Available online at ScienceDirect. Energy Procedia 48 (2014 )

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1 Available online at SieneDiret Energy Proedia 48 (2014 ) SHC 2013, International Conferene on Solar Heating and Cooling for Buildings and Industry September 23-25, 2013, Freiburg, Germany A simple method to alulate Central Solar Heating Plants with Seasonal Storage Mateo Guadalfajara a, *, Miguel A. Lozano a, Luis M. Serra a a Aragon Institute of Engineering Researh (GITSE-I3A), Universidad de Zaragoza, C/ María de Luna s/n, Zaragoza 50018, Spain Abstrat Central Solar Heating Plants with Seasonal Storage (CSHPSS) are systems produing heat from solar radiation for a distrit heating system. These systems are able to produe thermal energy during all the year providing a signifiant part (high solar fration) of the demands required for spae heating and Domesti Hot Water (DHW). The design and alulation of the behaviour of these systems during the year is a omplex proess requiring detailed limati and demand data in order to properly design/sizing the plant omponents to reah the desired behaviour (e.g. a speifi solar fration). The loation of the plant and the different demands orresponding to different limati areas affet very signifiantly the behaviour of these systems. As a onsequene, the sizing and design riteria of the piees of omponents of these systems are very different in the North and the South of Europe. The utilization of simple methods for the alulation of these systems allows the design of the main omponents and provides an estimate of the behaviour of the system during the year. In this paper is proposed a simple method for the alulation of CSHPSS using demand data and simple and easy to find available publi limati data. The proposed method is ompletely desribed and applied to speifi Spanish loations to pre-design the main omponents of these systems. The model also provides a preliminary eonomi evaluation of the system and is very useful to perform parametri analysis to evaluate the CSHPSS system performane, as well as to establish optimization and design riteria of CSHPSS The The Authors. Published by by Elsevier Elsevier Ltd. Ltd. Seletion and and peer peer review by by the the sientifi sientifi onferene onferene ommittee ommittee of SHC of 2013 SHC under 2013 responsibility under responsibility of PSE AG of PSE AG. Keywords: solar thermal energy; distrit heating; seasonal storage; renewable energy; * Corresponding author. Tel.: address: mateog@unizar.es; mlozano@unizar.es; serra@unizar.es The Authors. Published by Elsevier Ltd. Seletion and peer review by the sientifi onferene ommittee of SHC 2013 under responsibility of PSE AG doi: /j.egypro

2 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) Introdution The development of solar systems overing part of the residential thermal energy is an eonomially viable option that redues the onsumption of fossil fuels [1]. The Spanish normative on buildings [2] requires for new buildings, depending on the limati loation, a prodution with solar energy of 30% to 70% of thermal energy demand of domesti hot water (DHW). This prodution represents a small solar fration of the total thermal energy demand of DHW and spae heating of buildings. Therefore, onsidering also the overage of other heating demands in buildings as spae heating or even ooling with absorption mahines, the real potential of the solar thermal energy soure is very high. The World energy demand in the residential setor (2035 Mtoe) represents roughly 27% of the final energy onsumption [3]. Hene, the prodution of a signifiant part of this demand with solar energy might solve an important part of the energy problems: shortage, dependeny, high pries flutuation, pollution, limate hange, among others [1]. Central solar heating plants with seasonal storage (CSHPSS) an over with a high solar fration the spae heating and domesti hot water demands of big ommunities at an affordable prie. These systems already supply heat to big ommunities through distrit heating systems in the north and enter of Europe. The evaluation of the performane and the design of these entralized solar systems is a omplex proess, due to their dynami behavior both during the day and along the year. The prodution of the solar olletor field depends on the solar radiation and the ambient temperature hanging along the day, as well as on the operation temperature of the seasonal storage tank. The behavior and operation temperature of the seasonal storage depends on the demand and solar prodution distribution along the year. Further, the loation and the size of the demand affets to the performane of the system in suh way that the sizing between the north and south of Europe is very different. As a result, the proess of predesign and study in initial stages of the projet beomes a real hallenge. Dynami simulations with TRNSYS [4] of CSHPSS provide an evaluation of the performane of its behavior with a high auray [5, 6, 7] but it requires exhaustive and detailed information and a high omputational effort. Simple alulation methods requiring less detailed data and a lower omputational effort an omplement TRNSYS for a preliminary quik evaluation of the size of the main omponents of an installation failitating the design task and providing an estimate of its annual performane [8, 9]. In this paper is presented an original simple method for the alulation of CSHPSS built on the Engineering Equation Software [10], using demand data and publi limati data that an be easily obtained. The proposed method alulates the behaviour of the system on a monthly basis and an be used to pre-design the solar field and the volume of the seasonal thermal energy storage of CSHPSS, as well as to perform easily parametri analysis for the evaluation of these systems. It is also shown how this method is useful to perform feasibility studies in preliminary stages of a projet, as well as to establish optimization and design riteria of CSHPSS. 2. Simple method The simple method is based on the possibility of performing an approximate alulation on a monthly basis of the solar olletor field prodution and the apaity of the seasonal thermal energy storage to math prodution and demand. Fig. 1 shows the system sheme and identifies the main energy flows that appear in the simple model. The radiation reeived, Q r, over the solar olletor is harvested and the prodution of the solar field, Q, is alulated simulating its hourly operation during a representative day of the month. It is onsidered a omplete mixture in the thermal energy storage, i.e. without stratifiation; so it keeps uniform the aumulator temperature, T au, along the alulation period, whih is a month in the proposed model. Thus, the solar olletor performane and the heat losses, Q l, of the seasonal storage are alulated onsidering the tank temperature. In a seasonal storage tank, the premise of onsidering onstant the water tank temperature along the month is reasonable due to its high thermal inertia (high volume). A monthly energy balane is used to alulate the temperature in the thermal energy storage at the end of the month. This temperature of the water tank at the end of the month is used to alulate the solar olletor performane at the next month.

