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A thermo-economical optimization of a domestic solar heating plant with seasonal storage A. Ucar *, M. Inalli Department of Mechanical Engineering, Firat University, 23279 Elazıg˘, Turkey Received 3 June 2005; accepted 29 June 2006 Available online 1 September 2006

Abstract In this study, the thermo-economic optimization analysis to determinate economically optimal dimensions of collector area and storage volume in domestic solar heating systems with seasonal storage is presented. For this purpose, a formulation based on the simpliﬁed P1 and P2 method is developed and solved by using MATLAB optimization Toolbox for ﬁve climatically diﬀerent locations of Turkey. The results showed that the required optimum collector area in Adana (37 °N) for reaching maximum savings is 36 m2/house and 65 m2/house in Erzurum (39 °N) for same storage volume (1000 m3). The eﬀects of collector eﬃciency on solar fraction and savings are investigated. The simulation results showed that the solar fraction and savings of the selective ﬂat plate collector systems are higher than the other black paint ﬂat plate collector systems. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Solar heating; Thermo-economic; Optimization

1. Introduction The store of solar heat from the summer to the winter for space heating is important because of large diﬀerences between solar energy supply and heat demand. The large solar thermal energy systems are always characterized by expensive components. Solar collectors and storage are the most important economic parameters within these systems and most of the remaining costs can often be parameterized using these two components. Nordell and Hellstro¨m [1] evaluated performance of a solar-heated low temperature space-heating system with seasonal storage in the ground using the simulation models TRNSYS and MINSUN together with the ground storage module DST. They implied an economically feasible design for a total annual heat demand of about 2500 MW h. It was found that total annual cost of the solar heating system

*

Corresponding author. Tel.: +90 424 2370000/5233; fax: +90 424 2415526. E-mail address: [email protected]ﬁrat.edu.tr (A. Ucar). 1359-4311/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.06.010

was reduced by about 20% to about 800 SEK MW h1, which was lower than the best conventional alternative. Lindenberger et al. [2] developed the dynamic energy, emission and cost optimization model deeco and applied to the analysis of solar district heating systems with seasonal storage in a pilot project of the Bavarian Research Foundation. They computed the optimum integration of condensing boilers, compression and absorption heat pumps and cogeneration of heat and power for 100 well insulted housing units and collector areas between 1 and 2.5 m2 per MW h heat demand and water storage volumes between 1.2 and 4.2 m3 per m2 collector area satisfy between 32 and 95 percent of the total heat demand. Michaelides and Wilson [3] developed simulation model concerned with the optimization of some design criteria for water based active solar space heating systems intended for residential applications in Cyprus. They used the TRNSYS simulation program for correlate the performance and cost eﬀectiveness of the system with a number of key design criteria. The simulation results showed that the system is not viable when compared with a diesel oil alternative but the system is cost eﬀective when compared with electricity.

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Nomenclature Ac bo bp CA CE CF cf df F FR IT i MS N Np P1 P2

collector area, m2 collector constant characteristic coeﬃcient of heat pump area dependent cost, $/m2 ﬁxed cost, $ cost of fuel, $/GJ speciﬁc heat of ﬂuid, J/kg K down payment solar fraction collector heat removal factor monthly average daily solar radiation incident on the collector per unit area, MJ/m2 assumed annual interest rate on mortgage solar system performance degrade period of economic analysis, year the payback period of system, year ratio of the life cycle solar savings to the ﬁrst year solar savings ratio of the life cycle expenditures to the initial investment

Turkey has abundant reserves of renewable energy, such as solar, wind and geothermal. Solar energy seems one of the most promising sources because of the country’s climate, as seen in Fig. 1. Turkey has an average 2640 h of sunshine per annum and the average solar ﬂux exceeds 5.8 GJ/m2 annually. But, Turkey’s solar thermal is used directly to a small extent: 52 ktoe in 1995 [4]. So far solar energy is utilized only for domestic hot water usage in small scale systems. Solar heating systems with the seasonal storage have studied theoretically in the last decade. The utilization of solar energy and its contribution to the economy of Turkey has been increased in the recent years. A thermo-economic feasibility study is necessary before installing a seasonal storage solar system. The present study is dealt with the thermo-economic optimization of collector area (Ac) and storage volume (V) for solar heating systems in Turkey, using MATLAB optimization Toolbox. An original formula is developed for the economically opti-

