Identifying periods of clear sky direct normal irradiance

1 Identifying periods of clear sky direct normal irradiance Larrañeta, M.1, Reno, M. J. 2, Lillo-Bravo, I.3, Silva-Pérez, M.A.3 1 Andalusian Association for Research and Industrial Cooperation (AICIA). 2 Sandia National Laboratories. 3 Department of Energy Engineering, University of Seville. Corresponding author: Miguel Larrañeta, Andalusian Association for Research and Industrial Cooperation, Camino de los Descubrimientos s/n. 41092, Seville, Spain. Phone/Fax number: (+34)954487237/ (+34)954487233 E-mail: mlarr[email protected]s Abstract 1 When modeling the effect of the cloud transients in the Direct Normal Insolation (DNI), it is 2 particularly relevant to identify those moments in which there are no clouds between the 3 observer and the sun. In this paper, we present a simple algorithm for offline detection of 4 situations where the sun path to the observer is not obstructed by any cloud. The algorithm is 5 based on the characterization of the relations between the measured and the clear sky curves. 6 The clear sky identification module consists of three evaluation and detection metrics: hourly 7 mean, slope, and line length criterion. All of them rely on the assessment of the measured data 8 against the clear sky generated data. The conjunction of the fulfillment of the three criteria leads 9 to the clear sky hour identification. We validate our algorithm by comparing our results with 10 those obtained from a recently published clear sky detection algorithm that uses high temporal 11 resolution Global Horizontal Irradiation (GHI) as the input. We obtain a 98% agreement when 12 having more than 50 minutes identified as clear. 13 Keywords 14 DNI; clear sky; solar radiation models 15 1 Introduction 16 There are several alternatives when defining the clear sky condition and the clear sky irradiance 17 [1]. The most common definition is the absence of visible clouds across the entire sky dome and 18 the irradiance occurring these conditions is the clear sky irradiance. In Concentrated Solar Power 19 (CSP) systems it is also interesting to identify periods where there are no visible clouds between 20 the observer (solar field) and the sun although there may be clouds in the rest of the sky dome 21 since DNI is not affected by diffuse radiation scattered by the clouds and plant production will 22 be similar than under clear sky conditions. We use the term “clear sky equivalent DNI” to refer 23 to either DNI during clear sky conditions or DNI during all-sky conditions that is similar to clear 24 Elsevier. Versión aceptada con Licencia Creative Commons CC BY-NC-ND 2 sky irradiance. This paper is valuable to identify both clear sky periods and periods with 25 irradiance similar to clear sky irradiance relying on hourly DNI data. 26 In an automated performance evaluation of a CSP system, the determination of periods with 27 irradiance similar to clear sky irradiance would result of great interest for the detection of 28 system degradations and faults. 29 Many clear sky detection methods rely on measured irradiance, mainly in GHI and Diffuse 30 Horizontal Irradiation (DHI) of high temporal resolution [1] but only few use DNI measurements 31 and none of them in an hourly time step. Perez et al. [2] proposed a formulation of sky clearness 32 ε using the diffuse irradiance and beam irradiance. Reno et al. [3] developed an endogenous 33 statistical model for GHI observations. This method uses five criteria to compare a 10-min sliding 34 window containing ten observations to a corresponding clear sky model for the same period. 35 Each 1-min measurement is classified as clear only if threshold values for all five of the clear-sky 36 criteria are met. Inman et al. [4] applied the same methodology for DNI time series. In this case, 37 the thresholds for DNI were slightly relaxed because of the increased variability in the 38 observational DNI time series. Nou et al. [5, 6] applied a multi-resolution analysis based on the 39 discrete wavelet transform for the same purpose using also 1-min data. The signal was 40 decomposed into approximations and details through Low-Pass and High-Pass filters 41 highlighting significant changes in DNI related to the presence of clouds. 42 High temporal resolution DNI series are needed for the design and evaluation of CSP plants. Due 43 to the relative difficulty of having extensive time series, these are in some cases, synthetically 44 generated. When modeling high temporal resolution DNI data, it is particularly relevant to 45 identify periods with irradiance similar to the clear sky irradiance to decide if disturbances in the 46 solar radiation should be generated [7] especially in hazy days when the DNI may show negligible 47 fluctuations [8]. 