3 1098 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) Fig. 1. Energy flow hart of the simple model of entral solar heating plant with seasonal storage. The monthly operation of the seasonal storage tank has two different operation modes during the year: i) harge and ii) disharge. The harge operation mode ours when the prodution of the solar field, Q, is higher than the heat demand, Q d. Then part of the olleted heat will be used to attend the immediate demand, Q b, and the surplus of the olleted heat will be sent to the seasonal storage for its later onsumption, Q e. In the disharge operation mode, the heat demand, Q d, is higher than the prodution of the solar olletors, Q, and the seasonal storage tank is disharged, Q s, in first instane and if it is still not enough, then the auxiliary system, Q g, will provide the required heat to over the demand. The thermal energy storage operation is onstrained by two temperature limits, maximum and minimum. When the limit of the minimum temperature is reahed, the thermal energy storage an not be disharged anymore and the auxiliary system provides the required heat, Q g, to fulfil the demand. The thermal energy storage an not be harged either over the maximum temperature. When it reahes this maximum temperature limit, part of the heat prodution is rejeted, Q x, to avoid overheating and equipment damage. As the thermal energy storage is warm, the heat losses to the environment, Q l, are also alulated. The thermal energy aumulated in the storage tank is denoted by the variable EA (Fig. 1). As shown in Fig. 2 the simple method onsists of four sequential modules for the alulation of the annual and monthly performane of a CSHPSS. In base of publi data that an be easily obtained the Module 1 elaborates the hourly and monthly limati and demand data required to alulate the system performane (hourly radiation on tilted surfae, hourly ambient temperature, monthly demand ). The Module 2 alulates the monthly prodution of the solar field based on the hourly radiation and hourly ambient temperature of a typial day for eah month, and on the tank temperature at the beginning of the onsidered month. The alulation of the solar olletor is based on the performane equation of the solar olletor field. The effiieny equation of the heat exhanger between the primary and the seondary iruits (between the solar field and the seasonal storage tank) is also onsidered. Data elaboration (Demand, limati and design) Climati data Demand data Design data Module 1 Module 2 Module 3 Module 4 Q d Q l Q Q r Q x Solar olletor prodution System monthly energy balane Q b Q e Q s Q g Annual system results T au Aumulator temperature Solar fration System effiieny Fig. 2. Information flow hart and sheme of the simple method alulation modules. Eah month an energy balane, onsidering prodution, demand and losses, alulates the energy harged/disharged/aumulated in the seasonal storage and if required the auxiliary energy, as well as the final

4 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) temperature of the water in the tank and the heat rejeted, in ase the storage tank would be fully harged (Module 3). The Module 4 alulates and presents the tehnial results: annual energy balane, global effiieny of the system and of the onsidered omponents, solar fration, among others, as well as an estimation of the investment, operation and maintenane osts of the system and the solar heat ost. 3. Base ase To make easier the evaluation of CSHPSS systems with the simple method a few publi and available data are used. The minimum input data required are the next: annual demand of DHW and spae heating; latitude of the loation of the plant; monthly average of the daily global radiation over horizontal surfae, H (monthly data); average medium, minimum and maximum ambient temperature, Ta ave, Ta min and Ta max (monthly data); monthly degree-days (base 15ºC), DD 15 (monthly data); old water temperature from the net, T net (monthly data); ground temperature, T ter ; and ground refletane, ρ g. In the onsidered base ase the installation is loated in Zaragoza and it supplies heat for spae heating and domesti hot water for a ommunity of 1000 dwellings of 100 m 2. The demand onsidered has been taken from the referene values in Spain for new multifamily buildings [11]. In Zaragoza the annual demand for spae heating in multifamily buildings is 40.6 kwh/m 2 and the domesti hot water demand is 12.9 kwh/m 2. The limati data have been obtained from multiple soures: radiation [12], degree-days [13], average medium, average minimum and average maximum ambient temperatures [14] and old water temperature of the supply network [15]. The design variables onsidered in the simple model presented in this paper are the next: Area of solar olletor, A (or RAD, whih is the ratio of the area of the solar field, m 2, divided by the annual demand in MWh/year); volume of the seasonal storage tank, V (or RVA, whih is the ratio of the volume of the seasonal storage tank, m 3, divided by the area of the solar field in m 2 ); effiieny urve of the solar olletor (η 0, k 1, k 2 ); tilt and orientation of the solar olletors; speifi mass flow rate of working fluid irulating through the solar olletors, m s ; heat exhanger effiieny of the solar field, E ff ; temperature of the water supplied to the distrit heating network, T SH ; temperature of the water returning from the distrit heating network, T ret ; maximum temperature in the seasonal storage tank (aumulator), T max ; global heat transfer oeffiient in the aumulator for the alulation of the heat losses, U au. The parameters for the base ase are presented in Table 1. Table 1: Design parameters for the base ase Solar Colletor field Heating Demand Parameter Value Parameter Value RAD: ratio olletor area / demand 0.6 m 2 /(MWh/yr) Seasonal RVA: ratio volume area 6 m 3 /m 2 A: area of solar olletors 3210 m 2 Storage V: volume of seasonal storage 19,260 m 3 η 0 : opti effiieny T min: minimum storage temperature 30 ºC k 1: heat loss oeffiient W/(m 2 K) T max: maximum storage temperature 90 ºC k 2: heat loss oeffiient W/(m 2 K 2 ) RHD: ratio height diameter in the storage 0.6 m/m Β: tilt 45º U au: heat transfer oeffiient 0.12 W/(m 2 K) Θ: orientation 0º A au: heat transfer area 4101 m 2 m s: solar field flow 20 kg/(h m 2 ) ρ p: speifi heat 4180 kj/(m 3 K) Eff: heat exhanger effiay 0.9 EA max: max energy aumulated 1342 MWh Q SH: annual spae heating demand 4060 MWh/year Distrit T sup: supply temperature 50 ºC Q DHW: annual DHW demand 1290 MWh/year Heating T ret: return temperature 30 ºC Qd: annual demand 5350 MWh/year The seasonal storage is assumed as an underground ylindrial tank with a shape ratio RHD = 0.6 (height divided by diameter). One the volume is known the other dimensions an be alulated. D ( 4 V /( RHD)) H RHD D 1/ 3 (1) (2)

5 1100 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) A au ( RHD 0.5) D 2 (3) The ground temperature, T ter, has been onsidered onstant along the year and with the same value than the average ambient temperature (15.0ºC in Zaragoza). The maximum energy stored an be alulated with the next equation: EA max V p ( T max T min 9 ) /( ) (4) 3.1. Module 1: Data elaboration In the Module 1 are alulated the hourly environmental temperature T a [m, for a representative day of eah month and the hourly radiation over tilted surfae q r [m, in W/m 2. The Erbs s orrelation for the ambient temperature is used to estimate the ambient temperature along the day; it uses the minimum, the maximum and the monthly average of the daily temperatures of a typial day [17, 18] Ta Ta ave 2 ( 1) 24 ( Tamax Tamin ) a os( k b ) 4 k 1 k k (5) (6) where is the solar hour of the day ( = 12 is the solar high noon). With the average daily radiation over horizontal surfae and the extraterrestrial radiation over horizontal surfae, whih depends on the ity latitude (Zaragoza, 41.6º) and the date, the sky learness index an be alulated [19]. This index is used to alulate the daily diffuse radiation with Erbs s orrelation [20]. The total radiation over horizontal surfae an be hourly distributed with the Collares-Pereira & Rabl orrelation [21]. The diffuse radiation an also be hourly distributed with Liu & Jordan orrelation [22]. The differene between total radiation and diffuse radiation is the diret radiation over horizontal surfae. The hourly radiation over tilted surfae an be alulated using the isotropi sky model [19]. Further in the Module 1 the annual spae heating demand an be monthly distributed with the degree-days method. As entralized systems tend to be unplugged when the demand is low, then the spae heating demand supplied is onsidered 0 in those months in whih the degree-days, DD SH, are lower than the monthly days (N). DDSH [ if DD15[ N[ Then DDSH[ DD15[ Else DDSH[ 0 (7) Q SH [ Q SH DD SH [ / m 12 m 1 DD SH [ (8) The domesti hot water demand is monthly distributed with the method proposed by the standard UNE [15], in whih the DHW demand is estimated as a funtion of the temperature of the water supply network, T net, and the number of the days of eah month. The total monthly demand of the system is the sum of both, spae heating demand and DHW demand. DD Q DHW DHW [ N[ ( T T [ ) [ Q DHW DD DHW DHW [ / d SH DHW net m 12 m 1 DD DHW [ (9) (10) (11) Note that the simple method does not require the elaboration data performed in the Module 1 for the evaluation of the CSHPSS if equivalent data are provided (monthly demand and hourly radiation over tilted surfae and ambient temperature for a representative day for eah month).

