Generation of synthetic solar datasets for risk analysis

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Solar Energy, Vol. 187, on July 2019, , available at: https://doi.org/10.1016/j.solener.2019.05.042 © 2019 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND 1 Generation of synthetic solar datasets for risk analysis 1 Larrañeta, M.1, Fernandez-Peruchena, C.2, Silva-Pérez, M.A.3, Lillo-bravo, I.3, Grantham, A.4, 2 Boland, J.4 3 1 Andalusian Association for Research and Industrial Cooperation (AICIA). Seville, Spain 4 2 National Renewable Energy Centre (CENER). Seville, Spain 5 3 University of Seville. Department of Energy Engineering. Seville, Spain. 6 4 Centre for Industrial and Applied Mathematics, University of South Australia. Mawson Lakes, 7 Australia 8 Corresponding author: 9 Miguel Larrañeta, Andalusian Association for Research and Industrial Cooperation, Camino de 10 los Descubrimientos s/n. 41092, Seville, Spain. 11 Phone: (+34)954487237 12 E-mail: mlarr[email protected]s 13 Abstract 14 In this paper, we present a method for the synthetic generation of long-term time series of 15 coupled 1-min global horizontal solar irradiance (GHI) and direct normal solar irradiance (DNI). 16 This method requires an input of 10-15 annual time series of hourly DNI and GHI values that can 17 be retrieved from satellite-based irradiance databases, and produces 100 years of 1-min solar 18 radiation values that can be used for risk analysis or as input for solar plants performance 19 simulation in a wide range of scenarios. 20 The method consists of the conjunction of three steps. The first one, based on a stochastic 21 procedure, is used to generate 100 years of monthly DNI and GHI values. The second step 22 consists of the subsequent generation of daily irradiation values. To that end we have used a 23 bootstrapping technique. The synthetic daily sequences have the same serial correlation 24 structure as the observed data. The last step consists of the generation of 100 years of 1-min 25 solar irradiance data out of the daily values based on the non-dimensionalization of the daily 26 profiles by the clear sky envelope approach. The method has been applied for the location of 27 Seville showing satisfactory results in terms of cumulative distribution functions (CDFs) of the 28 synthetic data. We obtain an average monthly KSI (Kolmogorov-Smirnov test integral) index of 29 0.11 kWh/m2 for GHI and 0.26 kWh/m2 for DNI. The minimum KSI value is 0.07 kWh/m2 for GHI 30 and 0.15 kWh/m2 for DNI obtained in January. The maximum KSI value is 0.19 kWh/m2 for GHI 31 and 0.34 kWh/m2 for DNI obtained in June and August respectively. 32 Keywords 33 Typical meteorological year; high frequency; synthetic sequences; cloud transients; solar 34 variability 35 2 1 Introduction 36 Concentrated solar power (CSP) and photovoltaic (PV) plants simulation tools typically use a 1- 37 year meteorological series representative of “typical” conditions, defined as typical 38 meteorological year (TMY) (Hall et al., 1987)). Accordingly, their results represent the “typical” 39 yield values defined as specific values (with no confidence intervals), rather than “distributions 40 of values” expected given the actual uncertainties of the model and inputs. As a result, it is not 41 suited for designing systems to meet the worst-case conditions occurring at a location (Wilcox, 42 S., & Marion, 2008), which is a common practice in feasibility analysis and is currently carried 43 out through the definition of several probabilities of exceedance scenarios. 44 An approach of growing interest to take into account the inherent variability of the performance 45 of solar plants is the consideration of a probability distribution for each input variable in the 46 plant model for assessing both their uncertainty and variability (Ramirez et al., 2017). In 47 particular, for generating the probability distributions of annual energy yield, simulation tools 48 require as input a large number of plausible meteorological years (PMYs), whose generation is 49 the objective of this work. 50 Solar-power financing is mainly based on the statistical characterization of the solar resource 51 and its uncertainty. Current methods usually rely on the use of satellite-derived solar radiation 52 time series (typically 15-20 years) locally adapted with coincident validated ground 53 