- Email: [email protected]
The influence of climate and location on collector performance
Renewable Energy 25 (2002) 499–509 www.elsevier.nl/locate/renene
The influence of climate and location on collector performance M. Adsten
a,*
, B. Perers b, E. Wa¨ckelga˚rd
a
The A˚ngstro¨m Laboratory, Uppsala University, Box 534, S-751 21 Uppsala, Sweden Vattenfall Utveckling AB, c/o Miljo¨konsulterna, Box 1046, S-611 29 Nyko¨ping, Sweden
a b
Received 20 February 2001; accepted 8 March 2001
Abstract The influence of annual climate variations on the performance of solar thermal collectors in the northern part of Europe has been investigated. The annual solar collector energy output has been calculated with the MINSUN simulation program using hourly, measured climatic data for the years 1983–98 for three cities situated in the south (Lund), central (Stockholm) and north (Lulea˚) of Sweden. A synthetic year created with the Meteonorm weather simulation program was also used in the simulations. Two solar thermal collectors were modelled: a flat plate solar collector and a tubular vacuum collector, both of commercial standard. The thermal energy output is strongly correlated to the annual global irradiation at a horizontal surface. The annual average energy delivered from the flat plate collector was 337 kWh/m2 for Stockholm (337 for Lund and 298 for Lulea˚), and from the vacuum tube collector 668 kWh/m2 for Stockholm (675 for Lund and 631 for Lulea˚) at an operating temperature of T=50°C. Maximum deviations from the average value for this 16-year period are around 20% for the flat plate and 15% for the vacuum tube collector, at T=50°C. The relation between global irradiation on a horizontal surface and the annually collected thermal energy at a constant operating temperature could be fitted to a linear equation: qu=aG(0°)+bT, where qu is the energy output from the collector, G(0°) the global irradiation at a horizontal surface, T the average temperature of the collector fluid, and a and b fitting parameters in a double linear regression analysis. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Solar thermal collector simulations; Climate variation
* Corresponding author. Tel.: +46-18-471-00-00; fax: +46-18-50-01-31. E-mail addresses: [email protected] (M. Adsten), [email protected] (B. Perers). 0960-1481/02/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 1 ) 0 0 0 9 1 - X
500
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
Nomenclature pu qu F⬘(ta)b G F⬘(ta)d ⌬T F⬘UL1 F⬘UL2 (mC)e Tf t q
collector array thermal power (W/m2) collector delivered annual energy output (kWh/m2) zero loss efficiency for beam radiation (at normal incidence) solar irradiation, beam or diffuse (W/m2) zero loss efficiency for diffuse radiation (in collector plane) temperature difference between Tf and ambient temperature (K) first order heat loss coefficient (W/m2K) temperature dependence in heat loss coefficient (W/m2 K 2) effective thermal capacitance for the collector (J/m2 K) mean fluid temperature in the collector (K) time (s) incidence angle for the beam solar radiation onto the collector plane (°)
1. Introduction Simulations of solar collector performance are often used when dimensioning of solar thermal systems is carried out and also in tests of real collectors. Climatic data in some form has to be used in the collector model in order to simulate the real conditions of in-service performance. The time resolution in the models is often annual, monthly or hourly, leading to different levels of accuracy in the simulated performance. In most cases beam and global irradiation and ambient temperature are required in the model. These data can be obtained in two ways, either through weather simulation programs or by using real measured data. The weather simulation programs are often based on measured data in some form, such as monthly average data that are used to generate hourly values. An example of such a program is Meteonorm [1]. Real data on an hourly basis can often be obtained from authorised meteorological measurement stations. The climate data used in simulations, synthetic or real, are often considered to be an average type of climate for a specific geographic location and the location itself should be representative for a larger geographic region. However, the collector performance can be considerably different for a year with an extreme climate. A comparative study of simulated annual energy output from a solar collector using climatic data for three locations in Sweden for 16 different years, 1983–98 has been made in order to elucidate the impact of climatic variations such as annual global irradiation and ambient temperature. It comprises results presented in a more extensive study of six solar collectors [2]. Two of them, a flat plate and a vacuum tube collector, are reported here. A comparison with a synthetic year produced with Meteonorm has also been included in this paper. The symbols used in the paper are identified in the nomenclature.