6 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) Module 2: Solar olletor field prodution The prodution of the solar olletor, q [m,, is alulated hourly using the effiieny urve of large solar olletors. This alulation requires the solar radiation q r [m, and the temperature differene among the solar olletor, T, and the ambient temperature, T a. Note that only is onsidered heat olleted when the effiieny value of the solar olletor is positive (eq. 12). q [ m, Max 2 ( 0 qr[ m, k1 T[ m, k2 T[ m, ; 0) (12) T[ m, T [ m, T [ m, a (13) The solar olletor temperature is the average value between inlet and outlet temperature of the fluid in the solar olletor. T [ m, ( T [ m, T [ m, )/ 2 in out (14) The outlet temperature of the solar olletor fluid depends on its inlet temperature, the mass flow rate m s = 20 kg/(h m 2 ) and its speifi heat p,sf = 4180 J/(kg K). T out [ m, Tin[ m, q[ m, 3600 /( ms p,sf ) (15) One the inlet temperature, T in, is known, then the rest of variables q, T, T, T out an be obtained from the previous eqs The fluid irulating through the solar olletor transfers the heat to the seasonal storage through a ounterurrent plate heat exhanger. Considering that the heat apaity of the fluids irulating through the primary iruit (solar olletor) and through the seondary iruit (load iruit harging the aumulator) is the same, and that the temperature of the water in the aumulator remains onstant during the whole month, then the next equation is obtained: T [ m, T [ m, E ( T [ m, T [ m 1]) in out ff out au (16) The monthly prodution of the solar field Q [ is the sum of the hourly values multiplied by the solar olletor area A and the number of the days of the month (N). A N[ h 1 q [ m; The monthly radiation Q r [ reeived by the solar field is alulated in a similar way, hanging q [m, by q r [m, in eq Module 3: Monthly energy balane The monthly energy balane of the system requires a ontrol of the minimum and maximum load of the seasonal storage tank. This guarantees the alulation of the harge and disharge of the aumulator fulfilling these limits and affets the auxiliary energy required to over the demand and the heat rejeted in ase the tank would be fully harged. All the thermal energy flows appearing in the equations of the Module 3 are expressed in MWh/month. The system is operated in suh a way that eah month the heat harvested in the solar olletors, Q, firstly will attend the demand, Q b, and one it has been overed, the remaining heat, Q e, will be introdued in the thermal energy storage tank (see Fig. 1). (17) Max( ;0) e b e d (18) (19)

7 1102 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) Heat loss of the seasonal storage tank, Q l, is alulated multiplying the global heat transfer oeffiient of the aumulator U au in W/(m 2 K) by the tank area A au in m 2, and by the temperature differene between the tank T au and the ground T ter, and by the number of hours of the month. The onsidered tank temperature is the temperature at the beginning of the month (temperature at the end of the previous month). U l au A au ( T au [ m 1] T ter ) 24 N[ 10 6 (20) In order to alulate the tank disharge an auxiliary variable, Q sx, whih expresses the maximum amount of heat that ould be disharged, is used. This maximum amount depends on the aumulated energy, EA, the heat introdued, Q e, and thermal losses, Q l. Max( EA[ m 1] ;0) sx e l (21) The monthly auxiliary energy required (Q g ) is alulated as follows: Max( Q [ Q [ ;0) g d b sx (22) Finally the disharged heat, Q s, is alulated as a differene of the demand minus the solar diret prodution and the auxiliary energy required. s d b g (23) The monthly solar heat produed, Q solar, is Q solar [ b s (24) The theoretial energy aumulated, EA x, at the end of the month is alulated without onsidering the temperature limit. In real installations there are seurity systems that stop the pumps when the maximum temperature inside the seasonal storage tank is reahed, T max = 90ºC in this ase. In the simple model this effet is modeled alulating the heat rejeted, Q x. Thus, the theoretial energy aumulated, EA x, at the end of the month is, EA [ EA[ m 1] x e l s (25) If this energy is higher than the maximum amount, part of the solar prodution will be rejeted, Q x. The final energy aumulated, EA, and the heat rejeted, Q x, are given by the following equations: EA[ Min ( EAx[ ; EAmax ) EA [ EA[ x x (26) (27) The aumulator temperature at the end of the month is alulated onsidering the real energy stored. T au [ T EA min ( Tmax Tmin ) EA[ / max All the alulations are performed for an annual yle in whih the load and the aumulator temperature at the end of the year is the same than that at the beginning. EA[ 0] EA[12] T au [ 0] Tau[12] In the alulations have not been onsidered: the eletri onsumption of pumps, the heat losses in pipes, heat exhangers and auxiliary equipment nor the distrit heating network. (28) (29) (30)