measurements at the project site. These series allow a deep understanding of the solar radiation 54 dynamics over different temporal scales (intraday, day, season, year), and in particular the inter- 55 annual variability which defines the probability of exceedance scenarios. These scenarios are 56 modeled to evaluate a project's ability to meet the risk and return requirements of investors 57 (Fernández-Peruchena et al., 2018). On the other hand, statistical approaches are taking a 58 growing interest in CSP projects requiring high capital-intensive investments, through the 59 implementation of probabilistic approaches addressing the variabilities in both energy yield and 60 system costs (Eck et al., 2012; Ho and Kolb, 2010). In this new scheme, the characterization of 61 the solar resource variability (at both short-term and long-term scales) is an essential issue, as 62 the DNI is the most decisive variable in the CSP plant energy yield. The research community is 63 addressing this issue and making substantial progress: several approaches have already been 64 tested and presented in the literature (Nielsen et al., 2017). This new scheme relies on the 65 concept of PMY, defined as a high-frequency yearly series of GHI, DNI and other relevant 66 meteorological variables (temperature, relative humidity, wind speed), which are consistent 67 with the corresponding monthly and annual series, thus preserving natural variability 68 characteristics (Fernández-Peruchena et al., 2015). It is worth noting that, besides solar 69 irradiance, also other meteorological variables are required for solar plants yield simulation, 70 among which the wind speed and ambient temperature stand out, as well as additional variables 71 of interest (circumsolar radiation, surface level radiation extinction, soiling, etc.). Site-specific 72 features of these variables should be assessed for accurate PMY generation. 73 One approach for generating PMYs is based on sampling from a data bank of measured data. 74 Usaola et al. (2014) presented a method based on Bootstrap Sampling, useful in the event of 75 having a database with enough representative data. The bootstrap methodology has been also 76 tested in (Ramírez et al., 2015) using 4 years of data, but without satisfactory results. Other 77 approaches rely on the synthetic generation of PMYs. Röttinger et al. (2015) assumed the annual 78 3 DNI values to be normally distributed for defining a generation scheme, with a 1- width 79 equivalent to the diagnosed data set uncertainty. In the multiscale stochastic model (MUS) 80 scheme (Fernández-Peruchena et al., 2015), GHI annual values are generated by randomly 81 sampling its Normal distribution (characterized by means of available GHI series at the site). 82 From these annual series, each temporal scale generated (monthly, daily, intra-daily) reproduces 83 the natural characteristics at that scale and also accounts for the boundary conditions imposed 84 by the lower temporal resolution series previously generated (e.g., monthly series must 85 reproduce annual values). DNI and other meteorological variables of interest for the plant 86 simulation are generated from the corresponding GHI series. 87 This hierarchy of models is a valuable method of ensuring the consistency across time scales. 88 This provided the basis for the multiple time scale synthetic generation of rainfall data in 89 Piantadosi et al. (2009). As referred to in that paper, a number of other papers focusing on 90 generating rainfall on different time scales start at a high frequency, say daily, and then progress 91 to lower frequencies such as monthly and yearly. However, what was remarked was that if one 92 followed that progression, even for the situation where the synthetic daily totals are statistically 93 indistinguishable from the observed data, when one amalgamated those into monthly totals, 94 the monthly means matched well but the variance of the synthetic monthly totals significantly 95 underestimated those of the data. Thus, this alternative progression from lower to higher 96 frequency is adopted. 