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
501
2. Collector model The solar collector array part (UMSORT) of the simulation program MINSUN [3] for a solar heating plant with seasonal storage is used in the simulations. The program has been updated according to the latest results about dynamic collector modelling and solar radiation processes. By only simulating the collector array, system performance is disregarded. The advantage of this approach is that modelling of collector specific system designs is not needed and cannot influence the simulated collector performance. It is therefore possible to single out the impact of climatic annual variations on different types of collector designs. Operation conditions are described by one parameter in the collector model, a constant average fluid temperature, which is the arithmetic average of the inlet and outlet temperature. The instantaneous optical and thermal responses of a solar collector are described by the useful power, pu, in Eq. (1): pu⫽F⬘(ta)bKtab(q)Gb⫹F⬘(ta)dKtad(q)Gd⫺F⬘UL1⌬T⫺F⬘UL2(⌬T)2
(1)
⫺(mC)e dTf/dt The model is based on the Hottel Whillier Bliss equation with improvements that account for correction terms such as thermal capacitance, incident angle effects and temperature dependence of the heat loss coefficient. The basic model and correction terms are described elsewhere [4]. The incidence angle dependence is modelled with the standard equation [4] Kta⫽(1⫹b0(1/cos q⫺1))
(2)
where b0 is a collector-specific incidence angle coefficient. Two different collector designs have been modelled. One flat plate collector with a selective absorber having high U-value and a low iron glass cover, and one vacuum tube collector of through flow type. These two were chosen because it can be expected that they respond differently to climatic variations. The parameters of the collector model are found in Table 1. These are taken from a solar heating nomogram [5] and are typical for collectors of commercial standard. Simulations were performed for three operating temperatures, 25, 50 and 75°C unless otherwise stated. These temperatures are representative for pool heating or extreme low-temperature systems (25°C), domestic hot water heating (50°C) and space heating (75°C). The collector tilt from the horizontal ground plane is 45° and Table 1 Collector parameters used in the collector model Collector
F⬘(ta)b
F⬘(τα)d
b0
F⬘UL1 (W/m2 K)
F⬘UL2 (W/m2 K 2)
(mC)e (kJ/m2 K)
Flat plate Vacuum tube
0.79 0.80
0.71 0.72
0.15 0.10
4.80 0.80
0.03 0.01
6.0 6.0
502
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
south facing (azimuth angle 0°). A tilt angle of 45° was chosen because it is approximately the optimum tilt for all three latitudes studied in this work. The optimum tilt function for the studied latitudes is rather flat around 45°, the difference between using the absolute optimum for Lund and Lulea˚ compared to 45°-tilt is only a couple of kilowatt hours. Ground reflection, rg, was set to 0.2, the standard value for nonsnow season [4]. Climate data was obtained from the Swedish Meteorological and Hydrological Institute, SMHI, as hourly average values for beam and global irradiation and ambient temperature from 1983 to 1998 for three Swedish cities: Lulea˚ (65.55° N, 22.13° E), Stockholm (59.33° N, 18.10° E) and Lund (55.72° N, 13.30° W). The Hay and Davies model was used to calculate the diffuse contribution on a tilted surface. A synthetic year produced with the Meteonorm weather simulation program was also used.
3. Results The collector energy output for 50°C operating temperature and global irradiation are plotted in Fig. 1(a) and (b) as the deviations from the average values of these quantities. As seen in the figure, 1997 represents the year with the largest solar irradiation and 1998 the year with the lowest. 1986 is a typical year for Stockholm within the recorded period. The solar collector yield follows the trends of global irradiation for the flat plate collector (Fig. 1(a)) and the vacuum collector (Fig. 1(b)). Table 2 contains the average and extreme values of annual solar irradiation, temperature and collector energy output for all three cities and operating temperatures. The temperatures are the average annual ambient temperatures accounting for hours when the global irradiation on a 45°-tilted surface is larger than 300 W/m2. This selection represents the operation hours of the collector since solar radiation intensity must exceed 300 W/m2 in order to heat the collector so it can deliver energy. The delivered collector energy outputs are in the same order for Stockholm and Lund, and lower for Lulea˚ . It is found in Table 2 that the relative standard deviation for the flat plate collector is higher than that found for the vacuum collector. The solar irradiation data for Stockholm 1986 (average), 1997 (high) and 1998 (low) is presented in Fig. 2 as the global irradiation on a 45°-tilted south facing surface sorted in different power intervals. The main part of extra solar irradiation during 1997 falls into the power interval 500–900 W/m2. The largest relative difference occurs for the highest irradiation levels from 1000 W/m2, but these only represent a small part of the annual irradiated solar energy. Fig. 3 can be used when designing a solar collector system to dimension the pipes and heat exchanger in a cost-effective way. The span in power shown in Fig. 3(a) and (b) is narrower than for the solar irradiation in Fig. 2 which is due to the fact that solar irradiation below about 300 W/m2 is not utilised by the collector. It is seen that the excess energy is not distributed exactly as the global irradiation in Fig. 2, which indicates that a certain power interval of solar irradiation is not directly carried over to the power interval in Fig. 3 showing delivered energy output. The
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
503
Fig. 1. Simulated solar collector output and solar irradiation on horizontal and 45°-inclined surface compared to the average output for 1983–98 and a synthetic year produced with the Meteonorm weather simulation program (M) for (a) a flat plate collector with high U-value and (b) a vacuum tube collector of through flow type. Three different average collector temperatures were simulated for Stockholm, 1983–98.
main reason for this is that the thermal losses depend on the difference between operation temperature and ambient temperature. The main trend is however similar, and hence results from the collector simulations show that the solar irradiation has a major influence on the total annual energy delivery of the collector and ambient temperature has a minor impact. We therefore propose a simple model, which can be used to estimate the annual collector yield, qu from the global irradiation on a horizontal surface, G(0°) at constant operation temperature, T (given in °C): qu⫽aG(0°)⫹bT
(3)
The constants a and b are found from double-linear regression. All parameters are presented in Table 3, together with the standard deviation for each of the parameters, the R2 value and the standard deviation for the whole model. R2 is the coefficient of determination, a value between one and zero. For perfect correlation between model output and the simulated or measured values, the R2-value is equal to one.