8 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) Module 4: Annual results and eonomi evaluation The annual energy flows of the system (Q d, Q r, Q, Q b, Q e, Q x, Q l, Q s, Q g and Q solar ) are alulated in the Module 4. The annual net energy balane of the system should be equal to ero. Balane annual The solar fration, SF, and the solar olletor effiieny, oll, an be alulated in monthly and annual basis. SF Q solar / Q d Q / Q oll r Q Q Q Q Q g d l x The thermal energy storage effiieny, au, and the annual system effiieny, sys, an be alulated only in annual basis. (31) (32) (33) au sys Q / Q Q / Q s solar e r (34) (35) In Table 2 are shown the obtained results for the analyzed ase. Table 2: Monthly and annual results of the system for the analyzed base ase (Zaragoza, 1000 dwellings, RAD = 0.6, RVA = 6). Jan Feb Mar Apr May Jun Jul Aug Sep Ot Nov De Year Q d (MWh) Q r (MWh) Q (MWh) Q b (MWh) Q e (MWh) Q s (MWh) Q l (MWh) Q x (MWh) Q solar (MWh) Q g (MWh) EA (MWh) T au (ºC) SF (%) η oll (%) η au (%) η sys (%) Furthermore, the Module 4 provides an eonomi evaluation of the proposed installation. With data from previous works [7, 23] the ost of the main equipment has been estimated: solar olletor field (Inv ol ) and seasonal storage (Inv au ) expressed in Euro ( ). Inv oll = 740 A (36) Inv au = α 4660 V (37) The exponents in previous equations explain the sale eonomies of the solar olletor field and the seasonal storage tank. Note that the aumulator ost per unit of volume dereases signifiantly with the size, whih has been verified by other authors [24-29]. The parameter α inluded in eq. 37 is useful to onsider the eonomi behavior of different tehnologies of thermal energy storage [24-29] (e.g. water tank, pit or borehole) or the expeted future prie redution assoiated to the tehnology development. The value α = 1 orresponds with the experiene gained

9 1104 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) in the demonstration projets of the two last deades using a hot water tank for thermal energy storage. Empirial evidenes [30-32] indiate that the investment ost of the seasonal storage is still very high. The investment ost of the rest of the equipment existing in a CSHPSS (pumps, heat exhangers, pipes, valves, et.) has been inluded with an inreasing fator of 25% (f aux = 25%). The indiret osts (engineering projet, projet management, assuranes, et.) are onsidered with an inreasing fator of 12% (f ind = 12%). Therefore, the total investment is. Inv = (1+f ind ) (1+f aux ) (Inv oll +Inv au ) =1036 A α 6524 V (38) The annual ost of the equipment, Z in /year, is alulated applying the annual amortization fator and the operation and maintenane osts. The amortization fator is alulated onsidering an annual interest rate, i in year -1, of 3.0%, whih is at present a ommon interest rate in ountries in whih CSHPSS are being installed, e.g. Denmark. The amortization osts are distributed along the equipment lifetime. The estimated lifetime is 25 years (na = 25 years) for the solar olletor and 50 years for the seasonal storage (nv = 50 years). The annual operation and maintenane osts are estimated in 1.5% (f ope = year -1 ) of the investment ost aording to the riteria proposed by the IEA [1]. Therefore, the annual osts are alulated with the next equations: Z oll = Inv oll (f ope +i (1+i) na /((1+i) na - 1) = 54 A (39) Z au = Inv au (f ope +i (1+i) nv /((1+i) nv 1)) = α 251 V (40) Z = (1+f ind ) (1+f aux ) (Z oll +Z aux ) =75 A α 352 V tank (41) For the analyzed base ase (1000 dwellings loated in Zaragoza) the initial investment required is Inv = The annual ost is Z = 229,445 /year. The unit ost of the solar heat, solar, is alulated as the quotient between the annual ost and the solar heat produed. As the solar prodution is Q solar = 2979 MWh/year, then the unit ost of the solar heat is solar = 77.0 /MWh. Based on the simple method presented, next in setions 4 to 6, several parametri studied are presented and applied to the analysis of the performane of CSHPSS as well as to the evaluation of design riteria. 