48 To distinguishing clear sky periods, some authors have also classified cloud types using 49 measured radiation data combined with other devices. In the recent years, cloud cover and 50 types have been generally addressed using sky imagers. Martínez-Chico et al. [9] defined the sky 51 condition by means of the levels of attenuation of the DNI reaching the earth surface. The most 52 representative characteristics the type of cloud producing each sky condition were described 53 using a total sky imager. Other measurements like illuminance scan data [10], ground-based 54 radar data [11], Lidar backscatter measurements [12], longwave downwelling radiation along 55 with shortwave downwelling radiation [13] or with other meteorological parameters [14] have 56 been also used in cloud type detection. 57 In this paper, we present a methodology for the identification of periods with clear sky 58 equivalent DNI only from hourly DNI data, without the necessity of using other devices. The 59 approach is performed comparing the differences between the means, the slopes and the 60 lengths of the measured and theoretical clear sky curves. For this purpose, an empirical clear 61 sky fit has been performed. The algorithm is not sensitive to the choice of the clear sky model 62 because we have implemented an iterative adaptive method; nevertheless, the methodology 63 relies on the proper fit of the clear sky model. The performance of the model has been addressed 64 comparing the results with a recently published algorithm showing satisfactory results besides 65 having a simpler structure. 66 3 2 Clear sky fit 67 The algorithm proposed in this paper is strongly dependent on the clear sky model fit. In this 68 sense, two handicaps are found; the clear sky definition and the limitation on the use of only 69 hourly DNI data. 70 The clear sky definition involves identifying periods with high clouds or cirrus as non-clear sky 71 instants while the instantaneous radiation fairly reflect fluctuations from the clear sky shape. 72 Because this work is intended to be an intermediate block when generating high temporal 73 resolution synthetic irradiance data, identifying those moments as non-clear would lead to the 74 generation of unreal fluctuations. 75 The selected clear sky model requires an empirical adjustment to the clear sky DNI that in this 76 case is only hourly data. In the implementation of this methodology, some of the generated 77 clear sky data overcome the physical limits due to the shortage of hours per day that can be 78 used to fit the model. In the analyzed latitude, daylight hours vary from 9-15, including hours 79 with low solar elevations. 80 The first handicap is assumed the main source of error in the methodology while the second is 81 solved by imposing extreme values in the parameters that define the clear sky profiles calculated 82 from the analysis of the behavior of these parameters on the same site for a period of 14 years. 83 In the present methodology any of the well-known DNI clear sky models [15] could be used, 84 based on the available information. Here in this case, we use the clear sky model A-B Proposed 85 by Silva-Perez [16] 86 Ibncs =Ics ∙E0∙A 1+B∙mR (1) 87 Where mR is the relative air mass determined according to the expression of Kasten and Young, 88 [17] Ics is the solar constant, E0 the correction due to Earth-Sun distance and A and B are empirical 89 parameters intended to model the state of transparency or turbidity of the atmosphere. This 90 model is a modification of the kastov´s formula quoted, among others, by Kondayev [18]: 91 Ibncs =Ics ∙E0∙1 1+c∙mR (2) 92 The introduction of the second parameter is justified by the fact that, as noted by Murk [19], at 93 least two parameters are required to model the time evolution of the solar irradiance. This 94 results from the effect described by the Scottish physicist James David Forbes, known as virtual 95 diurnal variation: the transparency of the atmosphere depends on the solar height nonlinearly, 96 even in the case of a stationary atmosphere and azimuthally homogeneous, because when 97 passing through a large air mass, the radiation in wavelengths with higher monochromatic 98 extinction coefficients expires before, remaining mainly components with lower monochromatic 99 extinction coefficients. 100 The parameter A mainly realizes the processes of absorption in certain spectral bands, 101 particularly those in which the absorption is stronger, while B realizes primarily scattering 102 phenomena, but also of weak absorption phenomena. In any case, A and B are not independent. 103 Consider that certain elements (including aerosols) play an important role in both processes of 104 4 dispersion and the absorption; therefore, their presence in the atmosphere will be reflected in 105 both parameters. 