Average annual collector energy Top=25°C output (kWh/m2a) Top=50°C Top=75°C Span in output (kWh/m2a), Top=25°C relative highest and lowest Top=50°C Top=75°C Standard deviation (kWh/m2a) Top=25°C Top=50°C Top=75°C
Average annual irradiation on 45°-tilted surface (kWh/m2a) Span insol. (kWh/m2 year) Relative highest lowest insol. Standard deviation (kWh/m2a) Average annual temperature (°C) for hours with G(45°)⬎300 W/m2 Temperature span (°C) Relative highest and lowest Standard deviation (°C)
603 337 145 ⫺103+113 ⫺71+76 ⫺39+40 57 (9%) 42 (12%) 24 (16%)
Flat plate
Flat plate 781 675 564 ⫺79+85 ⫺77+83 ⫺59+78 55 (7%) 54 (8%) 53 (9%)
+1.8 (+13%) ⫺4.1 (⫺30%) 1.4 (10%)
+2.1 (+16%) ⫺3.3 (⫺25%) 1.3 (10%)
610 337 141 ⫺73+84 ⫺61+65 ⫺36+36 57 (9%) 45 (13%) 25 (18%)
+115 (+10%) ⫺144 (⫺13%) 77 (7%) 13.6
+113 (+10%) ⫺103 (⫺9%) 69 (6%) 13.4
Vacuum
1113
772 668 559 ⫺111+114 ⫺108+112 ⫺99+105 59 (8%) 58 (9%) 55 (10%)
Vacuum
Stockholm (59.33° N)
1124
Lund (55.72° N)
543 298 124 ⫺96+91 ⫺67+59 ⫺38+29 55 (10%) 37 (13%) 19 (16%)
Flat plate
+1.4 (+14%) ⫺1.7 (⫺17%) 1.1 (11%)
+146 (+14%) ⫺126 (⫺12%) 80 (7%) 9.8
1077
Lulea˚ (65.55° N)
733 631 526 ⫺98+109 ⫺95+103 ⫺88+94 61 (8%) 59 (9%) 54 (10%)
Vacuum
Table 2 Average and extreme values and standard deviations of annual solar irradiation, temperature and collector energy output for collector delivered energy simulations for three Swedish cities
504 M. Adsten et al. / Renewable Energy 25 (2002) 499–509
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
505
Fig. 2. Annual incident solar energy (Q) on a 45°-surface sorted in different power intervals when the solar irradiation is within different power intervals for an average year (1986), a good year (1997) and a bad year (1998) for Stockholm.
The delivered energy obtained by the collector array model (Eq. (1)) and the double linear regression equation (Eq. (3)) show good agreement, as can be seen in Fig. 4(a) and (b). Deviations are found for example for years with extreme ambient temperatures or with a very high or low beam radiation content in relation to the horizontal global solar radiation. An example of the latter is Stockholm 1992 with a high horizontal global irradiation, G(0°)=978 kWh/m2a (average 926 kWh/m2a), and low beam radiation, Gbeam=881 kWh/m2a (average 972 kWh/m2a), resulting in a too high energy output with the regression model compared to the collector array model. When studying Table 3 it is found that the a coefficients are quite close to one, so a deviation in solar irradiation of 100 kWh leads to a change of about 100 kWh in collector delivered energy. For an operating temperature of 50°C the maximum deviation from the average value for the 16-year period is found to be 18–23% for the flat plate and 11–17% for the vacuum tube collector, depending on location. The standard deviations are 12% (Stockholm) and 6% (Lulea˚ and Lund) for the flat plate, 9% (Stockholm) and 3% (Lulea˚ and Lund) for the vacuum tube collector (50°C operating temperature). Collector manufacturers are interested in providing an energy guarantee for their solar collectors. A guarantee consisting of a fixed value is not satisfactory due to the large deviations from year to year shown in Fig. 1. A collector certification of average delivered annual energy with a standard deviation is a more appropriate guarantee for the collector manufacturers to use. Fig. 1 shows the simulated energy output obtained with weather data from the Meteonorm compared to the 16-year average. When the energy output is simulated with Meteonorm synthetic data it is found that the output for a collector placed in Stockholm is higher than the average for the vacuum collector; it is within the top 25% in the studied 16-year period. The flat plate collector energy output is above the average for operating temperature 25 and 50°C and below for 75°C. For Lund
506
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
Fig. 3. Simulated energy output (Q) for (a) a flat plate solar collector with high U-value and (b) a vacuum tube collector of through flow type sorted in different collector power intervals. Data from Stockholm for an average year (1986) a good year (1997) and a bad year (1998) was used in the simulation. Average collector temperature 50°C.
