1. I

ARCHIVES OF CIVIL ENGINEERING, LIV, 3, 2008

DIFFUSE SKY RADIATION MODELS’ ACCURACY ANALYSIS BASED ON MEASUREMENT DATA FOR LOWER SILESIA REGION D. WŁODARCZYK1 , H. NOWAK2

In most cases, in order to design solar energy systems one needs to know the solar radiation as divided into direct radiation and diffuse radiation. If only global radiation is known, one can employ empirical models to calculate the diffuse radiation fraction in the global radiation. The paper presents a comparison between the values generated by empirical models of diffuse sky radiation on a horizontal plane, i.e. the ORGILL HOLLANDS model [1], the E model [2] and CLIMED2 [3], with measurement data for the period 2000-2004 from the Meteorological and Hydrological Institute’s measuring station in Legnica (Poland). Measurement data quality conditions were imposed on the database whereby erroneous or statistically insignificant data were eliminated. The models were evaluated using standard statistical indices: MBE, RMSE and CC and the relative values of the mean bias error and the root mean square error, i.e. MBE[%] and RMSE[%]. The ORGILL HOLLANDS model proved to be the most accurate, followed by CLIMED2 and the ERBS model. Keywords: solar energy, diffuse radiation, theoretical models, actinometric measurements.

1. I As the awareness of fossil fuels depletion increases so do the prices of resources on the energy market. Renewable energy sources can provide an alternative to the conventional energy sources. The energy source which holds high prospects is solar radiation energy. It can be actively utilized in solar energy collectors or photovoltaic cells or passively exploited through architectonic designs improving the thermal balance of buildings. The global solar radiation on a horizontal plane consists of two parts: direct radiation and diffuse radiation. From the solar power engineering point of view it is essential to accurately determine the two components for at least two reasons. Firstly, calculations of solar radiation on variously inclined and oriented surfaces require separate input data in the form of direct and diffuse radiation on a horizontal plane. 1

PhD., Institute of Building Engineering, Wrocław University of Technology, Wrocław, Poland, e-mail: [email protected] 2 Prof., PhD., DSc., Institute of Building Engineering, Wrocław University of Technology, Wrocław, Poland, e-mail: [email protected]

624

D. W, H. N

Secondly, any power system based on the concentration of sunrays must be designed for the local direct solar radiation availability data. The measurement of solar radiation on a horizontal plane is a basic actinometric measurement. Unfortunately, despite the dual nature of global solar radiation only the latter is measured in many weather stations. But in order to properly design solar power systems one must know the global solar radiation on a horizontal plane, divided into direct and diffuse radiation. Therefore one needs empirical mathematical models which would estimate the diffuse radiation fraction in the global solar radiation on a horizontal plane. In this paper empirical models of diffuse sky radiation on a horizontal plane, making it possible to calculate the diffuse radiation value from the global solar radiation on a horizontal plane, are compared. The comparison is based on the solar radiation measurement data for the years 2000-2004 from the Meteorological and Hydrological Institute’s actinometric station in Legnica (Poland).

2. T        Empirical models usually calculate diffuse radiation fraction ID [W/m2 ] in global radiation I [W/m2 ] on the basis of clearness index kT . The clearness index is a ratio of the global solar radiation on a horizontal plane on the earth’s surface (I) to a corresponding quantity on the boundary of the earth’s atmosphere (circumterrestrial radiation) (I0 ) [W/m2 ]: (2.1)

kT =

I . I0

In 1977 O and H [1] proposed one of the first models of this kind, based on actinometric data for Toronto (Canada):

(2.2)

 ID    f = = 1.0 − 0.249 kT    IG    f = 1.577 − 1.84 kT      f = 0.177

for 0 ≤ kT ≤ 0.35, for 0.35 < kT ≤ 0.75, for kT > 0.75.

Five years later E [2] proposed another model actinometric data:  ID    = 1.0 − 0.09 kT f =    IG     f = 0.9511 − 0.1604 kT + 4.388 k 2 T (2.3)    4 3   + 12.336 k −16.638 k  T T     f = 0.165

based on American and Australian

for 0 ≤ kT ≤ 0.22, for 0.22 < kT ≤ 0.80, for kT > 0.80.

