Energy Yield Assessment of the Photovoltaic Power Plant

Transcription

1 Energy Yield Assessment of the Photovoltaic Power Plant ******** Municipality of ********, *********(Country) Nominal power ******** kwp DC Reference No /2013 Date: 18 August 2016 Customer Supplier *************** Solargis s.r.o. Contact: Mr. Marcel Suri Pionierska 15, Bratislava, Slovakia Phone marcel.suri@solargis.com

2 TABLE OF CONTENTS Acronyms... 3 Glossary Summary Characteristics of site and PV power plant Site description Configuration of photovoltaic power plant Solargis data Satellite-derived solar radiation Meteorological data Solargis PV simulation methods PV simulation assumptions and uncertainties Inter-row shading of fixed modules and related electricity losses Air temperature, wind speed and precipitation Global and Diffuse Horizontal Irradiation Monthly statistics of GHI and DIF Comparing GHI data with other data sources Global Tilted Irradiation Monthly, daily and hourly GTI statistics Comparing different azimuth and inclination of PV modules Theoretical PV power production Estimation of system losses and performance ratio Monthly statistics of theoretical PV power production Interannual variability of PV power output Uncertainty of PV power production PV electricity production over 20 years Conclusions List of figures List of tables References Support information Background on Solargis Legal information Solargis page 2 of 54

3 ACRONYMS GHI GTI DNI DIF TEMP WS MACC CFSR GFS Meteosat MSG Meteosat MFG Global Horizontal Irradiation, if integrated solar energy is assumed. Global Horizontal Irradiance, if solar power values are discussed. Global Tilted Irradiation irradiation impinging to the plane of photovoltaic modules defined by the tilt and azimuth. Direct Normal Irradiation, if integrated solar energy is assumed. Direct Normal Irradiance, if solar power values are discussed. Diffuse Horizontal Irradiation, if integrated solar energy is assumed. Diffuse Horizontal Irradiance, if solar power values are discussed Air Temperature at 2 metres Wind speed at 10 metres Monitoring Atmospheric Composition and Climate meteorological model operated by the European service ECMWF (European Centre for Medium-Range Weather Forecasts) Climate Forecast System Reanalysis. The meteorological model operated by the US service NOAA (National Oceanic and Atmospheric Administration) Global Forecast System. The meteorological model operated by the US service NOAA (National Oceanic and Atmospheric Administration) Meteosat satellite Second Generation data Meteosat satellite First Generation data 2016 Solargis page 3 of 54

4 GLOSSARY Bias Represents systematic deviation (over- or underestimation) and in context of solar irradiation it is determined by systematic or seasonal issues in cloud identification algorithms, coarse resolution and regional imperfections of atmospheric data (aerosols, water vapour), terrain, sun position, satellite viewing angle, microclimate effects, high mountains, etc. Capacity Factor (CF) The net capacity factor of a PV power plant is the ratio of its annual specific output to the potential output if it were possible for it to operate at full nameplate capacity indefinitely. Capacity factor is calculated by dividing specific power output (in kwh/kwp) by 8760 hours per year. Ground Cover Ratio (GCR) Ratio between area of PV modules to the total land area. Interannual variability Is derived from 19 years of data (1994 to 2012), and it is calculated from the unbiased standard deviation of monthly and yearly summaries of GHI, multiplied by number Thus interannual variability represents a range of values at 80% probability of occurrence. The lower boundary of interannual variability represents 90% probability of exceedance, and it is also used for calculating the P90 value. Monthly values of interannual variability indicate year-by-year instability of solar radiation for each month. The yearly values give an idea of weather fluctuation when comparing yearly GHI sums. P50 value Best estimate or median value. For annual and monthly solar irradiation summaries it is close to average, since multiyear distribution of solar radiation resembles closely normal distribution. P90 value Conservative estimate, assuming 90% probability of exceedance (with the 90% probability the value should be exceeded). When assuming normal distribution, the P90 value is also a lower boundary of the 80% probability of occurrence. P90 value can be calculated by subtracting uncertainty from the P50 value. Root Mean Square Deviation (RMSD) Represents spread of deviations given by random discrepancies between measured and modelled data and is calculated according to this formula: = On the modelling side, this could be low accuracy of cloud estimate (e.g. intermediate clouds), under/over estimation of atmospheric input data, terrain, microclimate and other effects, which are not captured by the model. Part of this discrepancy is natural - as satellite monitors large area (of approx. 3 x 4 km) while sensor can see only micro area of approx. 1 squared centimetre. On the measurement side, the discrepancy may be determined by accuracy/quality and errors of the instrument, pollution of the detector, misalignment, data loggers, insufficient quality control, etc. Solar irradiance Solar power (instantaneous energy) falling on a unit area per unit time [W/m 2 ]. Solar resource or solar radiation is used when considering both irradiance and irradiation. Solar irradiation Amount of solar energy falling on a unit area over a stated time interval [Wh/m 2 ] Solargis page 4 of 54

5 Theoretical PV power production Uncertainty Electricity production from the PV power plant at the start-up of operation. The performance degradation of PV modules and interannual variability is not considered at the calculations. Is a parameter characterizing the dispersion of the values attributed to an estimated irradiance/irradiation values. In this report, uncertainty assessment of the solar resource estimate is based on a detailed understanding of the achievable accuracy of the solar radiation model and its data inputs (satellite, atmospheric and other data), which is confronted by an extensive data validation experience. The second important source of uncertainty information is the understanding of quality issues of ground measuring instruments and methods. In this report, the uncertainty assumes 80% probability of occurrence of values. Thus, the lower boundary of uncertainty represents 90% probability of exceedance, and it is also used for calculating the P90 value Solargis page 5 of 54

6 1 SUMMARY This report estimates electricity yield from a planned photovoltaic (PV) power plant *********, located in *********. The report analyses also solar resource and meteorological conditions of the site. The projected total installed capacity of the PV power plant is ********* kwp. The power plant is of open-space free-standing type, and it is to be built using polycrystalline silicon PV modules mounted at fixed angle of 10 North with decentralized (string) inverter topology. Chapter 2 gives description of the site and PV power plant configuration. Solar and meteorological data All analyses in this report are based on the use of Solargis database developed by GeoModel Solar. The data are computed from satellite, atmospheric and meteorological models (Chapter 3). In this report, 15 and 30- minute time series data are used, covering a period of the most recent 19 years (period 1994 to 2012). Solar resource parameters are validated for selected sites, and it shows high data accuracy and consistency in the region (Chapter 3.1). For calculation in this study, an improved Solargis model (version 1.9) is used. Satellite data are used for quantification of cloud attenuation, and two satellites are used: Meteosat MFG and MSG (source EUMETSAT). Important benefit for the accuracy of the output data is use harmonised and accurate aerosol inputs derived from the new version MACC database (source ECMWF). Global Horizontal Irradiation (GHI) and Diffuse Horizontal Irradiation (DIF) are characterized as they serve the purpose as reference values. Solargis database includes also meteo parameters, and three of them are analysed for the site: Air Temperature (TEMP) at 2 meters, Wind Speed (WS) at 10 meters and Precipitation (Chapter 3.2). These parameters are calculated from the outputs of global atmospheric models GFS and CFSR (source NOAA NCEP) and are made available in the delivered data products. Meteo parameters are validated using measurements from meteo stations in the region (source NOAA NCDC). Compared to solar resource, spatial and temporal resolution of meteo data are lower; therefore the temperature, wind and precipitation parameters have higher uncertainty. PV simulation assumptions Simulation of photovoltaic electricity (PVOUT) generated by the power plant is based on Solargis 15-minute time series and software tools developed by Solargis. This simulation considers site-specific interaction of solar radiation and temperature with the PV modules and other components of the PV power plant (Chapter 4). The AC output at the feeding point to the grid will be lower than nominal installed capacity since there are losses associated with energy transformation in several stages. These comprise losses due to PV conversion, mismatch, interconnections, dirt, dust, bird droppings, soiling, reflections, inter-row shading, inverter losses and AC cabling and power transformer losses. Breakdown of losses is presented in Chapter 4.1, and it is summarized in Chapter 8.1. Far horizon, defined by terrain features, is considered and there is no influence of far-distance shading. Fixed mounted PV modules are to be installed on the structures with relative row spacing of 1.7. For such configuration, annual summary of losses due to near shading is negligible about 0.2% (Chapter 4.2). Technical availability of the power plant (i.e. excluding downtime due to maintenance, failures, and grid blackouts) in this report is considered to be 99%. The PV plant is to be built in the close future and year 2014 is assumed in this study as the first year of operation Solargis page 6 of 54