in the southern part, simulated output and solar irradiation using the Meteonorm data are fairly average when comparing with real data for 1983–98. In the northern part, the solar irradiation for Lulea˚ and the simulated output for the vacuum collector are close to average, but the delivered energy for the flat plate collector is within the bottom 25%. If the irradiation data for a 45°-tilted surface is calculated in the Meteonorm program, the irradiation levels are found to be in accordance with the top years. This is explained by Meteonorm using the Perez method when calculating irradiation in the tilted plane. According to Brunger and Hollands [6], the Perez method overpredicts the irradiation on a tilted plane for high latitudes.
0.86 0.88 0.85 0.86 0.98 0.95 0.92 0.94
Lulea˚ Stockholm Lund All three cities Lulea˚ Stockholm Lund All three cities
Flat plate
Vacuum tube
a
City
Collector
0.011 0.010 0.010 0.008 0.010 0.008 0.007 0.008
SDa
0.98 0.98 0.98 0.97 0.95 0.97 0.97 0.91
⫺8.36 ⫺9.13 ⫺9.36 ⫺8.82 ⫺4.22 ⫺4.31 ⫺4.36 ⫺4.15 0.183 0.179 0.176 0.142 0.157 0.135 0.118 0.129
R2
b (kWh/m2 °C) SDb (kWh/m2 °C)
26 26 25 35 22 19 17 32
SDmodel (kWh/m2 °C)
Table 3 Multiple linear regression to obtain parameters for qu=aG(0°)+bT, where G is the global horizontal irradiation in kWh/m2 and T is the average collector temperature in °C. Regression was performed using simulated collector delivered thermal energy data for two different solar collectors with climate data for three Swedish cities, Lulea˚ , Stockholm and Lund from 1983 to 1998
M. Adsten et al. / Renewable Energy 25 (2002) 499–509 507
508
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
Fig. 4. Simulated (Sim) and calculated (Mod), solar collector thermal energy output vs. annual horizontal irradiation for (a) a flat plate collector with high U-value and (b) a vacuum tube collector of through flow type. Three different average collector temperatures were simulated and calculated for Stockholm, 1983–98.
4. Conclusions The solar irradiation varies considerably from year to year causing a large variation in the solar collector delivered heat. The span around the average value for the 16year period is around 20% for the flat plate and 15% for the vacuum tube collector for an operating temperature of 50°C. A guarantee consisting of a fixed value is not satisfactory due to the large deviations from year to year. Instead a guarantee involving the average output and a standard deviation is suggested. As can be expected the performance of the vacuum tube collector is better than that of the flat plate collector. The standard deviation of the vacuum tube collector is lower than for the flat plate, indicating that the vacuum tube collector is less dependent on climate variations due to smaller thermal losses. The thermal energy output can be determined by the relation Q=aG(0°)+bT with
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
509
reasonable accuracy. There are some small deviations from this relation, and they are found to be due to very large variations in solar irradiation (relation of beam to total) or ambient temperature. A deviation in solar irradiation leads to a change in collector delivered energy of almost equal size since the a coefficient is close to unity. It is important to use local climate data in order not to over/underestimate the thermal performance of the collector. In the work presented here it is shown that the same climate data can be used for the southern and central part of Sweden with reasonable accuracy. For the northern part, however, local climate data must be used to avoid overestimation. Synthetic data produced with the Meteonorm weather simulation program lead to simulated results that are within the limits defined by the results obtained from the measured data. It is however not equal to the average of the 16-year period as would have been preferable.
Acknowledgements This work was financed by the Foundation for Strategic Research (SSF) within the Energy Systems program and Vattenfall Utveckling AB. A number of people have been very supportive during the progress of this work, among others we would like to mention Bjo¨ rn Karlsson and Arne Roos. Thank you!
References [1] Remund J, Kunz S. METEONORM — solar engineering handbook, 1997. [2] Adsten M, Perers B. Influence on solar collector energy output by annual climate variation. Report UPTEC 99005R, Uppsala University, Uppsala, Sweden, 1999 [ISSN 0346-8887]. [3] Chant VG, Ha˚ kansson R. The MINSUN simulation and optimisation program. Application and users guide. Ottawa: IEA SH & C Task VII, 1985. [4] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. New York: Wiley & Sons Inc., 1991. [5] Perers, B. Solar heating in Northern and Central Europe — Nomogram. CEC Thermie B Project: ¨ lvkarleby, Sweden, 1997. Solar heating in Northern and Central Europe. A [6] Brunger AP, Hollands KGT. Solar irradiance modelling for high latitudes. Final report, CANMET, Solar Thermal Engineering Centre, Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada, 1995.
