slightly compressed

Fig. 2 e SOFC subsystem.

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by the FC in order to overcome the relative pressure drops. Then, it is pre-heated in HEF, using the thermal energy of stream 16. The fuel exiting the HEF can be brought directly to the combustor C or to the mixer M which mixes anode recirculated stream (stream 5) with fresh fuel (stream 24). Then, the resulting flow (stream 25) is pre-reformed and re-heated in PR, using the thermal energy of stream 26 leaving SOFC stack. The pre-reformed fuel (stream 2) enters the anode compartment of the fuel cell where participates at the electrochemical reaction producing electricity and heat. Simultaneously, air is slightly compressed by AC, pre-heated by HEA, and brought to the cathodic side of the Fuel Cell (stream 22). Here, it is further pre-heated by HEC and then enters the cathode compartment (stream 6) acting as oxidant in the electrochemical process. Unreacted fuel (stream 4) and air (stream 7) are burnt in C increasing the temperature of the outlet stream (8), which is employed to supply heat first to HEC and then to PR. By-passes at streams 9, 18 and 1 can be used by system control manager in order to achieve the desired thermal balance in the plant. The stack outlet flow (28) is divided in two streams for pre-heating air and fuel respectively. Then, pre-heaters exhaust gases are mixed in a mixer (stream 10) and brought to cogenerative side of the system. Here, a feedback controller reads the temperature of the HF entering the HEHF and modules the upstream diverter, in order to achieve the desired HF temperature exiting the HEHF. The outlet gas stream (30) is mixed with the bypassed flow (21): the resulting stream (32) heat flow is recovered by a second heat exchanger (HEDHW) producing Domestic Hot Water. Thus, HEHF and HEDHW are respectively the hightemperature and the low-temperature cogenerative heat exchangers. The SOFC subsystem was modeled in MATLAB and then linked to the main TRNSYS project, using the appropriate module (Calling Matlab) included in TRNSYS package. In conclusion, the considered HSSOFC provides space heating and cooling and domestic hot water to the building. The same building test case (university building with thermal demand for the fitness center) used in previous analyses [11,40] was here considered. Thus, it is possible to compare the results of this study with those achieved by the previously analyzed systems [11,40]. Data regarding building walls, occupancy, equipments and loads are diffusely discussed in Ref. [11]. The duration curve of the building electric load is given in Ref. [40]. Finally, the considered DHW daily demand was set at 25 m3/day at 45  C.

3.

System simulation

layout investigated in this paper was originated from the layout developed in previous works [11,12,15e17,29,40], where the models of both built-in and user-developed components are described in detail. As discussed in Refs. [11,12,15e17,29,40], the majority of the components models (e.g. pumps, mixers, diverters, valves, controllers, auxiliary heater, absorption chiller, cooling tower, plate-fin heat exchanger, building, etc.) were taken from TRNSYS library whereas some new models (defined types, in TRNSYS) were developed by the authors in Fortran and linked to the TRNSYS (e.g. DHW heat exchangers, Parabolic-Trough Collectors, Hydraulic Separator, Fan-coils, Primary Energy Calculator, Economic Costs Calculator, etc). Conversely, the SOFC subsystem (consisting of several components, as shown in Fig. 2) was completely modeled by a proprietary simulation code, developed by the author in MATLAB [5,43]. In conclusion, a full presentation of the simulation model would require the description of the models of dozens of components. Therefore, for sake of brevity, the thermodynamic models of the main components will be only briefly summarized in Appendix, whereas the full description of the models is available in references. Conversely, the models for the calculation of economic and energetic balances are discussed in detail in the followings. The main input data regarding the HSSOFC are provided in Table 1. Table 2 shows the input parameters of tanks, pumps and chiller. Building parameters are shown in Ref. [11] and here omitted for brevity.

3.1.

Calculation of energy saving

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 e with respect to a traditional HVAC system assumed as a reference (RS) e can be evaluated, too. To this scope, a reference system was also implemented and simulated in TRNSYS, using the same building served by the HSSOFC. In the case study presented in the paper, an air-towater electric-driven heat pump (EHPRS) was considered as the reference system, producing hot water during the winter and refrigerated water during the summer. The RS also includes a gas-fired heater, for DHW production. This system

Table 1 e Parameters for solar collectors. Parameter

The HSSOFC polygeneration system described in the previous section was dynamically simulated in TRNSYS, which is a well-known software diffusely adopted for both commercial and academic purposes. As mentioned above, the TRNSYS project is also linked with the MATLAB code developed by the author, simulating the SOFC subsystem. In particular, TRNSYS, for each simulation, calls MATLAB routine and then uses the results of MATLAB simulation, for the calculation of the overall system performance. The TRNSYS software includes a large library of built-in components, often validated by experimental data [44]. As mentioned above, the HSSOFC

ASC cSC (sa)n FRUL cf Nseries Nparallel TSC,set,s TSC,set,w TSC,max lpump

Value

Unit

600 35 0.7 4.17 2.8 10 15 170 55 300 5

2

m / e W/(m2 K) kJ/(kg K) / /  C  C  C %

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Table 2 e Parameters for pumps (P), tanks (TK ), absorption chiller (ACH ), auxiliary heater (AHB) and Heat Exchanger (HE2). Parameter UAHE2 QP4 vTK1,s vTK1,w TK1 overall loss coefficient TK1 nodes TK1 height TK2 Volume 4P2 COPAHC,n Tset,out,ACH

Value

Unit

1.0 106 10750 20 20 3.0 5 2.0 2.0 50 1.21 6.5

kJ/(h K) kg/h L/m2 L/m2 kJ/(h m2 K) e m m3 kg/h/m2 /  C

electric energy delivered to the grid by the HSSOFC and the last is the thermal energy for DHW produced by the HSSOFC. Note that this last term includes only the amount of domestic hot water actually produced by the HSSOFC and demanded by the building. If the daily DHW production of the HSSOFC is higher than building demand, the exceeding part of this energy will be dissipated. The primary energy required by the HSSOFC is only due to the yearly natural gas volume consumed by the fuel cell and to the fossil fuels consumed by the thermoelectric power plant (average efficiency, hel,t ¼ 0.461) in order to supply the auxiliary electric energy (Eel,,i) required by the building and system and not supplied by the HSSOFC. Therefore, the HSSOFC primary energy is: PEHSSOFC ¼

is commonly considered as the reference HVAC system for Mediterranean climates, since it is largely more efficient than the combination of gas-fired heater and electric water chiller used for continental climates. Thus, the primary energy consumed by the EHPRS was calculated by the TRNSYS simulation and then used in HSSOFC simulation in order to evaluate primary energy savings. As above mentioned, this study was performed using the same building (as a consequence the same hourly space heating, space cooling and DHW demand) adopted in previous works [11,29,40], in order to better compare this layout with the ones previously developed. In particular, in Ref. [40] the electric load profile of the building under investigation is reported, whereas in Ref. [11] building space heating and cooling loads are described in detail. Note also that a correct energy comparison between the two investigated systems (HSSOFC versus RS) 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 HSSOFC 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 HSSOFC system also produces DHW and eventually some electric energy in excess, to be sold to the grid. This is also due to the fact that the SOFC is assumed to operate at full load all the time, when the system is active. In addition, as shown in Figs. 1 and 2, the exceeding thermal energies produced by the SC and by the SOFC are converted in DHW. 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 excess electric energy produced by the HSSOFC and sold to the grid (Eel,þ). Therefore, considering the sum over all the time-steps, the RS primary energy is: "   X   1 X Qc;i Qh;i þ þ Eaux;RS;i þ Eel;b;i PERS ¼ hel;t i COPEHP;RS;i COPEHP;RS;i i # X X QDHW;i  þ Eel;þ;i þ hb;i i i

(1)

The first term in Eq. (1) represents the primary energy consumed by the HVAC system, the second one is the primary energy required by building equipments, the third one is the

6135

X Eel;SOFC;i i

hel;SOFC;i

þ

1 X 1 X Eel;;i ¼ VNG LHV þ Eel;;i hel;t i hel;t i

(2)

In fact, the simulation model presented in this paper also includes a subroutine for the calculation of the electricity balances. The model consists of a data reader which obtains, from an external file (provided graphically in Ref. [40]), the electrical energy demanded by equipments and lights (Eel,b), for each time step. Simultaneously, the model also calculates the amount of electricity produced by the fuel cell (Eel,SOFC) and the one consumed by the auxiliary devices (pumps, fans, etc) included in the system (Eaux). Thus, for each time step, the model calculates the net electric energy required by the HSSOFC. Eel;HSSOFC ¼ Eaux þ Eel;b  Eel;SOFC

(3)

Obviously, if this quantity is positive, the HSSOFC is demanding electric energy from the grid. Conversely, when this quantity is negative, the HSSOFC is providing electricity to the grid. The system energy performance is also evaluated using the Solar Fraction (Fsol), which can be defined as: Fsol ¼

QSC QSC þ QAH þ QHEHF

(4)

Finally, the overall energy saving is calculated using the well-known Primary Energy Saving (PES): PES ¼

PERS  PEHSSOFC PERS

3.2.