D   ’   . . .

625

In 2001 D M et al. [3] proposed the CLIMED2 model based on Mediterranean data:  ID    f = = 0.995 − 0.081 kT for kT ≤ 0.21,    IG     f = 0.724 + 2.738 kT − 8.32 k 2 T (2.4)   for 0.21 < kT ≤ 0.76,  3   +4.967 k  T     f = 0.180 for kT > 0.76.

The latter model yielded very good results in different researches ([4], [5]) carried out on independent measurement databases. In the present paper calculation results generated by selected empirical models are compared with the results of solar irradiance measurements carried out in Legnica in the years 2000-2004.

3. M  The global solar radiation and diffuse sky radiation on a horizontal plane, measured in the Meteorological and Hydrological Institute’s centre in Legnica in the years 2000-2004 were used for the comparative analysis of the empirical models of diffuse sky radiation. Consistently with the general worldwide trend in the investigation of such models, hourly data were adopted for the analyses. The data were recorded automatically from 4:00 to 21:00 of local time all year round using a computer controlled data logger. The database was verified by the CIE (Commission Internationale de l’Eclairage) standard data quality conditions [6]. The conditions eliminate garbage (produced by, for example, measuring system failures, terrain obstacles, etc.). For this purpose equations eliminating from the database the elements which do not come up to the required quality level are used. The CIE quality conditions have this form:    0 ≤ ID ≤ 1.1 IG        0 ≤ IG ≤ 1.2 I0 . (3.1)    0 ≤ ID ≤ 0.8 I0       0 ≤ I B ≤ I0

where ID – hourly diffuse radiation on a horizontal plane [Wh/m2 ], IG – hourly global radiation on a horizontal plane [Wh/m2 ], I0 – hourly solar radiation on the atmosphere’s boundary [Wh/m2 ], I B – hourly direct radiation on a horizontal plane [Wh/m2 ]. After the CIE conditions were imposed, i.e. after data not satisfying the conditions were eliminated, a database made up of 20482 measured values was obtained. Atmosphere clearness index kT versus diffuse radiation fraction f in global radiation for the database is shown in Fig. 1.

626

D. W, H. N

Fig. 1. Global radiation clearness index kT versus diffuse radiation fraction f in global radiation on a horizontal plane for hourly actinometric quantities measured in Legnica in years 2000-2004. Rys. 1. Zależność pomiędzy współczynnikiem jasności promieniowania całkowitego kT i udziałem promieniowania rozproszonego w promieniowaniu całkowitym na płaszczyznę horyzontalną f dla godzinowych danych aktynometrycznych pomierzonych w Legnicy w okresie 2000-2004

Figure 1 shows that there are some data which are far off the trend set by the other trend data. According to M [7], data for the diffuse radiation fraction ( f ) in the global radiation on a horizontal plane (roughly equal to 1.00) at clearness index kT ≥ 0.40 may be erroneous due to the improperly adjusted shading ring during the measurement of diffuse radiation on a horizontal plane. This means that the CIE solar data quality conditions should not be the only tool verifying measurement data validity. In 2005 Y et al. [8] found that the standard quality conditions might be insufficient and so they proposed shape patterns for the atmosphere clearness index (kT ) – diffuse to global irradiance ratio diagram. A standard database is created by accepting only the measuring points situated within the area delineated by two curves produced by the least squares method on the basis of points located at a distance of two standard deviations from the average diffuse radiation fraction ( f ) in the global radiation in a specified interval of atmosphere clearness index kT . In addition, the area of such a database is bounded by the boundary values of f , i.e. 0 and 1. After the average diffuse radiation fractions f in the global radiation and the standard deviations for all the 50 intervals of 0.02 were calculated, the equations of

D   ’   . . .

627

the curves limiting the database to the “pattern” were formulated by the least squares method. The curves are shown in Fig. 2 and Fig. 3.