The influence of climate and location on collector performance M. Adsten
a,*
, B. Perers b, E. Wa¨ckelga˚rd
a
The A˚ngstro¨m Laboratory, Uppsala University, Box 534, S-751 21 Uppsala, Sweden Vattenfall Utveckling AB, c/o Miljo¨konsulterna, Box 1046, S-611 29 Nyko¨ping, Sweden
a b
Received 20 February 2001; accepted 8 March 2001
Abstract The influence of annual climate variations on the performance of solar thermal collectors in the northern part of Europe has been investigated. The annual solar collector energy output has been calculated with the MINSUN simulation program using hourly, measured climatic data for the years 1983–98 for three cities situated in the south (Lund), central (Stockholm) and north (Lulea˚) of Sweden. A synthetic year created with the Meteonorm weather simulation program was also used in the simulations. Two solar thermal collectors were modelled: a flat plate solar collector and a tubular vacuum collector, both of commercial standard. The thermal energy output is strongly correlated to the annual global irradiation at a horizontal surface. The annual average energy delivered from the flat plate collector was 337 kWh/m2 for Stockholm (337 for Lund and 298 for Lulea˚), and from the vacuum tube collector 668 kWh/m2 for Stockholm (675 for Lund and 631 for Lulea˚) at an operating temperature of T=50°C. Maximum deviations from the average value for this 16-year period are around 20% for the flat plate and 15% for the vacuum tube collector, at T=50°C. The relation between global irradiation on a horizontal surface and the annually collected thermal energy at a constant operating temperature could be fitted to a linear equation: qu=aG(0°)+bT, where qu is the energy output from the collector, G(0°) the global irradiation at a horizontal surface, T the average temperature of the collector fluid, and a and b fitting parameters in a double linear regression analysis. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Solar thermal collector simulations; Climate variation
* Corresponding author. Tel.: +46-18-471-00-00; fax: +46-18-50-01-31. E-mail addresses: [email protected] (M. Adsten), [email protected] (B. Perers). 0960-1481/02/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 1 ) 0 0 0 9 1 - X
500
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
Nomenclature pu qu F⬘(ta)b G F⬘(ta)d ⌬T F⬘UL1 F⬘UL2 (mC)e Tf t q
collector array thermal power (W/m2) collector delivered annual energy output (kWh/m2) zero loss efficiency for beam radiation (at normal incidence) solar irradiation, beam or diffuse (W/m2) zero loss efficiency for diffuse radiation (in collector plane) temperature difference between Tf and ambient temperature (K) first order heat loss coefficient (W/m2K) temperature dependence in heat loss coefficient (W/m2 K 2) effective thermal capacitance for the collector (J/m2 K) mean fluid temperature in the collector (K) time (s) incidence angle for the beam solar radiation onto the collector plane (°)
1. Introduction Simulations of solar collector performance are often used when dimensioning of solar thermal systems is carried out and also in tests of real collectors. Climatic data in some form has to be used in the collector model in order to simulate the real conditions of in-service performance. The time resolution in the models is often annual, monthly or hourly, leading to different levels of accuracy in the simulated performance. In most cases beam and global irradiation and ambient temperature are required in the model. These data can be obtained in two ways, either through weather simulation programs or by using real measured data. The weather simulation programs are often based on measured data in some form, such as monthly average data that are used to generate hourly values. An example of such a program is Meteonorm [1]. Real data on an hourly basis can often be obtained from authorised meteorological measurement stations. The climate data used in simulations, synthetic or real, are often considered to be an average type of climate for a specific geographic location and the location itself should be representative for a larger geographic region. However, the collector performance can be considerably different for a year with an extreme climate. A comparative study of simulated annual energy output from a solar collector using climatic data for three locations in Sweden for 16 different years, 1983–98 has been made in order to elucidate the impact of climatic variations such as annual global irradiation and ambient temperature. It comprises results presented in a more extensive study of six solar collectors [2]. Two of them, a flat plate and a vacuum tube collector, are reported here. A comparison with a synthetic year produced with Meteonorm has also been included in this paper. The symbols used in the paper are identified in the nomenclature.