(5)

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 Refs. [11,12,15,17,29] for the SHC components and in Ref. [5] for the SOFC subsystem. The operating costs due to natural gas and electric energy consumptions were evaluated, whereas maintenance costs 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 HSSOFC polygeneration was expressed as: P Ctot ¼

Ji

i

AF

þ Cop

(6)

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 1 2 8 e6 1 5 0

The operating costs were evaluated for both HSSOFC and RS system in order to calculate the cost savings due to the use of the HSSOFC. As regards the HSSOFC system, the operating cost, Cop, is due both to the natural gas consumption required to supply the HSSOFC fuel cell and to the eventual electricity purchased from the grid in the periods in which SOFC electrical power is lower than building and system demand. The operating costs are calculated by taking into account also the electric energy flows exchanged with the grid. In fact, the model considers the eventual purchase/selling from/to the grid at the current price ( pEE) or cost (cEE), respectively. According to the algorithm shown in Eq. (3), the model evaluates for each time step the eventual amount of energy purchased or sold. Then, another algorithm evaluates the current cost/price values for the considered time step, on the basis of a time-dependent tariff system. Thus, the model is capable to evaluate the economic value of the electric energy sold or purchased by taking into account the periods in which this energy is purchased or sold: X  VNG;i cNG;i þ Cel;i (7) Cop;HSSOFC ¼ i

Note that in Italy, as in many other countries, the electric energy 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 peak, medium and off-peak periods. Typically, F1 occurs during the working days between 8.00 a.m. and 6.00 p.m., F2 is typical of the daylight of Saturdays and late evenings and 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 cost of electric energy to be purchased were assumed equal to 0.14 €/kW h, 0.11 €/kW h and 0.090 €/kW h, in F1, F2 and F3, respectively. The prices for electric energy sale were equal to 0.090 €/kW h, 0.070 €/kW h and 0.045 €/kW h, in F1, F2 and F3, respectively. The calculation of electricity costs is dynamically performed by the simulation tool. In fact, the user may upload the file containing 8760 rows and indicating which tariff timeframe corresponds to each hour. Then, the code evaluates Equation (3) and calculates the actual electrical cost. It evaluates, for each time step, the logical variable ael, whose possible values are only 0 and 1:   (8) ael ¼ Eel;HSSOFC;i > 0 if i ¼ F1 Cel;i ¼ ael cEE;F1 Eel;HSSOFC;i þ ael pEE;F1 Eel;HSSOFC;i else if i ¼ F2 Cel;i ¼ ael cEE;F2 Eel;HSSOFC;i þ ael pEE;F2 Eel;HSSOFC;i else Cel;i ¼ ael cEE;F3 Eel;HSSOFC;i þ ael pEE;F3 Eel;HSSOFC;i

(9)

Then, the model compares the present time step with the time-dependent cost map, in order to evaluate the corresponding timeframe (F1, F2 or F3). Finally, the model evaluates the present cost of electrical energy. If the net electrical energy (Eel,HSSOFC,i) is positive, this amount of energy must be purchased from the grid at the current costs (cEE). Conversely, if the net electrical energy (Eel,HSSOFC,i) is negative, such amount of energy is sold to the grid at the current price ( pEE).

Obviously, if in the considered time step, Cel,i is positive, the quantity is a cost, otherwise it represents an income for the owner of the HSSOFC. As for 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 i

þ

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

XQDHW;i cNG;i  LHVhb;i i

(10)

In particular, an algorithm similar to the one shown in Eq. (9) can calculate which is the actual value of cEE,i for the considered time step. 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 two possible public funding strategies are considered in this work: the first is based on a public capital cost contribution equal to 30% of the extra cost of the HSSOFC with respect to the RS; the second is based on a feed-in tariff equal to 0.20 € per kW h of primary energy saved by the HSSOFC with respect to the RS. Thus, Simple Pay Back Periods (SPB), Net present Value (NPV) and Profit Index (PI ) are calculated as follows SPB ¼

  ð1  jÞ Jtot;HSSOFC  Jtot;RS Cop;RS  Cop;HSSOFC þ ðPERS  PEHSSOFC Þcft

  NPV ¼ Cop;RS  Cop;HSSOFC þ ðPERS  PEHSSOFC Þcft FA    ð1  jÞ Jtot;HSSOFC  Jtot;RS PI ¼

NPV   ð1  jÞ Jtot;HSSOFC  Jtot;RS

(11)

(12)

(13)

In these equations, the values of j and cft are 0.30 and 0 €/ kW h if the capital cost contribution is considered (in this case, the economic indexes are indicated as SPBcc, NPVcc and PIcc), whereas their values are respectively 0 and 0.20 €/kW h in case of feed-in tariff (in this case, the economic indexes are indicated as SPBft, NPVft and PIft).

4.

Results and discussion

On the basis of the model presented in the previous sections, a case study has been implemented. This case study was developed for the university building located in Naples, South of Italy, previously investigated by the author [11]. The building consists of 7 classes, a common area and is located close to the university fitness center, so that the produced DHW can be delivered to that user. The building is used from Monday to Saturday, from 8.00 a.m. to 6.00 p.m., all year long. The activation periods of the heating and cooling systems are compliant with Law [11,40]. The power demand of the building (only lights and equipments) is evaluated on the basis of its historical data, graphically shown in Ref. [40]. The total cooling capacity of the HSSOFC system is 250 kW. The collector field area was set at 600 m2 which is significantly lower than the theoretical value (approximately 1000 m2) required to

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 1 2 8 e6 1 5 0

achieve the demanded cooling power. In fact, in this polygeneration system, the heat required to drive the ACH must be supplied both by SC and SOFC. Therefore, it is mandatory to select a lower size of SC area in order maximize the SOFC thermal energy utilization. The main parameters adopted as input in this case study are summarized in Tables 1e3. Note that the parameters shown in the above mentioned tables are only a small percentage of the total number of parameters, which are extensively reported in Refs. [11,12,15,17,40] for the TRNSYS model and in Refs. [43,46] for the SOFC subsystem. The electric capacity of the SOFC was set at 95 kW. This value comes from the results obtained in Ref. [40], where the Fuel Cell was designed on the basis of the thermal capacity demanded by the ACH. This selection determined a dramatic disproportion between Fuel Cell electrical production and building electricity demand, causing a large amount of electricity sold to the grid. Therefore, in this study the SOFC was designed on the basis of the duration curve of the building power load [40], in order to better balance the quantity of electrical energy to be sold and purchased. This procedure allows one to set SOFC nominal power. However, that power target could be achieved by different possible combinations of SOFC synthesis/design parameters. The selection of the synthesis/design parameter is a key point in the design procedure of the system, since it dramatically affects system efficiency and costs. In particular, an appropriate design could be performed using an optimization procedure minimizing a specific objective function. Such optimization algorithms can calculate the values of the synthesis/design parameters which minimize the selected objective function. In this study, the subsystem total cost (owning and operating) was assumed as the objective function and the same genetic algorithm