Fig. 2. Measurement data removed from analyzed database by applying bounding curves. Rys. 2. Dane pomiarowe usunięte z analizowanej bazy danych po zastosowaniu krzywych ograniczających

Fig. 3. Measurement data left in database after bounding curves were applied. Rys. 3. Dane pomiarowe pozostawione w analizowanej bazie danych po zastosowaniu krzywych ograniczających

628

D. W, H. N

For low values of clearness index kT Y et al. [8] propose to manually enter a constant value, otherwise because of the minimum standard deviation in this interval of kT the lower bounding curve would eliminate a large number of measurement data lying very close to average f . In the analyzed case, 0.9168 was entered as the value bounding the “pattern” at kT : < 0; 0.20 >. After the “pattern” was applied 853 measuring points, amounting to 4.06% of all the measuring points which had passed the CIE data quality control test, were left outside the enveloping curves. The data removed from the database are shown in Fig. 2. In sum, 20176 measuring points, amounting to 95.94% of the data which had passed the CIE data quality control test, remained within the pattern. The data within the pattern, forming the final database for the statistical analysis of empirical models of diffuse irradiance on a horizontal surface, are shown in Fig. 3.

4. S     The database was used to verify the accuracy of calculating of the fraction of diffuse radiation in the global solar radiation on a horizontal plane. In order to evaluate the particular models three standard statistical indices: MBE, RMSE and CC, described by formulas (4.1), (4.2), (4.3), (4.4), (4.5), were used. MBE (Mean Bias Error) informs us about the average of model results. The lower the MBE of a model, the more accurate the latter is. RMSE (Root Mean Square Error) is a measure of the measurement data deviation from the theoretical model. Similarly as for MBE, a lower RMSE is desirable for a model. MBE and RMSE can also be expressed in relative values (related to the average measured value of diffuse radiation) i.e. MBE[%] and RMSE[%]. This was proposed in, among others, [4]. CC (Correlation Coefficient) informs us about the degree of correlation between measurement data and empirical model calculations.

(4.1)

(4.2)

(4.3)

MBE =

RMSE =

N P

(yi − xi )

i=1

v u u u N tP

MBE[%] =

,

N

(yi − xi )2

i=1

N P

,

N

(yi − xi )

i=1

N · x¯

,

629

D   ’   . . .

v u u N tP

(yi − xi )2

i=1

(4.4)

RMSE[%] =

(4.5)

CC = s"

N P

N x¯

,

(yi − y)(x ¯ i − x) ¯

i=1 N P

i=1

(yi − y) ¯2

#"

N P

(xi − x) ¯2

i=1

#,

where xi – the i-th measurement value, yi – the i-th theoretical model value, x¯i – the average measurement value, y¯i – the average theoretical model value, N – the number of analyzed data. The results of the statistical analysis for all the models are shown in Table 1. A comparison between the data generated by the particular models and the measurement data is shown in Fig. 4, Fig. 5 and Fig. 6. Table 1 Statistical indices of analyzed models. Wskaźniki statystyczne analizowanych modeli

ORGILL HOLLANDS [1]

MBE [Wh/m2 ] 0.23

RMSE [Wh/m2 ] 32.55

MBE[%] [%] 0.18

RMSE[%] [%] 24.98

CC [–] 0.9437

ERBS [2]

−4.25

34.83

−3.26

26.73

0.9367

CLIMED2 [3]

−4.00

33.50

−3.07

25.71

0.9428

Statistical index

If one analyzes MBE and relative MBE[%] for a measurement data sample generated by each theoretical model, it becomes apparent that the ORGILL HOLLANDS model generates the lowest errors: 0.23 Wh/m2 and 0.18%. The other two models scored almost equally: the ERBS model −4.25 Wh/m2 and −3.26% and CLIMED2 −4.00 Wh/m2 and −3.07%. A regards RMSE and RMSE[%], again the ORGILL HOLLANDS model generates the lowest errors: 32.55 Wh/m2 and 24.98%. The CLIMED2 model generates higher errors: 33.50 Wh/m2 and 25.71%. The ERBS model scored the worst in this category: 34.83 Wh/m2 and 26.73%. In the case of CC, the ORGILL HOLLANDS model and CLIMED2 scored similarly, i.e. respectively 0.9437 and 0.9428. The ERBS model result was 0.9367. So high CC values are achieved owing to the latest measurement data quality conditions in the form of standard deviations curves, proposed in [8]. If only the standard CIE solar measurement data quality conditions [6] are used, the presented models achieve CC values of about 0.85 ([4], [5]).