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
501
2. Collector model The solar collector array part (UMSORT) of the simulation program MINSUN [3] for a solar heating plant with seasonal storage is used in the simulations. The program has been updated according to the latest results about dynamic collector modelling and solar radiation processes. By only simulating the collector array, system performance is disregarded. The advantage of this approach is that modelling of collector specific system designs is not needed and cannot influence the simulated collector performance. It is therefore possible to single out the impact of climatic annual variations on different types of collector designs. Operation conditions are described by one parameter in the collector model, a constant average fluid temperature, which is the arithmetic average of the inlet and outlet temperature. The instantaneous optical and thermal responses of a solar collector are described by the useful power, pu, in Eq. (1): pu⫽F⬘(ta)bKtab(q)Gb⫹F⬘(ta)dKtad(q)Gd⫺F⬘UL1⌬T⫺F⬘UL2(⌬T)2
(1)
⫺(mC)e dTf/dt The model is based on the Hottel Whillier Bliss equation with improvements that account for correction terms such as thermal capacitance, incident angle effects and temperature dependence of the heat loss coefficient. The basic model and correction terms are described elsewhere [4]. The incidence angle dependence is modelled with the standard equation [4] Kta⫽(1⫹b0(1/cos q⫺1))
(2)
where b0 is a collector-specific incidence angle coefficient. Two different collector designs have been modelled. One flat plate collector with a selective absorber having high U-value and a low iron glass cover, and one vacuum tube collector of through flow type. These two were chosen because it can be expected that they respond differently to climatic variations. The parameters of the collector model are found in Table 1. These are taken from a solar heating nomogram [5] and are typical for collectors of commercial standard. Simulations were performed for three operating temperatures, 25, 50 and 75°C unless otherwise stated. These temperatures are representative for pool heating or extreme low-temperature systems (25°C), domestic hot water heating (50°C) and space heating (75°C). The collector tilt from the horizontal ground plane is 45° and Table 1 Collector parameters used in the collector model Collector
F⬘(ta)b
F⬘(τα)d
b0
F⬘UL1 (W/m2 K)
F⬘UL2 (W/m2 K 2)
(mC)e (kJ/m2 K)
Flat plate Vacuum tube
0.79 0.80
0.71 0.72
0.15 0.10
4.80 0.80
0.03 0.01
6.0 6.0
502
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
south facing (azimuth angle 0°). A tilt angle of 45° was chosen because it is approximately the optimum tilt for all three latitudes studied in this work. The optimum tilt function for the studied latitudes is rather flat around 45°, the difference between using the absolute optimum for Lund and Lulea˚ compared to 45°-tilt is only a couple of kilowatt hours. Ground reflection, rg, was set to 0.2, the standard value for nonsnow season [4]. Climate data was obtained from the Swedish Meteorological and Hydrological Institute, SMHI, as hourly average values for beam and global irradiation and ambient temperature from 1983 to 1998 for three Swedish cities: Lulea˚ (65.55° N, 22.13° E), Stockholm (59.33° N, 18.10° E) and Lund (55.72° N, 13.30° W). The Hay and Davies model was used to calculate the diffuse contribution on a tilted surface. A synthetic year produced with the Meteonorm weather simulation program was also used.
3. Results The collector energy output for 50°C operating temperature and global irradiation are plotted in Fig. 1(a) and (b) as the deviations from the average values of these quantities. As seen in the figure, 1997 represents the year with the largest solar irradiation and 1998 the year with the lowest. 1986 is a typical year for Stockholm within the recorded period. The solar collector yield follows the trends of global irradiation for the flat plate collector (Fig. 1(a)) and the vacuum collector (Fig. 1(b)). Table 2 contains the average and extreme values of annual solar irradiation, temperature and collector energy output for all three cities and operating temperatures. The temperatures are the average annual ambient temperatures accounting for hours when the global irradiation on a 45°-tilted surface is larger than 300 W/m2. This selection represents the operation hours of the collector since solar radiation intensity must exceed 300 W/m2 in order to heat the collector so it can deliver energy. The delivered collector energy outputs are in the same order for Stockholm and Lund, and lower for Lulea˚ . It is found in Table 2 that the relative standard deviation for the flat plate collector is higher than that found for the vacuum collector. The solar irradiation data for Stockholm 1986 (average), 1997 (high) and 1998 (low) is presented in Fig. 2 as the global irradiation on a 45°-tilted south facing surface sorted in different power intervals. The main part of extra solar irradiation during 1997 falls into the power interval 500–900 W/m2. The largest relative difference occurs for the highest irradiation levels from 1000 W/m2, but these only represent a small part of the annual irradiated solar energy. Fig. 3 can be used when designing a solar collector system to dimension the pipes and heat exchanger in a cost-effective way. The span in power shown in Fig. 3(a) and (b) is narrower than for the solar irradiation in Fig. 2 which is due to the fact that solar irradiation below about 300 W/m2 is not utilised by the collector. It is seen that the excess energy is not distributed exactly as the global irradiation in Fig. 2, which indicates that a certain power interval of solar irradiation is not directly carried over to the power interval in Fig. 3 showing delivered energy output. The
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
503
Fig. 1. Simulated solar collector output and solar irradiation on horizontal and 45°-inclined surface compared to the average output for 1983–98 and a synthetic year produced with the Meteonorm weather simulation program (M) for (a) a flat plate collector with high U-value and (b) a vacuum tube collector of through flow type. Three different average collector temperatures were simulated for Stockholm, 1983–98.
main reason for this is that the thermal losses depend on the difference between operation temperature and ambient temperature. The main trend is however similar, and hence results from the collector simulations show that the solar irradiation has a major influence on the total annual energy delivery of the collector and ambient temperature has a minor impact. We therefore propose a simple model, which can be used to estimate the annual collector yield, qu from the global irradiation on a horizontal surface, G(0°) at constant operation temperature, T (given in °C): qu⫽aG(0°)⫹bT
(3)
The constants a and b are found from double-linear regression. All parameters are presented in Table 3, together with the standard deviation for each of the parameters, the R2 value and the standard deviation for the whole model. R2 is the coefficient of determination, a value between one and zero. For perfect correlation between model output and the simulated or measured values, the R2-value is equal to one.
