Generation of a Test Reference Year of global solar radiation from a Test Reference Year of Temperature

Transcription

1 Generation of a Test Reference Year of global solar radiation from a Test Reference Year of Temperature J. Bilbao, A. Miguel & J. A. Franco Department ofapplied Physics, Valladolid University, Spain Abstract The paper shows an alternative method for generating a Typical Reference Year of global solar radiation from data sets of climatic variables obtained by automatic meteorological stations in Valladolid (Spain). Data sets of climatic variables used were obtained between 1988 and 1998 in ten minute steps. Climatic variables used in this method are maximum, average and minimum daily temperature, maximum, average and minimum daily relative humidity and maximum and average wind speed. With this method solar radiation measured is only necessary in order to compare experimental data with data generated by the Typical Reference Year. The method proposed is a simplified version of the modified Festa-Ratto method and generates a Typical Reference Year corresponding to the above climatic variables. From hourly and monthly average temperature data corresponding to the Typical Reference Year obtained, monthly average clearness indices are obtained by using Erbs's model. Finally, a daily series of clearness indices is obtained using the Aguiar and Collares-Pereira algorithm. Daily global solar radiation is obtained and compared with measured data between 1991 and Introduction Expected solar radiation values constitute an important tool to characterise the climate of a given locality and to design renewable energy conversion devices. Unfortunately, the number of years during which solar radiation is measured is usually too small to obtain regular patterns of the average evolution over the year. Many authors have proposed the development of methodologies for generating so-called Typical Meteorological Years (TMYs), a term mainly used

2 408 Computer Techniques in Environmental Studies in the USA, or Test Reference Years (TRYs) as they are called in Europe. The TRY has been used in order to predict the thermal performance of buildings, namely thermal comfort conditions, heating and cooling loads and the performance of solar thermal and photovoltaic systems [1]. Various TRY generation methodologies are available in the literature. Most of them promote the idea of using sequences of real measured data to compose a TRY [2-7]. This is a drawback because these methodologies can be used only in sites which have enough meteorological and radiation data sets. In cases where insufficient radiation data sets are available, the TRY will not be generated. The aim of this paper is to show an alternative method for generating a Test Reference Year of solar radiation from purely meteorological data sets corresponding to a TRY generated by using a new version of the Festa-Ratto method. 2 Methodology A TRY provides a standard data series for daily solar radiation and other meteorological parameters for a period of one year, representing climatic conditions considered to be typical over a long time period. The methodology used in this paper can be structured in the following steps. 2.1 New version of the Festa-Ratto method The original Festa-Ratto method is an empirical methodology for generating the Test Reference Year by using data sets of individual months selected from different years over the available period. The individual months are selected as is described in the following procedure. For each available month (y,m), daily values of several meteorological variables x(y,m,d) (y=l,...,ny; m-j,...,12; d=l,...,nd(m)) corresponding to a day d of a month m of a year y and a variable x are available. The meteorological variables are converted into standardised residuals with respect to the smoothed long-term trend (,Y variables): (1) where X(y,m,d) are the standardised residual of variable x(y,m,d) with respect to the smoothed mean and standard deviation ^ (m,d) and a^(m,d) respectively. The procedure of smoothing the average and deviation is free whenever the monthly averages are preserved:,,d) = -- -Y^(m,d) (2) nd(m)-ny,.,</ nd(m) d In our method we did not smooth the average and the deviation but worked

3 Computer Techniques in Environmental Studies 409 directly with them. First order products and their standardised residuals were calculated likewise: (3) a z(m,d) 0... (4) For each X, Z variable, the average, standard deviation and cumulative distribution of each individual month (y,m) are calculated (short-term parameters) and are compared with the same magnitudes calculated for each month but for the complete period available (long-term parameters). Thus the distances between the short and long term means d^, standard deviations d^ and Kolmogorov-Smirnov parameters are calculated for each X, Z variable and for each month (y,m) [6,7]. Then a composite distance is calculated for each variable according to:, /) = (1 - a - 6)^ (),, m, /) + ad^ (_y, m, y ) where a = b = 0.1 and d(y, m, j) denotes the respective distance for year y, month m and A" or Z parameter j. Thus, by using daily maximum and mean air temperature (T^x > T), mean relative humidity (RH), wind speed (W) and daily global irradiation (G), 10 distances are calculated for each candidate month. In the method which is proposed, global radiation is not used and so only 8 distances were calculated. The original Festa-Ratto method uses a min-max approach, assigning the maximum of the ten distances to the candidate month. The candidate month m belongs to that year _y# with the minimum assigned distance: where month m year y Q o d(yq,m)= min \d(y,m\ {l < y < ny} J (6) d-(y,m) = max[d();,m,./),{l < ; < loj] (7) A variation of the method was implemented by Argiriou [7], assigning to each candidate month a weighted sum of the distances instead of the maximum distance. Following the same method, we have assigned to each candidate month a weighted sum of the distances. However, in our method we did not calculate any global radiation distance but merely duplicated the weighting coefficients used by Argiriou [7] and ignored the weighting coefficient of global radiation. These weighting factors are shown in Table 1.