630

D. W, H. N

Fig. 4. Comparison between data calculated by ORGILL HOLLAND model and data measured at M&HI’s actinometric station in Legnica in years 2000-2004. Rys. 4. Porównanie danych obliczonych za pomocą modelu ORGILLA i HOLLANDA z danymi pomierzonymi na stacji aktynometrycznej IMGW w Legnicy w latach 2000-2004

Fig. 5. Comparison between data calculated by ERBS model and data measured at M&HI’s actinometric station in Legnica in years 2000-2004. Rys. 5. Porównanie danych obliczonych za pomocą modelu ERBSA z danymi pomierzonymi na stacji aktynometrycznej IMGW w Legnicy w latach 2000-2004

D   ’   . . .

631

Fig. 6. Comparison between data calculated by CLIMED2 model and data measured at M&HI’s actinometric station in Legnica in years 2000-2004. Rys. 6. Porównanie danych obliczonych za pomocą modelu CLIMED2 z danymi pomierzonymi na stacji aktynometrycznej IMGW w Legnicy w latach 2000-2004

5. C The most accurate empirical models of diffuse irradiance on a horizontal surface for a given location should be selected by comparing the statistical indices with the measurement results for this location. The ORGILL HOLLANDS model scored the best in all the three statistical indices (MBE, RMSE and CC). The other models, i.e. the ERBS model and CLIMED2, were characterized by a much higher mean error. Considering all the statistical indices, CLIMED2 proved to be more accurate than the ERBS model. One should note that besides the actinometric measurement data location also the measurement data quality checking procedure, the class of the measuring devices and the measuring period length affect the theoretical models’ results. In the authors’ previous paper [5], in which a similar analysis of the theoretical models in comparison with the actinometric data recorded at the meteorological station of the Meteorology and Climatology Unit of Wrocław University Institute of Geography and Regional Development in 2004 was carried out, CLIMED2 achieved the best results whereas the ORGILL HOLLANDS model performed rather poorly. This confirms the fact that for solar energy calculations one should use calculation models which take into account the local actinometric conditions and the measuring period length. Conclusions drawn from measurement data covering a period of five years are more reliable those for

632

D. W, H. N

a period of one year. Therefore the authors recommend the ORGILL HOLLANDS model for designing solar energy systems for the Lower Silesia region. It is also important to use sensors characterized by a low measuring error, otherwise the measuring device error may turn out to be larger than the difference between the analyzed models. Standard Kipp&Zonen instruments, ensuring high measurement accuracy, were used to measure solar radiation intensity in the present research work. Another important aspect of such comparative analyses is the length of the measurement period. It should be at least a few (or more than 10) years long in order to ensure the possibly maximum range of analyzed actinometric conditions. But when even longer measurement periods are to be used, one should consider the following two negative aspects. Firstly, because of the climate changes and the atmosphere pollution today’s actinometric conditions may differ somewhat from the conditions that prevailed tens years ago. Secondly, the measuring instruments that were used years ago were not so accurate as the present ones.