97 There are a limited number of papers dealing specifically with the generation of daily solar 98 radiation datasets, among which it is worth mentioning that of Aguiar et al. (1988). They 99 generated daily sequences using only average monthly radiation and a library of Markov 100 transition matrices for each month. The approach taken here is similar to that of Boland (2008), 101 Magnano et al. (2010), and Boland (2010), and which was utilized in Grantham et al. (2018). In 102 those papers, the daily solar irradiation data series was standardized by subtracting a Fourier 103 series model which replicates the seasonality of the series, and dividing by an exponentially 104 weighted moving average of the standard deviation of the series over the year. Then, a first 105 order autoregressive AR (1) model was constructed for the standardized series and finally a 106 white noise series is calculated from the differences between the data and the AR(1) model. 107 When it comes to downscaling high resolution time series, there has been many approaches 108 based on Markov chains (Morf, 1998; Ngoko et al., 2014; Bright et al., 2015; Bright et al., 2017; 109 Munkhammar et al., 2018), the partition of solar radiation into a deterministic and a stochastic 110 component (Polo et al., 2011; Larrañeta et al., 2015; Larrañeta et al., 2018; Grantham et al., 111 2017) and the non-dimensionalization of the daily profiles (Fernández-Peruchena et al., 2015; 112 Fernández-Peruchena et al., 2018; Larrañeta et al., 2018), but at the moment, there is still room 113 to improve the reproduction of the solar variability in the high resolution temporal scale 114 (Lohmann, G., 2018). In this paper, we rely on the methods recently published in Grantham et 115 al. (2018) and Larrañeta et al. (2018) to present a 3-step methodology for generating 100 PMYs 116 of coupled DNI and GHI at 1-min time resolution, using hourly input series of 10-15 years at the 117 site that can be easily retrieved from satellite estimates. This work presents for the first time, to 118 our knowledge, a globally applicable method for the synthetic generation of multiple annual 119 solar radiation time series in high resolution (1-min) going beyond previous approaches that 120 reached the monthly (Fernández-Peruchena et al., 2015) or daily resolution (Grantham et al., 121 4 2018). This methodology is oriented towards the new paradigm described on probabilistic 122 approaches addressing the plant feasibility. 123 Fully stochastic analyses that take into account the uncertainty and variability in different 124 parameters or factors affecting the energy yield of solar energy projects during their lifetime 125 have been identified as a promising approach to overcome the limitations of traditional, 126 deterministic feasibility analysis (Nielsen et al., 2017). Since variability and uncertainty in the 127 solar irradiance is the first source of uncertainty in the estimation of the energy yield, the 128 elaboration and assessment of realistic multi-year generation has been identified as one key 129 research task for the creation of Advanced Meteorological Data Sets for CSP Performance 130 Simulations (Ramírez et al., 2017) 131 The idea of the synthetic generation of long term series is not new: it was presented together 132 with the concept of Plausible Meteorological Years (PMY) in Fernandez-Peruchena et al., 2015. 133 That paper presented a general and functional methodology for the generation of such PMYs 134 based in a number of sub-methodologies and models that perform adequately. However, the 135 ultimate aim of that paper was to encourage other experts to contribute to an improved 136 methodology with present or future methods for each of the steps that could lead to better 137 results. In this context, the present work is based on the availability of long-term, high-precision 138 series at the site, from which valuable information is extracted through novel synthetic 139 generation techniques (Grantham et al., 2018). 140 The paper is organized as follows. Section 2 describes the data used for the testing the method 141 performance. Section 3 describes the algorithm step by step. In Section 4, we present the results 142 analysis and the discussion of the performance of the method, and in Section 5 the conclusion 143 and future lines of work are drawn. 