7 Solar resource and air temperature summary The calculations based on satellite-derived multiyear time series shows long-term annual and monthly statistics (Chapters 5, 6 and 7). Long-term average value is often referred to as P50, i.e. 50% probability of exceedance (i.e. median). Considering the long-term yearly average to be equal to P50 is simplification, but it is widely accepted within the industry. The time series summarise to the following longterm yearly averages: Global Horizontal Irradiation: 1851 kwh/m 2, with uncertainty of the estimate 5.0% Global Tilted Irradiation at 10 : 1851 kwh/m 2, with uncertainty of the estimate 5.5% Ratio of Diffuse Horizontal to Global Horizontal Irradiation: 53% Air temperature at 2 meters: 20.9 C with uncertainty of the estimate ±1.0. PV electricity yield summary Considering time series of Solargis GTI and TEMP parameters and 99% technical availability, the following theoretical PV energy yield parameters are calculated, constituting the best (P50) estimate (Chapter 8): Theoretical specific electric output: 1455 kwh/kwp Theoretical performance ratio: 78.6% Capacity factor: 16.6% Uncertainty of the PV electric output calculation: ±7.2%. Long-term average value is often referred to as P50, i.e. 50% probability of exceedance (median). On condition of using many years of data (19 years in case of Solargis), the average annual estimate can be considered as equal or close to P50. This assumption is a simplification, but it is widely accepted within the industry. Overall, combined uncertainty determining the minimum expected electricity output is considered, constituting a base for an estimate of the conservative production scenario, P90 (Chapter 9). It is given by two elements: i. Uncertainty of PV output estimate: ±7.2%, which is determined by the uncertainty of solar radiation estimate ±5.5% and PV simulation model ±4.7%; ii. Uncertainty due to weather variability: with 80% probability year-by-year PV power production may differ from the longterm average by up to ±3.3%. Assuming a period of 20 years, this uncertainty decreases to about ±0.7%. For long-term energy yield calculations, performance degradation of PV modules and other components has to be considered. In the calculations the annual reduction of conversion efficiency of PV modules is considered as follows: 0.8% performance degradation for the first year and 0.5% for the remaining years, for a period of 20 years. Assuming combined uncertainty and annual degradation of conversion efficiency of PV modules, average (P50) and conservative (P90) estimates of PV energy generation are calculated for the first year of operation, and for a period of 20 years (Chapter 9). The key performance numbers are summarised in the table below. Theoretical power production per year Estimated longterm production in year 2014 Annual average power production over 20 years Average power production at P50 [kwh/kwp] Average performance ratio at P50 Combined uncertainty Conservative power production at P90 [kwh/kwp] [MWh] [%] [±%] [MWh] Total uncertainty for first year of operation and for a period of 20 years combines: (i) uncertainty of solar radiation and PV estimate and (ii) uncertainty due to interannual variability. The production estimate assumes annual reduction of conversion efficiency of PV modules 0.8% for the first year and 0.5% for the remaining years for a period of 20 years Solargis page 7 of 54

8 At the end of the first year of the PV power plant operation, the P50 (average) yearly power plant production is estimated at 1443 kwh/kwp (14.4 GWh). Assuming combined uncertainties, in the first year, the minimum specific production at P90 should exceed 1328 kwh/kwp. For a period of 20 years, the average electricity production at P50 is estimated to 1377 kwh/kwp per year and performance ratio of the power plant to 74.4%. When considering combined uncertainty of all elements, it is expected at P90 that specific yearly electricity production of the power plant averaged over 20 years exceeds 1277 kwh/kwp. Comment on uncertainty The Solargis data in this report have not been site-adapted due to the missing ground measurements. Correlation and site adaptation of Solargis data with local measurements has a potential for reduction of uncertainty - by about 2% to 2.5% for GHI. Therefore it is recommended to start measuring solar resource at the site. Possible man-induced climate change or extreme natural events are not considered in this study Solargis page 8 of 54

9 Energy Yield Assessment of ******* kwp photovoltaic power plant *******, *******. 2 CHARACTERISTICS OF SITE AND PV POWER PLANT 2.1 Site description Site name: ********* *********(Map) Municipality ********* ********* Geographical coordinates of the point within the power plant: *********************** Elevation above sea level: Approx m a.s.l. Terrain inclination: Flat Terrain azimuth: - Location of the site with planned PV power station in the map: Fig. 1: Detailed geographical position of the site ( 2013 Solargis, Google Maps 2013 Google) 2016 Solargis page 9 of 54

10 ********* Fig. 2: Geographical position of the site in the region ( 2013 Solargis, Google Maps 2013 Google) ********* Fig. 3: Annual sum of Global Horizontal Irradiation - position of the site (green circle) in the detailed solar map ( 2013 Solargis) Terrain shading and ground albedo The site is located in a flat terrain, and it is not affected by terrain shading. The PV power plant is to be located in a rural area. Effects of the ground reflectance (albedo) are very limited as PV panels will be mounted at very low inclination angle (tilt is 10 ). Two graphs in Fig. 4 show: a) Change of the day length and solar zenith angle during a year; b) Change of the sun path over a year. Terrain horizon is drawn in grey colour and has negligible effect on solar radiation. Black dots show hours in True Solar Time. Blue labels indicate Central Africa Time (UTC +2 hours). a) Day length and solar zenith angle b) Sunpath and terrain horizon Fig. 4: Astronomical and geographical situation 2016 Solargis page 10 of 54

11 2.2 Configuration of photovoltaic power plant The concept of the photovoltaic power plant is outlined as follows: Installed capacity: ********* PV modules: Polycrystalline silicon *********: Total module count: units Modules with power tolerance ±3% NOCT 45ºC Temperature coefficient of the P max [%/K] Dimensions: 1956 x 990 x 50 mm Warranty: 10 years product warranty loss per year shall not exceed 0.7% 25 years 80.7% performance warranty Inverters: ********* String inverter, nominal AC output of one piece 27.6 kw CEC weighted efficiency: 98.0% *CEC efficiency is used in the calculations Mounting: Fixed mounting option, modules are going to be mounted on the fixed racks 2 rows of 21 panels in portrait mode Inclination of modules 10º Azimuth of modules: 0º (North) Relative row spacing 1.7 Transformer: Distribution transformers ********* Transformer units: ********* No-load losses estimated to 0.2% Short-circuit losses estimated to 1% Technological components of the photovoltaic power plant mutually match (Fig. 5). Due to varying nominal power of modules, however, it can be expected that real installed power in the start-up will be slightly higher. Summary of connected modules slightly exceeds recommended direct current (DC) input power of inverters. This may lead to some losses during sunny hours with high irradiation and lower temperature, because inverters will not be able to consume all produced DC input. Design with decentralized inverters ensures lower demands on DC cabling and lower losses in DC circuits. It also increases the reliability of the PV power plant as a whole, because in case of failure of one or more inverters, electricity production can continue without interruption. The disadvantage of the selected topology is lower efficiency of inverters and higher demands on production data collection compared with high power inverters used in photovoltaic power plants with central inverters concept Solargis page 11 of 54

12 Energy Yield Assessment of ******* kwp photovoltaic power plant *******, *******. Fig. 5: PV module layout of the ********* power plant Solargis page 12 of 54

13 3 SOLARGIS DATA 3.1 Satellite-derived solar radiation Solar radiation is calculated by numerical models, which are parameterized by a set of inputs characterizing the cloud transmittance, state of the atmosphere and terrain conditions. The methodology is described in several papers [1, 2, 3]. The related uncertainty and requirements for bankability are discussed in [4, 5]. Sun-tracking strategies on the example of South Africa are discussed in [6]. In Solargis approach, the clear-sky irradiance is calculated by the simplified SOLIS model [7]. This model allows fast calculation of clear-sky irradiance from the set of input parameters. Sun position is deterministic parameter, and it is described by the algorithms with satisfactory accuracy. Stochastic variability of clear-sky atmospheric conditions is determined by changing concentrations of atmospheric constituents, namely aerosols, water vapour and ozone. Global atmospheric data, representing these constituents, are routinely calculated by world atmospheric data centres and delivered at a spatial resolution of about 125 km. The calculation accuracy of the clear-sky irradiance is especially sensitive to the information about aerosols. The key factor determining short-term variability of all-sky irradiance is clouds. Attenuation effect of clouds is expressed by the means of a parameter called cloud index, which is calculated from the routine observations of meteorological geostationary satellites. In *********, spatial resolution of satellite data used in Solargis is about 3.0 x 3.5 km and time step is 15 and 30 minutes. To retrieve all-sky irradiance in each time step, the clear-sky global horizontal irradiance is coupled with cloud index. The clouds are the most influencing factor, modulating clear-sky irradiance. Effect of clouds is calculated from the Meteosat MFG and MSG satellite data ( EUMETSAT) in the form of cloud index (cloud transmittance). The cloud index is derived by relating irradiance recorded by the satellite in four spectral channels and surface albedo to the cloud optical properties. In Solargis, the modified calculation scheme Heliosat-2 has been adopted to retrieve cloud optical properties from the satellite data. A number of improvements have been introduced to better cope with specific situations such as snow, ice, or high albedo areas (arid zones and deserts), and also with complex terrain. In Solargis, the new generation aerosol data set representing Atmospheric Optical Depth (AOD) is used. This data set is developed and regularly updated by MACC project ( ECMWF) [8]). Important feature of this AOD data set is that it captures daily variability of aerosols and allows simulating more precisely the events with extreme atmospheric load of aerosol particles [9]. Thus it reduces uncertainty of instantaneous estimates of GHI and allows for improved distribution of irradiance values. It is to be noted that coverage of high frequency (daily) aerosol data is limited to the period from 2003 onwards; the remaining years (1994 to 2002) are represented in the calculation only by monthly long-term averages. Water vapour is also highly variable in space and time, but it has lower impact on the values of solar radiation, compared to aerosols. The daily GFS and CFSR values ( NOAA NCEP) are used in Solargis, thus representing the daily variability from 1994 to the present. Ozone absorbs solar radiation at wavelengths shorter than 0.3 µm, thus having negligible influence on the broadband solar radiation. Diffuse irradiance for tilted surfaces is calculated by Perez model [11]. Primary parameters are Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI). All the other data are derived from these two quantities Solargis page 13 of 54