Table 3 e SOFC subsystem parameters. Parameter Fuel inlet mass flow rate Air inlet mass flow rate Fuel inlet temperature Air inlet temperature Fuel inlet pressure Air inlet pressure AC compression factor FC compression factor SOFC active area HEA area HEF area PR heat transfer area Fuel utilization factor Anode thickness Cathode thickness Electrolyte thickness SOFC length Number of SOFC tubes SOFC tube diameter PR tube length Number of PR tubes SOFC tube diameter UAHEHF

Value

Unit

0.0042 0.360 25.0 25.0 1.00 1.00 1.50 1.50 551070 74.5 0.850 1.79 0.850 0.010 0.22 0.0040 1.50 750 0.0156 0.22 30 0.0156 3000

kg/s kg/s  C  C bar bar / / cm2 m2 m2 m2 / cm cm cm m / m m / m kJ/h K

6137

adopted in Ref. [5] was adopted for the system optimization. Such procedure, defined thermoeconomic optimization, is widely adopted in industry and academia for optimal system design. The optimization procedure was performed by using the same guidelines shown in Ref. [5], varying the main design parameters of the SOFC (such as: air and fuel mass flow rates, SOFC number of tubes, heat exchanger number of plates, etc.) described in Ref. [5]. Additional details regarding the selected thermoeconomic optimization procedure are given in Ref. [5]. The values of the design parameters calculated by the genetic algorithm are shown in Table 3. This table also shows some boundary conditions set in the simulation. Additional parameters of the SOFC subsystem are given in Ref. [5]. The overall results of this optimization procedure are reported in Tables 4 and 5, respectively showing the thermodynamic properties of the system key points and the overall efficiency parameters for the plant as a whole and for the main components. Table 4 also shows that the optimization procedure returned results compliant with those reported in literature:  SOFC operating temperature is very close to its optimal value (1000  C);  SOFC longitudinal thermal gradient is within acceptable ranges;  The amount o of un-reacted fuel (stream 3), burnt in the catalytic burner (C), is able to increase C outlet temperature up to 1079  C. Such additional thermal flow is then used for stream pre-heating in PR, HEC, HEF and HEA;  AC and FC pressure increase is higher than pressure drops in the system;  Temperature of gas exhaust stream (10) is high enough for the thermal demand of HEF included in HSSOFC layout. Note also that the thermodynamic properties of state points 29-33 are not reported in Table 4. In fact, such state properties dynamically vary during the HSSOFC operation, as discussed in the following. Conversely, the thermodynamic states of points 1e28 do not vary, as a consequence of the steady state operation of the SOFC subsystem during HSSOFC activation. Table 4 also presents chemical (Exch) and physical exergy (Exph) flows of the state points, showing that chemical exergy conversion mainly occurs in the IRSOFC, whereas physical exergy is mainly varies in the heat exchangers included in SOFC subsystem. Table 5 shows some of the main energetic/electrochemical results of the SOFC subsystem under investigation. In particular, the heat exchange efficiency of HEF and HEA is in the same order of magnitude of the ones achieved for the hybrid optimized configuration shown in Ref. [5]. Similarly, HEC heat exchange efficiency is very low: in fact this component is not a real heat exchanger, since it only models the heat exchange section, placed on the top of the SOFC stack, as discussed in the previous sections. The overall electrical efficiency of the system is slightly lower than 47%, which is the typical value achieved by the majority of the existing SOFC prototypes [3]. Note also that this efficiency is significantly lower than the one achieved in the previous study [5]. This is due to the fact that the SOFC considered in the present analysis does not include the GT, so that it is not possible to recover energy from

6138

Table 4 e SOFC subsystem: state point thermodynamic properties. t ( C)

p (bar)

H (kW)

S (kW/K)

Exph (kW)

Exch (kW)

m (kg/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

404.7 925.9 1006.0 1006.0 1006.0 831.9 1006.0 1079.0 1061.0 303.4 130.5 25.0 70.5 25.0 63.9 1004.0 1004.0 813.4 305.4 813.4 1005.0 813.4 404.7 404.7 825.4 1061.0 1005.0 1005.0

1.500 1.500 1.499 1.499 1.499 1.497 1.497 1.497 1.497 1.491 1.496 1.000 1.500 1.000 1.500 1.496 1.496 1.498 1.491 1.498 1.496 1.498 1.500 1.500 1.500 1.497 1.496 1.496

4.74E þ 00 4.85E þ 01 6.67E þ 01 3.08E þ 01 3.59E þ 01 3.23E þ 02 3.81E þ 02 4.44E þ 02 4.36E þ 02 1.17E þ 02 5.70E  01 9.07E þ 00 2.57E þ 01 2.20E  01 5.83E  01 4.74E þ 00 4.06E þ 02 3.16E þ 02 1.16E þ 02 0.00E þ 00 4.11E þ 02 3.16E þ 02 0.00E þ 00 4.74E þ 00 4.07E þ 01 4.36E þ 02 4.11E þ 02 4.11E þ 02

9.57E  03 8.72E  02 1.08E  01 5.00E  02 5.84E  02 5.46E  01 5.81E  01 6.75E  01 6.69E  01 3.19E  01 2.07E  03 8.51E  02 9.49E  02 9.81E  04 1.26E  03 7.49E  03 6.42E  01 5.39E  01 3.16E  01 0.00E þ 00 6.50E  01 5.39E  01 0.00E þ 00 9.57E  03 7.50E  02 6.69E  01 6.50E  01 6.50E  01

1.96E 2.77E 3.90E 1.80E 2.10E 1.77E 2.23E 2.65E 2.59E 4.44E 2.13E 0.00E 1.37E 0.00E 2.81E 2.77E 2.37E 1.71E 4.43E 0.00E 2.40E 1.71E 0.00E 1.96E 2.24E 2.59E 2.40E 2.40E

þ 00 þ 01 þ 01 þ 01 þ 01 þ 02 þ 02 þ 02 þ 02 þ 01  01 þ 00 þ 01 þ 00  01 þ 00 þ 02 þ 02 þ 01 þ 00 þ 02 þ 02 þ 00 þ 00 þ 01 þ 02 þ 02 þ 02

2.11E þ 02 2.67E þ 02 8.29E þ 01 3.83E þ 01 4.47E þ 01 1.61E þ 00 1.64E þ 00 4.36E þ 00 4.36E þ 00 4.36E þ 00 5.02E  02 1.61E þ 00 1.61E þ 00 2.11E þ 02 2.11E þ 02 5.02E  02 4.31E þ 00 1.61E þ 00 4.31E þ 00 0.00E þ 00 4.36E þ 00 1.61E þ 00 0.00E þ 00 2.11E þ 02 2.55E þ 02 4.36E þ 00 4.36E þ 00 4.36E þ 00

4.20E  03 2.57E  02 3.99E  02 1.84E  02 2.15E  02 3.60E  01 3.46E  01 3.64E  01 3.64E  01 3.64E  01 4.20E  03 3.60E  01 3.60E  01 4.20E  03 4.20E  03 4.20E  03 3.60E  01 3.60E  01 3.60E  01 0.00E þ 00 3.64E  01 3.60E  01 0.00E þ 00 4.20E  03 2.57E  02 3.64E  01 3.64E  01 3.64E  01

xH2 O 0.00E 3.32E 5.67E 5.67E 5.67E 0.00E 0.00E 3.97E 3.97E 3.97E 3.97E 0.00E 0.00E 0.00E 0.00E 3.97E 3.97E 0.00E 3.97E 0.00E 3.97E 0.00E 0.00E 0.00E 4.40E 3.97E 3.97E 3.97E

þ 00  01  01  01  01 þ 00 þ 00  02  02  02  02 þ 00 þ 00 þ 00 þ 00  02  02 þ 00  02 þ 00  02 þ 00 þ 00 þ 00  01  02  02  02

xCO

xH2

xO2

xN2

0.00E þ 00 1.28E  01 6.65E  02 6.65E  02 6.65E  02 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 5.16E  02 0.00E þ 00 0.00E þ 00 0.00E þ 00

