Post-processing of COSMO-REA6 direct and diffuse radiation components 84

The generated power of photovoltaic modules mainly depends on the incidental irradiance to the solar module. For modules mounted with an arbitrary orientation estimates of the tilted radiation becomes necessary. Therefore, not only the global horizontal irradiance (GHI), which is given as post-processed product from Frank et al. [2018], is necessary but also its decomposition in direct and diffuse radiation. The components allow a precise estimation of the radiation on inclined surfaces, taking into account their different propagation characteristics. Thus, a post-processing for the radiation components direct and diffuse radiation is developed and applied to COSMO-REA6.

In order to develop a method to adjust the direct and diffuse components for all individual time steps and grid cells the procedure relies on reanalyses data only. The post-processed GHI (Q_GHI,pp) derived in Chapter 3 pre-defines the aimed sum of the post-processed direct (Q_dir,pp) and diffuse (Q_dif,pp) radiation by the relation

Q_dir,pp+ Q_dif,pp= a Q_dir+ b Q_dif = Q_GHI,pp (5.1) with Q_dir, Q_dif the radiation components provided by the COSMO reanalysis, and a and b the unknown relation coefficients. With two unknowns and one equation a further relation is necessary to solve for a and b. This second relation needs to provide information of a realistic ratio r of the direct and diffuse radiation components after the post-processing. Therefore, I use the climatological ratio distributions derived from reanalysis for various GHI-classes and assume the percentile of the ratio being unchanged by the post-processing. The following describes the developed procedure in detail.

Defining the radiation component ratio r at each grid point and each time step as r = T_dir

T_dir+ T_dif with T_dir= Q_dir

Q_{T OA} and T_dif = Q_dif

Q_{T OA}. (5.2)

Fig. 5.1 illustrates the derived ratio distributions from COSMO-REA6 alternating with dis-tributions derived from baseline surface radiation network (BSRN) measurements in Linden-berg. Note, the BSRN measurements have highest quality standards with uncertainties of 2 and 5 W m⁻², respectively [Heimo et al., 1993]. The general behavior of increasing ratios with increasing transmissivity values between 0 and 0.7 is well represented by the reanalysis. Not

5.2 Material and methods 85

Figure 5.1: Distribution of the radiation component ratios r (direct component divided by GHI) as function of GHI transmissivity at the BSRN site Lindenberg. Grey boxplots represent the distributions derived from BSRN measurements (10 min averages), red ones from COSMO-REA6, and blue ones are artificially approximated using reanalysis radiation only. Percentiles shown are the 5, 25, 50, 75, and 95th.

represented at all is the observed decrease of the ratio for transmissivity values above ~0.7.

This is expected, since the high irradiance values are not simulated at all due to the use of the overestimated aerosol optical thickness in COSMO-REA6. However, the decreasing ratios indicate the physical limit of the direct radiation component in clear sky situations. Even higher transmissivities are only possible with increased diffuse radiation values. A typical effect leading to particularly high diffuse radiation is scattering at local cloud edges. Such effects can not be simulated by the COSMO-REA6 model which represents a grid cell mean. Consequently, based on COSMO-REA6 it is not possible to derive the climatological component ratio in situations of particularly high transmissivities (>0.7). However, since the climatological ratio distributions are intended to be used for a realistic adaptation of the individual radiation components an approximation of those is necessary.

Approximations of median ratios for the high transmissivity values are derived for each reanalysis pixel by assuming the direct radiation related to the median ratio of the highest transmissivity class (median(r(T = max))) in the reanalysis to be the maximum of physically possible direct radiation (T_dir,max). The maximum direct radiation per pixel can then be written as

T_dir,max = median(r(T = max)) T_GHI,max (5.3)

with T_GHI,max the mean value of the highest transmissivity bin in the reanalysis. Given the constant direct radiation the median ratios of the missing ratio distributions (T>~0.7) can then be estimated by

r(TGHI > TGHI,max) = T_dir,max TGHI

. (5.4)

This procedure provides the median values of r as a function of the transmissivity but not the corresponding distributions. As a pragmatic approach for all T_GHI > T_GHI,max the frequency distribution of the T_GHI class 0.06 less than T_max is used. The resulting approximated ratio distributions are additionally drawn in Fig. 5.1. Testing the derived approach for ratio distribu-tion approximadistribu-tions at eight BSRN sites shows that the site Lindenberg is a good representative for all ratio distribution plots. With the completed estimates of the ratio distributions for all grid points of COSMO-REA6 it is now possible to estimate the post-processed ratios. The only further assumption is that the percentile of the ratio in its ratio distribution is maintained.

The first step in the estimation of the post-processed radiation components is to calculate with the COSMO-REA6 provided radiation components the ratio r_pre before post-processing. In a second step its percentile in the ratio distribution in the related transmissivity class T_GHI,precan be calculated. Subsequently, the ratio of the post-processed radiation r_pp is determined by the calculated percentile in the target ratio distribution related to T_GHI,pp. This ratio information is the second condition necessary to determine the relation coefficients a and b. Based on the relations

rpp= a Tdir,pre

T_GHI,pp (5.5)

and

rpre = Tdir,pre

T_dir,pre+ T_dif,pre (5.6)

the coefficient a can easily be derived by substituting T_dir,pre in eq. 5.6 by the corresponding expression derived from eq. 5.5. After rearranging, a can be determined by:

a = T_GHI,pprpp− T_GHI,pprpprpre

r_preT_dif,pre . (5.7)

The coefficient b is then calculated from the relation given in Eq. 5.1. This post-processing has the advantage to adjust the individual radiation components in compliance with the post-processed GHI values from [Frank et al., 2018] and at the same time it maintains case individual

5.2 Material and methods 87

radiation component ratio discrepancies from the climatological median ratio given by the re-analysis. The post-processed radiation components are prerequisites for a realistic simulation of PV power based on COSMO-REA6.

5.2.3 PV reference data

For the assessment and calibration (Sec. 5.3.2) of derived PV estimates based on COSMO-REA6 real-world data of PV power are necessary. One provider of freely available wind- and PV power records is the Open Power System Data (OPSD) platform⁶. OPSD is funded by the German Federal Ministry for Economic Affairs and Energy in order to collect, check and uniform open data required by energy system models.

As the OPSD generation data is based on all currently installed capacities per country, while the simulated PV generation is only based on a subset of real installed capacity, generation data cannot be directly compared. An established detour to compare the production of two PV data sets with different installed capacities is to normalize the production in the respective data set with the theoretical production of the total installed capacity under standard test conditions (25^◦Celsius and 1000 Wm⁻²). To determine the resulting factor, which is also called the capacity factor CF, the installed capacities per country of the OPSD product are required.

Focusing on the whole European domain uniform generation and capacity data from OPSD are only available on country scale. The data packages made use of are the time-series data package version 2019-06-05 [OPSD, 2019b] and the national generation capacity package version 2019-02-22 [OPSD, 2019a]. The packages provide power generation as well as installed capacity since 2010 for a steadily increasing number of European countries. While the generation package encompasses hourly resolved power data the capacity package comprises yearly data only. Thus, in order to derive capacity factors (CFs), yearly capacity values are linearly interpolated to the hourly scale.