14 Tab. 1: Input data used in the Solargis model Solargis data input Source of primary data Time coverage Original time step Approx. grid resolution Cloud index Atmospheric Optical Depth (aerosols) Water vapour Elevation and horizon Meteosat MFG Meteosat MSG (EUMETSAT) MACC (ECMWF) CFSR/GFS (NOAA) SRTM-3 (SRTM) 1994 to to minutes 15 minutes 2003 to hours (monthly averages before 2003) 3.0 to 3.5 km 125 km 1999 to and 3 hours 35 and 55 km m Solar data accuracy from Solargis has been compared with high-quality solar radiation measurements from more than 100 stations, and with AERONET data from 230 stations, worldwide. Quality indicators of GHI for the validation sites in South and Central Africa are presented in Tabs. 2 to 4. Bias measures a difference between Solargis value and the observation at the meteorological station. Absolute values of Bias are calculated for daytime hours only. Tab. 2: Selected validation sites in Africa (Source of validation data: BSRN, Eskom, UKZN Howard College Durban, Stellenbosch University, AMMA) Site name Country Latitude [º] Longitude [º] Altitude [m] Aggeneis South Africa De Aar South Africa Durban South Africa Paulputs South Africa Sonbesie South Africa Tellerie South Africa Upington South Africa Tamanrasset Algeria Agoufu Mali Bamba Mali Banizoumbou Niger Djougou Benin Ilorin Nigeria Tab. 3: Global Horizontal Irradiance quality indicators in Africa Global Horizontal Irradiance, Bias Root Mean Square Deviation, RMSD GHI [W/m 2 ] [%] Hourly [%] Daily [%] Monthly [%] De Aar Durban Sonbesie Tellerie Tamanrasset Agoufu Bamba Banizoumbou Djougou Ilorin Solargis page 14 of 54

15 Tab. 4: Direct Normal Irradiance quality indicators in Africa Direct Normal Irradiance, DNI Bias Root Mean Square Deviation, RMSD [W/m 2 ] [%] Hourly [%] Daily [%] Monthly [%] Aggeneis De Aar Durban Paulputs Sonbesie Upington Tamanrasset The IEA SHC Task 36 data inter-comparison has identified Solargis as the best quality solar database on the market [12]. Additional information can be found in [13, 14]. Further information about the data and methodology can be consulted at the links below: In Central Africa, typical uncertainty of yearly solar radiation summaries of raw Solargis data is as follows: Global Horizontal Irradiation ±5.0% Global Tilted Irradiation for fixed PV ±5.5% Direct Normal Irradiation ±8.0% In more complex geographies, uncertainty of yearly GHI and GTI can be higher, especially in regions where aerosol content is high and dynamically changing, along the coast, in mountains and urbanized and industrialized areas. The Solargis data in this report have not been adapted, for the developmental site, due to the missing ground measurements. Site adaptation of Solargis data with local measurements has a potential for reduction of uncertainty - by about 2% to 2.5% for GHI. Therefore it is recommended to start measuring solar resource by a professional service at the site Solargis page 15 of 54

16 3.2 Meteorological data The meteo data stored in Solargis database are calculated from two principal data sources. Solargis algorithms and Digital Elevation Model SRTM-30 have been used in the data post-processing. The following are the features of the Solargis meteo database: Sources of primary data (both are copyright of NOAA NCEP): o CFSR (Climate Forecast System Reanalysis), years 1994 to 2009 o GFS (Global Forecast System), years 2010 to 2013 Parameters available: o Air temperature at 2 metres (dry bulb temperature), TEMP [ C] o Relative humidity, RH [%] o Wind speed at 10 metres, WS [m/s 2 ] o Wind direction, WD [ ] o Atmospheric pressure, AP [hpa] o Precipitation [mm] Original temporal resolution of 1 hour (CFSR) and 3 hours (GFS) is interpolated and harmonised to the time step of 15 minutes Original spatial resolution of the primary parameters is 35 km (CFSR) and 55 km (GFS). Both data resolutions are post-processed and recalculated to the spatial resolution of 1 km Period covered in Solargis by meteo parameters: 01/1994 to the present time (19+ years). Important note: meteo parameters are derived from the numerical weather model outputs (GFS and CFSR) and they have lower spatial and temporal resolution. Thus they do not represent the same accuracy as the solar resource data. Especially wind, relative humidity and precipitation data have higher uncertainty, and they provide only overview information for solar energy projects. Thus local microclimate of the site may deviate from the values derived from the Solargis global database. Data from CFSR model are considered as more accurate than data from GFS model. The validation procedure was carried out by comparison of modelled data with ground-measured data for meteo stations in the region (sourced from NOAA NCDC) for a time period 2007 to Validation The accuracy of meteorological models depends on the input data. Being a mathematical representation of dynamic processes the models are based on a set of partial differential equations, solution of which strongly depends on initial and boundary conditions. The initialisation parameters come from meteo measurements at different levels of atmosphere. The accuracy in the lowest layer of the atmosphere (2 m for air temperature, and humidity, 10 m for wind speed and wind direction) depends on spatial distribution and quality of measurements from the meteo observation networks. Following, original outputs from the meteo models are validated using the data from selected meteorological stations in Africa (Tab. 5). In general, meteo data from the meteo models represent larger area, they are smoothed and therefore they are not capable to represent accurately the local microclimate. Visual verification of the performance of the GFS and CSFR models is shown in scatterplots for air temperature, relative humidity and wind speed using an example of Kigali Airport. Tab. 5: Meteo stations considered in the validation of GFS and CFSR model outputs Meteo station (airport) Data source Latitude [º] Longitude [º] Elevation [m a.s.l.] Kigali Airport NOAA NCDC Nyeri NOAA NCDC Nairobi Kenyatta Airport NOAA NCDC Embu NOAA NCDC Meru NOAA NCDC Eldoret Airport NOAA NCDC Solargis page 16 of 54

17 Energy Yield Assessment of ******* kwp photovoltaic power plant *******, *******. Air temperature at 2 metres The air temperature at 2 m data is calculated from the GFS data (2010 to 2012) and from the CFSR data (1994 to 2009) by the Solargis algorithms and Digital Elevation Model SRTM-30. Original time resolution is 1 hour (CFSR) and 3 hours (GFS), spatial resolution is recalculated to 1 km. Considering spatial and time interpolation, for instantaneous hourly values the deviation of modelled values to the ground observations can reach several degrees. The comparison of modelled air temperature with ground measurements in the region is summarized in Tab. 6 and Figs. 6 and 7. The results exhibit good correlation between measured and modelled temperature. The biases in minimum night-time and maximum daytime temperature ( Bias min and Bias max ) are also presented in the table. Tab. 6: Air temperature at 2 m: accuracy indicators of the model outputs [ºC]. CFSR model (2007 to 2009) Meteo station RMSD RMSD RMSD Bias hourly daily monthly mean GFS model (2010 to 2012) Bias min Bias max RMSD RMSD RMSD Bias hourly daily monthly mean Bias min Bias max Kigali Airport Nyeri Nairobi Kenyatta Embu Meru Eldoret Airport Fig. 6: Air Temperature at 2 m at Kigali Airport meteo station for the period 2007 to Agreement between measured values (horizontal axis) and the values derived from the GFS/CFSR models (vertical axis) is shown. Source: NOAA 2016 Solargis page 17 of 54

18 Fig. 7: Air temperature at 2 m Kigali Airport meteo station. for CFSR (red colour) and GFS (green colour). Measured values (black colour, source NOAA) and the values derived from the GFS/CFSR models (source NOAA). Variability of the modelled data in Fig 7 matches variability in the measurements. However, CFSR and GFS data represent larger area, they are smoothed and therefore they are not always capable to represent values of the local microclimate, mainly the night minima. Relative humidity Relative humidity for a period is calculated from the humidity, air pressure and air temperature parameters derived from CFSR model. For a period 2010 to 2012 the relative humidity is taken directly from the GFS database. Original time resolution is 1 hour for CFSR and 3 hours for GFS. The indirect calculation of relative humidity for the CFSR period may result in slightly higher deviations especially for the night values. The results of comparison of the simulated relative humidity with on-site ground measurements are summarized in Tab. 7 and Figs. 8 and 9. Tab. 7: Relative humidity: quality indicators of the model outputs [%]. CFSR model (2007 to 2009) GFS model (2010 to 2012) Meteo station RMSD hourly RMSD daily RMSD monthly Bias mean Bias min Bias max RMSD hourly RMSD daily RMSD monthly Bias mean Bias min Bias max Kigali Airport Nyeri Nairobi Kenyatta Embu Meru Eldoret Airport Solargis page 18 of 54

19 Energy Yield Assessment of ******* kwp photovoltaic power plant *******, *******. Fig. 8: Relative humidity at 2 m at Kigali Airport meteo station. for the period 2007 to Agreement between measured values (horizontal axis) and the values derived from the GFS/CFSR models (vertical axis) is shown. Source: NOAA Fig. 9: Relative humidity at 2 m at Kigali Airport meteo station. for CFSR (red colour) and GFS (green colour) Measured values (black colour, source NOAA) and the values derived from the GFS/CFSR models (source NOAA) Solargis page 19 of 54