106 Water vapor and atmospheric aerosols are predominant components in the absorption 107 processes. Regarding dispersion processes, aerosols play an imperative role. Furthermore, the 108 presence of these two components in the atmosphere is quite variable. According to the above 109 reasoning, the presence of water vapor will be reflected mainly in the parameter A, which will 110 be lower the greater the presence of water vapor in the atmosphere, and the presence of 111 aerosols is mainly reflected in the B parameter, whose value will be greater the higher content 112 of aerosols. 113 In a first approach, intending to have an initial envelope clear sky curve, we use the parameters 114 A and B fitted to the maximum irradiance values divided by the correction due to Earth-Sun 115 distance obtained for each solar angle higher than 5°. The hourly direct fraction index kbh [20] is 116 afterwards calculated as: 117 𝑘𝑏ℎ=𝐼𝑏𝑛ℎ/𝐼𝑏𝑛𝑐𝑠ℎ (3) 118 Where, Ibn h is the observed hourly average direct normal irradiance and 𝐼𝑏𝑛𝑐𝑠ℎ is the hourly 119 average clear-sky DNI. The initial clear sky hours are defined as hours whose kbh is higher than 120 0.65. 121 The process continues with the analysis of the initial number of clear sky hours for each day. If 122 it is higher than two hours, we run the empirical fit again but in this time, matching it to the 123 points identified as initial clear sky hours and using a least squares procedure. Under the 124 assumption that the state of the atmosphere does not change substantially from one day to the 125 next, the fitted A and B parameters will remain constant until the exposed conditions appear 126 again. As explained before, the posed conditions may not entail a proper fit, therefore if the 127 fitted A and B parameters reach a threshold maximum and minimum value, they will remain 128 constant from the previous day. 129 Those threshold maximum and minimum values are calculated from an extensive database. In 130 this case, we use measurements of direct solar radiation during 14 years (2000–2013) for the 131 location of Seville. The measurements were taken with a sampling and storing frequency of 0.2 132 Hz. A first class Eppley NIP pyrheliometer coupled to a sun tracker Kipp&Zonen 2AP measured 133 the DNI. The devices are located at the meteorological station of the Group of Thermodynamics 134 and Renewable Energy of the University of Seville. We calculate the A and B parameters 135 assuming the same conditions as exposed in the previous paragraph, but in this case, due to the 136 high resolution of the available data, three hours of clear hours corresponds to much more 137 points and therefore, the fit is generally more concrete. The threshold maximum and minimum 138 values are the Percentile 99 and Percentile 01 of the obtained A and B values for the entire 139 dataset. Figure 1 represents the boxplot of the A and B values calculated for 14 years at the 140 location of Seville. 141 5 142 Fig 1. A-B clear sky model parameters boxplot for 14 years at the location of Seville. 143 In order to appreciate the strength of correlation between both parameters we present a scatter 144 plot of the daily fitted values in figure 2. Outliers have not been included in the plot 145 146 Fig 2. A-B clear sky model parameters scatter plot for 14 years at the location of Seville. 147 3 Clear sky identification 148 Once obtained a clear sky curve fitted to each day, the next step consists of identifying periods 149 with irradiance similar to the clear sky irradiance from the comparison of both curves hour by 150 hour. The criteria used are based on [3] but because of the lower resolution data, we use only 3 151 of the 5 metrics originally proposed. Each hour is defined by two points, which leads to the 152 comparison of linear segments. In clear conditions, at lower solar angles the variation of the 153 hourly mean from one hour to the next is greater than for solar angles close the solar noon 154 because the daily clear sky solar radiation curve is similar to a Gaussian curve. Therefore, we 155 divide the daily curves into three intervals, each space covers 1/3 of the maximum solar angle. 156 Figure 2 presents an example of the threshold values for each interval on the clear sky curve of 157 a summer day. 158 6 159 Fig 3. Example of the three independently analyzed intervals depending on the maximum solar 160 elevation for a summer day. 161 The identification of clear sky equivalent DNI consists on the concurrence of three criterion 162 depending on the hourly mean and the slope and length of the straight line. Note that each 163 criterion is not overly restrictive on its own, but the combination of the three of them would 164 determine whether the analyzed hour is clear or not. 165 3.1 Hourly mean criterion 166 The first criterion involves the comparison of the hourly clear sky and measured means. The 167 analysis consist in the calculation of the absolute percentage differences of the measured and 168 clear sky radiation Dcs-mi: 169 𝐷𝑐𝑠−𝑚𝑖=abs (100∙𝐼𝑏𝑛𝑐𝑠𝑖−𝐼𝑏𝑛𝑖 I𝑏𝑛𝑖) (4) 170 Whenever Dcs-mi is lower than 2.5%, the hour is classified as clear regardless the rest criteria 171 output. This statement includes points where the measured DNI is higher than the clear sky DNI. 172 Table 1 presents the limit values for each solar interval. 