4 410 Computer Techniques in Environmental Studies Table 1. Weighting factors (x 20) used with the modified Festa-Ratto method [7] and our method. Argiriou [1] Our method T,,,a> zr,,,^ T ZT RH Z&f/ W zw/ G ZC Monthly average clearness index K^ As soon as the temperature Test Reference Year is generated, the monthly average clearness index K^ of each month can be fitted by using the least squares method if we agree with Erbs' formula [8] : cos(f-3.805) cos(2f-0.360) cos(3f ) cos(4f ) (8) where 12 (9) and = 25.8^^ (10) In these equations T^ is the average hourly temperature of the month m and hour h (12 at solar noon), 7^ is the average monthly temperature of the month m, KM is the average monthly clearness index of the month m and A is the temperature amplitude. The temperatures used in calculations belong to the Test Reference Year Daily clearness index generation The last step in the generation of daily solar radiation series consists of the daily clearness index generation from the monthly average clearness index. Many methodologies of generation are available in the literature. For example, Bilbao [10] has made a compilation of these methodologies. The methodology used in this paper is the Aguiar method [9]. This is a Markov Transition Matrix type model with a library of 10 matrices from 10 classes of monthly average daily clearness indices. Using the previous monthly average clearness index A^./ and KM as inputs, a daily clearness index kj series corresponding to the month m can be created and an annual daily solar radiation series can then be generated.

5 3 Results and discussion Computer Techniques in Environmental Studies 41 1 To generate the TRY temperature for Valladolid, data sets of temperature, relative humidity and wind velocity, obtained between the period 1988 and 1998 in ten minute steps, were used. Daily averages of the required variables were made with the available data. The root mean square error (RMSE) test was used to evaluate the model. The following expression for RMSE as a percentage of the average value was used: AT' y (r - r V * L^ V" im ir / (11) where N is the number of data, F^ is the simulated value, /],. is the measured value and F is the average of the measured values. This estimator was calculated for the following variables: monthly average daily global irradiation, monthly average temperature, daily global irradiation and daily temperature. An average year of global solar irradiation (AYG) was made with the experimental data belonging to the period , and the results were compared with the Test Reference Year. Table 1 shows the values of the monthly average daily global irradiation of each year and the RMSE obtained by comparing these data with the TRY data. In general, the RMSE is below 20% and the most unfavourable results correspond to the winter period. Asterisks indicate missing data. Table 1. Monthly average values of daily global solar irradiation (MJ m" ) for each year and RMSE of the TRY with respect to each year. Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec RMSE (%) AYG TRY As regards temperature, the RMSE has also been calculated with data corresponding to the period between 1988 and With this time interval, we

6 412 Computer Techniques in Environmental Studies have built an Average Year of Temperature (AYT) which has been compared with the TRY temperature. The results are shown in Table 2. Table 2. Monthly average temperature values for each year ( C) and RJVISE (R) of the TRY with respect to each year. Year AYT TRY Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec R (%) Each RMSE has been calculated with available data sets. RMSE values are generally between 5.2% and 14.6%. The most favourable year (with the lowest RMSE value) is the Average Year of Temperature and the most unfavourable year is Nevertheless, the maximum difference between the average monthly temperature value is 3.5 C (June 1992 and June of TRY) and this difference corresponds to a summer month. Obviously the years with many selected months will have lower RMSE values. These were 1995 (February and March), 1996 (July and October) and 1998 (May, August and September). It is important to note the RMSE obtained in 1989 and 1990 was lees than 14% despite no months being selected to generate the Test Reference Year. It can also be seen that the Test Reference Year fits in very well with all the available period used in its generation. RMSE for daily global radiation has also been calculated. In general the RMSE for daily global radiation is between 19.6% and 38.8%. The most unfavourable year is 1993 whose RMSE is 38.8% and the most favourable result corresponds to the Average Year of Global solar irradiation whose RMSE value is 19.6%. In Figure 1 the values of daily global solar irradiation of each day of the Test Reference Year (G^) are plotted versus the corresponding values of the Average Year of Global solar irradiation (G^). With regard to daily temperature values, RMSE values range between 22.3% and 39%. The most unfavourable result corresponds to 1993 whose value is 39% and the most favourable result is the Average Year of Temperature (AYT) whose value is 22.3%. In Figure 2 the daily average temperature values of the Test

7 Computer Techniques in Environmental Studies 413 Reference Year (TY^,) are plotted versus the corresponding values of the Average Year of Temperature (7^). 30 -j- L ^.u_^ i^_^. - Data number: 351 i Correlation coefficient: Site: VALLADOLID (SPAIN) N 20 - E ] i 15 J '!,/>, 0 :/-^^: /L_^A^_ G ( M J m "^) Figure 1: Daily global solar irradiation values of the TRY (G^) vs. daily global solar irradiation values of the AYG (G^g) ^ i.^. - J Data number: 351 i Correlation coefficient: Site: VALLADOLID (SPAIN) T ayt ( C) \ ' Figure 2: Daily average temperature values of the TRY (T^) vs. daily average temperature values of the AYT (7^,).