20 Wind speed Wind speed is calculated from the CFSR and GFS databases, from 10 m wind u- and v- components. The original 3 hourly values (in case of GFS database) are interpolated by nearest neighbour method to hourly values. The results of comparison of modelled wind speed with on-site ground measurements are summarized in Tab. 7 and Figs. 10 and 11. Wind speed data from both meteorological models have high uncertainty and can be only considered as indicative. Tab. 8: Wind speed: quality indicators of the model outputs [m/s]. CFSR model (2007 to 2009) GFS model (2010 to 2012) Meteo station RMSD hourly RMSD daily RMSD monthly Bias mean Bias min Bias max RMSD hourly RMSD daily RMSD monthly Bias mean Bias min Bias max Kigali Airport Nyeri Nairobi Kenyatta Embu Meru Eldoret Airport Fig. 10: Wind speed at 10 m at Kigali Airport meteo station. for the period 2007 to Comparison of the measured values (horizontal axis) and the values derived from the CFSR/GFS models (vertical axis) is shown. Source: NOAA 2016 Solargis page 20 of 54

21 Energy Yield Assessment of ******* kwp photovoltaic power plant *******, *******. Fig. 11: Wind speed at 10 m at Kigali Airport meteo station for CFSR (red colour) and GFS (green colour). Measured values (black colour, source NOAA) and the values derived from the GFS/CFSR models (source NOAA). Precipitation *********. Fig. 12: Precipitation at *********meteo station for period Comparison of CFSR (red colour) and measured values (dark blue colour, source NOAA) 2016 Solargis page 21 of 54

22 4 SOLARGIS PV SIMULATION METHODS 4.1 PV simulation assumptions and uncertainties Photovoltaic power production has been calculated using numerical models developed or implemented by Solargis. Simulations of the power plant and its components are carried out by Solargis PV model, which uses 15 and 30-minute time series of solar radiation and air temperature data representing a period of 19 years (1994 to 2012). In PV simulation, the energy losses can be classified in two groups: Static: module surface pollution, losses in cables, and mismatch between PV modules Dynamic: these losses depend on the irradiance/temperature conditions, which change over the day and over the seasons. More about the simulation procedure including background publications can be consulted at Step 1: Global irradiation on the tilted surface of PV modules Global irradiation impinging on a tilted plane of PV modules G INCLINED (GTI) is calculated from Global Horizontal Irradiance (G h), Direct Normal Irradiance (DNI), terrain albedo, and instantaneous sun position within 15 minutes time interval (S POS): G INCLINED=f DIFF (G h, DNI, Albedo, S POS) Perez model is used [10]. Global irradiation received by North-facing PV modules tilted at angle 10 is estimated to 1851 kwh/m 2 (Chapter 7.1). Based on the expert evaluation and data validation, the uncertainty of this estimate is ±5.5%. Step 2: Losses due to terrain shading Shading by terrain features is calculated by disaggregation using SRTM-3 DEM and horizon height. Shading of local features such as from nearby building, structures or vegetation is not relevant: G INCLINED-SHAD = f SHAD(G INCLINED, S POS, Horizon) Method by Ruiz-Arias et al [12] is used. For open space systems the uncertainty of this estimate is very low due to high resolution of DEM (~80 m). For urban areas, where buildings mainly influence shading, an additional analysis must be undertaken to consider the detailed surface model. For the analysed location there is very low surrounding terrain horizon with virtually no effect on the availability of solar radiation. The loss caused by far horizon shading is estimated on the level of 0.1%. The uncertainty of this estimate is ±0.1%. Step 3: Losses due to angular reflectivity The resulting irradiation is subject to losses from angular reflectivity (angle of incidence effects) on the surface of PV modules, and the magnitude of effects depends on relative position of the sun and plane of the module: G ANGULAR = f ANGULAR(G INCLINED-SHAD, S POS) The model by Martin and Ruiz is used [13]. The accuracy of calculations of angular reflectivity losses depends on cleanness and specific properties of the module surface (antireflection coating, texture, etc.). In this study a typical low iron float glass and average effect of dirt and dust are assumed. The modelled losses of solar radiation due to reflectivity of module surface are 3.3%. The uncertainty of this step is below ±0.5% Solargis page 22 of 54

23 Step 4: Losses due to frost and snow Considering the climatic conditions at the ********* site no losses due to frost and snow are considered. Step 5: Losses due to dirt and soiling Losses of solar radiation at the level of surface of PV modules depend mainly on the environmental factors and cleaning of the PV modules surface during the power plant lifetime. The longterm effects are not satisfactorily known. In this study the losses due to these effects were estimated to be 3.0%. The uncertainty has been set to ±1.5%. Step 6: Losses due to performance of PV modules outside of STC conditions Global irradiation (G ANGULAR) reaching modules of the given type (M TYPE) along with the air temperature (T AIR) are the input parameters to the PV performance model: PV DC = f PV(G ANGULAR, T AIR, M TYPE) The conversion efficiency is non-linear and depends on the distribution of both the values of irradiance and temperature. Relative change of produced energy from this stage of conversion depends on module technology and mounting type. Typically the losses at this step are higher for crystalline silicon modules than thin films due to higher negative thermal power coefficient of crystalline silicon and better behaviour of thin film at low light levels (different spectral sensitivity). The approach by King et al is used in the modelling of this physical process [14], further developed by Huld et al [15, 16] and very recently published in [17, 18]. The losses at this stage of energy conversion for polycrystalline modules are 10.6%. The uncertainty of this estimate is about ±3.0%. Step 7: Losses by inter-row (near-distance) shading In this study the relative spacing of rows of 1.7 is assumed for fixed inclined modules. Such spacing ensures negligible near-distance shading losses less than 0.2% with uncertainty below ±0.1% (Chapter 4.2). Crystalline silicon modules are sensitive to partial shading, and losses depend on the topology of module interconnections. Step 8: Power tolerance of modules From the module power tolerance result bigger or smaller mismatch losses of the modules connected in strings. If modules with higher power tolerance are connected in series, the losses are higher. The power tolerance of modules increases uncertainty of power output estimation. In this study the uncertainty was set to ±3.0% as defined in modules datasheet. Step 9: Mismatch and DC cabling losses Mismatch due to different MPP operating point of modules connected into an inverter and heat losses in the interconnections and cables depend on the design and components of the PV power plant. If classification of modules is considered according to the measurements of the nominal conversion efficiency performed by the manufacturer, grouping the modules from the same class is an effective measure to minimize the mismatch losses of the modules connected within one string [21]. Overall DC losses from all these effects are estimated to be 0.9% (0.4% DC cabling and 0.5% mismatch losses) with uncertainty of ±0.7%. Step 10: Inverter losses from conversion of DC to AC Although power efficiency of inverter is high, each type of inverter has its own efficiency function (dependence of the inverter efficiency on the inverter load and inverter input voltage) f INVERTER. PV AC= f INVERTER (PV DC, DC LOSS) Losses due to performance of inverters can be estimated using inverter power curve with 30-minute pairs of DC data or using the less accurate pre-calculated value given by the manufacturer and representing the weighted average efficiency (CEC, California Energy Commission). The CEC efficiency of the inverters, provided by the manufacturer, is used in this simulation. The average losses at this stage are considered at the level of 2.0% (CEC 98.0%) with uncertainty of estimate of ±0.5% Solargis page 23 of 54

24 Step 11: AC and transformer losses The inverter output is connected to the grid through the transformer. The additional AC side losses reduce the final system output by a combination of cabling (AC LOSS) and transformer losses (TR LOSSES): PV OUT=f AC(AC LOSS, TR LOSSES) The combined AC losses are estimated to 2.2% (1.0% for transformers and 1.2% AC cabling) with ±0.5% uncertainty. Step 12: Technical availability This empirical parameter quantifies electricity losses incurred by shutdown of a PV power plant due to maintenance or failures. In the analysis of theoretical production, the technical availability of 99% is considered with ±0.7% uncertainty. Step 13: Long term degradation Many years of operation of PV power plants is the ultimate test for all components, placing the module encapsulants, cell interconnections, junction boxes, cabling, and inverters under stress during the weather cycles [19]. Currently produced modules and system components represent a mature technology, and low degradation can be assumed. Manufacturer of modules in this study provides a limited power warranty for 25 years. Although it has been observed in different studies that performance degradation rate of PV modules is higher at the beginning of the exposure (initial degradation), and then stabilizes at a lower level, an assumption of linear annual degradation rate is good approximation for the payback time of the investment costs. Based on existing in-field experiences of commercial projects the long term annual performance degradation of well-manufactured modules may be close to value of 0.8% for the first year and 0.5% for the next ones and these values are used in this study of long-term degradation. It has to be noted that the uncertainty for the estimate of the degradation rate PV modules performance in tropical countries is not satisfactorily studied. Simulations were followed according to expert knowledge, monitoring results and recommendations of [28] Solargis page 24 of 54

25 4.2 Inter-row shading of fixed modules and related electricity losses Inter-row shading of fixed mounted PV modules, mounted on the structures, was simulated taking into account sun geometry, varying terrain properties and solar radiation data. The terminology used below is explained in Fig. 13. Absolute row spacing (x 3) is the distance between the lowest parts of the two successive mounting structures (rows with modules). Relative row spacing is defined as a ratio of absolute row spacing (x 3) and the table width (x 2). For the analysed power plant the relative row spacing of 1.7 was assumed. Fig. 13: Inter-row shading - description of terminology Considering relative row spacing of fixed mounted PV modules at the ********* site as 1.7, the minimum sun height on 21 June at noon is approx Depending on the sun height during different seasons of the year there will be different shading losses. Seasonal variability of near-shading losses in this site is very low (Fig. 14). Fig. 14: Patterns of electrical losses in PV modules mounted on a table. Three plots represent energy loss patterns in December, June and cumulative losses over the whole year in different parts of the table surface for the modules mounted in part located on the northern slope Solargis page 25 of 54