144 2 Meteorological database 145 In this work, an extensive database is used for testing the proposed method (Table 1). This 146 database is composed of 1-min average values of DNI and GHI recorded during 14 consecutive 147 years (2002–2015) for the location of Seville (Spain). The measurements were taken with a 148 sampling and logging frequency of 0.2 Hz. An ISO first class Eppley NIP pyrheliometer mounted 149 on a sun tracker Kipp & Zonen 2AP measured the DNI. A secondary standard Kipp and Zonen 150 CMP21 measured the GHI. The devices are located at the meteorological station of the Group 151 of Thermodynamics and Renewable Energy of the University of Seville and have been 152 periodically calibrated, at least once every two years. Data used in this work have been subjected 153 to quality-control procedures following the BSRN recommendations (McArthur, 2004). We have 154 performed a gap filling procedure for the identification and replacement of missing or incorrect 155 data in order to prepare a complete database (Moreno et al., 2016). Only 1% of the data has 156 been filled for the entire training database. 157 Table 1. Location selected for the training the method. 158 Latitude (°N) Longitude (°W) Altitude (m) Climate Period Seville 37.4 6.0 12 Mediterranean 2002-2015 159 5 We use the observed 1-min GHI and DNI data obtained from the Australian Bureau of 160 Meteorology website (Bureau of Meteorology, 2015) for the location of Adelaide, the capital of 161 South Australia (Table 2) to generate the synthetic high temporal resolution synthetic time series 162 for the location of Seville (step 3). GHI and DNI data were observed with a secondary standard 163 Kipp and Zonen CM11 and a first class Carter Scott DN5 respectively 164 Table 2. Data used for the generation of the dimensionless database. 165 Latitude (°N) Longitude (°W) Altitude (m) Climate Period Adelaide -34.9 -138.5 2 Hot Mediterranean 2003-2017 166 3 Methodology 167 In this section we describe the implemented algorithm for the multiyear synthetic generation 168 step by step. Figure 1 shows the flow diagram of the implemented algorithm. The input to the 169 algorithm is the available 10-15 years series at the site, either registered or modeled (referred 170 to as 10-15 “observed” years in Fig. 1). In step 1 we generate synthetic monthly data from the 171 observed data. In step 2, both the output of the first step and the observed data are required as 172 input. In the last step, we require as input an extensive normalized 1-min database from any 173 location and the output of the second step. 174 175 Fig. 1. Flow diagram of the implemented algorithm for the multiyear synthetic generation. 176 3.1 Step 1: From monthly observed to monthly synthetic 177 In the first step of the methodology, from the available initial series (hereafter observed series, 178 even if they can also come from models), we generate 100 annual series at monthly scale, 179 corresponding to the annual probability of exceedance from 1 to 100. The annual probability of 180 exceedance is the probability that a given solar radiation total accumulated over one year will 181 be exceeded in any year. For 100 years, the probability of exceedance is complementary to the 182 Step 1 10-15 “observed” years Hourly DNI+GHI Step 2 Step 3 100 synthetic years 1-min DNI+GHI 100 synthetic years Monthly DNI+GHI 100 synthetic years Daily DNI+GHI Dimensionless database 6 percentile (P). For instance, a PoE10 corresponds to a P90. Given a random variable X with 183 continuous and strictly monotonic probability density function 𝑓(𝑥), a quantile function 𝑄𝑓 184 assigns to each probability p attained by f the value x for which 𝑃𝑟(𝑋≤𝑥)=𝑝. Symbolically, 185 the quantile function can be represented as follows: 186         1inf ; ,0 1Q p F p x F x p p       The kth n-tile Pk is that value of x, say xk, which corresponds to a cumulative frequency of N∙k/n. 187 If n = 4, the quantity is called a quartile, and if n = 100, it is called a percentile. 188 We use 10-15 years of observed data as input since it is a commonly available length of satellite 189 derived time series, but the size of the sample may not be enough to statistically characterize 190 the annual and monthly distribution of the solar radiation. The larger the sample size, the better 191 the characterization of the annual and monthly distribution of the solar radiation. For smaller 192 sample sizes than 10 years of observed data, the characterization of the distributions may not 193 be statistically representative. We calculate the synthetic monthly values following the 194 probability integral transform method to generate independent random monthly values. The 195 procedure for generating a monthly GHI and DNI coupled pair is briefly described below: 196 i. Calculate the cumulative distribution function (CDF) of the observed GHI monthly series 197 for each month. Since input data is obtained in the hourly resolution, we firstly integrate 198 the observed hourly data into the monthly resolution. 