0.00E þ 00 2.47E  01 9.47E  02 9.47E  02 9.47E  02 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 7.35E  02 0.00E þ 00 0.00E þ 00 0.00E þ 00

0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 2.10E  01 1.81E  01 1.66E  01 1.66E  01 1.66E  01 1.66E  01 2.10E  01 2.10E  01 0.00E þ 00 0.00E þ 00 1.66E  01 1.66E  01 2.10E  01 1.66E  01 0.00E þ 00 1.66E  01 2.10E  01 0.00E þ 00 0.00E þ 00 0.00E þ 00 1.66E  01 1.66E  01 1.66E  01

2.00E  02 8.43E  03 6.76E  03 6.76E  03 6.76E  03 7.90E  01 8.19E  01 7.74E  01 7.74E  01 7.74E  01 7.74E  01 7.90E  01 7.90E  01 2.00E  02 2.00E  02 7.74E  01 7.74E  01 7.90E  01 7.74E  01 0.00E þ 00 7.74E  01 7.90E  01 0.00E þ 00 2.00E  02 9.73E  03 7.74E  01 7.74E  01 7.74E  01

xCO2 0.00E 1.61E 2.65E 2.65E 2.65E 0.00E 0.00E 1.99E 1.99E 1.99E 1.99E 0.00E 0.00E 0.00E 0.00E 1.99E 1.99E 0.00E 1.99E 0.00E 1.99E 0.00E 0.00E 0.00E 2.05E 1.99E 1.99E 1.99E

þ 00  01  01  01  01 þ 00 þ 00  02  02  02  02 þ 00 þ 00 þ 00 þ 00  02  02 þ 00  02 þ 00  02 þ 00 þ 00 þ 00  01  02  02  02

xCH4 9.80E  01 1.24E  01 1.72E  08 1.72E  08 1.72E  08 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 9.80E  01 9.80E  01 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 0.00E þ 00 9.80E  01 2.20E  01 0.00E þ 00 0.00E þ 00 0.00E þ 00

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 1 2 8 e6 1 5 0

Par./Unit

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 6 1 2 8 e6 1 5 0

Table 5 e SOFC subsystem main results. Parameter HEA heat efficiency HEF heat efficiency HSC heat efficiency Combustion efficiency Net electrical efficiency Net exergetic efficiency Inverter efficiency Air Compressor Isent. efficiency Fuel Compres. Isent. efficiency Max cell theoretical efficiency Stack Electrical efficiency Total electrical power CH4 moles reacted H2 moles electroch. reacted Steam to carbon ratio: Air utilization factor: Fuel utilization factor: Max cell theoretical potential Actual cell potential Cell current Cell current density Anode resistance Cathode resistance Interconnections Resistance Anode activation overpotential Cathode activation overpotential Global activation overpotential Concentration overpotential Ohmic overpotential Anode exchange current density Cathode exchange current density Cross-over current density

6139

Table 6 e HSSOFC Case Study: main energetic results.

Value

Unit

Parameter

0.795 0.929 0.072 1.00 0.469 0.447 0.920 0.800 0.750 0.729 0.531 95.1 0.000253 0.000888 2 0.169 0.850 0.779 0.665 171.4 311.0 0.03846 1.00E-05 0.00286 0.0608 0.0225 0.0277 0.0260 0.0418 0.0382 754.5 2

/ / / / / / / / / / / kW kmol/s kmol/s / / / V V A mA/cm2 Ohm cm2 Ohm cm2 Ohm cm2 V V V V V mA/cm2 mA/cm2 mA/cm2

Eel,aux,HSSOFC Eel,SOFC QHE1 QAH QAH,s QSC QSC,s hSC Itot Fsol Eel,þ,F1 Eel,þ,F2 Eel,þ,F3 Eel,,F1 Eel,,F2 Eel,,F3 Eel,þ Eel, Eel,RS,F1 Eel,RS,F2 Eel,RS,F3 QHEHF QHEDHW Eel,RS PERS PEHSSOFC DPE PES EDHW,rej COPACH

SOFC exhaust gases to produce additional electricity. On the other hand, such circumstance determines a significant increase of the amount of thermal energy and of the “quality” such energy, since it is available at a higher temperature. Note also that the stack efficiency is significantly higher than that of the system as a whole, as a consequence of the electric energy consumed by auxiliary equipment. Finally, Table 5 also shows that the SOFC electrochemical parameters are similar to the ones shown in literature. In fact, the current density and the operating voltage are respectively close to 310 mA/cm2 and 0.66 V, which are usual values for this kind of Fuel Cell. As for the HSSOFC system, the main results are displayed in Table 6, where the main annual energy flows are shown. The SOFC produces 1.07  109 kJ/year of electric energy. This amount is significantly higher of the electricity required for all auxiliary equipment (CT, pumps, etc.). In fact, the electricity produced by the SOFC is basically used for building electrical equipments (1.01  109 kJ/year). The amount of electric energy produced by the SOFC and delivered to the grid is significantly lower (4.32  108 kJ/year) than the one used for internal demand (building and auxiliary devices). A small part of electricity (7.43  107 kJ/year) is also bought from the grid when HSSOFC power production is lower than building demand. However, this circumstance is rare and occurs mainly during the peak hours (F1 and F2). Similarly, the exceeding electric energy is delivered from the HSSOFC to the

Value 5.32E 1.07E 6.38E 5.24E 4.94E 1.10E 9.14E 2.64E 4.16E 8.67E 3.02E 1.28E 2.39E 5.28E 2.09E 6.53E 4.32E 7.43E 7.84E 1.17E 4.18E 1.16E 8.98E 9.05E 4.14E 2.55E 1.58E 3.83E 5.46E 1.38E

þ 07 þ 09 þ 08 þ 07 þ 07 þ 09 þ 08  01 þ 09  01 þ 08 þ 08 þ 06 þ 07 þ 07 þ 05 þ 08 þ 07 þ 08 þ 08 þ 06 þ 08 þ 08 þ 08 þ 09 þ 09 þ 09  01 þ 08 þ 00

Unit kJ kJ kJ kJ kJ kJ kJ / kJ / kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ kJ / kJ /

grid mainly during the peak hours (F1 and F2). This circumstance is due to the fact that the HSSOFC operates mainly during the peak hours. The SOFC also produces a significant amount of thermal energy which is used both for DHW production (8.98  108 kJ/year) and for HF heating (1.16  108 kJ/year). Therefore, this result clearly shows that the thermal energy required for space heating and cooling is low for maximizing the utilization of the thermal energy available from SOFC cogenerative heat exchanger. Thus, the simultaneous production of DHW by the SOFC is crucial in order to optimize the utilization of such thermal energy. Note also that the SC field, although undersized, produces a large amount of heat (1.10  109 kJ/year), mainly during the summer. In fact, concentrating SC maximize their efficiency only in case of high direct solar irradiation. In fact, the average SC average thermal efficiency (26.4%) is quite low. Conversely, the peak efficiency of SC may also overcome 60%. Note also that thermal energy produced by SC is not always required by space heating or cooling system. In fact, a large amount of QSC is used for DHW production. Table 6 also shows that the amount of DHW produced by the HSSOFC is higher than building demand, causing an annual thermal energy dissipation of 5.46  108 kJ/year. Finally, it can be observed that the thermal energy produced by the AH is not negligible. In fact, the SOFC is not sized for the maximum heating demand. Thus, some thermal energy is demanded to the AH during the heat peak loads. Nevertheless, the considered HSSOFC system shows a very good performance from the energetic point of

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view, presenting a primary energy saving ratio (PES) of 38.3%. This is due to the simultaneous contribution of solar energy and cogeneration. In fact, the sole SOFC electrical efficiency is not competitive with the thermoelectric efficiency, assumed as reference system. Note also that the Primary Energy (PE) demand of the HSSOFC is mainly due to the natural gas consumed by the SOFC. Table 7 shows the main economic results of the system under investigation. In particular, it is clear that the HSSOFC is dramatically more expensive than RS system, showing an extra capital cost slightly lower than 400 k€. On the other hand, the HSSOFC allows one to save more than 24 k€ per year. In fact, the HSSOFC pays approximately 41.1 k€ per year of natural gas supplying the Fuel Cell and the AH. Such gas is used to produce both heat and electricity. The amount of electricity sold to the grid is significantly higher than the one bought from the grid by the considered SOFC. Therefore, the balance between these two cash flows is an annual income of 7.36 k€. Finally, space heating and cooling and DHW are not considered as additional costs for the HSSOFC, since they are produced by cogeneration and/or solar energy. The main costs of the reference systems are due to the electricity needed for building equipments and for space heating and cooling. In particular, the electricity used for equipments, lights and space heating and cooling costs 34.2 k€/year. In addition, for the reference system, the cost of DHW production is 20.6 k €/year. The economical feasibility of the HSSOFC system can be analyzed by using some common economic indexes, as discussed in the previous section. In these calculations, the life span of the system and the actualization factor were assumed as 20 years and 5%, respectively. The SPB period is 16.5 year.