26 The estimation of the impact of the modules arrangement on the electricity yield of partially shadowed PV modules is not a trivial task. A high number of factors need to be addressed to estimate the magnitude of these effects, such as: Energy yield reduction in modules themselves, the mismatch between non-uniformly shaded modules, Characteristics of photovoltaic inverter, Shape of particular shading pattern and its orientation in relation to electrical connection within the module the orientation of strings. The silicon-wafer based modules are very sensitive to partial shading. The loss in performance at partially shaded c-si photovoltaic modules in the rows can be nearly proportional to the loss at the most shaded PV cell for the cells connected in series within the module, if proper counter-measures are not applied [20]. As a consequence the cells near the ground can reduce the performance of the whole module considerably when shaded. The standard technique to counterbalance the effect of shading is utilization of the bypass diodes incorporated within module structure and proper topology of modules interconnections. At the site, terrain is nearly flat, without significant shading from the long-distance (terrain) horizon what allows for uniform row spacing for the whole power plant. For the period of the whole year, the inter-row shading losses are estimated at the level about 0.2% Solargis page 26 of 54

27 5 AIR TEMPERATURE, WIND SPEED AND PRECIPITATION Tab. 9 shows monthly characteristics of selected meteorological parameters; they represent diurnal statistics, i.e. they are calculated over 24-hour cycle. The meteo data are derived from GFS and CFSR meteorological models (see Chapter 3.2) by Solargis post-processing, and they represent regional climate patterns rather than local microclimate. This means that extreme values may be smoothed and not always well represented in the below-shown statistics. The meteo parameters, especially precipitation, have higher uncertainty compared to solar parameters. Tab. 9: Monthly statistics of air temperature at 2 m, relative humidity, wind speed at 10 m and precipitation (period 1994 to 2012) Air temperature at 2 m [ C] Relative humidity Average wind speed Precipitation* Average Minimum Maximum [%] at 10 m [m/s] [mm] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YEAR * The precipitation data is calculated for the period 1994 to 2009 (CFSR model) Uncertainty of annual average of air temperature at 2 meters (TEMP) is approximately ±1.0. Fig. 15 shows hourly statistics of wind speed at 10 metres as it is derived from the meteorological models for the region. The prevailing wind speed is shown in a duration curve. Fig. 15: Duration curve of wind speed at 10 m in ********* 2016 Solargis page 27 of 54

28 For air temperature at 2 metres, monthly averages of minimum and maximum daily values show their typical daily amplitude in each month (Fig. 16). Fig. 16: Air temperature at 2 meters - monthly average, and average minimum and maximum values Fig. 17: Precipitation - monthly average, and average minimum and maximum values (period ) 2016 Solargis page 28 of 54

29 6 GLOBAL AND DIFFUSE HORIZONTAL IRRADIATION 6.1 Monthly statistics of GHI and DIF Tab. 10 shows long-term average of monthly and daily summaries of Global Horizontal Irradiation (GHI) and Diffuse Horizontal Irradiation (DIF). GHI minimum and maximum monthly summaries are identified for a period 1994 to Important note: monthly values of GHI minimum do not sum up to the annual minimum; therefore the annual minimum is marked by blue colour. Tab. 10: Monthly statistics of Global Horizontal Irradiation (GHI) and Diffuse Horizontal Irradiation (DIF). Daily GHI and DIF average Monthly GHI average, minimum and maximum GHI DIF DIF/GHI ratio Average Yearly share Minimum Maximum [kwh/m 2 ] [kwh/m 2 ] [%] [kwh/m 2 ] [%] [kwh/m 2 ] [%] [kwh/m 2 ] [%] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YEAR Direct horizonal average 8 Diffuse horizonal average Diffuse horizonal av horizonal av Global Global horizontal Min minimum/maximum Max ntal minimum/maximum Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Daily sum of global horizontal irradiation [kwh/m 2 ] 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fig. 18: Global Horizontal Irradiation and its direct and diffuse components: monthly statistics of daily sums Solargis page 29 of 54

30 Fig. 18 shows long-term averages of daily sums for Global Horizontal Irradiation (GHI) and its diffuse and direct components for each month. Minimum and maximum monthly averages of GHI daily sums are identified in the data set representing years 1994 to Tab. 11 shows variability of monthly and annual summaries of GHI in a period 1994 to The bottom row shows long-term averaged values. This table shows year-by-year weather fluctuation (interannual variability). Tab. 11: Global Horizontal Irradiation: monthly and yearly summaries. Global and Diffuse Horizontal Irradiation summary of yearly values: Long-term yearly average: 1851 kwh/m 2 (average daily sum 5.07 kwh/m 2 ) Minimum year (1997): 1783 kwh/m 2 (average daily sum 4.88 kwh/m 2 ) Maximum year (2010): 1942 kwh/m 2 (average daily sum 5.32 kwh/m 2 ) Diffuse to global ratio (DIF/GHI): 53% Uncertainty of annual GHI ±5.0%* *Note: more information about uncertainty can be consulted in Chapter Solargis page 30 of 54

31 6.2 Comparing GHI data with other data sources Global Horizontal Irradiation is calculated from Solargis data (Chapter 3.1). In this Chapter, the annual Solargis average is compared to five other data sources with different temporal and spatial resolution and different time coverage (Tab. 12). Comparison of other databases with Solargis shows discrepancies, which are determined by their inherent characteristics, namely by: Applied model approaches; Type and quality of input data; Time representation; Spatial and temporal resolution of the output database. In general, the databases relying on the interpolation of ground-measured data, such as Meteonorm [22] are unreliable in regions with sparse spatial coverage of meteorological stations. The global database NASA SSE [24] is computed by empirical models from satellite and atmospheric data with very coarse spatial resolution, which results in smooth and regionally unreliable climate patterns. SWERA/NREL database has medium spatial resolution and is computed by CSR model by NREL [25], thus only showing overview perspective. Satellitebased PVGIS-CMSAF database is not updated regularly and the data are available only as long-term averages [26]. Implementation of all these databases is static (data for the recent history are not available), and they cannot be site-adapted using local measurements [27]. In general, higher uncertainties may be expected when comparing data representing different decades due to changes in air pollution, land use and complex climate cycles. In addition, ground observations from the last decades may have been measured with instruments of lower quality and measuring standards. The modern satellite-based databases, such as Solargis, have high spatial and temporal resolution, they are routinely updated, and they are considered as the mainstream source of solar information for solar energy applications - for prefeasibility studies, project optimisation, financing, and for operation and management of solar power plants. Solargis database shows its high reliability (Chapter 3.1). The Solargis data in this report have not been adapted due to the missing ground measurements. In this context, high quality ground measurements play an important role for validation and site-adaptation of satellitebased data time series. It is recommended to adapt Solargis data by local DNI and GHI measurements once they are available. Tab. 12: Comparing long-term yearly average of GHI from different data sources. Database Data source Data spatial resolution Time resolution of available data Period GHI [kwh/m 2 ] NASA SSE Satellite + model 110 km x 100 km Long-term monthly Meteonorm Ground + satellite Interpolation Long-term monthly PVGIS-HC1 satellite 28 km x 28 km Long-term monthly PVGIS/CMSAF satellite 4 km x 4 km monthly (hourly) SWERA/NREL model 40 km x 40 km Long-term monthly Solargis Meteosat MFG and MSG satellites 3 km x 4 km 30 minutes Standard deviation of GHI annual values 2.7% Schematic assessment of GHI uncertainty (80% confidence) ±3.3% Expected Solargis GHI uncertainty (80% confidence) ±5.0% 2016 Solargis page 31 of 54

32 In a simplified way, the GHI uncertainty can be estimated from comparing the variability of the data sets by calculating the standard deviation (Tab. 12), which is still applied by some consultants. In case of the ********* site, this schematic approach results in uncertainty estimate of approx. ±3.3%. Based on the analysed accuracy of Solargis data (Chapter 3.1), the conservative expert-calculated uncertainty for Global Horizontal Irradiation is estimated to ±5.0% in this report (Tab. 4) Solargis page 32 of 54

33 7 GLOBAL TILTED IRRADIATION 7.1 Monthly, daily and hourly GTI statistics Tab. 13 shows long-term average of monthly and daily summaries of Global Tilted Irradiation (GTI) and minimum and maximum monthly summaries for a period 1994 to 2012 for the ********* site. GTI is calculated for fixed-mounted PV modules North-oriented and tilted at 10. Fig. 19 shows long-term averages of daily GTI sums for each month, as well as minimum and maximum monthly averages of GTI daily sums for years 1994 to Tab. 13: Monthly statistics of Global Tilted Irradiation (GTI) for North-facing PV modules, tilt 10. Daily GTI Average Average Yearly share Monthly GTI Minimum Maximum [kwh/m 2 ] [kwh/m 2 ] [%] [kwh/m 2 ] [%] [kwh/m 2 ] [%] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YEAR Global tilted average Global tilted minimum/maximum 8 Jan Global tilted average Feb Mar Global tilted minimum/maximum -3 Apr May Jun Jul Aug Sep Oct Nov Dec Daily sum of global tilted irradiation [kwh/m 2 ] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fig. 19: Global Tilted Irradiation: monthly statistics of daily sums. North-facing PV modules with tilt 10 are assumed Solargis page 33 of 54