199 The probability integral transform method is then applied (steps ii and iii): 200 ii. Generate an independent random number R from a uniform distribution in the interval 201 between 0 and 1. 202 iii. Identify the value whose cumulative probability corresponds to the value generated 203 with the random number R to obtain the monthly synthetic GHI value (𝐺𝐻𝐼𝑠𝑦𝑛𝑡ℎ 𝑚). Figure 204 2 illustrates this step. 205 To maintain the relation between the GHI and the DNI at the site, we include limitations for the 206 calculation of the monthly synthetic DNI values (steps iv and v): 207 iv. Find the values of DNI in the observed monthly data of the month of the year under 208 treatment in the range of the 𝐺𝐻𝐼𝑠𝑦𝑛𝑡ℎ 𝑚 ± 5%. 209 v. Calculate the CDF of the identified possible values of DNI in the range 𝐺𝐻𝐼𝑠𝑦𝑛𝑡ℎ 𝑚 ± 5%. 210 The probability integral transform method is then applied again for the DNI (steps vi and vii): 211 vi. Generate an independent random number Y from a uniform distribution in the interval 212 between 0 and 1. 213 vii. Identify the monthly synthetic DNI value (𝐷𝑁𝐼𝑠𝑦𝑛𝑡ℎ 𝑚) such as the value whose cumulative 214 probability corresponds to the value generated with the random number Y. 215 216 7 i. 217 Fig. 2. Graphical reproduction of the stage iii of the procedure for the dynamic generation of 218 synthetic monthly values. Example for the month of January for the location of Seville. 219 We repeat this procedure for each of the 12 months of the year, thereby obtaining the annual 220 synthetic cumulative values by adding the monthly synthetic values. We calculate 10,000 annual 221 synthetic values running therefore the procedure 120,000 times. The complete procedure of 222 generating 10,000 synthetic annual values results in a low computational cost. In Fig. 3, we 223 represent a scatter plot of the annual values of DNI versus the corresponding annual values of 224 GHI of both the observed (dark blue squares) and the 10,000 synthetic data (light blue circles). 225 226 Fig. 3. Annual DNI versus their corresponding GHI values of both observed (dark blue squares) 227 and 10,000 synthetic data (light blue circles) for the location of Seville. 228 Even if the procedure presented here provides synthetic monthly irradiation data within the 229 limits of the observed values, it can generate annual irradiation values upper or lower than the 230 extreme values of the observed annual series, as can be observed from Fig. 3. 231 To generate the 100 sets of annual synthetic values, a preliminary statistical analysis of annual 232 solar irradiation probability density functions has been carried out. We have considered that the 233 annual GHI and DNI series follow Normal and Weibull distributions, respectively (Peruchena et 234 al. 2016). The assumption of normal distribution for annual GHI series is validated by the 235 Kolmogorov–Smirnov and Shapiro–Wilk normality tests (p > 0.05), and the Weibull distribution 236 8 assumption for annual DNI series is analyzed by a set of goodness of fit tests (p > 0.05) (for more 237 details, the reader is referred to Peruchena et al. (2016)). 238 We calculate the annual DNI and GHI expected probabilities of exceedance (𝑃𝑜𝐸𝐷𝑁𝐼 𝑛 and 𝑃𝑜𝐸𝐺𝐻𝐼 𝑛, 239 respectively) by fitting the observed annual values to a Weibull and a Normal distribution, 240 respectively. Then, we seek for the lower absolute values of the differences of the synthetic 241 annual coupled DNI and GHI values to the theoretical annual PoEs within the 10,000 generated 242 synthetic values. In Fig. 4 we present a scatter plot of the annual values of DNI versus the annual 243 values of GHI of the observed data (dark blue squares ) and the 100 synthetic data corresponding 244 to the PoEs from 1 to 100 (light blue circles). 245 246 Fig. 4. Annual values of DNI versus the corresponding GHI values of the observed data (dark blue 247 squares), along with the 100 synthetic values corresponding to the PoEs from 1 to 100 (light blue 248 circles) for the location of Seville. 