4. Physial analysis 4.1. Critial volume of the seasonal storage In the analyzed base ase the maximum allowed temperature (90ºC) in the seasonal storage, indiating that the thermal energy storage tank is full, is not reahed (80.3ºC is the maximum value in Table 2). A reasonable design riteria is based on the next premises: 1) do not rejet any fration of the solar heat olleted (Q x = 0), whih means that a thermal energy storage is required; and 2) maximum usage of the aumulation installed apaity, whih means that the tank should be fully harged (the maximum allowed temperature in the tank should be reahed just at the end of the harging period and the beginning of the disharge period). Therefore it is interesting to study the effet of varying the volume of the storage tank from the base ase (RVA = 6 m 3 /m 2 ). If the ratio RVA is redued, maintaining the olletor area onstant, the seasonal storage tank temperature rises until it is obtained the maximum temperature at the end of the harging season, and the solar fration dereases due to the inrease of heat losses (see Fig. 3). For a value of the ratio RVA lower than 4,7 m 3 /m 2 the solar fration dereases faster, beause the volume of the seasonal storage tank does not allow to store all the heat produed and as a onsequene part of this heat is rejeted (Q x > 0). The ritial value of RVA without heat rejetion is alled RVA. In Fig. 3 is also shown that when dereasing the volume of the storage tank the solar fration dereases. The slope of the solar fration is higher when RVA is lower than the ritial volume, RVA.

10 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) ,56 0,55 Qx SF 0,54 0,53 0, Qx (MWh/year) 0,51 SF 0 0, ,5 5 5,5 6 RVA (m 3 /m 2 ) Fig. 3: Effet of the aumulation volume on the solar fration (SF) and the rejeted heat (Qx) 4.2. Effet of solar fration on the aumulation needs When the ritial volume, RVA, is onsidered a design riterion, then the number of free design variables is redued just to one: the area of the solar field. In Fig. 4 is shown the relationship between the ritial volume and the olletor area as a funtion of the solar fration. Inreasing the olletor area, the solar fration rises up linearly. However, the aumulation needs do not rise up linearly. The need of thermal energy storage inreases quikly for low values of solar fration (SF), and inreases in a slower way for high values of SF. For low solar fration values (SF < 20%) it is almost not neessary to aumulate heat in summer (RVA < 0.7 m 3 /m 2 ) sine the solar prodution in summer almost do not overpass the demand of domesti hot water. But the aumulation needed to obtain a solar fration lose to 50% is RVA = 4.5 m 3 /m 2 and to obtain a solar fration lose to 100% is RVA = 6.1 m 3 /m 2. Other obtained results not depited in Fig. 4 for a variation of the solar fration from 20% to 100%, are summarized next: i) the olletor effiieny, oll, dereases linearly from 59% to 51%; ii) the thermal storage tank effiieny, au, rises from 75% at SF = 20% to 87% at SF = 50% and then it rises more smoothly to 89% at SF = 100%; iii) the global effiieny of the system, sys, dereases with the solar fration from 58% at SF = 20% to 48% at SF = 100%. 1,4 1,2 RAD (m 2 /(MWh/year) RVA (m 3 /m 2 ) 7 6 RAD (m 2 /(MWh/year)) 1 0,8 0,6 0, RVA (m 3 /m 2 ) 0, ,2 0,4 0,6 0,8 1 SF Fig. 4: Solar olletor area and ritial volume of the seasonal storage as a funtion of the solar fration Trade off: Area of the solar olletors Volume of the seasonal storage A design option to obtain a speified solar fration is to size the CSHPSS onsidering the ritial volume of the seasonal storage tank. Nevertheless a speifi solar fration an be obtained with multiple ombinations of the solar olletor field area volume of the seasonal storage tank [33, 34]. Thus, with the simple method the solar fration has been alulated for different ombinations and, applying data interpolation, lines with the same solar fration values have been depited in Fig. 5. Following whatever line with onstant solar fration, several values of the area

11 1106 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) of the solar field orresponding to different volumes of the seasonal thermal storage tank are feasible. In the spae A the volume of the storage is smaller than the ritial value and part of the heat olleted is rejeted. In the spae B the thermal storage does not reah the maximum temperature, i.e. the seasonal storage tank is not ompletely full in any moment along the year. If the volume of the thermal storage is inreased over a ertain value, spae C, the design is not appropriate beause an inrease of the storage tank volume will maintain or even redue the solar fration. The most appropriate values for these design variables depend on the projet limits and on the seleted design riteria Eonomi analysis A (m 2 ) Fig. 5: Trade-off: solar olletor area and volume of seasonal storage, isoquant lines of solar fration. In Table 3 is shown the variation of the ost