R 1. J. O, K. H, Correlation equation for hourly diffuse radiation on a horizontal surface, Solar Energy, 19, 357-359, 1977. 2. D. E, S. K, J. D, Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation, Solar Energy, 28, 293-302, 1982. 3. A. D M, J. B, R. A, H. K, E. N, Diffuse solar irradiation model evaluation in the north Mediterranean belt area, Solar Energy, 70, 143-153, 2001. 4. G. N, C. C, M. M, P. P, Calculation of an hourly basis of solar diffuse irradiations from global data for horizontal surface in Ajaccio, Energy Conversion and Management, 45, 2849-2866, 2004. 5. D. W, H. N, Calculation of diffuse radiation fraction in global solar radiation on horizontal plane for Wrocław hourly actinometric data [in Polish], 1st International Conference on Solar Energy and Ecobuildings: “Renewable Energy. Innovative Ideas and Technologies for Buildings”, 549-556, Solina 2006. 6. D. K, Guide to recommended practice of daylight measurement, International Commission on Illumination (CIE), Report No. CIE-108, Wien, Austria 1994. 7. T. M, Solar radiation and daylight models, 2nd edition, Elsevier Butterworth-Heinemann, 2004. 8. S. Y, R. C, T. M, Quality control of solar radiation data: Present status and proposed new approaches, Energy, 30, 1533-1549, 2005. ANALIZA DOKŁADNOŚCI MODELU ROZPROSZONEGO PROMIENIOWANIA SŁONECZNEGO PRZY WYKORZYSTANIU DANYCH POMIAROWYCH DLA DOLNEGO ŚLĄSKA

Streszczenie Projektowanie słonecznych systemów energetycznych wymaga znajomości promieniowania słonecznego z podziałem na część bezpośrednią i rozproszoną. W przypadku posiadania jedynie danych promieniowania

D   ’   . . .

633

całkowitego można skorzystać z modeli empirycznych obliczających udział promieniowania słonecznego rozproszonego w promieniowaniu całkowitym. W pracy przedstawiono porównanie empirycznych modeli promieniowania słonecznego rozproszonego na płaszczyznę horyzontalną umożliwiających obliczenie tych wartości na podstawie znajomości całkowitego promieniowania słonecznego na płaszczyznę horyzontalną. Do porównania posłużyła baza danych pomiarowych promieniowania słonecznego ze stacji aktynometrycznej IMGW w Legnicy z lat 2000-2004. Tak przygotowaną bazę danych zweryfikowano za pomocą standardowych warunków jakości danych CIE (Commission Internationale de l’Eclairage). Warunki te eliminują dane błędne (związane z np. awariami systemu pomiarowego, przeszkodami terenowych itd.). Dodatkowo wykorzystano zaproponowane przez Younesa warunki ograniczające wykres zależności udziału promieniowania rozproszonego w całkowitym promieniowaniu słonecznym f od współczynnika jasności kT . Zaproponowane warunki mają postać krzywych, których równania otrzymuje się poprzez dopasowanie do punktów odpowiadających podwójnemu odchyleniu standardowemu od wartości średniej f w określonym przedziale kT . Około 4% danych, które przeszły pozytywnie procedurę CIE zostało odrzuconych poprzez wykorzystanie krzywych ograniczających. Ostateczna baza danych pomiarowych składała się z 20176 par punktów kT − f . Oceny modeli dokonano za pomocą standardowych wskaźników statystycznych: MBE, RMSE i CC. Wykorzystano także wartości względne wskaźników błędu średniego i błędu średniego kwadratowego: MBE[%] i RMSE[%]. Najdokładniejszy okazał się model Orgilla i Hollandsa i ten model autorzy zalecają stosować przy projektowaniu słonecznych systemów energetycznych na terenie Dolnego Śląska. Autorzy zwracają uwagę na fakt, że oprócz lokalizacji pomiaru danych aktynometrycznych na wyniki uzyskiwane przez modele teoretyczne ma także wpływ procedura sprawdzania jakości danych pomiarowych, klasa urządzeń pomiarowych oraz długość okresu pomiarowego. W poprzedniej pracy autorów dokonano analogicznej analizy modeli empirycznych względem wartości pomierzonych na stanowisku meteorologicznym Uniwersytetu Wrocławskiego, najlepsze wyniki uzyskał model CLIMED2, zaś model Orgilla i Hollandsa uzyskał wyniki bardzo przeciętne. Jest to zatem potwierdzenie faktu, że w obliczeniach energetyki słonecznej istotne jest stosowanie modeli obliczeniowych uwzględniających lokalne warunki aktynometryczne oraz długość okresu pomiarowego. Remarks on the paper should be sent to the Editorial Office no later than December 30, 2008

Received February 2, 2007 revised version July 12, 2007