249 3.2 Step 2: From monthly synthetic to daily synthetic 250 The second step of the methodology is to generate daily synthetic solar irradiation values out of 251 the monthly synthetic data generated in Step 1. The daily solar irradiation observed data series 252 are standardized by subtracting a Fourier series model which replicates the seasonality of the 253 series, and dividing by an exponentially weighted moving average of the standard deviation of 254 the series over the year. Then, a first order autoregressive AR(1) model is constructed for the 255 standardized series and finally a white noise series is calculated from the differences between 256 the data and the AR(1) model. This pool of random error terms is bootstrapped in the reverse 257 procedure to create any number of synthetic years before matching of monthly totals to the 258 generated synthetic monthly totals from Step 1. 259 We aim to generate synthetic quartets giving information about the energy, variability and 260 distribution of the daily solar irradiance profiles. We synthetically generate three daily indexes 261 that can be used to characterize or classify different types of days (Moreno et al., 2017): 262  Energy: We use the daily direct fraction index (Skartveit and Olseth, 1992) and the daily 263 clearness index (Black et al., 1954) to characterize the daily energy of a given day 264 following next equations: 265 15 408 Fig. 10. Scatter plot between DNI and GHI daily values, both of observed (dark blue hexagons) 409 and 100 synthetic (light blue hexagons) datasets broken down by months for the location of 410 Seville. 411 We can observe the consistent relation between both variables on a daily basis. In May, June, 412 July and December, there is a thinner cloud that is seemingly reproduced in the synthetic set. In 413 other months like February, March, October and November the dispersion of the cloud is also 414 reproduced in the synthetic set. To evaluate each radiometric variable separately, we calculate 415 the CDFs of the daily observed (opaque) and synthetic (translucent) GHI in an annual basis (Fig. 416 11) and monthly basis (Fig. 12). 417 418 Fig. 11. Cumulative distribution functions of all observed daily values of GHI for the location of 419 Seville (dark red), and the corresponding ones for each synthetic year (light red). 420 16 421 Fig. 12. Cumulative distribution functions of the observed (dark red) and synthetic (light red) 422 daily values of GHI for the location of Seville broken down by months. 423 The CDFs of the synthetic data (translucent) show a wider range of scenarios that could be very 424 useful to investors to understand the variability of the solar radiation and to evaluate its impact 425 on the energy yield of solar plants. From fig. 12 we can assure that the monthly CDFs of the 426 observed and synthetic daily values of GHI are almost overlapped for most of the months. It is 427 interesting to point out that in months like February, March, October and November, that 428 showed a disperse cloud pointsee Fig. 10, the CDFs are totally superimposed while in months 429 like May, June, July and December, when we could observe a thinner cloud pointsee Fig. 10, 430 the CDFs are slightly displaced. We also calculate the CDFs of the daily observed (dark blue) and 431 synthetic (light blue) DNI in annual (Fig. 13) and monthly (Fig. 14) basis. 432 433 Fig. 13. Cumulative distribution functions of all observed daily values of DNI for the location of 434 Seville (dark blue), and the corresponding ones for each synthetic year) (light blue). 435 17 436 Fig. 14. Cumulative distribution functions of the observed (dark blue) and synthetic (light blue) 437 daily values of DNI for the location of Seville broken down by months. 438 The annual CDFs of the daily synthetic DNI data (light blue) show again a wider range of scenarios 439 than the TMY. We can observe a slight mismatch in the CDFs of the synthetic sets for daily values 440 around 8.5 kWh/m2, suggesting a scope to improve in future approaches focusing on clear sky 441 situations. The monthly CDFs of the observed and synthetic daily values of DNI also show 442 similarity in most of the months, perhaps in February, March and August we can observe a slight 443 mismatch between CDFs. In Figs 15 and 16, we calculate the CDFs of the daily observed (opaque) 444 and synthetic (translucent) 𝑉𝐼 and 𝐹𝑚 broken down by months for the location of Seville. 