of the solar heat when the volume of the seasonal storage is modified. Starting with the base ase then the ratio RVA is redued from 6 m 3 /m 2 to 1 m 3 /m 2. From the obtained results, the positive effets of inreasing the volume of the seasonal storage (higher solar fration and higher system effiieny) do not ompensate the investment ost of inreasing the seasonal storage and the unit ost of the solar heat inreases. This effet ours even when the installed volume is not enough for storing all the heat produed and some solar heat is rejeted. It an be onluded that with the present investment osts of the water tank thermal energy storages the ritial volume is not the optimum eonomi design. RVA Table 3: Eonomi results as a funtion of the seasonal storage volume (Zaragoza, 1000 dwellings, RAD = 0.6). V (m 3 ) V (m 3 ) Minimum ost = 1/2 0.4 Critial volume 0.3 SF 0.2 Spae C limit T max (ºC) Spae C Q x (MWh/year) Spae B 0.7 FS η sys Inv (10 3 ) Z (10 3 /year) solar ( /MWh) Spae A It is estimated that if the investment ost of the seasonal storage is redued about 50%, keeping onstant the investment of the rest of the plant omponents, then the ritial volume ould be an interesting design option from an eonomi viewpoint. This an be ahieved with using other tehnologies for the onstrution of the seasonal storage, e.g. pit thermal energy storage. It has also been analyzed the ost of the solar heat when inreasing the solar olletor area in order to obtain a higher solar fration. In this ase the analysis has been performed using the ritial volume as design riterion. The obtained result is that the unit ost of the solar heat remains almost onstant when the solar fration is high ( 40%). The reason is that the ost of the heat loss is ompensated with the eonomies of

12 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) sale of inreasing the apaity of the installed equipment. When the number of dwellings is modified, then the annual demand hanges aordingly. Keeping onstant the design ratios, RAD = 0.6 and RVA = 6, the results obtained for different number of dwellings are shown in Table 7. The most signifiant result is the very important redution of the solar heat ost with the inrease of the demand. For a ommunity of 5000 dwellings the solar heat ost is 48 /MWh lose to the prie of the onventional heat in Spain, based on onventional fuel. Part of this ost redution is due to the slight inrease of the effiieny of the system when inreasing the size of the system, due to the redution of the thermal losses in the storage. Nevertheless, the dominant fator is the effet of the sale eonomy on the investment ost per dwelling, Inv/Dwell, whih is redued by a fator of 3.5 when inreasing from a size of 100 dwellings to a size of 5000 dwellings. Table 4: Parametri analysis varying the number of dwellings (Zaragoza, RAD = 0.6, RVA = 6). Number of A V Q solar SF η oll η au η sys Inv Inv/Dwell Z solar Dwellings (m 2 ) (m 3 ) (MWh/year) (%) (%) (%) (%) (10 3 ) ( /Dwell) (10 3 /year) ( /MWh) % 58.3% 75.9% 52.9% % 57.5% 85.1% 54.2% , % 57.2% 88.0% 54.6% ,050 96,300 15, % 56.8% 92.8% 55.2% 11, Sensitivity analysis with respet to the seasonal storage ost The variable ost of the thermal energy produed with entralized systems that use only natural gas boilers is about 50 /MWh [35]. From the unit osts presented in Table 4, it is shown that when the number of dwellings is bigger than 5000, the CSHPSS systems beome ompetitive. From the previous results it has been obtained that the unit solar heat ost mainly depends on the solar fration and on the aumulation volume. From an eonomi point of view the ritial volume that avoids the rejetion of heat in summer is not the optimum design (see Table 3) being preferable to invest more in solar olletors even when a part of the olleted heat is rejeted than invest in a bigger thermal energy storage [36, 37]. These results are onsistent with the results obtained by other authors [30-32]. Only large installations or a politial-legal regulation imposing a minimum solar fration or finanial support for the investment will foster the short term development of CSHPSS systems. All these results are referred to thermal energy storage in Water Tank Thermal Energy Storage whih is the more expensive tehnology per unit of volume but for universal appliation. Table 5: Optimum design for different solar frations and several senarios (Zaragoza, 1000 dwellings). α Solar Fration 20% 40% 60% 80% 90% 95% RVA opt (m 3 /m 2 ) solar ( /MWh) Q x/q (%) 0% 18% 29% 38% 4% 0% EA/EA Max (%) 94% 100% 100% 100% 100% 100% RVA opt (m 3 /m 2 ) ½ solar ( /MWh) Q x/q (%) 0% 18% 6% 0% 0% 0% EA/EA Max (%) 94% 100% 100% 100% 94% 92% RVA opt (m 3 /m 2 ) / 3 solar ( /MWh) Q x/q (%) 0% 18% 0% 0% 0% 0% EA/EA Max (%) 94% 100% 99% 93% 87% 85% RVA opt (m 3 /m 2 ) ¼ solar ( /MWh) Q x/q (%) 0% 0% 0% 0% 0% 0% EA/EA Max (%) 94% 93% 94% 88% 84% 83%