Table 7 e HSSOFC case study: main economic results. Parameter Jtot,HSSOFC Jtot,RS DJtot CDHW,HEDHW CDHW,HESC Cel, Cel,þ Cel, Cel,þ,RS Cel,RS Cop,RS Cop,HSSOFC Cft DCop DCop,ft SPB SPBft SPBcc CDHW,rej NPV NPVft NPVcc PI PIft

Value 4.76E þ 05 8.00E þ 04 3.96E þ 05 1.87E þ 04 1.33E þ 04 2.71E þ 03 1.01E þ 04 7.36E þ 03 1.57E þ 04 3.42E þ 04 5.48E þ 04 3.08E þ 04 8.80E þ 04 2.40E þ 04 1.12E þ 05 1.65E þ 01 3.54E þ 00 1.15E þ 01 1.14E þ 04 9.60E þ 04 1.00E þ 06 2.29E þ 04 2.42E  01 2.53E þ 00

Unit € € € €/year €/year €/year €/year €/year €/year €/year €/year €/year €/year €/year €/year year year year €/year € € € / /

This result is slightly worse than the ones achieved in PEM polygeneration system [40] or in CSHC system [29]. However, this is only due to the fact that, in the two above mentioned studies, the building DHW was not limited, and whatever amount of DHW produced by the solar system was used by the building. Here, the building DHW demand was more realistically limited in 2500 L/day at 45  C. Therefore, a large amount of heat produced by HSSOFC is dissipated and not delivered to the building. This energy dissipation corresponds to a cost dissipation of 11.4 k€/year. If such amount of thermal energy could be used, the SPB would be 11.2 year, which is slightly better than those achieved in the above mentioned studies. In addition, it is also well known that SPB is not a good economic index. In fact, in our case the estimated SPB (16.5 years) is lower than system operating life (20 years). However, the HSSOFC is far from being profitable, showing an NPV of 96.0 k€. In other words, this investment would determine a total loss of 96.0 k€. This circumstance is not surprising since it is quite common in fuel cells and renewable energy systems, which require some public incentive policy. A capital cost contribution of 30% would not be a satisfactory funding policy, since the corresponding SPBcc is 11.5 years but the NPVcc is low (22.9 k€). Conversely, a feed-in tariff of 0.20 € per kW h of primary energy saved by the HSSOFC would determine an additional annual income of 88.0 k€/year. This kind of incentive would completely change the economic balances, showing an SPBft of 3.54 years, an NPVft of 1.00 M€ and a PIft of 2.53. In this case, the considered HSSOFC would be extremely profitable. Note that the value proposed for the feed-in tariff is reasonable, since is dramatically lower than the one presently available for photovoltaic systems in Italy. The simulation tool developed for this work calculates temperature of all the state points and the energy flows of all the components included in the HSSOFC system, for each time step. The simulations were performed for a year (8760 h), using a time step of 2.4 min. Such short value is mandatory in order to get convergence in capacitive components such as building and tanks. Therefore, for each simulation, the tool returns a large amount of data. Obviously it is not possible to show here all these data. However, in the following figures a representative summer is selected, in order to show the typical trends of temperatures and energy flows. The presentation of the corresponding winter analysis is here omitted for brevity. During the summer, the HSSOFC operating temperature varies in a very large range. In fact, the CHW is produced by the ACH at 6.0  C, whereas the SC operates around 170  C. Therefore, for a better visualization of the results, the temperatures of some significant key point of the HSSOFC are displayed in two different figures, showing respectively low temperatures and high temperatures key points. In particular, Fig. 3 shows some low temperatures plots of the HSSOFC, during the 10 h of operation of a typical summer day. Here, the typical oscillating trend of the air node temperature of zone A1 (TA1) is displayed. These oscillations are due to the operation of the oneoff thermostat installed in each zone, which reactivates the fan-coils when the temperature is higher than 27  C and re-deactivates the fan-coils when the air temperature goes below 25  C. In other words, the controller operates using dead bands of 1  C. Lower values of these parameters

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Fig. 3 e HSSOFC main temperatures (1), summer day.

are not preferable since would determine a large number of fan-coil activation and deactivation. Note also that the building is dominated by internal loads and requires cooling even when the external (Text) is below 25  C. As regards CHW temperature entering (Tin,ACH,CHW) and exiting the ACH (Tout,ACH,CHW), Fig. 3 shows that the selected ACH is capable to cool the CHW to the fixed set point, except for the hottest day hours, when the ACH exiting temperature is around 7.5  C. However, this slight increase does not affect temperature control in the building zones. On the other hand, the temperature of the CHW entering the ACH (Tin,ACH,CHW) is dramatically oscillating as a consequence of the combinations of the load demands of the 7 zones included in the building. Furthermore, as expected, this temperature tends to increase when the load is maximum, i.e. during the hottest day hours.

Fig. 4 shows some HSSOFC high temperature key points during the operation of the selected summer day. Here, it is clearly shown that SC outlet (Tout,SC) temperature is often higher than the fixed set point. This means that P2 is operating at maximum flow rate. Note also that the peaks in Tout,SC are due to the feedback controller, managing P2, which operates using a secant method, determining some possible oscillations in the output control signal [44]. The fluid exiting from SC is then cooled down to 170  C (Tout,HE1,SCF) by the heat exchanger HE1. The temperature of the stream exiting TK1 is always higher than HEFC set point. Therefore, the temperature of the HF entering the HEFC is equal to the temperature exiting the HF (Tout,HEFC). Nevertheless, the TK1 average temperature (TTK1) is significantly lower, due to the thermal stratification of this component. Therefore, the additional

Fig. 4 e HSSOFC main temperatures (2), summer day.

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heat is provided by the cogenerative heat exchanger of the SOFC (HEFC). The outlet temperature of the HF exiting HEFC (Tout,HEFC,HF) is always higher than the set point required by the ACH. As a consequence, the temperature of the HF entering the ACH (Tout,AH) is always higher than the set point (168  C) and coincides with Tout,HEFC,HF, whereas the return temperature (Tout,ACH,HF) oscillates as a consequence of the variations of load demanded to the ACH. The main energy flows of the HSSOFC are shown in Fig. 5, regarding the same summer day selected above. Here, some of the results previously discussed are more clearly displayed. In particular, it is shown that the electric energy produced by the SOFC (PSOFC) is constant during the system operation. In addition, it is also clearly displayed that the cogenerative heat of the SOFC is always used for DHW production (QHEDHW is constant and QHEFC is zero, except for the last hour). The same figure also shows the total (Itot) and beam (Ib) radiation incident on SC, which can be compared to the heat produced by SC (QSC), concluding that the efficiency of the system is dramatically dependent on Ib. In fact, the efficiency of the PTC, calculated on Itot, is approximately 50% during the hottest day hours, whereas the annual efficiency is significantly lower (Table 6). Note also that a large amount of the QSC is used for DHW production by the HE1 (QHE1), specially during the early morning and late afternoon. Finally, Fig. 5 also depicts the cooling load demanded to the ACH (Qc,ACH) and the relative cooling energy provided by the CT (QCT), showing that the ACH operates at full load only during the early afternoon, corresponding to the time shown in Fig. 3, in which CHW outlet temperature is higher than the fixed set point. Fig. 6 shows the electric energy balances for the typical summer day under consideration. Here, it is clearly shown that during the summer, electric energy required for space cooling (Pel,EHP,RS) is dominant over the electric energy demanded for lights and equipments (Pel,b). Note that the considered 10 h of operation occur in F1. Therefore, the electric energy required by RS is Pel,RS,F1, that is the sum of Pel,EHP,RS and Pel,b. Furthermore, Fig. 6 also shows that the electrical

consumption of the auxiliary devices (Paux,HSSOFC) included in the HSSOFC is not negligible, specially due to the consumption of the CT. Finally, it is also clearly shown that, in the considered period, the power produced by the SOFC is largely higher than building (Pel,b) and system (Paux,HSSOFC) demand, determining a large amount of electric energy (Pel,þ,HSSOFC) delivered to the grid. Note that such energy is sold to the grid when the price is maximum (peak-load hours).