Qah Qae QH Qie Qloss Qu Rv S Ta Tiref Toref Tf V (UA)H UL W qf ðsaÞ

design house heat load, W energy accumulation rate in the storage tank, W heat load of building, W net energy input rate to storage, W heat loss to the surrounding earth from the storage tank, W monthly average of useful solar energy, W resale value of solar system, $ solar savings, $ ambient temperature, K inside design air temperature, K winter design outside air temperature, K ﬂuid temperature at the inlet to the collector, K storage volume, m3 building loss coeﬃcient, W/K collector overall energy loss coeﬃcient, W/m2 K heat pump power density of ﬂuid, kg/m3 average transmissivity absorptivity product

mal determination of collector area and storage volume. It is applied to ﬁve diﬀerent climate regions of Turkey. These regions, covering latitudes between 37 and 41 °N are illustrated in Fig. 3. 2. Thermal system A schematic diagram of seasonal solar heating system is illustrated in Fig. 2. The model system includes ﬂat plate solar collectors, a heat pump, an under ground storage tank and a heating load. Solar energy absorbed by the solar collectors is transferred to storage tank in the ground during the whole year. The heat pump operates only when the temperature of the water in the tank is in suﬃcient to keep the house at the required inside design air temperature [5]. 3. Simulation In the present study; the transient heat transfer between cylindrical storage and the surrounding ground is solved by using ﬁnite element code ANSYSTM. The problem has been introduced, by written the geometrical properties and boundary conditions in subprogram of ANSYS. Then ANSYS has solved this problem. The time-dependent heat conduction equation has been used in the ﬁnite element model of cylindrical type storage. Utilizing the cylindrical coordinate system, the time-dependent heat conduction equation is expressed as follows:

Fig. 1. Solar energy potential of Turkey.

1 o oT o2 T 1 oT r þ 2 ¼ r or or oz a ot

ð1Þ

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A. Ucar, M. Inalli / Applied Thermal Engineering 27 (2007) 450–456

Fig. 2. Schematic diagram of a central solar heating system with seasonal storage.

Fig. 3. The ﬁve diﬀerent climate locations in Turkey.

The data for monthly average of daily solar radiation and for the monthly average of daily outside air temperature for four diﬀerent climatically Turkey locations were transferred to ANSYS as data ﬁles. The input data to ANSYS are data for the monthly outside air temperature, the earth data and storage size data.

The heat loss coeﬃcient (UA)H of the building is calculated as ðUAÞH ¼ Qah =ðT iref T oref Þ

The useful energy gain of the ﬂat plate collectors is calculated by

Qu ¼ Ac F R ½ðsaÞI T U L ðT f T a Þ

4. Mathematical formulation Solar energy is supplied from the storage tank to a building. Instantaneous heat load for building is evaluated by using the equation QH ¼ ðUAÞH ðT iref T a Þ

ð2Þ

ð3Þ

ð4Þ

where Ac is the collector area, FR is the collector heat removal factor, ðsaÞ is the transmittance, UL is the collector overall loss coeﬃcient, IT is the instantaneous solar radiation incident on the collector per unit area, Ta is the ambient air temperature and Tf is the ﬂuid temperature at the inlet to the collector.

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Table 1 Weather data for the ﬁve locations Location

Latitude (°N)

Yearly ambient temperature (°C)

Maximum monthly temperature (°C)

Yearly solar radiation (MJ/m2 day)

Maximum monthly solar radiation (MJ/m2 day)

Winter design air temperature (°C)

Adana Izmir Elazıg˘ Erzurum _ Istanbul

37 38.2 38.7 39.5 40.5

18.7 17.3 13.0 7.9 13.8

28.1 27.5 27.2 19.6 23.2

13.5 12.1 12.9 14.3 13.1

17.0 16.9 19.2 18.0 18.8

0.0 0.0 12.0 21.0 3.0

The heat loss to the surrounding earth from the storage tank Qloss is given by Qloss ¼ Qie Qae

ð5Þ

where Qie is the net energy input rate and evaluated as follows: Qie ¼ Qu QH þ W

ð6Þ

where W is heat pump work. The energy accumulation rate in the storage tank is deﬁned as Qae ¼ qf Vcf

dT f dt

ð7Þ

The solar fraction is deﬁned as the utilized solar heat divided by the total heat demand and calculated as X F ¼ ½Qu Qloss =QH ð8Þ The simpliﬁed P1 and P2 method is used to determine optimum collector area and storage volume of domestic solar heating system [6]. Solar saving for solar heating systems are given by S ¼ P 1 C F QH F P 2 C S

