1、392 2008 ASHRAE ABSTRACT In this paper, several solar models based on Zhang et al.,Zhang and Huang, and Watanabe models are developed andtested against measured solar data obtained for several loca-tions throughout the world. The solar models can predicthourly global, direct normal, and diffuse sola
2、r radiation fromcloud cover information and non-solar data including dry-bulb temperature, wind speed, and relative humidity. Refinement of the Zhang and Huang model is also carriedout to improve its prediction accuracy for tropical climates.Specifically, new coefficients of the model were determine
3、dbased on regression analysis using measured hourly solar datafrom various tropical sites. Variations of the Zhang and Huangmodels requiring fewer input variables were also developed.These model variations were tested for both tropical and non-tropical climates. The analysis results indicated that w
4、hile onlytwo variables (solar angle and cloud cover) are required topredict hourly global solar radiation for high latitude loca-tions, dry-bulb temperature is required to accuratelypredict solar radiation for the tropical locations.INTRODUCTIONDynamic simulations using whole-building energy anal-ys
5、is programs, such as DOE-2 and EnergyPlus require hourlydata of weather data including solar radiation, dry-bulbtemperature, dew-point temperature or humidity, atmosphericpressure, wind direction, and wind speed. Weather files suit-able for building simulation programs are generally developedbased o
6、n measured data using various formats includingWYEC (Weather year for Energy Calculations), TMY (Typi-cal Meteorological Year), TRY (Typical Reference Year), andIWEC (International Weather For Energy Calculation). In particular, IWEC weather files were developed from adatabase of International Surfa
7、ce Weather Observations(ISWO) compiled and released by the National Climatic DataCenter (NCDC, 1998). The weather variables recorded in theISWO database include dry-bulb and dew-point temperatures,atmospheric pressure, wind speed and direction, and theamounts of cloud cover at various heights. Howev
8、er, no obser-vation data for solar radiation is reported by the ISWO data-base. To develop weather files suitable for building energysimulation, it is necessary to develop methods and models forestimating the amount of solar radiation based on other avail-able climatic parameters. For the developmen
9、t of IWECweather files, Kasten model was utilized (Thevenard andBrunger, 2002). The Kasten model, developed by Kasten(1980) and described in more details by Davies and McKay(1989), uses primarily total cloud amount to predict solar radi-ation. The model does not require cloud layer information oroth
10、er non-solar data such as temperature, relative humidityand wind speed.Some studies have indicated that cloud cover alone(combined with solar zenith angle) can produce reasonablyaccurate predictors of solar radiation for high latitude loca-tionsi.e., North America or Western Europe (Thevenard andBru
11、nger 2002, Zhang and Huang, 2002). However, cloudcover has to be combined with other parameters, such astemperature, humidity, or wind speed to adequately predictsolar radiation for tropical locations. For instance, Kastenmodel which was used to develop IWEC weather filesperformed well for the high
12、latitude locations in Europe andNorth America, but produced unreliable estimates of hourlysolar radiation for low latitude locations (Thevenard andBrunger, 2002). Development of Models for HourlySolar Radiation PredictionDonghyun Seo Joe Huang Moncef Krarti, PhD, PEStudent Member ASHRAE Member ASHRA
13、E Member ASHRAEDonghyun Seo is a graduate student and Moncef Krarti, PhD, PE is a professor in the Civil, Environmental, and Architectural Engineeringdepartment at the University of Colorado, Boulder, CO. Joe Huang is president of White Box Technologies, Inc., Berkeley, CA.NY-08-045 (RP-1309)2008, A
14、merican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 114, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior
15、written permission.ASHRAE Transactions 393Since solar zenith angle changes little on a daily basis inlow latitude locations and cannot be utilized as a determinantparameter for estimating hourly solar radiation, other param-eters have to be considered in addition to cloud cover to accu-rately predic
16、t solar radiation in tropical climates. For example,Chandel et al. (2004) reported significant improvements in adaily radiation model for Indian locations by adding a temper-ature term. In the regression models developed in Japan, theaddition of temperature change and relative humidityimproved the a
17、ccuracy of the models (Matsuo et al. 1974).Comparative analysis of four solar models (including Kastenmodel) against measured data have indicated that Zhang andHuang model (2002) is the best suited for estimating hourlysolar radiation for tropical sites (Krarti and Seo, 2006) as wellas other locatio
