Diseño de la Investigación

The basic methodology for obtaining an estimate of the annual solar resource suitable for prefeasibility analysis that can be used to make energy yield estimates is to acquire available long-term site estimates, such as satellite-derived estimates or nearby modeled station values (such as those available through the NSRDB or TMYs). These data sets and their uncertainties have already been described in previous chapters and sections. When short-term on-site

estimates from new solar radiation measurements are available, they can be used to reduce the uncertainty of the modeled estimates (Gueymard and Wilcox 2009). This process becomes critical in the project feasibility and due diligence stages of project development.

Three methods by which we can combine the short- and long-term data to obtain a more accurate estimate of the long-term solar resource (such as what may be needed for project feasibility studies) are discussed here.

The ratio method assumes that at least two independent data sets are available: an on-site

measurement data set (presumed to be relatively short term), and a long-term climatological data set, such as a satellite-derived database or a nearby long-term measurement station or modeled data. Ideally, at least part of the two data sets should be concurrent. If there is no concurrency in the data, the ratio method can still be applied, but the uncertainty of the resulting long-term on- site data profile will likely be much higher than if concurrent data periods are available. This method is described in Gueymard and Wilcox (2009). Basically, the method involves calculating the ratios of a selected averaging period of the concurrent data sets, such as hourly or monthly averages, then applying these ratios to the balance of the long-term data set to produce a long- term estimate for the site.

There are several important considerations to applying this approach, especially if the long-term data set involves the use of satellite-derived data for the same location as the site data. Although the ratio method removes biases between the short-term and long-term data sets, the biases may, in fact, vary from year to year or from season to season. Variations in biases suggest that the cross-correlation between the two concurrent measurement sources is less than 1.0, and lower cross-correlation values indicate more uncertainty associated with extrapolating short-term data to long-term means (Gueymard and Wilcox 2009). Consider these possible scenarios:

• In an ideal scenario, there is low month-to-month variability in biases between the reference data and on-site measurements. Under these circumstances, a simple correction factor based on the ratio method should be acceptable for extrapolating the short-term data set.

• A second scenario is high random variability between the short-term on-site data and the long-term reference data source, meaning that an accurate extrapolation to a longer-term value at the site will have high uncertainty.

• A third scenario is when there are strong seasonal trends in the data, which may require additional years of on-site data to better confirm or define the trend. This scenario would ultimately lead to long-term extrapolations with low uncertainty.

based on the inverse of the uncertainty of each data set. By assuming that the deviations from truth follow a normal distribution and are statistically independent, the Gaussian law for error propagation can be applied. Meyer et al. (2008) then provide curves showing how the additional data sets do not need to be of the same high quality as the base data set to add value to the combined data sets (Figure 6-5).

Figure 6-5. Resulting uncertainty when combining a base data set of 2%, 4%, 6%, or 8% overall uncertainty with an additional data set of varying quality. Figure from Meyer et al. (2008)

Meyer et al. (2008) show that by using more than two data sets, the resulting quality of the combined data set can be even further improved. For example, when the base data set has an uncertainty of 4%, the resulting data set can be improved by adding two data sets with a moderate 7% quality rather than 10%; however, if the two additional data sets have an

uncertainty of 10% or more, the base data set cannot be improved. Therefore, data sets with such high uncertainties should not be used. If the analyst uses this method, he or she should be

prepared to demonstrate that the incorporated data sets are truly independent and there are no correlations (similar instrumentation and measurement protocols, common estimates for model parameters such as aerosols or clouds). This methodology of combining the uncertainties of various input data sets to provide the resulting uncertainty of the “best guess” DNI estimate for a site is elaborated in a more recent paper by Meyer et al. (2008).

Another approach for reducing the uncertainty of long-term satellite-derived data sets using high- quality short-term ground data has been developed by Schumann et. al (2011). In this method, the frequency distribution of the ground-based data is used to improve the satellite-derived data. Their method has resulted in greatly reduced bias errors and improved Kolmogorov-Smirnov Integrals in the satellite data, especially for DNI estimates, even when as little as 3 months of ground data are available. In particular, their method shows that a full year of ground data are

sufficient to obtain significant improvements in long-term satellite-derived DNI data sets, resulting in greatly improved bankable data for purposes of financing large-scale CSP plants. Although their method was less successful in improving GHI data, they point out that there is generally less of a need to correct GHI data.

Their method builds on results from earlier studies (Carow 2008, Beyer et. al 2010) in which the frequency distribution, rather than a simple ratio technique, is employed to improve the satellite- derived data, noting that the frequency distribution of DNI has a strong influence on the power production of CSP plants, just as the wind speed frequency distribution has a strong influence on the power production of wind plants. The method of “training” the satellite data using

overlapping time series from ground measurements is demonstrated in Figure 6-6. The

differences in cumulative frequency distributions (training data) are applied to the test satellite data, producing a corrected data set (upper right image). The lower panels then show how the cumulative frequency distributions of the satellite data are “mapped” to a new frequency distribution based on the correction factors developed with the ground data.

Figure 6-6. Upper left: Cumulative frequency distribution for training time of overlapping ground data and satellite time series. The arrow illustrates the difference between the two curves. Upper right: Corrected satellite cumulative frequency distribution for test period. Lower left: Mapping of original satellite irradiance values to original cumulative frequency distribution (arrow and bottom right image). The original cumulative frequency distribution is first mapped to produce a corrected

cumulative frequency distribution, then the corrected cumulative frequency distribution is adjusted to satellite values. Green: ground data from training set; magenta: satellite data from

training set; purple: satellite data from test set; yellow: corrected satellite data. Figure from

method to reduce the bias errors to near zero, and especially to minimize the biases of the highest radiation values that are used for design purposes, has been presented by Mieslinger et al. (2014). The method was tested against two high-quality ground stations: Plataforma Solar de Almería (southern Spain) and Tamanrasset (Algeria); and four different satellite-derived methodologies: DLR, University of Oldenburg Department of Energy and Semiconductor Research, GeoModel Solar, and HelioClim-3. Unlike the previous methods, the method of Mieslinger et al. (2014) takes into consideration not only the systematic but also the random errors that are found when comparing satellite to ground data. Random errors are caused by parallax errors as well as by the difficulty in determining the vertical thickness of clouds from the satellite data used in the four methodologies applied here.

The basis of the adaption method is to apply a third order polynomial relationship rather than a simple regression model, to account for both the systematic and the random errors. The

polynomial function also addresses results in significant improvements in the differences

between measured and modeled data at high irradiance values. Using the criteria that an adapted data set should demonstrate a relative mean bias comparable to high-quality ground

measurements (+2%), the polynomial adaption method was shown to exceed this limit, especially when the HC3 data are removed from the testing. It was also demonstrated that forcing the bias to zero considerably reduces the Kolmogorov-Smirnov integrals of the satellite- derived values. Nevertheless, to validate this method further, it is clear that additional testing should be applied to more sites to investigate the performance of the method in different climatic zones and topographies.

Other methods have been proposed in the literature (Bender et al. 2011; Cebecauer and Suri 2010; Gueymard et al. 2012; Harmsen, Tosado-Cruz, and Mecikalski 2014; and Thuman, Schnitzer, and Johnson 2012), and they are typically used by commercial data providers. This is because the short-term measured data set must first be subjected to a stringent quality-control procedure and then to more or less complex statistical methods. There is currently no study that compares the performance of these methods, the details of which are often proprietary. Finally, an innovative optimal interpolation method has been proposed to perform the necessary

corrections to long-term data time series at a regional scale rather than for one specific site at a time (Ruiz-Arias et al. 2015).