173 Table 1. Threshold clear sky identification values for the hourly mean criterion 174 Solar elevation Condition Classification Interval 1 Dcs-mi < 35% Clear Interval 2 Dcs-mi < 15% Clear Interval 3 Dcs-mi < 10% Clear 175 The shadows that come from the horizon obstacles and the fact of working with hourly means 176 that carries a source of error, affect mainly low solar elevations (interval1). For these reasons, 177 the threshold clear sky identification values in this criterion are less restrictive the lower the 178 7 solar angle. The threshold Dcs-mi values correspond to quantiles of about 0.5 (0.46, 0.54 and 0.52 179 for the intervals 1, 2 and 3 respectively). Values adjusted to the location under study. 180 3.2 Slope criterion 181 The second step consists on the comparison of the slopes of the straight lines that joins two 182 hourly mean values. For each hour, the slope would be the variation of the hourly DNI divided 183 by the variation of time. 184 𝑆𝑐𝑠𝑖=𝐼𝑏𝑛𝑐𝑠𝑖−𝐼𝑏𝑛𝑐𝑠𝑖−1 𝑇𝑖−𝑇𝑖−1 ⁄ (5) 185 𝑆𝑚𝑖=𝐼𝑏𝑛𝑖−𝐼𝑏𝑛𝑖−1 𝑇𝑖−𝑇𝑖−1 ⁄ (6) 186 Where the subscript i represents the time instant, cs the clear sky and m the measured data. 187 We assume that a different measured and clear sky slope sign involves an alteration on the sky 188 condition caused to passing clouds. The condition for the clear sky identification in this criterion 189 is expressed in Table 2. 190 Table 2. Condition for the clear sky identification for the slope criterion. 191 Solar elevation Condition Classification Interval 1,2,3 Sign (𝑆𝑐𝑠𝑖) = Sign (𝑆𝑚𝑖) Clear 192 3.3 Line length criterion 193 The third step consist on the analysis of the length of the straight lines that joins two hourly 194 mean values and their corresponding absolute percentage differences calculated as follows: 195 𝐿𝑐𝑠𝑖=√(𝐼𝑏𝑛𝑐𝑠𝑖−𝐼𝑏𝑛𝑐𝑠𝑖−1)2+(𝑇𝑖−𝑇𝑖−1)2 (7) 196 𝐿𝑚𝑖=√(𝐼𝑏𝑛𝑖−𝐼𝑏𝑛𝑖−1)2+(𝑇𝑖−𝑇𝑖−1)2 (8) 197 𝐿𝐷𝑐𝑠−𝑚𝑖=abs (100∙𝐿𝑐𝑠𝑖−𝐿𝑏𝑛𝑖 L𝑏𝑛𝑖) (9) 198 Following a similar assumption as in the slope criterion, a great difference in the line length 199 longitude represents an alteration condition due to passing clouds. The line length that joins two 200 hourly mean clear sky values varies substantively depending on the solar elevation therefore we 201 combine the absolute differences on the line lengths and the clear sky line length. The 202 combination of these calculations leads to the line length clear classification as presented in 203 Table 3. 204 205 206 8 Table 3. Line length classification conditions for the clear sky identification. 207 Solar elevation Condition Classification Interval 1 LDcs-mi < 25 % & Lcsi > 220 Clear Interval 2 LDcs-mi < 35 % & Lcsi > 110 Clear Interval 3 LDcs-mi < 120 % & Lcsi < 30 Clear 208 For low solar angles, the absolute percentage condition is lower than for high solar angles 209 however, the line lengths follow the inverse pattern. The threshold LDcs-mi values correspond to 210 quantiles of 0.46, 0.54 and 0.52 for the intervals 1, 2 and 3 respectively. 211 4 Iterative process 212 Once identified the periods with irradiance similar to the clear sky irradiance, we execute a daily 213 iterative process that consists on the readjustment of the clear sky model to those periods 214 through the process exposed in paragraph 2 until the A and B parameters converge. Figure 3 215 shows the block diagram of the process. The subscript j represents the modeled day 216 217 Fig 4. Block diagram of the process 218 DNIhj , Aj-1, Bj-1 INPUT A1j, B1j = Aj-1, Bj-1 A1j, B1j CLEAR SKY FIT Clear sky hoursj Clear sky model parameters Aj, Bj Kb_hj > 0.65 for at least 3 hours NO YES CShj CLEAR SKY JDENTJFJCATJON A2j, B2j CLEAR SKY FIT A2j, B2j = A1j, B1j YES NO A1j, B1j = A2j, B2j DNIhj when Kb_hj > 0.65 DNIhj when CShj =1 DNIhj and DNIh_CSj with A1j, B1j 9 5 Results 219 To assess the performance of the model, we have utilized one year (2014) of measurements of 220 DNI and GHI reregistered with a sampling and storing frequency of 0.2 Hz at the meteorological 221 station of the Group of Thermodynamics and Renewable Energy of the University of Seville with 222 a secondary standard Kipp&Zonen CMP21 and a first class Eppley NIP pyrheliometer coupled to 223 a sun tracker Kipp&Zonen 2AP. The instantaneous DNI data has been integrated into hourly 224 means for the execution of the model and to 10-min resolution to observe the performance of 225 the model. Ten consecutive daily profiles are illustrated in Figure 4. The left figures show the 226 DNI hourly means of the daily profiles and the figures on the right show the daily profiles in 10- 227 min means. The measured data is printed in discontinuous blue, the identified clear sky 228 equivalent DNI periods are presented in continuous black and for the case of hourly means and 229 the clear sky fitted shape is presented in a doted cyan line. 230 231 232 233