445 18 446 Fig. 15. Monthly CDFs of the observed daily 𝑉𝐼 values (opaque) together with the monthly CDF 447 of the synthetic daily 𝑉𝐼 values (translucent) for the location of Seville 448 449 Fig. 16. Monthly CDFs of the observed daily 𝐹𝑚 values (opaque) together with the monthly CDF 450 of the synthetic daily 𝐹𝑚 values (translucent) for the location of Seville 451 Figs. 15 and 16 show a great concordance between observed and synthetically generated 452 variability and distribution. We can quantify the concordance between observed and synthetic 453 sets CDFs by using the KSI (Kolmogorov-Smirnov test integral) index, that is defined as the 454 integrated differences between the CDFs of the two data sets (Espinar et al., 2009). The unit of 455 this index is the same for the corresponding magnitude. The higher the KSI values, the worse 456 the model fit. 457 19 𝐾𝑆𝐼=∫ 𝐷𝑛𝑑𝑥 𝑥𝑚𝑎𝑥 𝑥𝑚𝑖𝑛 , (6) 458 where, 𝑥𝑚𝑎𝑥 and 𝑥𝑚𝑖𝑛are the extreme values of the independent variable, and 𝐷𝑛 are the 459 differences between the CDFs of the observed and synthetic datasets. In table 4 we show the 460 KSI values obtained for each synthetically generated variable in a monthly basis. 461 Table 4. KSI of the synthetic daily GHI, DNI VI and Fm for the location of Seville 462 463 Parameter KSI (kWh/m2) KSI (-) Variable GHI DNI VI Fm January 0.070 0.155 0.028 0.012 February 0.103 0.308 0.027 0.010 March 0.124 0.323 0.024 0.019 April 0.134 0.277 0.058 0.008 May 0.147 0.284 0.044 0.010 June 0.190 0.282 0.025 0.008 July 0.104 0.174 0.026 0.004 August 0.142 0.337 0.016 0.022 September 0.076 0.250 0.021 0.007 October 0.080 0.214 0.035 0.028 November 0.085 0.238 0.025 0.015 December 0.085 0.255 0.054 0.015 464 4.3 Step 3 evaluation 465 The qualitative assessment of the third step of the methodology, this is, the generation of 1-min 466 coupled DNI+GHI data from daily synthetic quartets of indexes, is presented in the following. In 467 Fig. 17, we present the annual CDFs of the 14 years of 1-min observed GHI (dark red) along with 468 the corresponding CDFs of the 100 years of 1-min synthetic GHI (light red). The same results but 469 for DNI are presented in Fig. 18. 470 471 Fig. 17. Annual CDFs of the 1-min observed GHI (dark red) and synthetic (light red) 1-min GHI 472 datasets. 473 20 474 Fig. 18. . Annual CDFs of the 1-min observed (dark blue) and synthetic (light blue) 1-min DNI 475 datasets 476 With this algorithm, we don´t intend to emulate only the distribution of the observed data, but 477 also other scenarios whether extreme or not. From Figs 17 and 18, we can observe that we are 478 capable of reproduce a larger range of scenarios including extreme years that would be useful 479 for risk analysis. In Fig 18 we observe a misalignment between the CDFs of the synthetic sets 480 and the CDFs of the observed data. The synthetic CDFs have a significantly increased probability 481 at 0-250 W/m2 resulting in a decrease in the cumulative probability around 750 W/m2. The use 482 of a dimensionless database from a location with a given climate (Adelaide) to reproduce the 483 high-resolution synthetic data for a location with a different climate (Seville) may be the main 484 cause of this deviations but also the slight deviation found in step 2 for clear sky days (Fig 13).In 485 Figs 19 and 20 we perform the analysis month by month. 486 487 Fig. 19. CDFs of the 14 observed 1-min GHI annual sets (dark red) together with the monthly 488 CDFs of the 100 synthetic 1-min GHI annual sets (light red) broken down by months for the 489 location of Seville. 490 21 491 Fig. 20. CDFs of the 14 observed 1-min DNI annual sets (dark blue) together with the monthly 492 CDFs of the 100 synthetic 1-min DNI annual sets (light blue) broken down by months for the 493 location of Seville. 494 The shapes of the typical CDFs for the different months are reproduced both for GHI (Fig. 19) 495 and DNI (Fig. 20). It is worth highlighting the high values and low dispersion of measured DNI 496 CDFs of July, from which the CDFs reduce their maximum values and dispersion (June and 497 August, and more markedly from May and September). Even if the typical values and variability 498 of CDFs are well reproduced by the synthetic series, there are few extreme CDFs of some months 499 (January and December), leading to a potential future improvement in the model 500 In figure 21 we present an example of the generated synthetic DNI and GHI time series by 501 showing five consecutive days at the same time of the year for four different years. 