ð9Þ

where CS is calculated as follows: C S ¼ C A Ac þ C E

ð10Þ

Substituting the solar fraction expression into Eq. (9) and it is we may further write S ¼ P 1 C F ðQH W Þ þ P 1 C F Qf V P 2 C A Ac P 2 C E

ð11Þ

where Qf is deﬁned as ratio of the energy accumulation rate in the storage tank to storage volume. Q ð12Þ Qf ¼ ae V By taking Eq. (11) as objective function and using MATLAB optimization Toolbox, optimum values of V and Ac are determined. The economic parameters P1 and P2 can be evaluated by [7] N

P 1 ¼ ½ð1 þ d f Þ=ðd f iÞ½1 ðð1 þ iÞ=ð1 þ d f ÞÞ P 2 ¼ 1 þ P 1 M S Rv ð1 þ d f Þ

N

ð13Þ ð14Þ

The payback period Np is given by Np ¼

ln½1 ðP 2 C A Aopt þ P 2 C E Þðd f iÞ=ðC F ðQH W Þ þ C F Qf V opt Þ ln½ð1 þ iÞ=ð1 þ d f Þ

ð15Þ

Fig. 4. Monthly heating load for the ﬁve diﬀerent climate locations.

Table 2 System simulation parameters Parameter Collector parameters Type Glazing Collector overall energy loss coeﬃcient, UL Collector heat removal factor, FR Average transmissivity absorptivity product, ðsaÞ Collector parameter, bo Parameter Load parameters Design house heat load, Qah Inside design air temperature, Tiref

Type I

Type II

Black paint ﬂat plate Double glass 4.5 W/m2 K

Selective ﬂat plate Double glass 3.2 W/m2 K

0.95

0.94

0.76

0.74

0.15

0.16

Value 10 kW (per house) 294 K

Table 3 Economic parameters [8] Collector types Parameter

Type I

Type II

Area dependent cost, CA (per house) Fixed cost, CE (per house) Solar system performance degrade, MS Down payment, df Assumed annual interest rate on mortgage, i Resale value of solar system, Rv (per house) Period of economic analysis, N

1200 $/m2 4000 $ 1% 5% 5% 4000 $ 50 years

1800 $/m2 6000 $ 1% 5% 5% 6000 $ 50 years

1 USD is equivalent to around 1.35 New Turkish Liras (YTL) at the market rate.

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Fig. 5. Solar fraction and savings as a function of optimal collector area for the three loads in Elazıg˘, Turkey: (a) One house; (b) 50 houses; (c) 500 houses.

_ _ Fig. 6. Solar fraction and savings as a function of optimal collector area for four diﬀerent climate locations of Turkey: (a) Adana; (b) Izmir; (c) Istanbul; (d) Erzurum.

A. Ucar, M. Inalli / Applied Thermal Engineering 27 (2007) 450–456

If i is equated df, the payback period Np can be calculated by Np ¼

ðP 2 C A Aopt þ P 2 C E Þð1 þ iÞ ½C F ðQH W Þ C F Qf V opt

ð16Þ

5. Simulation results and discussion In this study, the main objective is to ﬁnd optimal collector area and storage volume to assess the economic feasibility for loads. The optimum collector area and storage volume are solved from Eq. (11) by using MATLAB optimization Toolbox. Simulations were performed for ﬁve climatically diﬀerent locations of Turkey. The weather data of these locations are given in Table 1. The weather data used in the simulation are average values based on long years measurements of the meteorological stations in the ﬁve locations of Turkey. The data given in Table 1 indicates monthly average values of the daily radiation on tilted surfaces and ambient temperature. Fig. 4 shows monthly heating load for the ﬁve diﬀerent climate locations. The monthly heating load of a domestic solar heating system in Erzurum is 70% higher than of a system in Adana for December. The load sizes considered in this article were 1, 50 and 500 housing units. The simulation and economic parameters used in the present study are listed in Tables 2 and 3.