34 Global Tilted Irradiation (GTI) for North-facing PV modules, tilt 10 summary of yearly values: Long-term yearly average: 1851 kwh/m 2 (average daily sum 5.07 kwh/m 2 ) Minimum (1997): 1785 kwh/m 2 (average daily sum 4.89 kwh/m 2 ) Maximum (2010): 1942 kwh/m 2 (average daily sum 5.32 kwh/m 2 ) Uncertainty of annual GTI: ±5.5%* * Note: more information about uncertainty can be consulted in Chapter Solargis page 34 of 54

35 7.2 Comparing different azimuth and inclination of PV modules The theoretical optimum module azimuth and inclination for fixed mounting was calculated, at which the annual solar radiation is at maximum (Fig. 20). The optimisation was carried out using 15 and 30-minute values of Global Tilted Irradiance. The optimum inclination of c-si type modules is almost horizontal, tilt about 6, azimuth 45 (North-East) but considering the flat shape of the function, the useful range of optimum angles (the range where the annual output is negligibly affected by deviation from optimum) is much wider and this parameter is not critical. The modules oriented towards North with tilt of 10 will have lower annual yield by approximately 0.2% compared to optimum configuration. The shift of the optimum angle towards the East results from the asymmetry of global solar radiation around solar noon caused by different weather patterns in the morning and afternoon (more cloudy sky in the afternoon) and average temperature difference. The running temperature of the modules is lower in the morning than afternoon by few degrees. Since energy production strongly depends on temperature (negative dependence), small tilt of 10 of the PV modules with east azimuth helps in minimising running temperature of the module throughout the day and maximising the energy yield. Horizontal position is not recommended also because of dirt accumulation on the modules surface. Even small tilt should help with cleaning the modules both natural way (caused by precipitation) and periodical cleaning of the power plant. Fig. 20: Potential loss of PV electricity assuming that PV modules deviate from a theoretical optimum inclination and azimuth Solargis page 35 of 54

36 8 THEORETICAL PV POWER PRODUCTION 8.1 Estimation of system losses and performance ratio The annual and monthly power output from the photovoltaic power plant is calculated from 19 years time series of solar irradiance and temperature. The magnitude and uncertainty of the conversion losses is explained in Chapter 4.1. Option of fixed PV modules inclined at 10, azimuth 0 (North) is assumed in all calculations below. Technical availability is an empirical parameter that considers occasional energy losses due to complete shutdown of the power plant, which may occur during accidental failures, grid blackouts and maintenance operations. Occasionally, shutdown may be initiated also by the electrical utility. In reference to projects installed in Europe, 99% availability (i.e. annual energy losses 1%) can be considered as a "good practice". Validity of this assumption strongly depends on the operation routines, maintenance contracts, grid stability and in less favourable conditions it may be considered as too optimistic. Tab. 14 shows breakdown of energy losses, at the level of annual summary, providing an insight into the power plant performance, without considering efficiency degradation of PV modules. It must be stressed that blue rows in the tables refer to unit losses of Global Tilted Irradiation expressed in kwh/m 2, while the rest are electrical losses incurred in the system expressed in kwh/kwp. Such concept simplifies presentation of the results. Tab. 14: Conversion stages, losses, and performance ratio at the level of PV system Losses of solar radiation are blue [kwh/m 2 ]; electrical losses [kwh/kwp] in the PV system are black. Energy conversion stage and related losses Energy output GTI [kwh/m 2 ] PVOUT [kwh/kwp] [kwh/m 2 ] [kwh/kwp] Energy loss Uncertainty [%] [±%] Performance ratio Partial [%] Cumulative [%] Global irradiation - inclined plane (input) Terrain shading Angular reflectivity Snow, frost Dirt, dust and soiling Conversion of irradiation to DC in the modules Electrical losses due inter-row shading Power tolerance at PV modules Mismatch and cabling in DC section Inverters (DC/AC conversion) Transformer and AC cabling losses Total system performance Technical availability Total system performance considering technical availability Capacity factor 16.6% 2016 Solargis page 36 of 54

37 Specific theoretical energy output of the PV power plant is 1455 kwh/kwp with performance ratio of 78.6% and capacity factor of 16.6%. Combined uncertainty of this estimate is ±7.2%. This value constitutes the uncertainty of the GTI estimate (±5.5%) and the uncertainty in the energy conversion steps of the PV system (which totals to ±4.7%). It is important to note that most of energy losses are variable in time; they are determined by a season of the year, time of a day, weather conditions, and other effects. Losses due to atmospheric pollution (aerosols, humidity, dust) may have seasonal pattern, and in a short-term they may change rapidly, occasionally having strong impact. Soiling of modules due to permanent presence of dirt may affect the power plant performance in the longterm. Attentive operation and maintenance of the power plant may partially prevent losses in Steps 5 and 9, as described in Chapter Solargis page 37 of 54

38 8.2 Monthly statistics of theoretical PV power production Fig. 21 and Tab. 15 show theoretical solar electricity production and performance ratio from the PV power plant for each month. These values do not consider performance degradation of PV modules during their lifetime. Tab. 16 shows monthly values of specific electricity yield in kwh per 1 kwp. Average electricity production (at P50 probability) is complemented with absolute minimum and maximum monthly sums, which have been identified in the time series of Solargis data within the last 19 years. In Fig. 24 and Tab. 15, for demonstrating the extreme power production over this historical period, monthly PV power production is shown, monthly minima and maxima represent extremes found for individual months in 19 years period. Two extreme years are 1997 and 2010 (see Tab. 15 and Fig. 24). DaysInMon th Daily AC power output [kwh/kwp] 8 7 Specific PV out No shading Daily specific No shading Loss by inter-row shading Loss by inter-row shading AC power output Minimum/Maximum AC power AC power output PR Min Max Minimum/M aximum AC power Performance Ratio Perfornamce Ratio [%] 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 60 Fig. 21: Specific PV power production per 1 kwp (kwh/kwp) and performance ratio. The average theoretical PV power production (at P50) is estimated at 1455 kwh/kwp per year with performance ratio 78.6% and capacity factor of 16.6%. Tab. 15 shows also the share of monthly PV production relative to the yearly sum. In blue numbers the total production of the power plant in MWh is shown, assuming installed capacity kwp. The values in the table are mathematically rounded Solargis page 38 of 54

39 Tab. 15: Monthly statistics of PV electricity production of PV power plant. Min and max values are calculated form the extreme months found in the 19-years data history. Daily production Monthly production Monthly Specific Specific Min Specific Max Specific Avg Share Total PR [kwh/kwp] [kwh/kwp] [kwh/kwp] [kwh/kwp] [%] [MWh] [%] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Important note related to Tab. 15: minimum/maximum monthly power production is calculated for months within the data history with lowest/highest solar radiation. Minimum/maximum annual power production is calculated for the most (2010) and least (1997) sunny years within the available history. Thus summary of minimum/maximum months does not match with minimum/maximum yearly statistics. Tab. 16 shows variability of monthly and annual summaries of PV specific power production in a historical period 1994 to The bottom row shows long-term averaged values. This table shows year-by-year weather fluctuation (interannual variability). Numbers may slightly differ compared to the previous tables, due to mathematical rounding. Tab. 16: PV power production: monthly and yearly summaries. Assuming North-facing PV modules, tilt Solargis page 39 of 54

40 Fig. 22 shows histograms of daily PV specific output summaries for each month as calculated for years 1994 to The distribution of daily values is not symmetric: median is drawn by the vertical line, and percentiles P 10, P 25, and P 75, and P 90 are displayed with dark grey and light grey colour bands, respectively. The percentiles P 10 and P 90 show 80% occurrence of daily values within each month and percentiles P 25 and P 75 show 50% occurrence. Fig. 22: Histograms of daily values of theoretical power production by month assuming North-facing PV modules and tilt Solargis page 40 of 54

41 Fig. 23 shows distribution of PV output hourly statistics for each month and identifies typical daily patterns of PV power generation. The graphs show average as well as median and percentiles P 10, P 25, and P 75, and P 90 as calculated from PV output time series over the period 1994 to The power production values do not consider performance degradation of the modules over time. Fig. 23: Hourly probability statistics of theoretical power production by month assuming North-facing PV modules, tilt 10. UTC+2 time is used Solargis page 41 of 54

42 Tab. 17 is complementary to Fig. 22, and shows yearly distribution of hourly PV power production averages. Tab. 17: Hourly averages of PV power output [W/m 2 ]. UTC+2 time is used 2016 Solargis page 42 of 54

43 8.3 Interannual variability of PV power output Weather changes in cycles and has also stochastic nature. Therefore annual solar radiation in each year can deviate from the long-term average in the range of few percent this applies also to air temperature). The estimation of the interannual variability of PV power production (PVOUT) below shows the magnitude of this change. The uncertainty of PVOUT prediction is highest if only one single year is considered, but when averaged for a longer period, weather oscillations even out and approximate to the long-term average. In this report, the interannual variability is calculated from the unbiased standard deviation stdev of PVOUT over 19 years, considering, in the long-term, the normal distribution of the annual sums for n years, where x i is any particular year and is longterm yearly average:!" =# ( $ & & ) Annual specific PV out[kwh/kwp] Yearfic PV Output Out range up Out range dn erage PV Out Average 1497 specific 1417PV Output Years 1455 Fig. 24: Annual specific PV power output for the plane of the modules in period 1994 to 2012 including average (black line) and standard deviation (colour band) [kwh/kwp] Tab. 18 shows an expectation of PVOUT values that is to be exceeded at P90 for a consecutive number of years. The variability (var n) for a number of years (n) is calculated from the unbiased standard deviation (stdev): "() = *+ The uncertainty uncert, which characterises 80% probability of occurrence, is calculated from the variability (var n), multiplying it with !) = "() The lower boundary (negative value) of uncertainty represents 90% probability of exceedance, and it is used for calculating the P90 value Solargis page 43 of 54