13 1108 Mateo Guadalfajara et al. / Energy Proedia 48 ( 2014 ) The omparison of investment osts for different seasonal storage tehnologies [24-29] indiates that the ost for the thermal energy storage an be redued until ¼ when the aumulation in hot water tank is hanged to other tehnologies: Borehole Thermal Energy Storage, Pit Thermal Energy Storage and Aquifer Thermal Energy Storage. On the other hand, as the existing seasonal storage tehnologies are still in development, it an be expeted an important derease in the investment ost with the adjustment and optimization of the tehnologial onstrution proess. The optimum design from an eonomi point of view in several senarios α = (1; ½; 1 / 3 ; ¼) for different solar frations an be seen in Table 5 onsidering the demand of the base ase. The obtained results show that when the investment osts of the seasonal energy storage are redued by a fator of ½ or even more, then the next remarkable aspets our: i) the ost of the solar heat is lower than 50 /MWh; ii) the ost of the solar heat does not signifiantly hange with the solar fration, i.e. it is interesting from an eonomi viewpoint the design of CSHPSS with high solar fration; iii) sizing the CSHPSS onsidering the ritial volume of the seasonal storage tank is an appropriate design riterion. If the ost of the thermal energy storage tank is signifiantly redued, then it is interesting from an eonomi viewpoint the utilization of the storage tank instead of wasting part of the olleted heat. Even the oversizing of the heat storage tank an be justified in order to redue the temperature of the aumulator ( = ¼; SF = 95%; RVA = 7.8; T max = 79.6 ºC). Considering the limitations of the model presented in this paper for the alulation of the aurate behavior of solar systems with low thermal energy storage apaity, those ase studies with RVA < 1 m 3 /m 2 have not been alulated. Note that for eah value it exists a solar fration value that when surpassed the optimum design requires seasonal energy storage and, in the ase it is not reahed, the optimum design orresponds to a system without seasonal energy storage. In other words, for eah value there is a disontinuity orresponding to a speifi solar fration (ritial solar fration) whih determines if it interesting or not to install seasonal energy storage, but there are not intermediate ases. As the osts of the seasonal storage are redued it is more interesting to implement seasonal storage systems in order to store the surplus of the prodution ourring during summer instead of rejeting part of the olleted heat (Q x /Q = 0%). Even, it ould be profitable to design a seasonal storage with a volume higher than the ritial volume (EA/EA Max < 100%) as it is shown in Fig Conlusions A Simple Method for the alulation of CSHPSS using heat demand data and available publi limati data has been presented in this paper. The analysis of CSHPSS applying eonomi and other design riteria an be performed with the proposed method with redued alulation effort. It has been shown its appliation to a partiular ase of 1000 dwelling of 100 m 2 eah, loated in Zaragoza, Spain. The proposed Simple Method alulates the performane of the solar olletor field based on its physial behavior using hourly radiation and temperature data of a typial day per month. It also onsiders the performane along the month of the seasonal storage. These two features signifiantly redue the alulation effort ompared to present speialized dynami alulation software. The validation of results has not been presented in this paper, but when omparing the obtained results with those provided by TRNSYS and other simple methods, only small deviations are deteted [36,38]. The simplifiation of the alulations, e.g. the f-hart method [19], fostered the development of DHW solar systems. The Simple Method presented in this paper is not intended to ompete with speialized dynami alulation tools, but a omplementary and valuable tool for estimate the performane of CSHPSS systems as well as for the analysis oriented to establish optimization and design riteria, in order to pre-design the main omponents of these systems, as shown in this paper. Aknowledgements The present results have been developed in the frame of the researh projet ENE , partially funded by the Spanish Goverment (ENERGY researh program), the Government of Aragon and the Soial EU Fund (FEDER Program).

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