18、ns (Krarti and Seo, 2005 and Al-Anzi et al.2006). Unlike Kasten model that relies only on cloud coverdata (typically recorded based on human observation), Zhangand Huang model uses cloud cover as well as dry-bulbtemperature, relative humidity, and wind speed. In this paper, solar models based on Wat
19、anabe et al(1983), and Zhang models are tested and evaluated againstmeasured solar data obtained for several locations throughoutthe world. In addition, various Zhang and Huang modelvariations are defined using fewer input variables than theoriginal model to develop a refined Zhang and Huang modelth
20、at can be applicable to a wide range of world wide sites. Thepredictions of the refined solar model are tested againstmeasured solar data. The results of the testing analysis are thendiscussed. OVERVIEW OF SOLAR MODELSZhang and Huang ModelThe Zhang and Huang model is based on the Matsuomodel (1974)
21、developed for Japanese locations to predict solarradiation levels at 6-hour time intervals. Zhang and Huangextended the Matsuo model to predict solar radiation on anhourly basis. The model is originally developed using Chineselocations (Beijing and Guangzhou) with International SurfaceWeather Observ
22、ations (ISWO) weather data from the NationalClimatic Data Center (NCDC). The model relies on regressionanalysis to find model coefficients that provide the least squarefit between measured solar radiation data and climatic condi-tions including total cloud cover, relative humidity, windspeed, and dr
23、y-bulb temperature difference. Specifically,hourly average global solar irradiance (i.e., hourly averagesolar flux striking a surface) is estimated by Equation (1):(1)whereI = global solar irradiance in W/m2I0= solar constant, 13551W/m2SH = sine of solar altitude angle CC = cloud cover in tenthsRH =
24、 relative humidity in %DBTnand DBTn-3= dry-bulb temperature in at hours n and n-3, respectivelyWS = wind speed in m/s. c0, c1, c2, c3, c4, c5, d, k = regression coefficientsThe regression coefficients were determined from multi-parameter analyses against the measured data for Beijing andGuangzhou an
25、d were found to be as follows (Zhang andHuang, 2002):c0= 0.5598, c1= 0.4982, c2= -0.6762, c3= 0.02842c4= -0.00317, c5=0.014, d= -17.853, k = 0.843The correlation coefficient (R) was found to be 0.93, indi-cating that Equation (1) provides an accurate estimation of thehourly average total horizontal
26、solar irradiance in both Beijingand Guangzhou.Watanabe Diffuse/Direct Normal Solar ModelZhang and Huang used a model, developed by Watanabeet al. (1983) for Japanese locations, to separate the total globalsolar irradiance into direct and diffuse components as indi-cated by Equation (2):(2)whereI = g
27、lobal solar irradiance in W/m2Ib= direct normal solar irradiance in W/m2Id= diffuse solar irradiance in W/m2ZHANG DIFFUSE/DIRECT NORMAL SOLAR MODELRecently, Zhang introduced the Gompertz Function toestimate the direct and diffuse solar irradiance from the clear-ness index KT(Zhang et al., 2004). Whe
28、n KTis smaller thanI I03600 SH c0c1CC()c2CC()2+=c3DBTnDBTn 3()c4RH c5WS+d/k+when I 0I 0 when I 0=1.Currently, a more widely accepted value for the solar constant is1366 W/m2. In this paper, the value of 1355 W/m2used in the orig-inal Zhang and Huang model is considered throughout the study.It should
29、 be noted that the value of the solar constant does notaffect the accuracy of the results but only the values of the regres-sion coefficients. KTII0 SH KTC, 0.4268 0.1934 SH+=KDSKT1.107 0.03569 SH 1.681 SH2+()=1 KT()2when KTKTCKDS3.996 3.862 SH 1.540 SH2+ KT3when KTKTC=IbI0SH KDS1 KT()1 KDS()=IdI0SH
30、 KTKDS()1 KDS()=394 ASHRAE Transactions0.2, the direct normal irradiance and thus the direct beamtransmittance, Knas defined by Equation (4), are almost zero.As the global irradiance increases, the direct normal irradianceincreases and consequently the value of Knincreases and even-tually becomes eq
31、ual to KT, with KT= Kn=1.0. The globalhorizontal solar irradiance can be separated into direct normaland diffuse components at any solar angle using Equations (3),(4), and (5): (3)where Kn: is the direct beam transmittance and is defined asfollows:(4)KT: is the clearness index and is defined as foll
32、ows:(5)COMPARISON OF DIFFUSE AND DIRECT NORMAL SOLAR RADIATION MODELS To split the global solar radiation into diffuse and directnormal, two models have been tested: Watanabe model asexpressed by Equation (2) and Zhang et al. (2004) modeldefined by Equations (3-5). Figures 1 and 2 show the cumu-lati
33、ve frequency distributions of hourly average of directnormal irradiance and diffuse irradiance predicted by bothmodels and compared to measured data for Singapore (basedon measured data for 1999) and Honolulu (based on measureddata for 1990), respectively. Tables 1 and 2 summarize the prediction per