Average annual collector energy Top=25°C output (kWh/m2a) Top=50°C Top=75°C Span in output (kWh/m2a), Top=25°C relative highest and lowest Top=50°C Top=75°C Standard deviation (kWh/m2a) Top=25°C Top=50°C Top=75°C
Average annual irradiation on 45°-tilted surface (kWh/m2a) Span insol. (kWh/m2 year) Relative highest lowest insol. Standard deviation (kWh/m2a) Average annual temperature (°C) for hours with G(45°)⬎300 W/m2 Temperature span (°C) Relative highest and lowest Standard deviation (°C)
603 337 145 ⫺103+113 ⫺71+76 ⫺39+40 57 (9%) 42 (12%) 24 (16%)
Flat plate
Flat plate 781 675 564 ⫺79+85 ⫺77+83 ⫺59+78 55 (7%) 54 (8%) 53 (9%)
+1.8 (+13%) ⫺4.1 (⫺30%) 1.4 (10%)
+2.1 (+16%) ⫺3.3 (⫺25%) 1.3 (10%)
610 337 141 ⫺73+84 ⫺61+65 ⫺36+36 57 (9%) 45 (13%) 25 (18%)
+115 (+10%) ⫺144 (⫺13%) 77 (7%) 13.6
+113 (+10%) ⫺103 (⫺9%) 69 (6%) 13.4
Vacuum
1113
772 668 559 ⫺111+114 ⫺108+112 ⫺99+105 59 (8%) 58 (9%) 55 (10%)
Vacuum
Stockholm (59.33° N)
1124
Lund (55.72° N)
543 298 124 ⫺96+91 ⫺67+59 ⫺38+29 55 (10%) 37 (13%) 19 (16%)
Flat plate
+1.4 (+14%) ⫺1.7 (⫺17%) 1.1 (11%)
+146 (+14%) ⫺126 (⫺12%) 80 (7%) 9.8
1077
Lulea˚ (65.55° N)
733 631 526 ⫺98+109 ⫺95+103 ⫺88+94 61 (8%) 59 (9%) 54 (10%)
Vacuum
Table 2 Average and extreme values and standard deviations of annual solar irradiation, temperature and collector energy output for collector delivered energy simulations for three Swedish cities
504 M. Adsten et al. / Renewable Energy 25 (2002) 499–509
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
505
Fig. 2. Annual incident solar energy (Q) on a 45°-surface sorted in different power intervals when the solar irradiation is within different power intervals for an average year (1986), a good year (1997) and a bad year (1998) for Stockholm.
The delivered energy obtained by the collector array model (Eq. (1)) and the double linear regression equation (Eq. (3)) show good agreement, as can be seen in Fig. 4(a) and (b). Deviations are found for example for years with extreme ambient temperatures or with a very high or low beam radiation content in relation to the horizontal global solar radiation. An example of the latter is Stockholm 1992 with a high horizontal global irradiation, G(0°)=978 kWh/m2a (average 926 kWh/m2a), and low beam radiation, Gbeam=881 kWh/m2a (average 972 kWh/m2a), resulting in a too high energy output with the regression model compared to the collector array model. When studying Table 3 it is found that the a coefficients are quite close to one, so a deviation in solar irradiation of 100 kWh leads to a change of about 100 kWh in collector delivered energy. For an operating temperature of 50°C the maximum deviation from the average value for the 16-year period is found to be 18–23% for the flat plate and 11–17% for the vacuum tube collector, depending on location. The standard deviations are 12% (Stockholm) and 6% (Lulea˚ and Lund) for the flat plate, 9% (Stockholm) and 3% (Lulea˚ and Lund) for the vacuum tube collector (50°C operating temperature). Collector manufacturers are interested in providing an energy guarantee for their solar collectors. A guarantee consisting of a fixed value is not satisfactory due to the large deviations from year to year shown in Fig. 1. A collector certification of average delivered annual energy with a standard deviation is a more appropriate guarantee for the collector manufacturers to use. Fig. 1 shows the simulated energy output obtained with weather data from the Meteonorm compared to the 16-year average. When the energy output is simulated with Meteonorm synthetic data it is found that the output for a collector placed in Stockholm is higher than the average for the vacuum collector; it is within the top 25% in the studied 16-year period. The flat plate collector energy output is above the average for operating temperature 25 and 50°C and below for 75°C. For Lund
506
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
Fig. 3. Simulated energy output (Q) for (a) a flat plate solar collector with high U-value and (b) a vacuum tube collector of through flow type sorted in different collector power intervals. Data from Stockholm for an average year (1986) a good year (1997) and a bad year (1998) was used in the simulation. Average collector temperature 50°C.