44 Tab. 18: Uncertainty from interannual variability and value of annual sum of PV power output to be exceeded with 90% probability in the period of 1 to 10 and 20 years. Years Variability [±%] Uncertainty P(90) [±%] Minimum specific PV output, P(90) [kwh/kwp] Tab. 18 shows consequences of interannual variability if PV power output for different number of consecutive years. Few examples how this information can be interpreted In any individual year, it is expected at 90% probability that annual PV power output exceeds value of 1406 kwh/kwp. In other words, it is expected that approximately once in a ten years the annual PV power output sum is lower than 1406 kwh/kwp. Within a period of three consecutive years, it is expected at P90 that average annual PV power output exceeds value of 1427 kwh/kwp; Within a period of ten years, it is expected at 90% confidence that average PV power output exceeds 1440 kwh/kwp; for 20 years this expectancy is 1444 kwh/kwp. It is to be noted that prediction of the future power production is based on the analysis of historical data. Future weather changes may include longterm weather cycles, man-induced effects or large volcanic eruptions, which may have slight impact on this prediction. Based on the existing scientific knowledge [28, 29], an effect of extreme volcano eruptions, with an emission of large amount of stratospheric aerosols, can be estimated on the example of Pinatubo event in 1991 (the second largest volcano eruption in 20 th century). It can be expected that in such a case, the annual PV power output in the affected year may decrease by 2% or more, compared to the longterm average Solargis page 44 of 54

45 9 UNCERTAINTY OF PV POWER PRODUCTION Here we summarize the integrated effect of all uncertainties and performance characteristics of the PV power plant, thus identifying the conservative scenario of energy production, or P90. We explicitly show a relative uncertainty of the power production estimate in the first year and for a period of 20 years. All uncertainties are presented at P90, in other words we estimate annual electricity production that should be exceeded with 90% probability. Two components of the uncertainty are combined in PV electricity simulation: Uncertainty of the estimate of the PV electricity output (Tab. 14): the combined uncertainty of the PV power plant performance is ±7.2%; this value aggregates the uncertainty of the GTI (±5.5%) and the combined uncertainty of PV energy conversion steps (±4.7%). Uncertainty due to interannual variability of PV electricity production as a result of changing solar radiation and temperature: annual electrical output from a PV power plant in a particular year at P90 is ±3.3%. This uncertainty for a period of 20 years decreases to about ±0.7% (Tab. 18). Tab. 19 presents calculation of P90 probability of exceedance considering combination of both uncertainty of the PV estimate and uncertainty due to interannual variability. The P90 values, in Tab. 19, show the minimum expected power production with 90% probability of exceedance at the start-up, i.e. without considering the PV module degradation over the lifetime of PV power plant. The values in the column combined PV estimate uncertainty range from ±11.0% to ±13.6%, which is a result of monthly uncertainty of the GTI estimate (±5.5% annually, Chapter 7.1), PV model uncertainty of ±4.7% (Chapter 8.1) and interannual variability (Chapter 8.3). Tab. 19: Combined uncertainty and P50 and P90 monthly and yearly statistics of PV power plant Production Uncertainty at P90 Production Specific PV Estimate PV interannual Combined Specific Total at P50 uncertainty variability P90 P90 [kwh/kwp] [%] [%] [%] [kwh/kwp] [MWh] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Year Solargis page 45 of 54

46 10 PV ELECTRICITY PRODUCTION OVER 20 YEARS Theoretical average (P50) specific electricity yield, assuming 99% technical availability, is 1455 kwh/kwp (Chapters 8.1 and 8.2). For the unit power of ********* kwp power plant this represents an average yield of GWh respectively per year under theoretical assumption that there is no reduction of the PV module conversion efficiency. For prediction of electricity production of the PV power plant for a period of 20 years degradation (ageing) of nominal power (conversion efficiency) of PV modules has to be assumed. Since not only the modules are subject to ageing, the overall performance of the power plant depends also on cabling and performance of inverters during the planned 20 years respectively. Another possible source of uncertainty is non-uniform degradation of individual modules which results in higher mismatch losses. In the calculation below, a simplified assumption of annual linear degradation rate of 0.8% in the first year and 0.5% in the following years is considered (see Chapter 4.1, step 13). Taking into account uncertainty of the estimate, degradation rate, and uncertainty from interannual variability, which reduces in time (Chapter 9), a conservative scenario P90 for 20 years is calculated in Tab. 20. The first line shows uncertainty of PV estimate only, the rows for years 1 to 20 include also interannual variability. Tab. 20: Estimation of P50 and P90 yearly electricity production from the PV power plant assuming the lifecycle of 20 years End Combined Specific yield Expected yield PR Degradation Year of year uncertainty P50 P90 P50 P90 at P50 rate [± %] [kwh/kwp] [kwh/kwp] [MWh] [MWh] [%] [%] 0 Start Total Average Solargis page 46 of 54

47 Tabs. 21 and 22 below explicitly summarize the key information extracted from Tab. 20. At the end of the first year of the PV power plant operation, the average specific PV power production is estimated at 1443 kwh/kwp. Assuming all combined uncertainties at P90, a minimum specific production 1328 kwh/kwp can be expected with 90% confidence. Assuming period of 20 years of PV plant operation, the average yearly specific PV production is 1377 kwh/kwp. For the installed capacity of ********* kwp, the average total yield of the power plant is estimated to GWh per year. For combined P90 uncertainties, it can be expected that minimum specific production of 1277 kwh/kwp per year. Tab. 21: Average (P50) and minimum (P90) expected energy yield at the end of the first year of the operation of the PV power plant. Annual PV power production Uncertainty Combined Specific yield Total yield end of year 2014 [±%] uncertainty [±%] [kwh/kwp] [MWh] Average, best estimate at P P90 value considering uncertainty of the estimate P90 value considering also interannual variability in year Tab. 22: Average (P50) and minimum (P90) expected energy yield for a period of 20 years of the PV power plant operation. Annual PV power production Uncertainty Combined Specific yield Total yield over 20 years [±%] uncertainty [±%] [kwh/kwp] [MWh] Average, best estimate at P P90 value considering uncertainty of the estimate P90 value considering also interannual variability in 20 years Weather variability is estimated from the analysis of historical data, and this study does not take into account any prediction of man-induced climate change or extreme natural events Solargis page 47 of 54

48 11 CONCLUSIONS The ********* project has good potential of solar energy utilisation with stable electricity production during the year, only slightly influenced by seasonal weather changes (stable electricity production during the whole year). Fixed structures are robust, and not demanding for maintenance, and are utilised in the majority of projects all over the world. Since the power plant needs to be operational for many years the ease of service may become crucial, especially in remote areas. After the commissioning of the PV power plant, the behaviour of all components as well as natural and accelerated changes in their performance can only be better understood by implementation of the active monitoring and regular performance assessment. This service provided should be supported by numerical analysis of the monitored production data with simulations of the expected and reference performance numbers based on real-time satellite and meteorological observations. This approach ensures sustainable bankability of the information, enables fast identification of failures, and supports operation, control, and maintenance. The computation for this report includes a set of complex procedures and occasional marginal inconsistencies between numbers could be found as a result of the mathematical rounding. The Solargis time series data in this report have not been locally adapted due to the missing ground measurements. It is recommended to start measuring solar resource by a professional service at the site. Such measurements may be used for site-adaptation of Solargis long term time series data used in this report and significantly reduce the overall uncertainty of PV production estimates Solargis page 48 of 54

49 12 LIST OF FIGURES Fig. 1: Detailed geographical position of the site... 9 Fig. 2: Geographical position of the site in the region Fig. 3: Annual sum of Global Horizontal Irradiation - position of the site (green circle) in the detailed solar map 10 Fig. 4: Astronomical and geographical situation Fig. 5: PV module layout of the ********* power plant Fig. 6: Air Temperature at 2 m at Kigali Airport meteo station Fig. 7: Air temperature at 2 m Kigali Airport meteo station Fig. 8: Relative humidity at 2 m at Kigali Airport meteo station Fig. 9: Relative humidity at 2 m at Kigali Airport meteo station Fig. 10: Wind speed at 10 m at Kigali Airport meteo station Fig. 11: Wind speed at 10 m at Kigali Airport meteo station Fig. 12: Precipitation at *********meteo station for period Fig. 13: Inter-row shading - description of terminology Fig. 14: Patterns of electrical losses in PV modules mounted on a table Fig. 15: Duration curve of wind speed at 10 m in ********* Fig. 16: Air temperature at 2 meters - monthly average, and average minimum and maximum values Fig. 17: Precipitation - monthly average, and average minimum and maximum values Fig. 18: Global Horizontal Irradiation and its direct and diffuse components: monthly statistics of daily sums Fig. 19: Global Tilted Irradiation: monthly statistics of daily sums Fig. 20: Potential loss of PV electricity Fig. 21: Specific PV power production per 1 kwp (kwh/kwp) and performance ratio Fig. 22: Histograms of daily values of theoretical power production by month Fig. 23: Hourly probability statistics of theoretical power production by month Fig. 24: Annual specific PV power output for the plane of the modules in period 1994 to Solargis page 49 of 54