5. Parametric analysis and system optimization The study was also completed by a parametric analysis, aiming at analyzing the variation of the main energetic and economic parameters in function of some system design parameters, as usually performed in some previous studies [4,12,17]. To this scope, a parametric analysis was performed, by varying the following parameters: 1) SOFC size; 2) SC area; 3) SC winter set point temperature; 4) SC summer set point temperature; 5) TK1 summer volume; 6) TK1 winter volume. The configuration discussed in the previous sections is assumed as the initial one, and the above listed parameters are varied, one at the time. With regard to parameters from 3 to 6, conclusions similar to those drawn in Ref. [29] can be drawn, in which a high temperature CSHC system was investigated: the best energy and economic performance is achieved by using small TK1 volumes (both in summer and winter), low SC temperature winter set point and high SC summer temperature set point. In fact, such parameters mainly deal with the solar loop and are scarcely influenced by the use of the SOFC as auxiliary system. Comments regarding these results are provided in Ref. [29] and are here omitted for sake of brevity, also considering that such parameters affect very slightly the performance of the system under investigation. The discussion will be here focused on SC and SOFC capacities, which are the most significant parameters in the design of the HSSOFC system. Eleven possible SOFC sizes were

Fig. 5 e HSSOFC main thermal energy flows, summer day.

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Fig. 6 e HSSOFC electric energy flows, summer day.

considered, with a power capacity varying from 16 kW to 321 kW. For all of these configurations, the MATLAB code discussed in the previous sections was used in order to design the SOFC subsystem on the basis of the above discussed thermoeconomic optimization. For all the considered SOFC sizes, the electrical efficiency was close to 47%. The results of the analysis show that the performance of the HSSOFC is very sensitive to the variations of SOFC and SC capacities. In particular, Fig. 7 shows the main energetic parameters as functions of the two independent variables under discussion. Here, it is clearly shown that the PES is an increasing function of the SC area, although the rate of PES increase dramatically reduces with SC area. Conversely, PES is a non-monotonic function of SOFC size, showing a maximum, depending on SC area, varying from 63 kW to 95 kW. This trend is due to the management of thermal energy produced by the SOFC and SC. In fact, the amount of thermal energy produced by the HSSOFC and dissipated (EDHW,rej) dramatically increases with SC and SOFC sizes, as clearly shown in Fig. 7. As a consequence, the net thermal efficiency of the SOFC (i.e. the efficiency considering only the amount of thermal energy produced and delivered to the user) is generally decreasing

with SOFC nominal power. Results also show that the HSSOFCsolar fraction is significantly dependent on SC area but is almost insensitive to the SOFC nominal power, as expected. The electric balance is also dramatically affected by the variation of SOFC size. In Fig. 8, the electric energy flows are plotted as functions of the SOFC capacity, for an SC area of 600 m2. The amount of electric energy delivered to the grid becomes higher than the one purchased from the grid, only when SOFC size is higher than 63 kW. This plot is very important for sizing the SOFC, since a small and mediumscale cogeneration system could not be so profitable in case of high amount of power to be sold to the public grid. Fig. 8 also shows that both selling and purchasing occur during peakload hours (F1), whatever the size of the SOFC size. Finally, Fig. 9 shows the overall economic parameters for the HSSOFC, with respect to SC and SOFC capacities. In such figure, the economic indexes are shown in two cases: without any incentive (SPB, NPV and PI) and with a feed-in tariff (SPBft, NPVft and PIft). The considered HSSOFC system is not profitable without incentives, for whatever combination of SC and SOFC capacities. In fact, for the best configuration (600 m2 and 63 kW) the SPB is higher than 15 years, and both PI and NPV

Fig. 7 e Parametric analysis, energetic parameters.

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Fig. 8 e Parametric analysis, electric energy.

Fig. 9 e Parametric analysis, economic parameters.

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Fig. 10 e Thermoeconomic optimization of HSSOFC, objective function: SPBft.

are largely negative. Conversely, considering the feed-in tariff discussed in the previous section, all economic indexes become very good. In particular, the SPBft ranges between 3.5 and 8 years for the majority of the combinations. Similarly, the corresponding Net Present Value ranges from 200 k€ to 1000 k€. The Profit Index is also very positive ranging approximately from 0.6 to 2.60 The lowest SPBft and the highest PIft are achieved for ASC and PSOFC respectively of 400 m2 and 95 kW. A slightly different result is achieved if the NPVft, criterion is considered, suggesting the same SOFC size but an SC area of 800 m2. This parametric analysis is very important since provides important guidelines to the system designer regarding the selection of the system design parameters. However, it is not possible to assess that this procedure returns the set of design parameters minimizing (or maximizing) the selected objective function (SPB, VAN or PI). In fact, the parametric analysis here presented is not a rigorous mathematical procedure for the determination of the system optimal design. It is only a representative depiction of the system optimum response surface. In order to evaluate the set of design parameters minimizing the selected objective function, a rigorous mathematic optimization must be performed. To this scope, the author implemented an optimization procedure aiming at determining the set of operating and design parameters minimizing system Simple Pay Back, in case of feed-in tariff (SPBft). This optimization procedure was carried on using the TRNOPT plug-in included in the TRNSYS package [44]. This software links the TRNSYS dynamic simulation to the optimization algorithm. Such algorithms were developed by Lawrence Berkeley National Laboratory and included in the GENOPT package [51]. In this study the optimization was carried on using a Generalized Search Method (GPS) which allows to calculate the optimal value avoiding the calculation of the partial derivatives. In particular, the procedure presented in this paper uses appropriate algorithms [51] which

allows one to perform a robust and efficient optimization, taking into account the approximation of the objective function due to the TRNSYS solving technique and avoids the risk to achieve a local minimum point. This methodology is very efficient since the optimization usually terminates after 300 O 500 simulations, that is a number compatible with the present computational times. In fact, the optimization stopped after about 180 generations, as shown in Fig. 10.This optimization was performed, using as independent variable the 6 design parameters described above. The optimization procedure found the optimal configuration slightly better than the initial one (SPBft equal to 3.32 versus 3.54 in the initial configuration), for the following values of the considered design variables: 1) SOFC size: 95 kW; 2) SC area: 320 m2; 3) SC winter set point temperature: 50  C; 4) SC summer set point temperature: 175  C; 5) TK1 summer volume: 20 L/m2; 6) TK1 winter volume: 20 L/m2. The results of the optimization show that the selected initial point, discussed in the previous section, was very close to the optimal. These results are basically similar to the conclusions drawn by the above discussed parametric analysis. Therefore, it can be concluded that the appropriate selection of SC and SOFC capacities is crucial for achieving economically feasible HSSOFC systems. In particular, such parameters must be selected in order to limit as much as possible thermal energy dissipation.

6.