in the southern part, simulated output and solar irradiation using the Meteonorm data are fairly average when comparing with real data for 1983–98. In the northern part, the solar irradiation for Lulea˚ and the simulated output for the vacuum collector are close to average, but the delivered energy for the flat plate collector is within the bottom 25%. If the irradiation data for a 45°-tilted surface is calculated in the Meteonorm program, the irradiation levels are found to be in accordance with the top years. This is explained by Meteonorm using the Perez method when calculating irradiation in the tilted plane. According to Brunger and Hollands [6], the Perez method overpredicts the irradiation on a tilted plane for high latitudes.
0.86 0.88 0.85 0.86 0.98 0.95 0.92 0.94
Lulea˚ Stockholm Lund All three cities Lulea˚ Stockholm Lund All three cities
Flat plate
Vacuum tube
a
City
Collector
0.011 0.010 0.010 0.008 0.010 0.008 0.007 0.008
SDa
0.98 0.98 0.98 0.97 0.95 0.97 0.97 0.91
⫺8.36 ⫺9.13 ⫺9.36 ⫺8.82 ⫺4.22 ⫺4.31 ⫺4.36 ⫺4.15 0.183 0.179 0.176 0.142 0.157 0.135 0.118 0.129
R2
b (kWh/m2 °C) SDb (kWh/m2 °C)
26 26 25 35 22 19 17 32
SDmodel (kWh/m2 °C)
Table 3 Multiple linear regression to obtain parameters for qu=aG(0°)+bT, where G is the global horizontal irradiation in kWh/m2 and T is the average collector temperature in °C. Regression was performed using simulated collector delivered thermal energy data for two different solar collectors with climate data for three Swedish cities, Lulea˚ , Stockholm and Lund from 1983 to 1998
M. Adsten et al. / Renewable Energy 25 (2002) 499–509 507
508
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
Fig. 4. Simulated (Sim) and calculated (Mod), solar collector thermal energy output vs. annual horizontal irradiation for (a) a flat plate collector with high U-value and (b) a vacuum tube collector of through flow type. Three different average collector temperatures were simulated and calculated for Stockholm, 1983–98.
4. Conclusions The solar irradiation varies considerably from year to year causing a large variation in the solar collector delivered heat. The span around the average value for the 16year period is around 20% for the flat plate and 15% for the vacuum tube collector for an operating temperature of 50°C. A guarantee consisting of a fixed value is not satisfactory due to the large deviations from year to year. Instead a guarantee involving the average output and a standard deviation is suggested. As can be expected the performance of the vacuum tube collector is better than that of the flat plate collector. The standard deviation of the vacuum tube collector is lower than for the flat plate, indicating that the vacuum tube collector is less dependent on climate variations due to smaller thermal losses. The thermal energy output can be determined by the relation Q=aG(0°)+bT with
M. Adsten et al. / Renewable Energy 25 (2002) 499–509
509
reasonable accuracy. There are some small deviations from this relation, and they are found to be due to very large variations in solar irradiation (relation of beam to total) or ambient temperature. A deviation in solar irradiation leads to a change in collector delivered energy of almost equal size since the a coefficient is close to unity. It is important to use local climate data in order not to over/underestimate the thermal performance of the collector. In the work presented here it is shown that the same climate data can be used for the southern and central part of Sweden with reasonable accuracy. For the northern part, however, local climate data must be used to avoid overestimation. Synthetic data produced with the Meteonorm weather simulation program lead to simulated results that are within the limits defined by the results obtained from the measured data. It is however not equal to the average of the 16-year period as would have been preferable.
Acknowledgements This work was financed by the Foundation for Strategic Research (SSF) within the Energy Systems program and Vattenfall Utveckling AB. A number of people have been very supportive during the progress of this work, among others we would like to mention Bjo¨ rn Karlsson and Arne Roos. Thank you!
References [1] Remund J, Kunz S. METEONORM — solar engineering handbook, 1997. [2] Adsten M, Perers B. Influence on solar collector energy output by annual climate variation. Report UPTEC 99005R, Uppsala University, Uppsala, Sweden, 1999 [ISSN 0346-8887]. [3] Chant VG, Ha˚ kansson R. The MINSUN simulation and optimisation program. Application and users guide. Ottawa: IEA SH & C Task VII, 1985. [4] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. New York: Wiley & Sons Inc., 1991. [5] Perers, B. Solar heating in Northern and Central Europe — Nomogram. CEC Thermie B Project: ¨ lvkarleby, Sweden, 1997. Solar heating in Northern and Central Europe. A [6] Brunger AP, Hollands KGT. Solar irradiance modelling for high latitudes. Final report, CANMET, Solar Thermal Engineering Centre, Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada, 1995.