50 13 LIST OF TABLES Tab. 1: Input data used in the Solargis model Tab. 2: Selected validation sites in Africa Tab. 3: Global Horizontal Irradiance quality indicators in Africa Tab. 4: Direct Normal Irradiance quality indicators in Africa Tab. 5: Meteo stations considered in the validation of GFS and CFSR model outputs Tab. 6: Air temperature at 2 m: accuracy indicators of the model outputs [ºC] Tab. 7: Relative humidity: quality indicators of the model outputs [%] Tab. 8: Wind speed: quality indicators of the model outputs [m/s] Tab. 9: Monthly statistics of air temperature at 2 m, relative humidity, wind speed at 10 m and precipitation 27 Tab. 10: Monthly statistics of Global Horizontal Irradiation (GHI) and Diffuse Horizontal Irradiation (DIF).. 29 Tab. 11: Global Horizontal Irradiation: monthly and yearly summaries Tab. 12: Comparing long-term yearly average of GHI from different data sources Tab. 13: Monthly statistics of Global Tilted Irradiation (GTI) for North-facing PV modules, tilt Tab. 14: Conversion stages, losses, and performance ratio at the level of PV system Tab. 15: Monthly statistics of PV electricity production of PV power plant Tab. 16: PV power production: monthly and yearly summaries Tab. 17: Hourly averages of PV power output [W/m 2 ] Tab. 18: Uncertainty from interannual variability and value of annual sum of PV power output Tab. 19: Combined uncertainty and P50 and P90 monthly and yearly statistics of PV power plant Tab. 20: Estimation of P50 and P90 yearly electricity production from the PV power plant Tab. 21: Average (P50) and minimum (P90) expected energy yield at the end of the first year Tab. 22: Average (P50) and minimum (P90) expected energy yield for a period of 20 years Solargis page 50 of 54

51 14 REFERENCES [1] Cebecauer T., Šúri M., Perez R., High performance MSG satellite model for operational solar energy applications. ASES National Solar Conference, May 2010, Phoenix, USA. [2] Šúri M., Cebecauer T., Perez P., Quality procedures of Solargis for provision site-specific solar resource information. Conference SolarPACES 2010, September 2010, Perpignan, France. [3] Cebecauer T., Šúri M., Accuracy improvements of satellite-derived solar resource based on GEMS reanalysis aerosols. Conference SolarPACES 2010, September 2010, Perpignan, France. [4] Cebecauer T., Šúri M., Guyemard CH. Uncertainty Sources in Satellite-derived Direct Normal Irradiance: How can prediction accuracy be improved globally? Proceedings of the SolarPACES 2011 Conference, September 2011, Granada, Spain. [5] Šúri M., Cebecauer T., Requirements and standards for bankable DNI data products in CSP projects, Proceedings of the SolarPACES 2011 Conference, September 2011, Granada, Spain. [6] Šúri M., Cebecauer T., Skoczek A., Beták J., Solar electricity production from fixed-inclined and suntracking c-si photovoltaic modules in South Africa. 1st Southern African Solar Energy Conference (SASEC 2012), May 2012, Stellenbosch, South Africa. [7] Ineichen P., A broadband simplified version of the Solis clear sky model. Solar Energy, 82, 8, , [8] Morcrette J., Boucher O., Jones L., Salmond D., Bechtold P., Beljaars A., Benedetti A., Bonet A., Kaiser J.W., Razinger M., Schulz M., Serrar S., Simmons A.J., Sofiev M., Suttie M., Tompkins A., Uncht A., GEMS- AER team. Aerosol analysis and forecast in the ECMWF Integrated Forecast System. Part I: Forward modelling. Journal of Geophysical Research, 114, [9] Cebecauer T., Perez R., Šúri M., Comparing performance of Solargis and SUNY satellite models using monthly and daily aerosol data. Proceedings of the ISES Solar World Congress 2011, September 2011, Kassel, Germany. [10] Perez R., Ineichen P., Maxwell E., Seals R. and Zelenka A., Dynamic global-to-direct irradiance conversion models. ASHRAE Transactions-Research Series, pp , [11] Perez, R., Seals R., Ineichen P., Stewart R., Menicucci D.. A new simplified version of the Perez diffuse irradiance model for tilted surfaces. Solar Energy, 39, , [12] Ineichen P. Five satellite products deriving beam and global irradiance validation on data from 23 ground stations, university of Geneva/IEA SHC Task 36, 2011: [13] Ruiz-Arias J. A., Cebecauer T., Tovar-Pescador J., Šúri M., Spatial disaggregation of satellite-derived irradiance using a high-resolution digital elevation model. Solar Energy, 84, , [14] Martin N., Ruiz J.M. Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Material and Solar Cells, 70, 25 38, [15] King D.L., Boyson W.E. and Kratochvil J.A., Photovoltaic array performance model, SAND , Sandia National Laboratories, [16] Huld T., Šúri M., Dunlop E.D., Geographical variation of the conversion efficiency of crystalline silicon photovoltaic modules in Europe. Progress in Photovoltaics: Research and Applications, 16, , [17] Huld T., Gottschalg R., Beyer H. G., Topic M., Mapping the performance of PV modules, effects of module type and data averaging, Solar Energy, 84, 2, , [18] Skoczek A., Virtuani A., Cebecauer T., Chianese D., Energy Yield Prediction of Amorphous Silicon PV Modules Using Full Time Data Series of Irradiance And Temperature for Different Geographical Locations. 26th European Photovoltaics Solar Energy Conference, September 2011, Hamburg, Germany. [19] Huld T., Friesen G., Skoczek A., Kenny R.P., Sample T., Field M., Dunlop E.D., A power-rating model for crystalline silicon PV modules. Solar Energy Materials and Solar Cells, 95, 12, [20] Skoczek A., Sample T., Dunlop E. D., The results of performance measurements of field-aged crystalline silicon photovoltaic modules, Progress in Photovoltaics: Research and Applications, 17, , [21] The German Energy Society, 2008: Planning and Installing Photovoltaic Systems. A guide for installers, architects and engineers. Second edition. Earthscan, London, Sterling VA Solargis page 51 of 54

52 [22] Meteonorm handbook, Version 6.12, Part II: Theory. Meteotest, 2010 [23] Šúri M., Huld T., Cebecauer T., Dunlop E.D., Geographic Aspects of Photovoltaics in Europe: Contribution of the PVGIS Web Site. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 1, 1, [24] Surface meteorology and Solar Energy (SSE) release 6.0, Methodology, Version 2.4, [25] SWERA web site. Monthly and annual average global data at 40 km resolution for Africa, NREL, [26] Huld T., Müller R., Gambardella A., A new solar radiation database for estimating PV performance in Europe and Africa, Solar Energy, 86, 6, [27] Šúri M., Remund J., Cebecauer T., Dumortier D., Wald L., Huld T., Blanc T., First steps in the crosscomparison of solar resource spatial products in Europe. Proceeding of the EUROSUN 2008, 1 st International Conference on Solar Heating, Cooling and Buildings, 7-10 October 2008, Lisbon, Portugal [28] Lohmann S., Schillings C., Mayer B., Meyer R., Longterm variability of solar direct and global radiation derived from ISCCP data and comparison with reanalysis data, Solar Energy, 80, 11, , [29] Gueymard C., Solar resource e assessment for CSP and CPV. Leonardo Energy webinar, Solargis page 52 of 54

53 15 SUPPORT INFORMATION 15.1 Background on Solargis Primary business of the company Solargis (renamed from GeoModel Solar) is in providing support to the site qualification, planning, financing and operation of solar energy systems. We are committed to increase efficiency and reliability of solar technology by expert consultancy and access to our databases and customer-oriented services. The company builds on 20 years of expertise in geoinformatics and environmental modelling, and over 16 years in solar energy and photovoltaics. We strive for development and operation of new generation high-resolution quality-assessed global databases with focus on solar resource and energy-related weather parameters. We are developing simulation, management and control tools, map products, and services for fast access to high quality information needed for system planning, performance assessment, forecasting and management of distributed power generation. Members of the team have long-term experience in R&D and are active in the activities of International Energy Agency, Solar Heating and Cooling Program, Task 46 Solar Resource Assessment and Forecasting. Company Solargis operates a set of online services, integrated within Solargis information system, which includes data, maps, software, and geoinformation services for solar energy Legal information Considering the nature of climate fluctuations, interannual and long-term changes, as well as the uncertainty of measurements and calculations, the Solargis company cannot take guarantee of the accuracy of estimates. The Solargis company has done maximum possible for the assessment of climate conditions based on the best available data, software and knowledge. Solargis is the registered trademark of Solargis s.r.o. Other brand names and trademarks that may appear in this study are the ownership of their respective owners Solargis, all rights reserved Solargis is ISO 9001:2008 certified company for quality management. Authors: Ing. Branislav Schnierer; Artur Skoczek, PhD; Tomáš Cebecauer, PhD Project manager: Naďa Šúriová, MSc Approved by: Marcel Šúri, PhD 2016 Solargis page 53 of 54