34、formance ofboth Watanabe and Zhang et al. models expressed in terms ofmonthly MBE and RMSE values to predict respectively,hourly average direct normal and diffuse solar irradiances, forselected tropical and non-tropical sites. The results indicatethat both models provide close agreement for predicti
35、ons ofboth diffuse and direct normal solar radiation. Based on thecorrelation coefficient R-square values, Zhang et al. modelslightly outperforms the Watanabe model when predictingdiffuse solar radiation. However, the Watanabe modelprovides better predictions of direct normal solar radiation forSan
36、Diego, Honolulu, and Guam than the Zhang et al. model. Based on these findings as well as the reported results inZhang and Huang (2002), the Watanabe model is suitable toestimate direct normal and diffuse components of the hourlyaverage global solar irradiance for both tropical and non-trop-ical loc
37、ations. Zhang et al. model can be utilized to improveslightly the estimation of diffuse and direct normal radiationfor tropical climates.WEATHER DATA AND THE REGRESSION REFINEMENT PROCESS NCDC global surface hourly data sets, DSI-9956, wereused to extract values for input variables required for all
38、theZhang and Huang model variations considered in this study.The NCDC data sets provide hourly (in some cases, 3-hourly)values for wind direction and speed, ceiling height, cloud-cover (low, middle and high), visibility, dry-bulb and dewpoint temperature, sea level and station pressure, altimeter,pr
39、ecipitation, and snow depth. The relative humidity wascalculated using DOE-2 weather processor (LBL, 1980). To assess the prediction performance of the Zhang andHuang model and its variations, measured solar radiation datawere obtained from various sources for several locationsthroughout the world.
40、Table 3 shows the list of selected sitesand associated weather data (including measured solar radia-tion) used to assess the prediction performance of varioussolar models derived from the Zhang and Huang model.The variables used in the Zhang and Huang model, asoutlined in Equation (1), include:dry-b
41、ulb temperature (DBT) cloud-cover (CC) square of cloud-cover (CCS) relative humidity (RH) wind speed (WS) and solar altitude angle (SH) Several variations of Zhang and Huang solar model aredeveloped by reducing the number of input variables requiredto predict global solar radiation. Table 4 lists th
42、e solar modelvariations considered in the analysis presented in this paper.Solar altitude angle is an essential element of any solar modeland is considered in all the solar model variations. For themodel variation No. 5 and 6, dew point temperature is utilizedinstead of relative humidity. For each m
43、odel variation, aregression analysis is carried out to find the best correlationcoefficients. Then, the predictions of each model variation arecompared with the original Zhang and Huang model using twostatistical indicators: mean bias error (MBE) and root meansquare error (RMSE). EVALUATION OF ZHANG
44、 AND HUANG MODEL VARIATIONSThe performance of the six variations of the Zhang andHuang model listed in Table 4 for predicting hourly averageglobal solar irradiance is summarized in Figures 3 through 5for three sites including Singapore (Figure 3), Kuwait City(Figure 4), and Miami (Figure 5). These s
45、ites were selected toKnA1A2A3A2A4Kt=A10.1556 SH20.1028 SH 1.3748+=A20.7973 SH20.1509 SH 3.035+=A35.4307 SH 7.2182+=A42.990=KnIbSHI0SH-IbI0-=KTIbSH Id+I0SH-II0SH-=ASHRAE Transactions 395evaluate the Zhang and Huang model variations for a widerange of climatic regions (tropical wet, hot and arid, and
46、trop-ical monsoon, respectively). The results presented in Figure 3 indicate that model with5 variables as shown in Figure 3(b)- and 4 variables as indi-cated in Figure 3(c)- can predict fairly well global solar radi-ation for Singapore. However, the model with only 3 variables(SH, CC and CCS) provi
47、des poor predictions. The large scat-tering pattern obtained for almost all model variations shownin Figure 3 indicates that several variables are needed to accu-rately predict hourly global solar irradiance for Singapore.Indeed, as evident in Figure 3(c), solar radiation in the tropicalsites cannot
48、 be predicted accurately using only solar angle andcloud cover (i.e., the variables SH, CC, and CCS). Indeed, thesolar angle (SH) remains almost constant throughout the yearin the tropics and the cloud cover (CC) takes only discretevalues. This is not the case for the non-tropical climates asindicat
49、ed in Figure 4 (c) for Kuwait City. Figure 1 Cumulative frequency of hourly average diffuse and direct normal solar irradiances for Singapore (1999).(a) Direct normal solar irradiance.(b) Diffuse solar irradiance.1a 1b2a 2bFigure 2 Cumulative frequency of hourly average diffuse and direct normal solar irradiances for Honolulu (1990).(a) Direct normal solar irradiance.(b) Diffuse solar irradiance.Table 1. Prediction of Hourly Average Direct Normal Solar Irradiance Using Watanabe a