Conclusions

The results of the case study presented prove the technical feasibility of the HSSOFC polygeneration system analyzed in the paper. The dynamic simulation showed that the selection of a high-temperature cogeneration system, like the SOFC, is crucial in order to optimize the balance of the plant, specially balance between solar loop and absorption chiller. In addition, it also allows one to increase the overall operating

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temperature of the solar loop, so that PTC and double-stage absorption chiller can be used. These components significantly contribute to increase the overall performance of the system, especially during the summer. Conversely, during the winter, PTC dramatically suffers of the scarcity of solar radiation. Therefore, it may be concluded that the considered HSSOFC layout is indicated for applications in which the space cooling demand is dominant over the winter one. The results of the dynamic simulations presented also suggest that the HSSOFC may be efficient only where a simultaneous alternative heat demand is present, all year long (e.g. for DHW production). In fact, although both SC and SOFC are undersized, a lot of exceeding heat is produced, due to the phase shift between solar irradiation and thermal energy demand. As a consequence, the thermoeconomic optimization, performed in this study, suggested to accurately select SC and SOFC capacities in order to limit heat dissipations as much as possible. The economic analysis showed a profitability of the HSSOFC considered of the same order of magnitude than other SHC systems. In particular, the system is not profitable without public funding policies and becomes extremely convenient in case of feed-in tariff comparable to the green certificates presently adopted in many countries for the promotion of renewable energy sources. So, it can be concluded that the system evaluated is extremely efficient and flexible from a thermodynamic point of view, but a future commercialization of these prototypes will be only possible in case of dramatic reduction of SOFC capital cost and/or in presence of an effective funding policy, still required in order to make these systems economically competitive with the conventional ones.

Appendix. Thermodynamic simulation model Parabolic-trough collectors, PTC The collector consists of an evacuated tube, located at the focus of a parabolic concentrator. The evacuated tube is internally covered by an absorber, which transfers the beam solar irradiation, reflected by the parabolic surface, to the High Temperature Fluid, flowing inside. Such collectors can convert the sole beam fraction of the total irradiation. However, this deficiency is partly balanced by low thermal losses, only occurring at the external surface of the evacuated tube, which is typically small with respect to the total aperture area. In addition, such solar collectors are always equipped with a single axis tracking system, in order to keep the solar incidence angle in an acceptable range. Regarding collector orientation and tracking systems, a number of different possible configurations are available, showing significant differences in incident solar radiation and useful thermal energy. The most common arrangements are the following: i) horizontal collectors, NS axis orientation, tracking system following the solar azimuth angle; ii) horizontal collector, WE axis orientation, tracking system following the solar zenith angle. Usually, the former is more profitable for summer operation, and is commonly adopted for SHC applications. The simulation of Parabolic-Trough Collectors is developed on the basis of the equations given in Ref. [52]. Here,

a modified collector loss coefficient (F0 UL) is developed, based on the standard collector loss coefficient (FRUL, provided by manufacturer), corrected in function of the actual flow rate of the working fluid. The concentration ratio, cSC, is the ratio of the aperture area to the receiver area: cS ¼

ASC Areciever

(14)

The coefficient 2 is: 2¼

FR UL _ test cf cSC m

(15)

If 2  1, the corrected coefficient is equal to the manufacturer one (F0 UL ¼ FRUL). Otherwise, it is: FR UL   _ m cf cSC test _ test cf 1  e FUL ¼ m

(16)

Then, the useful energy gain from the solar collector is: QSC

   FR UL tin;SC  text ¼ R1 R2 ASC Nparallel FR IAMðsaÞn Ib  cSC

(17)

In Equation (17), three corrections factors are considered: R1 accounts for flow rates different from test conditions; R2 takes into account the series/parallel arrangement of the collectors; IAM, Incidence Angle Modifier, provides data regarding the variation of the transmittance and absorbance of the receiver as a function of the solar incidence angle. R1 and R2 can be calculated analytically [52]. IAM values are provided by the manufacturers. The solar collectors were also equipped with a feedback controller which calculates the control signal to be sent to P2 in order to maintain the controlled variable (SC outlet temperature) at the fixed set point. In addition, the controller stops P2 when the TK1 bottom temperature is higher than the SC outlet temperature, in order to prevent heat dissipation in SC in case of scarce solar irradiation and/or low external temperature. This way, a real PID feedback controller is simulated, that continuously adapts its output signal, using the secant method to calculate the control signal that minimizes the tracking error. A threshold value for non-zero output (lpump) was also introduced, in order to simulate the pump minimum flow rate, avoiding the use of unrealistic values (i.e.: mass flow rates for P2 lower than the minimum rated value) [11,12,15e17,29,40]. Finally, the tracking system of the SC under investigation was equipped with a maximum temperature control management. This device defocuses the receiver when the temperature of the HTF overcomes a fixed set point (tSC,max), depending on the maximum temperature allowed for both SC materials and HTF. However, this circumstance should be avoided by the HE1 which is activated in DHW production, when SC outlet temperature overcomes the fixed set point.

Heat exchanger diathermic oilewater, HE2 A cross-flow heat exchanger (HE2) was employed to transfer heat from the diathermic oil to the hot water circulating in the heating coils. Such device is simulated by using the type 5

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model included in TRNSYS library, based on the well-known 3NTU method [11,12,15e17,29,40].

Auxiliary gas-fired heater, AH As mentioned above, the AH produces auxiliary energy to be supplied to the ACH or to the HE2, in case of scarce availability of thermal energy from PTC and SOFC. The simulation model of this component is based on manufacturers data, providing both boiler and combustion efficiencies at different inlet temperatures and part load ratios. The heat to be supplied depends on the inlet temperature of the fluid (diathermic oil) and on the set point outlet temperature: _ f cf ðtset;out  tin Þ Q_ h;req ¼ m

(18)

If the heat flow rate required is higher than the AH maximum capacity, the AH works at nominal conditions, and the outlet temperature of the diathermic oil is calculated as follows: tout;AH

Q_ AH;n ¼ tin þ _ f cf m

(19)

In all other cases, a Part load ratio (PLR) is calculated, defined as: PLR ¼

Q_ h;req Q_ AH;n

(20)

Then, the values of PLR and inlet fluid temperature are used to enter the manufacturers’ data file, which returns both combustion and boiler efficiency. The primary energy required by the AH is: Q_ h;req Q_ fuel ¼ hAH

Absorption chiller, ACH A double-effect hot water LiBreH2O absorption chiller (ACH) was considered. The component is simulated by the TRNSYS Type 677 which uses a normalized catalog data lookup approach, calculating cooling capacity, electric energy consumption and outlet temperatures, once inlet CHW, CW and HF temperatures and flows are given [53]. The ACH can operate with HF inlet temperature in the range 120  Ce175  C. Lower temperatures cannot drive the double-effect generator. Similarly, higher temperatures are not acceptable for the thermodynamics of the machine. Here, the performance data were modified in order to comply with the data sheet of a 250 kW double-stage H2OeLiBr hot water fired absorption chiller.

Cooling tower, CT

Q_ exhaust ¼ Q_ fuel ð1  hcomb Þ

(22)

Q_ loss ¼ Q_ fuel  Q_ exhaust

(23)

Finally, the rate of mass flow of gas employed to produce the required heat is given by; Q_ h;req LHVgas

the thermal storage capacity should be lower. Thus, HF exiting HE1 is brought to the smaller tank of TK1 during the summer. In the winter, the diverters placed upstream TK1 are positioned at half position. Thus, the stream can use both tanks simultaneously, increasing system thermal capacity. Both tanks included in TK1 are simulated using Type 4; the second tank (TK2, modeled by Type 60) is used in the CHW loop to store chilled water in the cooling season and hot water in the heating season. Their models are based on the assumption that the tanks can be divided into N fully-mixed equal subvolumes. For each sub-volume, mass and energy balances are considered in transient state, allowing one to calculate thermal stratification in the component. The tanks are also equipped with a pressure relief valve, in order to account for boiling effects [11,12,15e17,29,40].

(21)

The energy exhausted and energy loss are as follows:

_ gas ¼ m

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(24)

The AH outlet set-point temperatures were fixed in function of those selected for the solar loop. In fact, the AH set-point temperatures were assumed to be 2  C lower than the corresponding winter or summer SC set point temperatures, in order to reduce the frequency of AH start-up and shut-down events.