455

Fig. 5 shows the calculated solar fraction and savings using optimum values of collector area and storage volume for the three loads. These results were obtained for the Elazıg˘ weather conditions and for the black paint ﬂat plate collector systems. It is observed that for reaching maximum savings per house collector area decreases with increasing load size. Taking as an example the required per house collector area to reach maximum savings is 50 m2/house for one house load and 45 m2/house for 500 houses load. Fig. 6 shows the calculated solar fraction and system savings for optimum values of collector area and storage volume in the case of the one house load and the four dif_ _ ferent locations of Turkey, Adana, Izmir, Istanbul and Erzurum, respectively. It can be seen that Adana has approximately 10–47% higher solar fraction values, compared with the other locations. The annual heating load is directly proportional to the temperature diﬀerence between the house and ambient. The heating load of the system decreases with increasing ambient temperature and hence less energy is extracted by heat pump from storage for house heating during heating season. A large part of total heating load for house heating is supplied from the sun, due to the annual ambient temperature and solar radiation are higher in Adana. Consequently, in order to obtain maximum saving the required optimum collector area in Adana is smaller than that of other locations. Using

Fig. 7. Eﬀect of collector eﬃciency on solar fraction and savings for the three loads in Elazıg˘: (a) One house; (b) 50 houses; (c) 500 houses.

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ing systems in ﬁve diﬀerent locations are given Table 4. The annual heating load of a house in Erzurum is higher than _ that of southern locations such as Adana and Izmir. Therefore, the required collector area for the northern locations such as Erzurum is bigger than that of other locations and the investment costs of the systems in these locations are higher. Consequently, the payback period of a system in Erzurum is 22%–25% longer, compared other locations. 6. Conclusions

Fig. 8. Payback periods of the ﬁve locations for 50 houses load. Table 4 Calculated minimal payback periods of the ﬁve locations Location

The payback period, Np,min (year)

Adana Izmir Elazıg˘ Erzurum _ Istanbul

13 15 23 35 26

same storage volume (1000 m3), the required optimum collector area for reaching maximum savings is 36 m2/house in Adana (37 °N) and 65 m2/house in Erzurum (39 °N). _ The required optimum collector area in Izmir is 36.7 m2/ house, i.e. 44% lower than for Erzurum. It can be seen that _ the required collector area for Elazıg˘ and Istanbul is 23% and 18% lower than for Erzurum, respectively. Fig. 7 shows eﬀect of collector eﬃciency on solar fraction and savings for the three load sizes. The solar fraction and savings of systems with the selective ﬂat plate collector which has high absorption and low emission are higher, compared other black paint ﬂat plate collector. It is observed that a larger optimum area for black paint ﬂat plate collector is required compared with other collector. The payback period of system is evaluated from Eq. (13) by using the optimum values of collector area and storage volume for ﬁve locations and the results are show in Fig. 8. These results show that the calculated payback period of a _ domestic solar heating system in Adana and Izmir is 53% and 44% lower than of a system in Erzurum, respectively. The payback period of a solar heating system under weather conditions of Elazıg˘ is less when compared with for Istanbul. The minimum payback periods of solar heat-

The collector area and storage volume in components of a seasonal storage solar heating system have a most important inﬂuence on investment cost. The thermo-economical optimization technique for determining the optimal sizes of collector area and storage volume of seasonal storage solar heating system in Turkey has been developed. The required optimum collector area and storage volume for reaching maximum savings are evaluated from an original formulation which is developed for solar heating systems under ﬁve climatically diﬀerent locations of Turkey. The required optimum collector area for reaching maximum savings is reduced as the latitude decreases. It can be seen that the required optimum collector area in Adana (37 °N) for reaching maximum savings is 45% lower than that of Erzurum (39 °N). Domestic solar heating systems with seasonal storage can be designed close to calculated optimal sizes using the method presented in this study. References [1] B. Nordell, G. Hellstro¨m, High temperature solar heated seasonal storage system for low temperature heating of buildings, Sol. Energy 69 (2000) 511–523. [2] D. Lindenberger, T. Bruckner, H.M. Groscurth, R. Ku¨mmel, Optimization of district heating systems: seasonal storage, heat pumps, and cogeneration, Energy 25 (2000) 591–608. [3] I.M. Michaelides, D.R. Wilson, Optimisation of design criteria for solar space heating systems through modelling and simulation, in: Proceedings of the Fifth International Conference on Building Simulation, Prague (1997) 315–319. [4] General directorate of electrical power resources survey and development administration (EIE). ¨ nsal, V. Tanyıldızı, A computational model of a [5] M. Inallı, M. U domestic solar heating system with underground spherical thermal storage, Energy 22 (1997) 1163–1172. [6] J.A. Duﬃe, W.A. Beckman, Solar Engineering of Thermal Process, John Wiley and Sons, New York, 1991. [7] M.S. So¨ylemez, On the thermo economical optimization of single stage refrigeration systems, Energy Buildings 36 (2004) 965–968. [8] M. Chung, J. Park, H. Yoon, Simulation of a central solar heating system with seasonal storage in Korea, Sol. Energy 64 (1998) 163–178.