8 414 Computer Techniques in Environmental Studies The simulation of a thermal system was carried out to validate the Test Reference Year. The Thermal System is a standard system configuration for heating water similar to that shown in Figure 3 and located in Valladolid. Relief valves Temper ing valve To tap Collector e f -» P \A/"it o r ^ heater Auxiliary Col lector-storage heat exchanger water supply Figure 3: Standard system configuration for water heating. The technical data of the system are given in Table 3. It provides domestic hot water delivered at 45 C minimum for a multi-storey building whose monthly consumption profile and thermal load required are described in Table 4. The parameter used in order to validate the results of the Test Reference Year was the solar fraction (solar load divided by the required load of the building). Monthly solar fractions were calculated by using f-chart Method [11] and results are shown in Table 4. It was assumed that the fresh water supply temperature was 1 rc during the year and thermal losses from duct, pipes and preheat storage tank were ignored. The only thermal load considered was domestic hot water. Monthly solar fractions obtained with the Test Reference Year data set were compared with those corresponding to the Average Year of Global irradiation (including the temperature). Diffuse irradiation of the Test Reference Year was calculated by using the Collares-Pereira and Rabl correlation [11]: k, kj k^ forkj<0.17 for0.17<k^<0.75 for0.75<kj<0.80 (12)

9 Computer Techniques in Environmental Studies 415 where D^ is the daily diffuse irradiation, G</ the daily global irradiation and k^ is the daily clearness index. Solar fraction values are also shown in Table 4. Table 3. Technical data of the Thermal system Flat plate collector Type Slope Orientation Area &Wn &c& &'/& (TO) / (TO) preheat storage tank volume MADE 400-E 45 South 224m' Wm^ C' m' Table 4. Average daily consumption, monthly thermal load and monthly solar fraction obtained from TRY and from AYG. Jan Feb Mar Apr May Jim Jul Aug Sept Oct Nov Dec Consumption (m* per day) Thermal load (MJ) ftry LOO LOO LOO /-> « LOO 1.00 LOO The annual solar fraction obtained with TRY is 0.68 and that corresponding to the AYG is The most unfavourable results correspond to the winter period. This is an obvious disagreement as the worst results of global irradiation are obtained for the winter months. Nevertheless, the RMSE of the monthly solar fraction is 14.5%. In general, the results obtained for each month are very similar, indicating that the thermal system works in the same way during both years and validates the use of a Test Reference Year instead of an Average Year. 4 Conclusions An alternative method for generating a Test Reference Year has been established. The Test Reference Year was implemented using meteorological

10 416 Computer Techniques in Environmental Studies data obtained from Valladolid between 1988 and The obtained Test Reference Year was an Average Year of global solar irradiation and with an Average Year of Temperature using several tests. The worst obtained results correspond to winter months and the monthly average temperature and global solar irradiation results were more favourable than daily results. 5 Acknowledgements The authors wish to acknowledge the financial support extended by the CICYT (Inter-Ministerial Commission for Science and Technology) (Contract 1FD ) and the information supported by MADE Tecnologias Renovables S.A. References [1] Bahadori M. N. & Chamberlain, M.J. A simplification of weather data to evaluate daily and monthly energy needs of residential buildings. Solar Energy 36(6), pp , [2] Hall, I.J., Prairie, R.R., Anderson, H.E. & Boes, E. Generation of Typical Reference Years for 26 SOLMET stations, Sandia Laboratories Report SAND , Sandia Laboratories, Albuquerque, NM, [3] Pissimanis, D., Karras, G., Notaridou, V. & Gavra, K. The generation of a typical meteorological year for the city of Athens. Solar Energy, 40 (5), pp , [4] Marion, W. & Urban, K. User's Manual for TMY2s Typical Meteorological Years, National Renewable Energy Laboratory, Golden, CO, USA, [5] Lund, H. The design reference year users manual Thermal Insulation Laboratory, Technical University of Denmark: Lyngby, [6] Festa, R. & Ratto, F. Proposal of a numerical procedure to select reference years. Solar Energy, 50 (1), pp. 9-17, [7] Argiriou, A., Lykoudis, S., Kontoyianidis S., Balaras C. A., Asimakopoulos, D., Petrakis, M. & Kassomenos, P. Comparison of methodologies for TMY generation using 20 years data for Athens, Greece. Solar Energy 66 (1), pp , [8] Erbs, D. G., Klein, S. A. & Beckman, W. A. Estimation of degree-days and ambient temperature bin data from monthly average temperatures. ASHRAE J., pp , June [9] Aguiar, R., Collares-Pereira, M. & Conde, J.P. Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices. Solar Energy, 40 (3), pp , [10] Bilbao, J., Miguel, A., Medina, J.A. & Lopez J.J. Climed selection of the best existing models, Laboratorio de Energias Renovables: Universidad de Valladolid, pp , [11] Duffie,J.A. & Beckman, W.A. Solar engineering of thermal processes. John Wiley & Sons, Inc: New York, 1991.