Storage tanks, TK The system layouts under evaluation included three storage tanks, all subject to thermal stratification. The storage system TK1 consists of two tanks, of different sizes. In fact, previous studies suggest that SHC systems during the winter need high thermal storage capacity. Conversely, in the summer, when the load is approximately simultaneous with solar radiation,

In this paper the 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 [54] that matches the manufacturers’ catalog data over a wide range of operating conditions. The model requires to set several parameters at design point (outdoor dry bulb and wet bulb temperatures, ambient air pressure, CT inlet and outlet CW temperatures, CW mass flow rate, process air mass flow rate, CT fan power). Cooling tower air mass flow rate, cooling capacity and CW mass flow rate are calculated using the equations reported in Refs. [11,12,15e17,29,40].

Heat exchanger for DHW production, HE1 As above mentioned, the DHW is produced in the solar loop 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 HE1 is equipped with a diverter placed upstream the DHW inlet, a bypass duct and a mixer downstream the DHW outlet. The diverter and the mixer are managed by the HE1 control system. The model of this heat exchanger was developed by the author using a modified version of the well-known 3-NTU method [55], calculating the by-pass factor and the DHW flow required in order to achieve both set point outlet temperatures of HF and DHW, respectively [11].

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Hydraulic separator This device is required in order to balance the flow rates between the primary and secondary loops of the system. In fact, the water flow rate in the primary loop is constant at the P4 nominal flow rate. On the other hand, the flow in the secondary loop is the sum of the flows circulating in the seven secondary pipelines. Therefore, the secondary loop flow rate may significantly vary during the day, depending on the heating/cooling loads of the different thermal zones. For such device, a new TRNSYS model was introduced, based on simple energy and mass balances [11].

Fan-coils Each zone is equipped with a 2-pipes loop, supplying hot/ chilled water to the respective fan-coils. Therefore, the same fan-coil operates in cooling mode during the summer and in heating mode in the winter. In this work, the fan-coil, for both cooling and heating modes is simulated, developing a new TRNSYS type, 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. Therefore, it is here adopted the new type developed in Ref. [11], calculating the fan-coil performance, from the design data combined with four correction factor, function of: actual fluid mass flow rate, inlet fluid temperature, air dry and wet bulb temperature, and air flow rate.

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 thermohygrometric 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 model considers also the air and energy coupling between adjacent zones and the radiative heat flows to the walls and windows. The walls are modeled according to the transfer function of Mitialas and Arsenault [44]. 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. Additional details concerning the mathematical models implemented in TRNBULD can be found in the TRNSYS mathematical in Ref. [44].

SOFC As discussed in the previous section, the model of the SOFC subsystem was derived from the one developed by the author [5,43], appropriately modified in order to comply with the need

to eliminate the gas turbine section and to re-design the cogenerative equipment. The SOFC is fed by natural gas whereas air is assumed as the oxidant. Considering input streams and chemical reactions, 7 different substances may be included in the subsystem streams: O2, N2, CH4, CO, CO2, H2O, and H2. For all these substances very detailed models were implemented for the calculation of properties (enthalpy, entropy, specific heats, viscosity, conductivity and density) [5,43]. The SOFC subsystem includes two compressors (air and fuel), simulated using the same approach shown in Refs. [5,43]. Compressors design points were appropriately modified varying their map scaling factors, in order to comply with flow rates and pressure ratio required by the HSSOFC under investigation. Due to its geometric arrangement, the HEC is simulated as a virtual counter-flow tube-in-tube heat exchanger, modeled on the basis of a modified iterative version of the 3-NTU method; the dependence of thermo-physical and transport properties on temperature and pressure drops is also taken into account [5,43]. Compact heat exchangers (HEA, HEF) are modeled using a further modified version the 3-NTU method, strictly related to the geometry of the component; the dependence of that specific heats, global heat transfer coefficients and outlet pressures on the temperature is also considered [5,43]. Finally, the HEDHW is simulated by the same technique described for HE1, whereas HEHF is a shell-and-tube heat exchanger, simulated replicating the same model included in the TRNSYS package [44]. The pre-reformer unit consists of a number of tubes located inside a shell and filled with a catalyst. The gas to be reformed flows inside these tubes. Hot gases, coming from the combustor, flow externally, supplying the thermal energy needed to support the process. In fact, the heat provided by the exothermic shift reaction is significantly lower than the one demanded by the endothermic demethanization or reforming processes. In order to simulate this component, the heat-exchange problem must be solved and the chemical composition of the outlet flows must be evaluated as well, taking into account both equilibrium and kinetics of the chemical reactions. To this scope, an appropriate model is developed based on the differential form of the energy balance equation, integrated along the reformer tubes to calculate the outlet temperatures starting from a set of inlet ones and taking into account the rate at which both the reforming and shift reactions occur in the cold stream. For the shift reaction, it is assumed that chemical equilibrium is controlling the process whereas for the reforming reaction both equilibrium and kinetic calculations are performed in order to ascertain the actual state of the reaction [5,43]. The internal reforming process was simulated by a similar approach, as shown in Refs. [5,43]. Combustion reaction was assumed complete. Therefore, the Combustor was simulated by simple energy and mass balances [5,43]. The core of the simulation model is the electrochemical process occurring in the fuel cell. SOFC are capable to convert electrochemically hydrogen into electricity and heat, using

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O2 as ion, by the anode and cathode semi-reaction, respectively as: H2 þ O2 /H2 O þ 2e

(25)

1 O2 þ 2e /O2 2

(26)

The rate of the above reported electrochemical reaction of was evaluated considering that the cell voltage is the Nernst Open Circuit Voltage, reduced of ohmic, activation and concentration overpotentials. Vcell ¼ ENernst  hact;A  hact;C  hU  hconc;A  hconc;C

(27)

The Nernst Potential was calculated using specific rigorous temperature dependent thermodynamic relations for the Gibbs free energy, avoiding the adoption of empirical equations [1,5]: ENernst ¼

Dg0f 2F

þ

1=2 RT pH2 pO2 ln pH2 O 2F

X

li di xi e T

(29)

The activation overvoltage was calculated by the implicit ButlereVolmer equation combined with semi-empirical relations for the anode and cathode exchange current density:    zF zF i ¼ i0 exp a hact  expð1  aÞ hact RT RT 

pH2 pamb

i0;an ¼ gA  i0;c ¼ gC

pO2 pamb

    pH2 O Eact;A exp  pamb RT

0;25

  Eact;C exp  RT

(30)

(31)

(32)

The concentration overvoltage was calculated taking into account transportation phenomena occurring in the cell, in function of anode and cathode limiting current densities, depending on an average diffusion factor [5]. hconc ¼

"   0;5 # RT i i $ 1 ln i  2F il;H2 il;O2

start-up and shut-down periods. Therefore, in this study it was assumed to operate the cell using the stand-by mode: when the power provided by the cell is not required, the current is brought to zero but the cell is kept warm in order to avoid thermal stresses. Obviously, keeping the operating temperature also during HSSOFC deactivation periods, determines an additional consumption of natural gas. However, this is largely compensated by the high electrical efficiency of the system. The main parameters showing the capacities of the SOFC subsystem are reported in Table 3. Details regarding geometry and materials of the system components (electrode thickness, heat exchanger geometry, tube length, PR catalyst density, etc.) are given in Ref. [5].

references

(28)

The Ohmic overvoltage was calculated considering the circumferential path of the charges [4e6,45,49]:

hU ¼ i

6149

(33)

The electrochemical model of the cell was validated using the experimental data published by Siemens [5]. Finally, the overall subsystem simulation algorithm, which iteratively calculates system thermodynamic properties, was here accordingly modified in order to comply with system layout modifications discussed above. The IRSOFC and the other components of the SOFC subsystem are also provided with thermal models calculating energy balances for each time step. In particular, the code also calculates the losses of the SOFC toward the environment. Note also that the SOFC subsystem is a part of the HSSOFC. Thus, it should be switched on or off, according to the user demand. However, this is not possible for SOFCs, since their high operating temperature require very long

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