502 503 22 Fig. 21. Five consecutive synthetically generated daily coupled GHI and DNI profiles at the same 504 time of the year for four different years. 505 The cumulative values should be preserved in order to maintain the consistency after each step 506 of the procedure, however slight differences are found. In table 5 we present the root mean 507 square error (RMSE) and the mean absolute error (MAE) between the outputs of each step of 508 the method. Calculations are performed in the annual, monthly and daily resolution by 509 integrating the synthetic data after each step of the procedure. We can observe a strong 510 consistency in the results given by the low values of RMSE and MAE. 511 Table 5. RMSE and MAE (kWh/m2) between the outputs of each step of the method. 512 RMSE (kWh/m2) Step 1-Step 2 Step 1-Step 3 Step 2-Step 3 GHI DNI GHI DNI GHI DNI Annual 5.7 6.1 13.4 2.7 11.6 6.3 Monthly 2.5 2.8 3.4 3.4 1.9 2.7 Daily - - - - 0.2 0.4 MAE (kWh/m2) GHI DNI GHI DNI GHI DNI Annual 4.5 3.7 11.7 2.3 11.1 4.1 Monthly 1.3 0.9 2.4 2.5 1.5 2.2 Daily - - - - 0.1 0.3 5 Conclusions and future improvements 513 In this work we present a method for the synthetic generation of 100 PMYs of coupled DNI and 514 GHI at 1-min time resolution using hourly input series of 10-15 years at the site that can be easily 515 retrieved from satellite estimates. The synthetic data can be used for the radiometric 516 characterization of any site in which satellite-derived solar data is available and for risk 517 evaluation of solar projects with the advantage of considering the interannual, seasonal and 518 intra-day variability of the solar radiation. 519 The method is divided in three main steps in a chain where we start generating synthetic 520 monthly, then daily and then 1-min values. For the generation of synthetic monthly values we 521 have used a Monte Carlo method and we have assumed a normal distribution form the annual 522 values of GHI and a Weibull distribution for the annual values of GHI. The correlations between 523 months has not been addressed in this study. In a future iteration of this work we intend to 524 develop tools to take care of this aspect. For the generation of synthetic daily values we have 525 used a first order autoregressive model and a nonparametric bootstrapping technique. The 526 relation between the daily GHI and DNI is kept and reproduced in the synthetic data. For the 527 downscaling from synthetic daily to 1-min values, we have used an algorithm based on the 528 normalization of the daily solar radiation profiles by the clear-sky envelope approach and the 529 extraterrestrial solar radiation, creating dimensionless profiles of observed solar radiation data 530 that can be used to generate synthetic 1-min data for any location and any day of the year. 531 Results show a great concordance between the synthetic and observed data in all the time 532 scales. We reproduce the Normal and Weibull distributions of the annual values maintaining the 533 23 particular relation between the DNI and GHI along each month of the year. We reproduce the 534 CDF of the observed daily values in terms of the energy, variability and distribution. We have 535 quantified the similarities in the CDFs by using the KSI in order to present comparable results for 536 future approaches. 537 The presented method sets the base for the multiyear synthetic generation, however, there are 538 several improvable issues in each step of the procedure. In step 1 we only generate synthetic 539 monthly values within the thresholds of the maximum and minimum observed monthly values. 540 Climate change trends should be included in order to generate extreme synthetic monthly 541 values and the worst case scenario (PoE99), should be addressed from volcanic eruptions’ 542 assessment. Step 2 would require a larger observed database to gather all possible stochastic 543 variations of the daily solar radiation. Regarding step 3, there is still room of improvement in the 544 intra-day variability characterization. The VI index shows a significant dependence on the day of 545 the year, location and time resolution. 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